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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>👋Hello</title>
<link href="/posts/37cb61b3.html"/>
<url>/posts/37cb61b3.html</url>
<content type="html"><![CDATA[<h1 id="text-stylefont-size-25px欢迎来到我的博客text"><a class="markdownIt-Anchor" href="#text-stylefont-size-25px欢迎来到我的博客text"></a> <text style="font-size: 25px;"><strong>欢迎来到我的博客</strong></text></h1><p><strong>24.9.28</strong></p><p>本站重构基本完成，依然基于Hexo框架，使用了<a href="https://github.com/ChrAlpha">ChrAlpha</a>大佬开发的Cards主题。</p><p>相比于花里胡哨的动效，我现在更喜欢简单一些（有点像老了）。上版博客的加载速度真的可以说是龟速。。。这版博客与原主题不同的地方基本都是我自写的，大部分资源都已经本地化，加载速度可以说有很大的提升2333</p><h2 id="一些素材声明"><a class="markdownIt-Anchor" href="#一些素材声明"></a> 一些素材声明</h2><table><thead><tr><th>名称</th><th>来源</th></tr></thead><tbody><tr><td>主题框架</td><td><a href="https://hexo.io/">Hexo</a></td></tr><tr><td>主题</td><td><a href="https://github.com/ChrAlpha/hexo-theme-cards">Cards</a></td></tr><tr><td>加载动画（Hello部分）</td><td><a href="Wokine.com">Wokine</a></td></tr><tr><td>主页图片</td><td><a href="https://www.freepik.com/free-vector/gradient-lake-scenery_19852064.htm#query=landscape%20svg&position=1&from_view=keyword&track=ais_hybrid&uuid=8fee4377-2332-49fc-8ff5-81f1ad25162f">Freepik</a></td></tr></tbody></table>]]></content>
<tags>
<tag> 其他 </tag>
</tags>
</entry>
<entry>
<title>快速破解seewo冰点还原</title>
<link href="/posts/9d27b799.html"/>
<url>/posts/9d27b799.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251432348.webp" class="lazy" data-srcset="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251432348.webp" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="写在最前"><a class="markdownIt-Anchor" href="#写在最前"></a> 写在最前</h2><p><big><strong>本文章只作技术交流之用，如果你的班主任要打你屁屁和我没关系捏</strong></big></p><p>据说seewo管家新版本这个方法不适用，不过嘛，学校一般不太会更新软件，试试，万一成功了呢。<s>反正我在浙江某末流985附属中学成功了</s></p><p>所需的文件：<br />1.<a href="https://www.123pan.com/s/Zk0Kjv-5kRx.html">希沃管家1.1.9 </a> 如果不想登录的话可以在<a href="https://www.iefans.net/soft/v1119124.html">这里</a>下载<br />2.<a href="https://wwp.lanzoum.com/iU7uB0cc5i6j">MD5对照表 </a>密码:96os</p><blockquote><p>对照表来自 <a href="https://www.bilibili.com/video/BV1424y1R74A">https://www.bilibili.com/video/BV1424y1R74A</a></p></blockquote><h2 id="summary"><a class="markdownIt-Anchor" href="#summary"></a> Summary</h2><p>老版的seewo管家的密码加密算法十分简单，所以只需要用老版seewo管家覆盖安装新版的seewo管家，获取密码后再关闭冰点还原就可以了。<strong>建议关闭后再安装回新版管家，有b友反馈反之会有无限重启的情况。</strong></p><h2 id="安装老版seewo管家"><a class="markdownIt-Anchor" href="#安装老版seewo管家"></a> 安装老版seewo管家</h2><p>1.<strong>断网</strong>后删除<code>C:\ProgramData\Seewo\SeewoCore\SeewoCore.ini</code>；</p><p>2.运行<code>C:\Program Files(x86)\Seewo\SeewoService\Uninstall.exe</code>卸载seewo管家<br /><strong>密码000000</strong> 不过似乎没有密码也能卸载；</p><p><img src="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251421627.png" class="lazy" data-srcset="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251421627.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20240725142119275" /></p><p>3.安装1.1.9版本的seewo管家。</p><p><strong>此时不要重启</strong></p><h2 id="获取密码"><a class="markdownIt-Anchor" href="#获取密码"></a> 获取密码</h2><p>1.显示学校名称后，打开<code>C:\ProgramData\Seewo\SeewoCore\SeewoCore.ini</code>记录下<code>PASSWORD</code>；</p><p><img src="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251413911.png" class="lazy" data-srcset="https://raw.gitmirror.com/Genkaim/blog_img/main/data/202407251413911.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20240725141307223" /></p><p>2.把<code>PASSWORD</code>转换成明文，成功查看到密码；</p><blockquote><p>用表格或一下两个网站转换<br /><a href="https://www.cmd5.com/">https://www.cmd5.com/</a><br /><a href="http://www.ttmd5.com/hash.php?type=0">http://www.ttmd5.com/hash.php?type=0</a></p></blockquote><p>3.关闭冰点还原后确认重启。</p>]]></content>
<tags>
<tag> 教程 </tag>
</tags>
</entry>
<entry>
<title>velaOS快应用快速入门</title>
<link href="/posts/3f1ce327.html"/>
<url>/posts/3f1ce327.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202311041820746.jpg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202311041820746.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><p>最近摸索了一下小米vela快应用的编写，写个教程顺便做个归纳 <s>蹭个hyperOS的热度。</s></p><p>本文章使用初学者 <s>毕竟我也是。</s></p><h2 id="概述"><a class="markdownIt-Anchor" href="#概述"></a> 概述</h2><p>在介绍之前，需要了解一个vela app基本的架构。</p><h3 id="项目结构"><a class="markdownIt-Anchor" href="#项目结构"></a> <a href="https://iot.mi.com/vela/quickapp/zh/content/framework/project-structure.html">项目结构</a></h3><p>基本架构：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line">├── manifest.json</span><br><span class="line">├── app.ux</span><br><span class="line">├── pages</span><br><span class="line">│ ├── index</span><br><span class="line">| | ├── index.ux</span><br><span class="line">| | ├── index.css</span><br><span class="line">| | └── index.js</span><br><span class="line">│ └── detail</span><br><span class="line">| ├── detail.ux</span><br><span class="line">| ├── detail.css</span><br><span class="line">| └── detail.js</span><br><span class="line">├── i18n</span><br><span class="line">| ├── defaults.json</span><br><span class="line">| ├── zh-CN.json</span><br><span class="line">| └── en-US.json</span><br><span class="line">└── common</span><br><span class="line"> ├── style.css</span><br><span class="line"> ├── utils.js</span><br><span class="line"> └── logo.png</span><br></pre></td></tr></table></figure><p>其中，</p><ol><li><p><code>manifest.json</code>记录app的基本信息</p><p>例如以下属性依次是：</p><p><strong>package</strong>: 包名，自己命名。</p><p><strong>name</strong>: app名称，会在手表上显示。</p><p><strong>versionName</strong>: 版本名称，自己命名。</p><p><strong>minPlatformVersion</strong>: 最低api版本。</p><p><strong>icon</strong>: 图标文件路径</p><p>hideToggle 资源和文件访问规则</p><p><strong><big> 资源和文件访问规则 </big></strong></p><p>应用资源路径分为绝对路径和相对路径，以"/“开头的路径表示绝对路径，比如 /common/a.png，不以”/"开头的路径是相对路径，比如 a.png 和 …/common/a.png 等。</p><p>应用资源文件分为代码文件和资源文件，代码文件是指 .js/.css/.ux 等包含代码的文件，其他文件则是资源文件，这类文件一般只当作数据来使用，比如图片、视频等。</p><ol><li>在代码文件中，导入其他代码文件时，使用相对路径，比如：…/common/component.ux；</li><li>在代码文件中，引用资源文件(如：图片、视频等)时，一般情况下使用相对路径，比如： ./abc.png；</li><li>当代码文件需要被导入时，如果导入文件与被导入文件在同一个目录，被导入文件引用资源文件时可以使用相对路径，但如果不在同一目录，必须使用绝对路径，因为被导入文件编译时会被复制到导入文件中，编译后目录会发生变化。比如 a.css 文件被 b.ux 导入，如果 a.css 与 b.ux 在同一个目录，a.css 引用资源文件时可以写相对路径：abc.png，如果不在同一个目录，必须写绝对路径：/common/abc.png，再比如当 a.ux 文件被 b.ux 文件导入时，如果 a.ux 与 b.ux 在同一个目录，a.ux 引用资源文件时可以写相对路径：a.png，如果不在同一个目录，a.ux 引用资源必须写绝对路径：/common/abc.png；</li><li>在 CSS 中，与前端开发一致，使用 url(PATH)的方式访问资源文件，如：url(/common/abc.png)。</li></ol><p>endhideToggle</p><p><strong>features</strong>： 调用的接口声明，有些敏感接口只有声明才可使用。</p><p><strong>designWidth</strong>： 设计稿的尺寸，具体看<a href="https://iot.mi.com/vela/quickapp/zh/content/framework/style/page-style-and-layout.html">页面样式与布局</a>。</p><p><strong>router</strong>: app中每个页面的定义。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br></pre></td><td class="code"><pre><span class="line">{</span><br><span class="line"> "package": "com.genkaim.muyu",</span><br><span class="line"> "name": "电子木鱼",</span><br><span class="line"> "versionName": "1.1.0",</span><br><span class="line"> "versionCode": 4,</span><br><span class="line"> "minPlatformVersion": 1000,</span><br><span class="line"> "icon": "/common/logo.png",</span><br><span class="line"> "deviceTypeList": [</span><br><span class="line"> "watch"</span><br><span class="line"> ],</span><br><span class="line"> "features": [</span><br><span class="line"> { "name": "system.storage" },</span><br><span class="line"> { "name": "system.file" },</span><br><span class="line"> { "name": "system.prompt" },</span><br><span class="line"> { "name": "system.vibrator" }</span><br><span class="line"> ],</span><br><span class="line"> "config": {</span><br><span class="line"> "logLevel": "log",</span><br><span class="line"> "designWidth": 600 </span><br><span class="line"> },</span><br><span class="line"> "router": {</span><br><span class="line"> "entry": "pages/index",</span><br><span class="line"> "pages": {</span><br><span class="line"> "pages/index": {</span><br><span class="line"> "component": "index"</span><br><span class="line"> },</span><br><span class="line"> "pages/settings": {</span><br><span class="line"> "component": "settings"</span><br><span class="line"> },</span><br><span class="line"> "pages/confirm": {</span><br><span class="line"> "component": "confirm"</span><br><span class="line"> },</span><br><span class="line"> "pages/about": {</span><br><span class="line"> "component": "about"</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></li><li><p><code>app.ux</code>为app基本的js语法例如生命周期中，app的onCreate、onDestroy在这调用</p><p>在下面的代码中，会在app打开时和退出时分别 log “onCreate”和"onDestroy"。</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line"><script></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">data</span>: {</span><br><span class="line"> <span class="attr">a</span>: <span class="number">1</span></span><br><span class="line"> },</span><br><span class="line"> <span class="title function_">onCreate</span>(<span class="params"></span>) { </span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"onCreate"</span>)</span><br><span class="line"> },</span><br><span class="line"> <span class="title function_">onDestroy</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"onDestroy"</span>)</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></script></span><br><span class="line"></span><br></pre></td></tr></table></figure></li><li><p><code>pages</code>下每个文件夹为当前页面的资源文件，包含<code>.ux</code>等等。</p></li><li><p><code>i18n</code>语言文件。</p></li><li><p><code>common</code>存放公用资源文件，比如logo。</p></li></ol><h3 id="生命周期"><a class="markdownIt-Anchor" href="#生命周期"></a> <a href="https://iot.mi.com/vela/quickapp/zh/content/framework/script/lifecycle.html?h=%E5%91%A8%E6%9C%9F">生命周期</a></h3><p>这里借用一下官方的图。</p><p>简单来说，<strong>app生命周期</strong>就是当打开app时，一次进行下面步骤，页面onShow前，先经历onInit和onReady两个阶段（这在export default中是具体的两个函数）。</p><p>当app退出时，为onDestroy。</p><img src="https://iot.mi.com/vela/quickapp/zh/content/images/life.png" class="lazy" data-srcset="https://iot.mi.com/vela/quickapp/zh/content/images/life.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="生命周期" style="width: 400px" /><h3 id="ux文件的基本认识"><a class="markdownIt-Anchor" href="#ux文件的基本认识"></a> <code>ux</code>文件的基本认识</h3><p>下面是一个简单的<code>.ux</code>文件的内容:</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <div class="page"></span><br><span class="line"> <text class="title">确定要清除所有功德吗</text></span><br><span class="line"> <input class="yes" type="button" value="确认" onclick="clearData" /></span><br><span class="line"> <input class="no" type="button" value="取消" onclick="goBack" /></span><br><span class="line"> </div></span><br><span class="line"></template></span><br><span class="line"></span><br><span class="line"><script></span><br><span class="line"> import prompt from '@system.prompt'</span><br><span class="line"> export default {</span><br><span class="line"> goBack(event) {</span><br><span class="line"> router.back()</span><br><span class="line"> },</span><br><span class="line"> clearData(event) {</span><br><span class="line"> router.back()</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></script></span><br><span class="line"></span><br><span class="line"><style></span><br><span class="line">.yes, .no {</span><br><span class="line"> width: 500px;</span><br><span class="line"> height: 150px;</span><br><span class="line"> color: white;</span><br><span class="line"> font-size: 40px;</span><br><span class="line"> font-weight: bold;</span><br><span class="line"> margin-top: 60px;</span><br><span class="line">}</span><br><span class="line">.page {</span><br><span class="line"> position: absolute;</span><br><span class="line"> background-color: black;</span><br><span class="line"> display: flex;</span><br><span class="line"> flex-direction: column;</span><br><span class="line"> display: flex;</span><br><span class="line"> justify-content: center; /* 水平居中 */</span><br><span class="line"> align-items: center; /* 垂直居中 */</span><br><span class="line">}</span><br><span class="line">.back {</span><br><span class="line"> position: absolute;</span><br><span class="line"> left: 0px;</span><br><span class="line"> top: 10px;</span><br><span class="line"> background-color: black;</span><br><span class="line"> color: white;</span><br><span class="line"> font-size: 80px;</span><br><span class="line"> font-weight: bold;</span><br><span class="line"> background-image: url('/common/icon-back.png');</span><br><span class="line">}</span><br><span class="line">.yes {</span><br><span class="line"> margin-top: 50px;</span><br><span class="line"> background-color: rgb(44, 44, 44);</span><br><span class="line">}</span><br><span class="line">.no {</span><br><span class="line"> margin-top: 30px;</span><br><span class="line">}</span><br><span class="line">.title {</span><br><span class="line"> color: white;</span><br><span class="line"> font-size: 50px;</span><br><span class="line"> font-weight: bold;</span><br><span class="line"> top: 5px;</span><br><span class="line">}</span><br><span class="line"></style></span><br><span class="line"></span><br></pre></td></tr></table></figure><ol><li><strong><a href="https://iot.mi.com/vela/quickapp/zh/content/framework/template/basic.html?h=templATE">template标签</a>：</strong> 类似于HTML的语言，vela提供多种<a href="https://iot.mi.com/vela/quickapp/zh/content/components/intro.html">组件</a>。例如这里出现两种不同的组件：</li></ol><p>text和input，分别会被渲染为文本块和按钮。</p><p><strong>其中：</strong></p><p>1.1 class为自己定义的类名type为组件类型，这里为按钮。</p><p>1.2 button标签的value值为按钮上显示的文字。</p><p>1.3 onclick为<a href="https://iot.mi.com/vela/quickapp/zh/content/components/general/events.html?h=%E4%BA%8B%E4%BB%B6">事件</a>绑定，意思为满足”点按“这一条件时，会调用指定函数，函数在export default定义。</p><blockquote><p>为什么要在template下再包一层div呢？</p><p>因为template下只允许存在一个根节点，必须先创建一个节点，内部再放并列节点。</p></blockquote><ol start="2"><li><strong><a href="https://iot.mi.com/vela/quickapp/zh/content/framework/script/basic.html?h=scri">script脚本</a>：</strong> 支持 ES5 / ES6 语法，这里的export default中，引用了一个模块来实现<a href="https://iot.mi.com/vela/quickapp/zh/content/features/basic/router.html?h=router">返回</a>的功能。</li><li>**<a href="https://iot.mi.com/vela/quickapp/zh/content/framework/style/page-style-and-layout.html?h=style">style层叠样式表</a>：**用选择器选择并设置属性即可。</li></ol><h2 id="简单示例电子木鱼基本功能实现"><a class="markdownIt-Anchor" href="#简单示例电子木鱼基本功能实现"></a> 简单示例：电子木鱼基本功能实现</h2><h3 id="基本功能"><a class="markdownIt-Anchor" href="#基本功能"></a> 基本功能：</h3><ol><li><p>页面元素：电子木鱼（图片），显示功德数值功能，”功德+1“动画。</p></li><li><p>实现点按木鱼计数功能。</p></li></ol><img src="https://www.bandbbs.cn/attachments/22569/" class="lazy" data-srcset="https://www.bandbbs.cn/attachments/22569/" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="muyu" style="width: 200px" /><p>页面资源：<a href="https://github.com/Genkaim/vela-apps/blob/main/wooden%20fish/src/pages/index/muyu.png">单击下载</a></p><h3 id="页面布局"><a class="markdownIt-Anchor" href="#页面布局"></a> 页面布局</h3><ol><li>放置木鱼图片可以用img组件或者css实现，这里使用的前者。</li></ol><p>因为需要实现点按反馈的功能，所以需要绑定onclick事件。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><img class="muyu" src="muyu.png" onclick="rpPlusPlus()" /></span><br></pre></td></tr></table></figure><ol start="2"><li>计数功能可以通过text组件显示，这里注意，动态的数据（变量）可以通过大括号的方式显示，例如下面的代码可以实现显示功德计数（变量在下文）。</li></ol><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><text class="cnt" >功德 {{localCnt}}</text></span><br></pre></td></tr></table></figure><ol start="3"><li>而动画的实现则是通过text组件+<a href="https://iot.mi.com/vela/quickapp/zh/content/framework/template/if.html?h=if">if条件渲染</a>+绑定动画（下文）实现的。</li></ol><blockquote><p>if条件渲染指if内表达式的值为true时，会渲染当前元素。</p></blockquote><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><text if="{{plus}}" class="showPlus">功德+1</text></span><br></pre></td></tr></table></figure><h3 id="脚本"><a class="markdownIt-Anchor" href="#脚本"></a> 脚本</h3><ol><li>数据处理：</li></ol><p>在上文中，需要几个变量：localCnt(int) 用于计数功德，plus(bool) 用于指示消息的显示。</p><p>定义变量需要这么写：</p><p>其中，</p><table><thead><tr><th>属性</th><th>类型</th><th>描述</th></tr></thead><tbody><tr><td>public</td><td>Object</td><td>页面级组件的数据模型，影响传入数据的覆盖机制：public 内定义的属性允许被传入的数据覆盖，如果外部传入数据的某个属性未被声明，在 public 中不会新增这个属性</td></tr><tr><td>protected</td><td>Object</td><td>页面级组件的数据模型，影响传入数据的覆盖机制：protected 内定义的属性，允许被应用内部页面请求传递的数据覆盖，不允许被应用外部请求传递的数据覆盖</td></tr><tr><td>private</td><td>Object</td><td>页面级组件的数据模型，影响传入数据的覆盖机制：private 内定义的属性不允许被覆盖</td></tr></tbody></table><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><script></span><br><span class="line">export default {</span><br><span class="line"> public: {</span><br><span class="line"> localCnt: 0,</span><br><span class="line"> plus: false</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></script></span><br></pre></td></tr></table></figure><ol start="2"><li>在上文中，需要定义rpPlusPlus函数，实现功德+1</li></ol><p>其中：</p><p>通过this.Name访问当前页面数据对象。</p><p>并设置plus为true，在400ms后设置为false，即让其显示400ms，因为它绑定了动画（下文），看起来的效果就是文字向上移动然后消失。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line">rpPlusPlus(event) {</span><br><span class="line"> this.plus = true;</span><br><span class="line"> this.localCnt++;</span><br><span class="line"> setTimeout(() => {</span><br><span class="line"> this.plus = false;</span><br><span class="line"> }, 400);</span><br><span class="line"> }</span><br></pre></td></tr></table></figure><h3 id="css"><a class="markdownIt-Anchor" href="#css"></a> css</h3><ol><li>绑定动画：</li></ol><p>上文已经定义了class为showPlus，所以通过<code>.showPlus</code>选择元素：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line">.showPlus {</span><br><span class="line"> position: absolute;/*定位*/</span><br><span class="line"> right: 70px;</span><br><span class="line"> top: 210px;</span><br><span class="line"> color: white;/*字体颜色*/</span><br><span class="line"> font-weight: bold;/*字体粗细*/</span><br><span class="line"> animation-name: moveUp;/*字体绑定动画*/</span><br><span class="line"> animation-delay: 0s;/*动画延迟时间*/</span><br><span class="line"> animation-duration: 200ms;/*动画持续时间*/</span><br><span class="line"> animation-iteration-count: 1;/*动画持续次数*/</span><br><span class="line"> }</span><br><span class="line"> @keyframes moveUp {/*定义动画*/</span><br><span class="line"> 0% {</span><br><span class="line"> transform: translateY(0);</span><br><span class="line"> }</span><br><span class="line"> 99% {</span><br><span class="line"> transform: translateY(-40px);</span><br><span class="line"> }</span><br><span class="line"> 100% {</span><br><span class="line"> visibility: hidden;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br></pre></td></tr></table></figure><ol start="2"><li>cnt、page和muyu元素：</li></ol><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br></pre></td><td class="code"><pre><span class="line">.muyu {</span><br><span class="line"> position: absolute;/*定位*/</span><br><span class="line"> height: 350px;</span><br><span class="line"> top: 250px;</span><br><span class="line"> background-color: transparent;/*背景颜色*/</span><br><span class="line"> width: 450px;/*大小*/</span><br><span class="line"> }</span><br><span class="line"> .cnt {</span><br><span class="line"> position: absolute;</span><br><span class="line"> bottom: 100px;/*定位*/</span><br><span class="line"> font-size: 70px;/*字体大小*/</span><br><span class="line"> color: white;/*字体颜色*/</span><br><span class="line"> }</span><br><span class="line"> .page {</span><br><span class="line"> background-color: black;/*背景颜色*/</span><br><span class="line"> display: flex;</span><br><span class="line"> flex-direction: column;</span><br><span class="line"> justify-content: center; /* 水平居中 */</span><br><span class="line"> align-items: center; /* 垂直居中 */</span><br><span class="line"> height: 100%; /* 确保容器占满整个视窗 */</span><br><span class="line"> }</span><br></pre></td></tr></table></figure><p>完整代码：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <div class="page"></span><br><span class="line"> <img class="muyu" src="muyu.png" onclick="rpPlusPlus()" /></span><br><span class="line"> <text if="{{plus}}" class="showPlus">功德+1</text></span><br><span class="line"> <text class="cnt" >功德 {{localCnt}}</text></span><br><span class="line"> </div></span><br><span class="line"></template></span><br><span class="line"></span><br><span class="line"><script></span><br><span class="line"> export default {</span><br><span class="line"> public: {</span><br><span class="line"> localCnt: 0,</span><br><span class="line"> plus: false</span><br><span class="line"> },</span><br><span class="line"> rpPlusPlus(event) {</span><br><span class="line"> this.plus = true;</span><br><span class="line"> this.localCnt++;</span><br><span class="line"> setTimeout(() => {</span><br><span class="line"> this.plus = false;</span><br><span class="line"> }, 400);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></script></span><br><span class="line"></span><br><span class="line"><style></span><br><span class="line"> .page {</span><br><span class="line"> background-color: black;/*背景颜色*/</span><br><span class="line"> display: flex;</span><br><span class="line"> flex-direction: column;</span><br><span class="line"> justify-content: center; /* 水平居中 */</span><br><span class="line"> align-items: center; /* 垂直居中 */</span><br><span class="line"> height: 100%; /* 确保容器占满整个视窗 */</span><br><span class="line"> }</span><br><span class="line"> .showPlus {</span><br><span class="line"> position: absolute;/*定位*/</span><br><span class="line"> right: 70px;</span><br><span class="line"> top: 210px;</span><br><span class="line"> color: white;/*字体颜色*/</span><br><span class="line"> font-weight: bold;/*字体粗细*/</span><br><span class="line"> animation-name: moveUp;/*字体绑定动画*/</span><br><span class="line"> animation-delay: 0s;/*动画延迟时间*/</span><br><span class="line"> animation-duration: 200ms;/*动画持续时间*/</span><br><span class="line"> animation-iteration-count: 1;/*动画持续次数*/</span><br><span class="line"> }</span><br><span class="line"> @keyframes moveUp {/*定义动画*/</span><br><span class="line"> 0% {</span><br><span class="line"> transform: translateY(0);</span><br><span class="line"> }</span><br><span class="line"> 99% {</span><br><span class="line"> transform: translateY(-40px);</span><br><span class="line"> }</span><br><span class="line"> 100% {</span><br><span class="line"> visibility: hidden;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> .muyu {</span><br><span class="line"> position: absolute;/*定位*/</span><br><span class="line"> height: 350px;</span><br><span class="line"> top: 250px;</span><br><span class="line"> background-color: transparent;/*背景颜色*/</span><br><span class="line"> width: 450px;/*大小*/</span><br><span class="line"> }</span><br><span class="line"> .cnt {</span><br><span class="line"> font-size: 70px;/*字体大小*/</span><br><span class="line"> bottom: 100px;/*定位*/</span><br><span class="line"> position: absolute;</span><br><span class="line"> color: white;</span><br><span class="line"> }</span><br><span class="line"></style></span><br><span class="line"></span><br></pre></td></tr></table></figure><p>如有错误，欢迎指出。</p>]]></content>
<tags>
<tag> Coding </tag>
</tags>
</entry>
<entry>
<title>RSS+Tinyletter+Zapier实现博客更新邮件推送</title>
<link href="/posts/d87f7e0c.html"/>
<url>/posts/d87f7e0c.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308240952291.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308240952291.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><p>hideToggle Update Log</p><p>timeline 2023,purple</p><!-- timeline 09-16 --><p>更新提醒</p><!-- endtimeline --><p>endtimeline</p><p>endhideToggle</p><p><s>rss很方便，但有人不会用（？</s></p><p>为了提供更多元的订阅方式(？</p><p><strong>提醒：Tinyletter会无理由封禁用户账户，我的账号已经被封了两次了，不建议使用。最近我会迁移邮件服务提供商并更新博客。在此之前，博客更新不会有邮件提醒（不过依然可以填写邮箱，我会迁移数据到新的服务商）</strong></p><h2 id="吐槽"><a class="markdownIt-Anchor" href="#吐槽"></a> 吐槽</h2><p>我查了很多网上的教程，包括mailChimp，mailsender还有power automate等等，但都不行，有各种各样的原因。。。不过最后还是找到了</p><h2 id="思路"><a class="markdownIt-Anchor" href="#思路"></a> 思路</h2><ol><li>在Zapier使用Rss作为触发器，给Tinyletter发送邮件。</li><li>Tinyletter分发邮件给填写过表单的访客。</li></ol><p>思路来自于 <strong><a href="https://backendology.com/2018/08/31/hugo-newsletter/">Newsletter for Hugo Blog</a></strong> 在此基础上增加了一些细节并翻译成中文。</p><p>link 获取网站的Favicon图标并显示在你的网页上,owen0o0,<a href="https://github.com/owen0o0/getFavicon">https://github.com/owen0o0/getFavicon</a></p><h2 id="tinyletter"><a class="markdownIt-Anchor" href="#tinyletter"></a> Tinyletter</h2><p>-> <strong><a href="https://app.tinyletter.com/">Tinyletter官网</a></strong></p><p>注册过程不再赘述。</p><ol><li>进入个人档案</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824094043823.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824094043823.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824094043823" /></p><ol start="2"><li>填写表单，Newsletter暂时不用管，随便填一些，填完记得保存。 <strong>如果出现跳转，那是有必填项目没填</strong> <small>（它这提示我当时不知道为什么就是没看到，卡了好久。。。 </small></li></ol><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> <strong>把这里打马赛克的地方复制下来，下一阶段要用</strong><br /><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> <strong>红色框出的网址是访客填邮箱用的，记得添加到博客，下一步会对其美化</strong></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824095925176.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824095925176.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824095925176" /></p><ol start="3"><li>个性化表单界面(views指不同情况下，报错、邮件格式错误…的界面)<br /><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824095940578.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824095940578.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824095940578" /></li></ol><p>Tinyletter部分完成了。<br /><strong>注意，每次博客文章更新，你会在Draft一栏看到Zapier发送的邮件，你需要手动发送给订阅者（不过是一键的）</strong></p><h2 id="zapier"><a class="markdownIt-Anchor" href="#zapier"></a> Zapier</h2><p>-> <strong><a href="https://zapier.com/">zapier官网</a></strong></p><p>注册过程不再赘述。</p><ol><li>进入仪表盘，新建zap</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092054322.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092054322.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092054322" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092212178.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092212178.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092212178" /></p><ol start="2"><li>设置触发器，按下图的红框依次操作</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092603376.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092603376.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092603376" /></p><p><strong>即当RSS更新时触发发送电子邮件</strong></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092641233.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092641233.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092641233" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092705303.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092705303.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092705303" /></p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092830760.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824092830760.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824092830760" height=50% width=50% /><ol start="3"><li>设置动作，按下图红框依次操作</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093013819.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093013819.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824093013819" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093103530.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093103530.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824093103530" /></p><p>下图的1、2、3依次填入：</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> <strong>To</strong> :刚才获取的tinyletter的邮件地址</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> <strong>Subject</strong> : 填你喜欢的名字</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> <strong>Body</strong> : 填入发件内容，可以参考我附在末尾的html代码</p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093142158.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093142158.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824093142158" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093647329.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093647329.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824093647329" /></p><p><strong>最后在仪表盘看到这种效果就行了</strong></p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093800196.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230824093800196.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230824093800196" /></p><p>附html代码：</p><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta"><!DOCTYPE <span class="keyword">html</span>></span></span><br><span class="line"><span class="tag"><<span class="name">div</span> <span class="attr">class</span>=<span class="string">"main"</span>></span></span><br><span class="line"><span class="tag"><<span class="name">div</span> <span class="attr">class</span>=<span class="string">"circle-cover"</span> <span class="attr">style</span>=<span class="string">"text-align: center;"</span>></span><span class="tag"><<span class="name">div</span> <span class="attr">class</span>=<span class="string">"circle"</span>></span><span class="tag"></<span class="name">div</span>></span><span class="tag"></<span class="name">div</span>></span></span><br><span class="line"><span class="tag"><<span class="name">img</span> <span class="attr">class</span>=<span class="string">"main-img"</span> <span class="attr">src</span>=<span class="string">"https://cdn.luogu.com.cn/upload/image_hosting/0xd4prt2.png"</span>></span></span><br><span class="line"><span class="tag"><<span class="name">h1</span>></span>本站更新了<span class="tag"></<span class="name">h1</span>></span></span><br><span class="line"><span class="tag"><<span class="name">P</span>></span>发送时间<span class="tag"></<span class="name">P</span>></span></span><br><span class="line"><span class="tag"><<span class="name">span</span> <span class="attr">id</span>=<span class="string">"time"</span>></span><span class="tag"></<span class="name">span</span>></span>/*这里的标题和链接都要改成自己的（插入的数据）*/</span><br><span class="line"><span class="tag"><<span class="name">div</span> <span class="attr">class</span>=<span class="string">"post"</span>></span><span class="tag"><<span class="name">p</span> <span class="attr">class</span>=<span class="string">"title"</span>></span>标题<span class="tag"><<span class="name">br</span>></span>{{205114825__title}}<span class="tag"></<span class="name">p</span>></span><span class="tag"></<span class="name">div</span>></span></span><br><span class="line"><span class="tag"><<span class="name">a</span> <span class="attr">href</span>=<span class="string">"{{205114825__link}}"</span>></span><span class="tag"><<span class="name">div</span> <span class="attr">class</span>=<span class="string">"link"</span>></span>跳转<span class="tag"></<span class="name">div</span>></span><span class="tag"></<span class="name">a</span>></span></span><br><span class="line"><span class="tag"><<span class="name">img</span> <span class="attr">class</span>=<span class="string">"footer"</span> <span class="attr">src</span>=<span class="string">"https://raw.gitmirror.com/genkaim/blog_img/main/data/line_s.png"</span>></span></span><br><span class="line"><span class="tag"></<span class="name">div</span>></span></span><br><span class="line"><span class="tag"><<span class="name">style</span>></span><span class="language-css"></span></span><br><span class="line"><span class="language-css"><span class="selector-class">.post</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-top</span>: <span class="number">25px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-left</span>: <span class="number">25px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>: <span class="number">300px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">height</span>: <span class="number">100px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">background</span>: <span class="number">#d5d5d5</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">border-radius</span>: <span class="number">8px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.post</span> <span class="selector-tag">p</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-top</span>: <span class="number">25px</span> <span class="meta">!important</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">display</span>: flex;</span></span><br><span class="line"><span class="language-css"><span class="attribute">align-items</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">justify-content</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">height</span>: <span class="number">100%</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.title</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">font-weight</span>: bold;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-tag">a</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">text-decoration</span>: none; <span class="comment">/* 去掉下划线 */</span></span></span><br><span class="line"><span class="language-css"><span class="attribute">color</span>: white;</span></span><br><span class="line"><span class="language-css"></span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-id">#time</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to right, <span class="number">#365262</span> <span class="number">0%</span>, <span class="number">#1c6a54</span> <span class="number">50%</span>, <span class="number">#254050</span> <span class="number">100%</span>);</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="selector-tag">text</span>-<span class="attribute">fill</span>-<span class="attribute">color</span>: transparent;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-id">#time</span> {</span></span><br><span class="line"><span class="language-css"> <span class="attribute">display</span>: block;</span></span><br><span class="line"><span class="language-css"> <span class="attribute">margin</span>: <span class="number">0</span> auto;</span></span><br><span class="line"><span class="language-css"> <span class="attribute">font-weight</span>: bold;</span></span><br><span class="line"><span class="language-css"><span class="attribute">text-align</span>: center;</span></span><br><span class="line"><span class="language-css"> }</span></span><br><span class="line"><span class="language-css"><span class="selector-tag">h1</span> {<span class="comment">/*这里可以改成自己喜欢的渐变色*/</span></span></span><br><span class="line"><span class="language-css"><span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to right, <span class="number">#365262</span> <span class="number">0%</span>, <span class="number">#1c6a54</span> <span class="number">50%</span>, <span class="number">#254050</span> <span class="number">100%</span>);</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="selector-tag">text</span>-<span class="attribute">fill</span>-<span class="attribute">color</span>: transparent;</span></span><br><span class="line"><span class="language-css"><span class="attribute">text-align</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-top</span>: <span class="number">20px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-tag">p</span> {<span class="comment">/*这里可以改成自己喜欢的渐变色*/</span></span></span><br><span class="line"><span class="language-css"><span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to right, <span class="number">#365262</span> <span class="number">0%</span>, <span class="number">#1c6a54</span> <span class="number">50%</span>, <span class="number">#254050</span> <span class="number">100%</span>);</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="attribute">background-clip</span>: text;</span></span><br><span class="line"><span class="language-css">-webkit-<span class="selector-tag">text</span>-<span class="attribute">fill</span>-<span class="attribute">color</span>: transparent;</span></span><br><span class="line"><span class="language-css"><span class="attribute">text-align</span>: center;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.main-img</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>:<span class="number">100%</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">overflow</span>:hidden;</span></span><br><span class="line"><span class="language-css"><span class="attribute">pointer-events</span>:none;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-top</span>: -<span class="number">120px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">border-radius</span>: <span class="number">8px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>: <span class="number">300px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">display</span>: block; </span></span><br><span class="line"><span class="language-css"><span class="attribute">margin</span>: auto;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-top</span>: <span class="number">40px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.main</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">padding</span>:<span class="number">40px</span> <span class="number">0px</span> <span class="number">20px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin</span>:<span class="number">0px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-color</span>: <span class="number">#f1e6e6</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>: <span class="number">350px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">height</span>: <span class="number">700px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">border-radius</span>: <span class="number">8px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.footer</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>: <span class="number">350px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin-left</span>: <span class="number">10px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"><span class="selector-class">.p</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">display</span>: flex;</span></span><br><span class="line"><span class="language-css"><span class="attribute">top</span>: <span class="number">10px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">align-items</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">justify-content</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">height</span>: <span class="number">100%</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">font-size</span>: <span class="number">10px</span> <span class="meta">!important</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"></span></span><br><span class="line"><span class="language-css"><span class="selector-class">.link</span> {</span></span><br><span class="line"><span class="language-css"><span class="attribute">font-size</span>: <span class="number">15px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">background</span>: <span class="number">#b3b3b3</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">border-radius</span>: <span class="number">8px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">margin</span>: <span class="number">40px</span> auto; <span class="comment">/* 设置左右外边距为 auto */</span></span></span><br><span class="line"><span class="language-css"><span class="attribute">padding</span>: <span class="number">5px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">color</span>: white;</span></span><br><span class="line"><span class="language-css"><span class="attribute">width</span>: <span class="number">150px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">height</span>: <span class="number">50px</span>;</span></span><br><span class="line"><span class="language-css"><span class="attribute">display</span>: block; <span class="comment">/* 设置元素为块级元素 */</span></span></span><br><span class="line"><span class="language-css"><span class="attribute">text-align</span>: center;</span></span><br><span class="line"><span class="language-css"><span class="attribute">font-weight</span>: bold;</span></span><br><span class="line"><span class="language-css"><span class="attribute">line-height</span>: <span class="number">50px</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"></span></span><br><span class="line"><span class="language-css"><span class="selector-class">.circle</span> {</span></span><br><span class="line"><span class="language-css"> <span class="attribute">width</span>: <span class="number">30px</span>;</span></span><br><span class="line"><span class="language-css"> <span class="attribute">height</span>: <span class="number">30px</span>;</span></span><br><span class="line"><span class="language-css"> <span class="attribute">border-radius</span>: <span class="number">50%</span>;</span></span><br><span class="line"><span class="language-css"> <span class="attribute">background-color</span>: <span class="built_in">rgb</span>(<span class="number">255</span>, <span class="number">255</span>, <span class="number">255</span>);</span></span><br><span class="line"><span class="language-css"> <span class="attribute">margin</span>: auto;</span></span><br><span class="line"><span class="language-css"><span class="attribute">box-shadow</span>: inset <span class="number">0</span> <span class="number">0</span> <span class="number">10px</span> <span class="built_in">rgb</span>(<span class="number">22</span>, <span class="number">22</span>, <span class="number">22</span>);</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-image</span>: <span class="built_in">url</span>(<span class="string">https://cdn.luogu.com.cn/upload/image_hosting/py13qt58.png</span>);</span></span><br><span class="line"><span class="language-css"><span class="attribute">background-size</span>: <span class="number">95%</span> <span class="number">100%</span>;</span></span><br><span class="line"><span class="language-css">}</span></span><br><span class="line"><span class="language-css"></span><span class="tag"></<span class="name">style</span>></span></span><br><span class="line"><span class="tag"><<span class="name">script</span>></span><span class="language-javascript"></span></span><br><span class="line"><span class="language-javascript"><span class="title function_">fetch</span>(<span class="string">'http://quan.suning.com/getSysTime.do'</span>)</span></span><br><span class="line"><span class="language-javascript"> .<span class="title function_">then</span>(<span class="function"><span class="params">response</span> =></span> response.<span class="title function_">json</span>())</span></span><br><span class="line"><span class="language-javascript"> .<span class="title function_">then</span>(<span class="function"><span class="params">data</span> =></span> {</span></span><br><span class="line"><span class="language-javascript"> <span class="comment">// 获取时间</span></span></span><br><span class="line"><span class="language-javascript"> <span class="keyword">var</span> timeString = data.<span class="property">sysTime2</span>;</span></span><br><span class="line"><span class="language-javascript"> <span class="comment">// 将时间显示在页面上</span></span></span><br><span class="line"><span class="language-javascript"> <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">'time'</span>).<span class="property">textContent</span> = timeString;</span></span><br><span class="line"><span class="language-javascript"> });</span></span><br><span class="line"><span class="language-javascript"></span></span><br><span class="line"><span class="language-javascript"></span><span class="tag"></<span class="name">script</span>></span></span><br><span class="line"><span class="tag"></<span class="name">html</span>></span></span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> 教程 </tag>
</tags>
</entry>
<entry>
<title>Hexo Butterfly优化合集-添加弹窗|修改加载动画|引入聊天机器人|css美化|修改链接悬停样式</title>
<link href="/posts/5c0d8670.html"/>
<url>/posts/5c0d8670.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100926980.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100926980.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><p>hideToggle Update Log</p><p>timeline 2023,purple</p><!-- timeline 08-23 --><p>更新了樱花特效添加到指定页面的实现方式</p><!-- endtimeline --><!-- timeline 08-21 --><p>更新更改链接鼠标悬停样式的修改</p><!-- endtimeline --> endtimeline <p>endhideToggle</p><p>内容较多，建议看侧边栏的目录。</p><h2 id="在右上角引入弹窗"><a class="markdownIt-Anchor" href="#在右上角引入弹窗"></a> 在右上角引入弹窗</h2><div style="text-align: center;"><button id="post-button" onclick="show()">单击预览</button><script>function show() { popup.style.opacity = 1; popup.animate([ { transform: 'translateX(110%)' }, { transform: 'translateX(0)' } ], { duration: 1000, fill: 'forwards', easing: 'ease-in-out' }); }</script><style>#post-button {background: #b3b3b3;border-radius: 8px;padding: 9px;color: white; transition: background 0.5s ease-in-out;} #post-button:hover { background: #c9c9c9;}</style></div><ol><li>引入<code>.js</code>文件</li></ol><p>在 <code>~\themes\butterfly\source\js\</code> 新建 <code>textWindow.js</code> 文件，复制下面的代码，<strong>注意注释</strong></p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">var</span> popup = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">"div"</span>);</span><br><span class="line"><span class="keyword">var</span> button = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">"button"</span>);</span><br><span class="line"></span><br><span class="line">button.<span class="property">id</span> = <span class="string">"close"</span>;</span><br><span class="line">button.<span class="property">textContent</span> = <span class="string">"X"</span>;</span><br><span class="line">popup.<span class="property">id</span> = <span class="string">"popup"</span>;</span><br><span class="line">popup.<span class="property">className</span> = <span class="string">"popup"</span>;</span><br><span class="line"><span class="keyword">var</span> title = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">"h1"</span>);</span><br><span class="line">title.<span class="property">textContent</span> = <span class="string">"<输入弹窗标题，注意下面也要改>"</span>;</span><br><span class="line"><span class="keyword">var</span> content = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">"p"</span>);</span><br><span class="line">content.<span class="property">textContent</span> = <span class="string">"<输入弹窗内容，注意下面也要改>"</span>;</span><br><span class="line">popup.<span class="title function_">appendChild</span>(title);</span><br><span class="line">popup.<span class="title function_">appendChild</span>(content);</span><br><span class="line"><span class="variable language_">document</span>.<span class="property">body</span>.<span class="title function_">insertAdjacentHTML</span>(<span class="string">"afterbegin"</span>, <span class="string">'<div id="popup" class="popup"><h1>输入弹窗标题</h1><p>输入弹窗内容</p></div>'</span>);</span><br><span class="line"><span class="variable language_">document</span>.<span class="property">body</span>.<span class="title function_">insertAdjacentElement</span>(<span class="string">"afterbegin"</span>, button);</span><br><span class="line"></span><br><span class="line"><span class="keyword">var</span> popup = <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">"popup"</span>);</span><br><span class="line"><span class="keyword">var</span> close = <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">"close"</span>);</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">function</span> <span class="title function_">show</span>(<span class="params"></span>) {</span><br><span class="line"> popup.<span class="property">style</span>.<span class="property">opacity</span> = <span class="number">1</span>;</span><br><span class="line"> popup.<span class="title function_">animate</span>([</span><br><span class="line"> { <span class="attr">transform</span>: <span class="string">'translateX(110%)'</span> }, </span><br><span class="line"> { <span class="attr">transform</span>: <span class="string">'translateX(0)'</span> }</span><br><span class="line"> ], {</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">1000</span>,</span><br><span class="line"> <span class="attr">fill</span>: <span class="string">'forwards'</span>, </span><br><span class="line"> <span class="attr">easing</span>: <span class="string">'ease-in-out'</span></span><br><span class="line"> }); </span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">function</span> <span class="title function_">hide</span>(<span class="params"></span>) {</span><br><span class="line"> popup.<span class="title function_">animate</span>([</span><br><span class="line"> { <span class="attr">transform</span>: <span class="string">'translateX(0)'</span> }, </span><br><span class="line"> { <span class="attr">transform</span>: <span class="string">'translateX(110%)'</span> }</span><br><span class="line"> ], {</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">1000</span>, </span><br><span class="line"> <span class="attr">fill</span>: <span class="string">'forwards'</span>, </span><br><span class="line"> <span class="attr">easing</span>: <span class="string">'ease-in-out'</span></span><br><span class="line"> });</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"><span class="variable language_">window</span>.<span class="property">onload</span> = <span class="keyword">function</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="title function_">show</span>()</span><br><span class="line">}<span class="comment">//这里选择触发方式，默认是加载完成出现弹窗</span></span><br><span class="line"><span class="comment">//要让弹窗出现调用show()，隐藏调用hide()即可</span></span><br><span class="line">popup.<span class="title function_">insertBefore</span>(close, popup.<span class="property">firstChild</span>);</span><br><span class="line">close.<span class="property">onclick</span> = <span class="keyword">function</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="title function_">hide</span>();</span><br><span class="line"> };</span><br></pre></td></tr></table></figure><p>然后在主题配置文件的bottom部分引入</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">- <span class="language-xml"><span class="tag"><<span class="name">script</span> <span class="attr">src</span>=<span class="string">"/js/textWindow.js"</span>></span><span class="tag"></<span class="name">script</span>></span></span></span><br></pre></td></tr></table></figure><ol start="2"><li>引入<code>.css</code>文件</li></ol><p>在 <code>~\themes\butterfly\source\css\</code> 新建 <code>textWindow.css</code> 文件，复制下面的代码，<strong>注意注释</strong></p><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"><span class="selector-attr">[data-theme=<span class="string">'light'</span>]</span> <span class="selector-id">#popup</span> {<span class="comment">/*根据网站明暗更改*/</span></span><br><span class="line"> <span class="attribute">background-color</span>: <span class="number">#e1e1e1</span>;<span class="comment">/*这里更改主体背景色*/</span></span><br><span class="line"> <span class="attribute">box-shadow</span>: <span class="number">0</span> <span class="number">0</span> <span class="number">10px</span> <span class="built_in">rgb</span>(<span class="number">114</span>, <span class="number">113</span>, <span class="number">113</span>);</span><br><span class="line"> }</span><br><span class="line"><span class="selector-attr">[data-theme=<span class="string">'dark'</span>]</span> <span class="selector-id">#popup</span> {</span><br><span class="line"> <span class="attribute">background</span>: <span class="number">#3b443e</span> ;<span class="comment">/*这里更改主体背景色*/</span></span><br><span class="line"> <span class="attribute">box-shadow</span>: <span class="number">0</span> <span class="number">0</span> <span class="number">10px</span> <span class="built_in">rgb</span>(<span class="number">29</span>, <span class="number">29</span>, <span class="number">29</span>);</span><br><span class="line"> } </span><br><span class="line"></span><br><span class="line"><span class="selector-id">#popup</span> {</span><br><span class="line"> <span class="attribute">position</span>: fixed;</span><br><span class="line"> <span class="attribute">right</span>: <span class="number">1vh</span>;</span><br><span class="line"> <span class="attribute">top</span>: <span class="number">2vh</span>;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">350px</span>; </span><br><span class="line"> <span class="attribute">height</span>: <span class="number">125px</span>; </span><br><span class="line"> <span class="attribute">border</span>: <span class="number">8px</span> ;</span><br><span class="line"> <span class="attribute">z-index</span>: <span class="number">1000000</span>;</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">8px</span>;</span><br><span class="line"> <span class="attribute">opacity</span>: <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"><span class="selector-id">#popup</span> <span class="selector-tag">h1</span> {</span><br><span class="line"> <span class="attribute">font-size</span>: <span class="number">20px</span> <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">margin-left</span>: <span class="number">15px</span>;</span><br><span class="line"> <span class="attribute">margin-top</span>: <span class="number">10px</span>;</span><br><span class="line"> <span class="attribute">margin-bottom</span>: <span class="number">0px</span>;</span><br><span class="line"> }</span><br><span class="line"><span class="selector-id">#popup</span> <span class="selector-tag">p</span> {</span><br><span class="line"> <span class="attribute">position</span>: absolute;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">250px</span>;</span><br><span class="line"> <span class="attribute">font-size</span>: <span class="number">15px</span> <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">margin-left</span>: <span class="number">15px</span>;</span><br><span class="line"> <span class="attribute">margin-top</span>: <span class="number">0px</span> ;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"><span class="selector-id">#close</span> {</span><br><span class="line"> <span class="attribute">position</span>: absolute;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">50px</span>; </span><br><span class="line"> <span class="attribute">height</span>: <span class="number">110px</span>; </span><br><span class="line"> <span class="attribute">margin-left</span>: <span class="number">292.5px</span>; </span><br><span class="line"> <span class="attribute">margin-top</span>: <span class="number">7.5px</span>; </span><br><span class="line"> <span class="attribute">border</span>: none; </span><br><span class="line"> <span class="attribute">color</span>: black; </span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">8px</span>;</span><br><span class="line"> <span class="attribute">z-index</span>: <span class="number">1000001</span>;</span><br><span class="line"> <span class="attribute">background-color</span>: <span class="number">#b3b3b3</span>;<span class="comment">/*这里更改按钮背景色*/</span> </span><br><span class="line"> }</span><br><span class="line"></span><br></pre></td></tr></table></figure><p>然后在主题配置文件的head部分引入</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">- <link rel="stylesheet" href="/css/textWindow.css"></span><br></pre></td></tr></table></figure><h2 id="更改加载动画本站同款"><a class="markdownIt-Anchor" href="#更改加载动画本站同款"></a> 更改加载动画（本站同款）</h2><p><a href="https://codepen.io/depy/pen/jOvymb">动画来源</a> 你也可以以我的代码为模板，在这个网站挑选自己喜欢的动画当作加载动画。</p><ol><li>修改源代码</li></ol><p>打开 <code>~\themes\butterfly\layout\includes\layout.pug</code> 按下面修改，大约在第十二行，<strong>注意缩进</strong></p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">- !=partial('includes/loading/index', {}, {cache: true})</span><br><span class="line">+ !=partial('includes/loading/loaded.ejs', {}, {cache: true})</span><br></pre></td></tr></table></figure><ol start="2"><li>在 <code>~\themes\butterfly\layout\includes\loading\</code> 新建<code>loaded.ejs</code> ，复制下面的代码</li></ol><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br></pre></td><td class="code"><pre><span class="line"><% if (theme.preloader.enable) { %></span><br><span class="line"> <script></span><br><span class="line"> document.body.style.overflow = 'hidden';</span><br><span class="line"> </script></span><br><span class="line"> <section class='loader'></span><br><span class="line"> <div class='loader-center'></span><br><span class="line"> <div class='chars'></span><br><span class="line"> <span class='char brace'>{</span></span><br><span class="line"> <span class='dots'></span><br><span class="line"> <span class='char dot _dot-1'>.</span></span><br><span class="line"> <span class='char dot _dot-2'>.</span></span><br><span class="line"> <span class='char dot _dot-3'>.</span></span><br><span class="line"> </span></span><br><span class="line"> <span class='char brace'>}</span></span><br><span class="line"> </div></span><br><span class="line"> </div></span><br><span class="line"> </section></span><br><span class="line"> </span><br><span class="line"> <script></span><br><span class="line"> var endLoading = function () {</span><br><span class="line"> document.body.style.overflow = 'auto';</span><br><span class="line"> var loader = document.querySelector('section.loader');</span><br><span class="line"> loader.classList.add('loading');</span><br><span class="line"> setTimeout(function() {</span><br><span class="line"> loader.style.display = 'none';</span><br><span class="line"> }, 1000);</span><br><span class="line"> }</span><br><span class="line"> setTimeout(function() {</span><br><span class="line"> window.addEventListener('load',endLoading);</span><br><span class="line"> }, 500);</span><br><span class="line"> </script></span><br><span class="line"> <% } %></span><br><span class="line"> </span><br></pre></td></tr></table></figure><ol start="3"><li>在 <code>~\themes\butterfly\source\css\</code> 新建<code>loaded.css</code> ，复制下面的代码</li></ol><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br><span class="line">160</span><br><span class="line">161</span><br><span class="line">162</span><br><span class="line">163</span><br><span class="line">164</span><br><span class="line">165</span><br><span class="line">166</span><br><span class="line">167</span><br><span class="line">168</span><br><span class="line">169</span><br><span class="line">170</span><br></pre></td><td class="code"><pre><span class="line"><span class="selector-tag">section</span><span class="selector-class">.loader</span> {</span><br><span class="line"> <span class="attribute">font-family</span>: Consolas, monaco, monospace;</span><br><span class="line"> <span class="attribute">position</span>:fixed;</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>; <span class="attribute">left</span>:<span class="number">0</span>; <span class="attribute">right</span>:<span class="number">0</span>; <span class="attribute">bottom</span>:<span class="number">0</span>;</span><br><span class="line"> <span class="attribute">background-color</span>:<span class="number">#232427</span>;</span><br><span class="line"> <span class="attribute">z-index</span>: <span class="number">100000</span>;</span><br><span class="line"> <span class="attribute">color</span>:<span class="number">#FF893A</span>;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">100%</span>;</span><br><span class="line">}</span><br><span class="line"><span class="selector-tag">section</span><span class="selector-class">.loader</span> <span class="selector-class">.loader-center</span> {</span><br><span class="line"> <span class="attribute">width</span>:<span class="number">300px</span>;</span><br><span class="line"> <span class="attribute">height</span>:<span class="number">100px</span>;</span><br><span class="line"> <span class="attribute">line-height</span>:<span class="number">100px</span>;</span><br><span class="line"> </span><br><span class="line"> <span class="attribute">margin</span>:<span class="number">0</span> auto;</span><br><span class="line"> <span class="attribute">text-align</span>:center;</span><br><span class="line"> <span class="attribute">font-size</span>:<span class="number">38px</span>;</span><br><span class="line"> <span class="attribute">letter-spacing</span>:-<span class="number">6px</span>;</span><br><span class="line"> </span><br><span class="line"> <span class="attribute">position</span>:absolute;</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">50%</span>; <span class="attribute">left</span>:<span class="number">50%</span>;</span><br><span class="line"> <span class="attribute">margin-left</span>:-<span class="number">150px</span>; <span class="attribute">margin-top</span>:-<span class="number">50px</span>;</span><br><span class="line"> </span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">section</span><span class="selector-class">.loader</span> <span class="selector-class">.loader-center</span> <span class="selector-class">.chars</span> <span class="selector-class">.dots</span> <span class="selector-class">.char</span> {</span><br><span class="line"> <span class="attribute">font-size</span>:<span class="number">150%</span>;</span><br><span class="line"> <span class="attribute">display</span>:inline-block;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">/* animation starts here */</span></span><br><span class="line"><span class="selector-class">.dots</span> <span class="selector-class">.dot</span> {</span><br><span class="line"> <span class="attribute">position</span>:relative;</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>; <span class="attribute">left</span>:<span class="number">0</span>; </span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dot</span>._dot-<span class="number">1</span> {</span><br><span class="line"> <span class="attribute">animation</span>:dot_1 <span class="number">1s</span> ease-in-out infinite;</span><br><span class="line"> <span class="attribute">animation-fill-mode</span>: backwards;</span><br><span class="line"> <span class="attribute">animation-direction</span>: alternate;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dot</span>._dot-<span class="number">2</span> {</span><br><span class="line"> <span class="attribute">animation</span>:dot_2 <span class="number">1s</span> ease-in-out infinite;</span><br><span class="line"> <span class="attribute">animation-fill-mode</span>: backwards;</span><br><span class="line"> <span class="attribute">animation-direction</span>: alternate;</span><br><span class="line"> <span class="attribute">animation-delay</span>:<span class="number">1s</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dot</span>._dot-<span class="number">3</span> {</span><br><span class="line"> <span class="attribute">animation</span>:dot_3 <span class="number">1s</span> ease-in-out infinite;</span><br><span class="line"> <span class="attribute">animation-fill-mode</span>: backwards;</span><br><span class="line"> <span class="attribute">animation-direction</span>: alternate;</span><br><span class="line"> <span class="attribute">animation-delay</span>:<span class="number">0.5s</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">@keyframes</span> dot_1 {</span><br><span class="line"> <span class="number">0%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">50%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">30px</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">20px</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">100%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0px</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">40px</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">@keyframes</span> dot_2 {</span><br><span class="line"> <span class="number">0%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">50%</span> {</span><br><span class="line"> <span class="attribute">top</span>:-<span class="number">30px</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">20px</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">100%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0px</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">40px</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">@keyframes</span> dot_3 {</span><br><span class="line"> <span class="number">0%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">50%</span> {</span><br><span class="line"> <span class="attribute">top</span>:-<span class="number">30px</span>;</span><br><span class="line"> <span class="attribute">left</span>:-<span class="number">40px</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="number">100%</span> {</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0px</span>;</span><br><span class="line"> <span class="attribute">left</span>:-<span class="number">80px</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">section</span> <span class="selector-class">.author</span> {</span><br><span class="line"> <span class="attribute">position</span>:fixed;</span><br><span class="line"> <span class="attribute">top</span>:<span class="number">0</span>; <span class="attribute">bottom</span>:<span class="number">0</span>;</span><br><span class="line"> <span class="attribute">left</span>:<span class="number">0px</span>;</span><br><span class="line"> </span><br><span class="line"> <span class="attribute">font-size</span>:<span class="number">80%</span>;</span><br><span class="line"> <span class="attribute">transform</span>:<span class="built_in">rotate</span>(-<span class="number">10deg</span>) <span class="built_in">translate</span>(<span class="number">50px</span>, <span class="number">20px</span>);</span><br><span class="line"> </span><br><span class="line"> <span class="attribute">padding</span>:<span class="number">5px</span> <span class="number">0</span>;</span><br><span class="line"> <span class="attribute">text-align</span>:center;</span><br><span class="line"> </span><br><span class="line"> <span class="attribute">color</span>:<span class="number">#eee</span>;</span><br><span class="line"> <span class="attribute">opacity</span>:<span class="number">0.8</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">section</span> <span class="selector-class">.author</span> <span class="selector-tag">a</span> {</span><br><span class="line"> <span class="attribute">color</span>:<span class="number">#78ECB4</span>;</span><br><span class="line"> <span class="attribute">text-decoration</span>:none;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">section</span> <span class="selector-class">.author</span> <span class="selector-tag">a</span><span class="selector-pseudo">:hover</span> {</span><br><span class="line"> <span class="attribute">color</span>:#<span class="number">60</span> D69D;</span><br><span class="line">}</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment">* Affiliate</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line"><span class="selector-class">.affiliate-container</span> <span class="selector-class">.the-text</span> {</span><br><span class="line"> <span class="attribute">background-color</span>: <span class="built_in">rgba</span>(<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>,<span class="number">0.5</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.affiliate-container</span> {</span><br><span class="line"> <span class="attribute">opacity</span>: <span class="number">0.6</span>;</span><br><span class="line"> <span class="attribute">position</span>: absolute;</span><br><span class="line"> <span class="attribute">right</span>: -<span class="number">20px</span>;</span><br><span class="line"> <span class="attribute">top</span>: <span class="number">0px</span>;</span><br><span class="line"> <span class="attribute">transform</span>: <span class="built_in">scale</span>(.<span class="number">8</span>);</span><br><span class="line"> <span class="attribute">transition</span>: <span class="number">0.2s</span> all ease-in-out;</span><br><span class="line"> <span class="attribute">margin-top</span>: <span class="number">0</span>;</span><br><span class="line"> <span class="attribute">justify-content</span>: flex-end;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.affiliate-container</span><span class="selector-pseudo">:hover</span> {</span><br><span class="line"> <span class="attribute">opacity</span>: <span class="number">0.8</span>;</span><br><span class="line"> <span class="attribute">transform</span>: <span class="built_in">scale</span>(<span class="number">1</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">/*退出，组件再loaded.ejs*/</span></span><br><span class="line"><span class="selector-class">.loader</span> {</span><br><span class="line"> <span class="attribute">opacity</span>: <span class="number">1</span>;</span><br><span class="line"> <span class="attribute">transform</span>: <span class="built_in">scale</span>(<span class="number">1</span>);</span><br><span class="line"> <span class="attribute">transition</span>: opacity <span class="number">1s</span> ease-in-out, transform <span class="number">1s</span> ease-in-out;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.loader</span><span class="selector-class">.loading</span> {</span><br><span class="line"> <span class="attribute">opacity</span>: <span class="number">0</span>;</span><br><span class="line"> <span class="attribute">transform</span>: <span class="built_in">scale</span>(<span class="number">2</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br></pre></td></tr></table></figure><p>然后在主题配置文件的head部分引入</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">- <link rel="stylesheet" href="/css/loaded.css" ></span><br></pre></td></tr></table></figure><h2 id="修改链接悬停样式"><a class="markdownIt-Anchor" href="#修改链接悬停样式"></a> 修改链接悬停样式</h2><p>打开 <code>~\themes\butterfly\source\css\_layout\post.styl</code> ，按下面修改，大约在80行</p><figure class="highlight stylus"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"> <span class="selector-tag">a</span></span><br><span class="line"> <span class="attribute">color</span>: <span class="variable">$theme</span>-link-color</span><br><span class="line"></span><br><span class="line"> <span class="selector-pseudo">&:hover</span></span><br><span class="line">- <span class="attribute">text-decoration</span>: underline </span><br><span class="line">+ <span class="attribute">color</span>: <span class="built_in">rgb</span>(<span class="number">215</span>, <span class="number">215</span>, <span class="number">215</span>)</span><br></pre></td></tr></table></figure><h2 id="接入aichatgpt机器人"><a class="markdownIt-Anchor" href="#接入aichatgpt机器人"></a> 接入ai（chatgpt）机器人</h2><h3 id="创建机器人new-bot"><a class="markdownIt-Anchor" href="#创建机器人new-bot"></a> 😆创建机器人New bot</h3><p>这次借助的是<a href="https://chatthing.ai/">Chat Thing</a> 网站，免费版支持gpt-3</p><ol><li>进入后注册登录，然后会看到仪表盘。</li><li>创建机器人，注意免费版只能创建一个机器人。</li><li>设置机器人的基础信息，注意催眠的地方在<strong>Advanced settings</strong>中最下面</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/image-20230809203623323.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/image-20230809203623323.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809203623323" /></p><h3 id="设置-data-source-数据来源"><a class="markdownIt-Anchor" href="#设置-data-source-数据来源"></a> 🫤设置 Data source 数据来源</h3><p><strong>注意免费版只能有一个数据来源</strong>，但一般也够了</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092140893.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092140893.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809214044613" /></p><p>有很多中不同方式，这里介绍两种方式：</p><ol><li>Website：（因为可以用sitemap）如图，输入网址即可</li></ol><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092043992.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092043992.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809204349728" width="50%" height="50%" /><ol start="2"><li><p>RSS订阅：点击你的xlog主页的RSS按钮，复制新打开网页的网址到下图位置即可即可</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100858296.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100858296.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810085810825" /></p></li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100859979.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100859979.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810085956865" /></p><p><big><strong>注意要保存并同步数据源</strong></big></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100901485.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100901485.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810090147307" /></p><p>这样，数据源也设置好啦</p><h3 id="嵌入博客-embed-bot"><a class="markdownIt-Anchor" href="#嵌入博客-embed-bot"></a> 🥰嵌入博客 Embed Bot</h3><p>点开Embed Bot，参考下图翻译，选择你想要的方式插入就好了</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092045929.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092045929.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809204552761" width="50%" height="50%"><p>如果是插入文章/页面，那么很简单，直接在对应<code>.md</code>插入你看到的代码就好了。</p><p>如果想要全局小组件，直接在bottom引入：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><script src="https://chatthing.ai/chat-widget.js" type="text/javascript" id="<替换为你在小组件代码中看到的id(保留引号)>" async defer></script></span><br></pre></td></tr></table></figure><p>效果分别如图</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092105044.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092105044.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809210531921" width="30%" height="30%" /><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092053443.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092053443.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809205358309" width="80%" height="80%" /><h2 id="引入樱花特效"><a class="markdownIt-Anchor" href="#引入樱花特效"></a> 引入樱花特效</h2><p>在 <code>~\themes\butterfly\source\js\</code> 新建 <code>sakura.js</code> 文件，复制下面的代码。</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">if</span> (<span class="variable language_">window</span>.<span class="property">location</span>.<span class="property">pathname</span> === <span class="string">'/'</span>) {</span><br><span class="line"> <span class="keyword">var</span> stop, staticx;</span><br><span class="line"> <span class="keyword">var</span> img = <span class="keyword">new</span> <span class="title class_">Image</span>();</span><br><span class="line"> img.<span class="property">src</span> = <span class="string">"data:image/png;base64,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"</span>;</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">Sakura</span>(<span class="params">x, y, s, r, fn</span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">x</span> = x;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">y</span> = y;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">s</span> = s;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">r</span> = r;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">fn</span> = fn;</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">Sakura</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">draw</span> = <span class="keyword">function</span> (<span class="params">cxt</span>) {</span><br><span class="line"> cxt.<span class="title function_">save</span>();</span><br><span class="line"> <span class="keyword">var</span> xc = <span class="number">40</span> * <span class="variable language_">this</span>.<span class="property">s</span> / <span class="number">4</span>;</span><br><span class="line"> cxt.<span class="title function_">translate</span>(<span class="variable language_">this</span>.<span class="property">x</span>, <span class="variable language_">this</span>.<span class="property">y</span>);</span><br><span class="line"> cxt.<span class="title function_">rotate</span>(<span class="variable language_">this</span>.<span class="property">r</span>);</span><br><span class="line"> cxt.<span class="title function_">drawImage</span>(img, <span class="number">0</span>, <span class="number">0</span>, <span class="number">40</span> * <span class="variable language_">this</span>.<span class="property">s</span>, <span class="number">40</span> * <span class="variable language_">this</span>.<span class="property">s</span>)</span><br><span class="line"> cxt.<span class="title function_">restore</span>();</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">Sakura</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">update</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">x</span> = <span class="variable language_">this</span>.<span class="property">fn</span>.<span class="title function_">x</span>(<span class="variable language_">this</span>.<span class="property">x</span>, <span class="variable language_">this</span>.<span class="property">y</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">y</span> = <span class="variable language_">this</span>.<span class="property">fn</span>.<span class="title function_">y</span>(<span class="variable language_">this</span>.<span class="property">y</span>, <span class="variable language_">this</span>.<span class="property">y</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">r</span> = <span class="variable language_">this</span>.<span class="property">fn</span>.<span class="title function_">r</span>(<span class="variable language_">this</span>.<span class="property">r</span>);</span><br><span class="line"> <span class="keyword">if</span> (<span class="variable language_">this</span>.<span class="property">x</span> > <span class="variable language_">window</span>.<span class="property">innerWidth</span> || <span class="variable language_">this</span>.<span class="property">x</span> < <span class="number">0</span> || <span class="variable language_">this</span>.<span class="property">y</span> > <span class="variable language_">window</span>.<span class="property">innerHeight</span> || <span class="variable language_">this</span>.<span class="property">y</span> < <span class="number">0</span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">r</span> = <span class="title function_">getRandom</span>(<span class="string">'fnr'</span>);</span><br><span class="line"> <span class="keyword">if</span> (<span class="title class_">Math</span>.<span class="title function_">random</span>() > <span class="number">0.4</span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">x</span> = <span class="title function_">getRandom</span>(<span class="string">'x'</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">y</span> = <span class="number">0</span>;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">s</span> = <span class="title function_">getRandom</span>(<span class="string">'s'</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">r</span> = <span class="title function_">getRandom</span>(<span class="string">'r'</span>);</span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">x</span> = <span class="variable language_">window</span>.<span class="property">innerWidth</span>;</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">y</span> = <span class="title function_">getRandom</span>(<span class="string">'y'</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">s</span> = <span class="title function_">getRandom</span>(<span class="string">'s'</span>);</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">r</span> = <span class="title function_">getRandom</span>(<span class="string">'r'</span>);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">list</span> = [];</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">push</span> = <span class="keyword">function</span> (<span class="params">sakura</span>) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">list</span>.<span class="title function_">push</span>(sakura);</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">update</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>, len = <span class="variable language_">this</span>.<span class="property">list</span>.<span class="property">length</span>; i < len; i++) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">list</span>[i].<span class="title function_">update</span>();</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">draw</span> = <span class="keyword">function</span> (<span class="params">cxt</span>) {</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>, len = <span class="variable language_">this</span>.<span class="property">list</span>.<span class="property">length</span>; i < len; i++) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">list</span>[i].<span class="title function_">draw</span>(cxt);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">get</span> = <span class="keyword">function</span> (<span class="params">i</span>) {</span><br><span class="line"> <span class="keyword">return</span> <span class="variable language_">this</span>.<span class="property">list</span>[i];</span><br><span class="line"> }</span><br><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">size</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">return</span> <span class="variable language_">this</span>.<span class="property">list</span>.<span class="property">length</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">getRandom</span>(<span class="params">option</span>) {</span><br><span class="line"> <span class="keyword">var</span> ret, random;</span><br><span class="line"> <span class="keyword">switch</span> (option) {</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'x'</span>:</span><br><span class="line"> ret = <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="variable language_">window</span>.<span class="property">innerWidth</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'y'</span>:</span><br><span class="line"> ret = <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="variable language_">window</span>.<span class="property">innerHeight</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'s'</span>:</span><br><span class="line"> ret = <span class="title class_">Math</span>.<span class="title function_">random</span>();</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'r'</span>:</span><br><span class="line"> ret = <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="number">6</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'fnx'</span>:</span><br><span class="line"> random = -<span class="number">0.5</span> + <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="number">1</span>;</span><br><span class="line"> ret = <span class="keyword">function</span> (<span class="params">x, y</span>) {</span><br><span class="line"> <span class="keyword">return</span> x + <span class="number">0.5</span> * random - <span class="number">1.7</span>;</span><br><span class="line"> };</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'fny'</span>:</span><br><span class="line"> random = <span class="number">1.5</span> + <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="number">0.7</span></span><br><span class="line"> ret = <span class="keyword">function</span> (<span class="params">x, y</span>) {</span><br><span class="line"> <span class="keyword">return</span> y + random;</span><br><span class="line"> };</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'fnr'</span>:</span><br><span class="line"> random = <span class="title class_">Math</span>.<span class="title function_">random</span>() * <span class="number">0.03</span>;</span><br><span class="line"> ret = <span class="keyword">function</span> (<span class="params">r</span>) {</span><br><span class="line"> <span class="keyword">return</span> r + random;</span><br><span class="line"> };</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> ret;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">startSakura</span>(<span class="params"></span>) {</span><br><span class="line"> requestAnimationFrame = <span class="variable language_">window</span>.<span class="property">requestAnimationFrame</span> || <span class="variable language_">window</span>.<span class="property">mozRequestAnimationFrame</span> || <span class="variable language_">window</span>.<span class="property">webkitRequestAnimationFrame</span> || <span class="variable language_">window</span>.<span class="property">msRequestAnimationFrame</span> || <span class="variable language_">window</span>.<span class="property">oRequestAnimationFrame</span>;</span><br><span class="line"> <span class="keyword">var</span> canvas = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">'canvas'</span>),</span><br><span class="line"> cxt;</span><br><span class="line"> staticx = <span class="literal">true</span>;</span><br><span class="line"> canvas.<span class="property">height</span> = <span class="variable language_">window</span>.<span class="property">innerHeight</span>;</span><br><span class="line"> canvas.<span class="property">width</span> = <span class="variable language_">window</span>.<span class="property">innerWidth</span>;</span><br><span class="line"> canvas.<span class="title function_">setAttribute</span>(<span class="string">'style'</span>, <span class="string">'position: fixed;left: 0;top: 0;pointer-events: none;'</span>);</span><br><span class="line"> canvas.<span class="title function_">setAttribute</span>(<span class="string">'id'</span>, <span class="string">'canvas_sakura'</span>);</span><br><span class="line"> <span class="variable language_">document</span>.<span class="title function_">getElementsByTagName</span>(<span class="string">'body'</span>)[<span class="number">0</span>].<span class="title function_">appendChild</span>(canvas);</span><br><span class="line"> cxt = canvas.<span class="title function_">getContext</span>(<span class="string">'2d'</span>);</span><br><span class="line"> <span class="keyword">var</span> sakuraList = <span class="keyword">new</span> <span class="title class_">SakuraList</span>();</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i < <span class="number">50</span>; i++) {</span><br><span class="line"> <span class="keyword">var</span> sakura, randomX, randomY, randomS, randomR, randomFnx, randomFny;</span><br><span class="line"> randomX = <span class="title function_">getRandom</span>(<span class="string">'x'</span>);</span><br><span class="line"> randomY = <span class="title function_">getRandom</span>(<span class="string">'y'</span>);</span><br><span class="line"> randomR = <span class="title function_">getRandom</span>(<span class="string">'r'</span>);</span><br><span class="line"> randomS = <span class="title function_">getRandom</span>(<span class="string">'s'</span>);</span><br><span class="line"> randomFnx = <span class="title function_">getRandom</span>(<span class="string">'fnx'</span>);</span><br><span class="line"> randomFny = <span class="title function_">getRandom</span>(<span class="string">'fny'</span>);</span><br><span class="line"> randomFnR = <span class="title function_">getRandom</span>(<span class="string">'fnr'</span>);</span><br><span class="line"> sakura = <span class="keyword">new</span> <span class="title class_">Sakura</span>(randomX, randomY, randomS, randomR, {</span><br><span class="line"> <span class="attr">x</span>: randomFnx,</span><br><span class="line"> <span class="attr">y</span>: randomFny,</span><br><span class="line"> <span class="attr">r</span>: randomFnR</span><br><span class="line"> });</span><br><span class="line"> sakura.<span class="title function_">draw</span>(cxt);</span><br><span class="line"> sakuraList.<span class="title function_">push</span>(sakura);</span><br><span class="line"> }</span><br><span class="line"> stop = <span class="title function_">requestAnimationFrame</span>(<span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> cxt.<span class="title function_">clearRect</span>(<span class="number">0</span>, <span class="number">0</span>, canvas.<span class="property">width</span>, canvas.<span class="property">height</span>);</span><br><span class="line"> sakuraList.<span class="title function_">update</span>();</span><br><span class="line"> sakuraList.<span class="title function_">draw</span>(cxt);</span><br><span class="line"> stop = <span class="title function_">requestAnimationFrame</span>(<span class="variable language_">arguments</span>.<span class="property">callee</span>);</span><br><span class="line"> })</span><br><span class="line"> }</span><br><span class="line"> <span class="variable language_">window</span>.<span class="property">onresize</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">var</span> canvasSnow = <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">'canvas_snow'</span>);</span><br><span class="line"> }</span><br><span class="line"> img.<span class="property">onload</span> = <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="title function_">startSakura</span>();</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">stopp</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">if</span> (staticx) {</span><br><span class="line"> <span class="keyword">var</span> child = <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">"canvas_sakura"</span>);</span><br><span class="line"> child.<span class="property">parentNode</span>.<span class="title function_">removeChild</span>(child);</span><br><span class="line"> <span class="variable language_">window</span>.<span class="title function_">cancelAnimationFrame</span>(stop);</span><br><span class="line"> staticx = <span class="literal">false</span>;</span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> <span class="title function_">startSakura</span>();</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>然后在bottom引入</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">- <script src="/js/sakura.js"></script></span><br></pre></td></tr></table></figure><p>hideToggle 旧版实现</p><p>如果你仅仅想在特定界面引入樱花特效，可以修改<code>~\themes\butterfly\layout\includes\header\index.pug</code> 文件，在你想添加的页面引入文件。</p><p>例如我只想在首页引入 <code>sakura.js</code> ，可以这样修改：<strong>注意缩进</strong></p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">if !theme.disable_top_img && page.top_img !== false</span><br><span class="line">+ if is_home()</span><br><span class="line">+ link(rel="stylesheet", href="/js/sakura.css")</span><br></pre></td></tr></table></figure><p>如果你使用了pjax，会发现尽管仅在首页引入 <code>sakuea.js</code> 但是樱花特效每个页面都会出现，这时我们需要修改代码。首先把之前引入的 <code>sakura.js</code> 删除 <strong>（不是删除文件，是删除引入）</strong> ，同一目录新建另外一个 <code>better_sakura.js</code> 文件，插入以下代码。</p><p>这里还加了一个移动设备判断，如果不需要把那句判断删去即可 <strong>（大括号也要删干净）</strong></p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 监听 pjax:complete 事件</span></span><br><span class="line"><span class="variable language_">document</span>.<span class="title function_">addEventListener</span>(<span class="string">'pjax:complete'</span>, <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">if</span> (!<span class="regexp">/Mobi|Android|iPhone/i</span>.<span class="title function_">test</span>(navigator.<span class="property">userAgent</span>)) {</span><br><span class="line"> <span class="keyword">if</span> (<span class="variable language_">window</span>.<span class="property">location</span>.<span class="property">pathname</span> === <span class="string">'/'</span>) {<span class="comment">//这里改成你想插入的页面的地址，例如首页是'/'，友链页面是'/link/'</span></span><br><span class="line"> <span class="keyword">var</span> script = <span class="variable language_">document</span>.<span class="title function_">createElement</span>(<span class="string">'script'</span>);</span><br><span class="line"> script.<span class="property">src</span> = <span class="string">'/js/sakura.js'</span>;</span><br><span class="line"> <span class="variable language_">document</span>.<span class="property">body</span>.<span class="title function_">appendChild</span>(script);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="variable language_">document</span>.<span class="title function_">addEventListener</span>(<span class="string">'pjax:send'</span>, <span class="keyword">function</span> (<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">var</span> canvasSakura = <span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">'canvas_sakura'</span>);</span><br><span class="line"> <span class="keyword">if</span> (canvasSakura) {</span><br><span class="line"> canvasSakura.<span class="property">parentNode</span>.<span class="title function_">removeChild</span>(canvasSakura);</span><br><span class="line"> }</span><br><span class="line"> });</span><br><span class="line">});</span><br></pre></td></tr></table></figure><p>endhideToggle</p><p>如果你仅仅想在特定界面引入樱花特效，可以在 <code>sakura.js</code> 代码大约51行的位置进行如下修改（对pjax同样有效）</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"> <span class="title class_">SakuraList</span>.<span class="property"><span class="keyword">prototype</span></span>.<span class="property">draw</span> = <span class="keyword">function</span> (<span class="params">cxt</span>) {<span class="comment">//如果不是主页就返回</span></span><br><span class="line">+ <span class="keyword">if</span> (<span class="variable language_">window</span>.<span class="property">location</span>.<span class="property">pathname</span> !== <span class="string">'/'</span>) {<span class="comment">//这里要填你想添加特效的网页相对位置。</span></span><br><span class="line">+ <span class="keyword">return</span>;<span class="comment">//例如想添加到友链界面，需要写window.location.pathname !== '/link/'</span></span><br><span class="line">+ }</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>, len = <span class="variable language_">this</span>.<span class="property">list</span>.<span class="property">length</span>; i < len; i++) {</span><br><span class="line"> <span class="variable language_">this</span>.<span class="property">list</span>[i].<span class="title function_">draw</span>(cxt);</span><br><span class="line"> }</span><br><span class="line"> }</span><br></pre></td></tr></table></figure><h2 id="文章标题美化"><a class="markdownIt-Anchor" href="#文章标题美化"></a> 文章标题美化</h2><p>随便引入一个 <code>.css</code> 文件，插入以下代码</p><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="selector-attr">[data-theme=<span class="string">'light'</span>]</span> <span class="selector-tag">h1</span> {<span class="comment">/*这里可以改成自己喜欢的渐变色*/</span></span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to right, <span class="number">#365262</span> <span class="number">0%</span>, <span class="number">#1c6a54</span> <span class="number">50%</span>, <span class="number">#254050</span> <span class="number">100%</span>);</span><br><span class="line"> <span class="attribute">background-clip</span>: text;</span><br><span class="line"> -webkit-<span class="attribute">background-clip</span>: text;</span><br><span class="line"> -webkit-<span class="selector-tag">text</span>-<span class="attribute">fill</span>-<span class="attribute">color</span>: transparent;</span><br><span class="line">}</span><br><span class="line"><span class="selector-attr">[data-theme=<span class="string">'dark'</span>]</span> <span class="selector-tag">h1</span> {<span class="comment">/*这里可以改成自己喜欢的渐变色*/</span></span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to right, <span class="number">#ffa9c4</span> <span class="number">0%</span>, <span class="number">#7fe6e1</span> <span class="number">50%</span>, <span class="number">#e68daa</span> <span class="number">100%</span>);</span><br><span class="line"> <span class="attribute">background-clip</span>: text;</span><br><span class="line"> -webkit-<span class="attribute">background-clip</span>: text;</span><br><span class="line"> -webkit-<span class="selector-tag">text</span>-<span class="attribute">fill</span>-<span class="attribute">color</span>: transparent;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="为site-icon添加alt属性"><a class="markdownIt-Anchor" href="#为site-icon添加alt属性"></a> 为site-icon添加alt属性</h2><h3 id="发现问题"><a class="markdownIt-Anchor" href="#发现问题"></a> 🫤发现问题</h3><p>我在bing站长工具扫描网站时，发现了一个问题，如图</p><p>网站的每个页面都有一张图片缺少了alt属性，借助bing url检查的帮助，我发现是网站的图标缺少了alt属性。</p><p><s>大佬也有百密一疏呢</s></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202307031844677.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202307031844677.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230703184447160" /></p><h3 id="解决问题"><a class="markdownIt-Anchor" href="#解决问题"></a> 😋解决问题</h3><p>需要在 <code>nav.pug</code>修改代码</p><p>将图示圈出的代码替换成下列代码</p><blockquote><p>如果是通过npm安装，</p><p>地址为<code>./node_modules/hexo-theme-butterfly/layout/includes/header/nav.pug</code></p><p>如果是从github clone下来的，</p><p>地址是<code>./themes/butterfly/layout/includes/header/nav.pug</code></p></blockquote><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">img.site-icon(src=url_for(theme.nav.logo), alt="Site Icon")</span><br><span class="line">#引号内的Site Icon可以替换</span><br></pre></td></tr></table></figure><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202307032047563.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202307032047563.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230703204759360" /></p>]]></content>
<tags>
<tag> 教程 </tag>
</tags>
</entry>
<entry>
<title>在xLog托管博客</title>
<link href="/posts/6b13026f.html"/>
<url>/posts/6b13026f.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/2021021012571650539.jpg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/2021021012571650539.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="介绍"><a class="markdownIt-Anchor" href="#介绍"></a> 介绍</h2><p><a href="https://xlog.app/about">xLog</a> 是一个基于Web3、区块链的在线博客平台。</p><h2 id="注册钱包"><a class="markdownIt-Anchor" href="#注册钱包"></a> 注册钱包</h2><p><strong>注意</strong>xLog完全开源，如果你对于“钱包”二字敏感，可以自行查阅它在github上的仓库。并且，你在xLog上的更新也是以交易的形式完成的，每次更改都需要你在钱包输入密码确认，<strong>但不会实际产生现实钱币数量的更改(仅限在xLog上的交易)</strong>。</p><p>如果你从未接触过，那么打开<a href="https://xlog.app/about">xLog</a>，在右上角找到连接，选择你喜欢的钱包（我用的是<a href="https://www.coinbase.com">Coinbase Wallet</a>），找到它的官网，下载APP，按照软件的提示操作，然后选择你注册的钱包登录。</p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230820162003780.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230820162003780.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230820162003780" height =40% width=40% /><h2 id="开始写作"><a class="markdownIt-Anchor" href="#开始写作"></a> 开始写作</h2><p>如图：</p><p>xLog支持文章、作品集、页面三个发布方式。</p><p>文章支持mardown格式，注意<strong>Latex公式需要套两个$$</strong>，页面同理，作品集支持发布其他平台的作品放入，并自动抓取信息，单击即可跳转。</p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230820164450362.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/image-20230820164450362.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230820164450362" height =25% width=25% /><h2 id="自定义你的博客"><a class="markdownIt-Anchor" href="#自定义你的博客"></a> 自定义你的博客</h2><p>xLog支持引入css在仪表盘的设置->自定义css即可添加代码。</p><p>下面附上我的css代码，<a href="https://genkaim.xlog.app">效果预览</a>，它基于<a href="https://birdgg.me/xlog-cutom-css">@birdgg分享的css</a></p><p>可以试试两个代码，哪个更合你的口味（</p><p>我修改的主要有：</p><ol><li>更改鼠标指针</li><li>更改标题字体</li><li>删除暗色模式下文章部分阴影</li></ol><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span 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class="line">285</span><br><span class="line">286</span><br><span class="line">287</span><br><span class="line">288</span><br><span class="line">289</span><br><span class="line">290</span><br><span class="line">291</span><br><span class="line">292</span><br><span class="line">293</span><br><span class="line">294</span><br><span class="line">295</span><br><span class="line">296</span><br><span class="line">297</span><br><span class="line">298</span><br><span class="line">299</span><br><span class="line">300</span><br><span class="line">301</span><br><span class="line">302</span><br><span class="line">303</span><br><span class="line">304</span><br><span class="line">305</span><br><span class="line">306</span><br><span class="line">307</span><br><span class="line">308</span><br><span class="line">309</span><br><span class="line">310</span><br><span class="line">311</span><br><span class="line">312</span><br><span class="line">313</span><br><span class="line">314</span><br><span class="line">315</span><br><span class="line">316</span><br><span class="line">317</span><br><span class="line">318</span><br><span class="line">319</span><br><span class="line">320</span><br><span class="line">321</span><br><span class="line">322</span><br><span class="line">323</span><br><span class="line">324</span><br><span class="line">325</span><br><span class="line">326</span><br><span class="line">327</span><br><span class="line">328</span><br><span class="line">329</span><br><span class="line">330</span><br><span class="line">331</span><br><span class="line">332</span><br><span class="line">333</span><br><span class="line">334</span><br><span class="line">335</span><br><span class="line">336</span><br><span class="line">337</span><br><span class="line">338</span><br><span class="line">339</span><br><span class="line">340</span><br><span class="line">341</span><br><span class="line">342</span><br><span class="line">343</span><br><span class="line">344</span><br><span class="line">345</span><br><span class="line">346</span><br><span class="line">347</span><br><span class="line">348</span><br><span class="line">349</span><br><span class="line">350</span><br><span class="line">351</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">@import</span> url(<span class="string">"https://cdnjs.cloudflare.com/ajax/libs/lxgw-wenkai-screen-webfont/1.7.0/lxgwwenkaiscreenr.css"</span>);</span><br><span class="line"></span><br><span class="line"><span class="keyword">@font-face</span> {</span><br><span class="line"> <span class="attribute">font-family</span>: <span class="string">'Candyshop'</span>;</span><br><span class="line"> <span class="attribute">src</span>: <span class="built_in">url</span>(<span class="string">https://ipfs.4everland.xyz/ipfs/bafkreiaztv4ex5zlllmz5jqkrc3uouggdwfy6rrenemtdf3erlbd6bmfwm</span>);</span><br><span class="line"> <span class="attribute">font-display</span>: swap;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-pseudo">:root</span> {</span><br><span class="line"> <span class="attr">--theme-color</span>: <span class="number">#f7e78e</span> <span class="meta">!important</span>;</span><br><span class="line"> <span class="attr">--font-fans</span>: <span class="string">'SF Compact Rounded'</span>, <span class="string">'PingFang SC'</span>, <span class="string">'Microsoft YaHei'</span>, Lato, sans-serif;</span><br><span class="line"> <span class="attr">--header-height</span>: <span class="built_in">max</span>(<span class="number">50vh</span>, <span class="number">450px</span>);</span><br><span class="line"> <span class="attr">--grey-0</span>: <span class="number">#fff</span>;</span><br><span class="line"> <span class="attr">--grey-1</span>: <span class="number">#fdfdfd</span>;</span><br><span class="line"> <span class="attr">--grey-2</span>: <span class="number">#f7f7f7</span>;</span><br><span class="line"> <span class="attr">--grey-3</span>: <span class="number">#eff2f3</span>;</span><br><span class="line"> <span class="attr">--grey-4</span>: <span class="number">#ccc</span>;</span><br><span class="line"> <span class="attr">--grey-5</span>: <span class="number">#999</span>;</span><br><span class="line"> <span class="attr">--grey-6</span>: <span class="number">#666</span>;</span><br><span class="line"> <span class="attr">--grey-7</span>: <span class="number">#333</span>;</span><br><span class="line"> <span class="attr">--grey-8</span>: <span class="number">#222</span>;</span><br><span class="line"> <span class="attr">--grey-9</span>: <span class="number">#000</span>;</span><br><span class="line"> <span class="attr">--grey-1-a0</span>: <span class="built_in">rgba</span>(<span class="number">253</span>, <span class="number">253</span>, <span class="number">253</span>, <span class="number">0</span>);</span><br><span class="line"> <span class="attr">--grey-1-a7</span>: <span class="built_in">rgba</span>(<span class="number">253</span>, <span class="number">253</span>, <span class="number">253</span>, .<span class="number">7</span>);</span><br><span class="line"> <span class="attr">--grey-1-a5</span>: <span class="built_in">rgba</span>(<span class="number">253</span>, <span class="number">253</span>, <span class="number">253</span>, .<span class="number">5</span>);</span><br><span class="line"> <span class="attr">--grey-1-a3</span>: <span class="built_in">rgba</span>(<span class="number">253</span>, <span class="number">253</span>, <span class="number">253</span>, .<span class="number">3</span>);</span><br><span class="line"> <span class="attr">--grey-9-a1</span>: <span class="built_in">rgba</span>(<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, .<span class="number">1</span>);</span><br><span class="line"> <span class="attr">--grey-9-a5</span>: <span class="built_in">rgba</span>(<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, .<span class="number">5</span>);</span><br><span class="line"> <span class="attr">--grey-2-a0</span>: <span class="built_in">rgba</span>(<span class="number">247</span>, <span class="number">247</span>, <span class="number">247</span>, <span class="number">0</span>);</span><br><span class="line"> <span class="attr">--color-pink-light</span>: <span class="number">#ffe6fa</span>;</span><br><span class="line"> <span class="attr">--color-cyan-light</span>: <span class="number">#e3fdf5</span>;</span><br><span class="line"> <span class="attr">--color-red</span>: <span class="number">#e9546b</span>;</span><br><span class="line"> <span class="attr">--color-pink</span>: <span class="number">#ed6ea0</span>;</span><br><span class="line"> <span class="attr">--color-orange</span>: <span class="number">#ec8c69</span>;</span><br><span class="line"> <span class="attr">--color-yellow</span>: <span class="number">#eab700</span>;</span><br><span class="line"> <span class="attr">--color-green</span>: <span class="number">#0a7426</span>;</span><br><span class="line"> <span class="attr">--color-aqua</span>: <span class="number">#3e999f</span>;</span><br><span class="line"> <span class="attr">--color-blue</span>: <span class="number">#38a1db</span>;</span><br><span class="line"> <span class="attr">--color-purple</span>: <span class="number">#9d5b8b</span>;</span><br><span class="line"> <span class="attr">--color-grey</span>: <span class="number">#869194</span>;</span><br><span class="line"> <span class="attr">--color-red-a1</span>: <span class="built_in">rgba</span>(<span class="number">233</span>, <span class="number">84</span>, <span class="number">107</span>, .<span class="number">1</span>);</span><br><span class="line"> <span class="attr">--color-red-a3</span>: <span class="built_in">rgba</span>(<span class="number">233</span>, <span class="number">84</span>, <span class="number">107</span>, .<span class="number">3</span>);</span><br><span class="line"> <span class="attr">--color-pink-a3</span>: <span class="built_in">rgba</span>(<span class="number">237</span>, <span class="number">110</span>, <span class="number">160</span>, .<span class="number">3</span>);</span><br><span class="line"> <span class="attr">--color-pink-light-a3</span>: <span class="built_in">rgba</span>(<span class="number">255</span>, <span class="number">230</span>, <span class="number">250</span>, .<span class="number">3</span>);</span><br><span class="line"> <span class="attr">--color-pink-light-a5</span>: <span class="built_in">rgba</span>(<span class="number">255</span>, <span class="number">230</span>, <span class="number">250</span>, .<span class="number">5</span>);</span><br><span class="line"> <span class="attr">--color-pink-light-a7</span>: <span class="built_in">rgba</span>(<span class="number">255</span>, <span class="number">230</span>, <span class="number">250</span>, .<span class="number">7</span>);</span><br><span class="line"> <span class="attr">--body-bg-shadow</span>: <span class="built_in">var</span>(--grey-<span class="number">2</span>);</span><br><span class="line"> <span class="attr">--box-bg-shadow</span>: <span class="built_in">var</span>(--grey-<span class="number">9</span>-a1);</span><br><span class="line"> <span class="attr">--text-color</span>: <span class="built_in">var</span>(--grey-<span class="number">7</span>);</span><br><span class="line"> <span class="attr">--header-text-color</span>: <span class="built_in">var</span>(--grey-<span class="number">0</span>);</span><br><span class="line"><span class="comment">/* cursor: url('https://img2.birdgg.me/iku-cursor.png') 0 0, auto;*/</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">html</span><span class="selector-class">.dark</span> {</span><br><span class="line"> <span class="attr">--grey-0</span>: <span class="number">#222</span>;</span><br><span class="line"> <span class="attr">--grey-1</span>: <span class="number">#21252b</span>;</span><br><span class="line"> <span class="attr">--grey-2</span>: <span class="number">#363636</span>;</span><br><span class="line"> <span class="attr">--grey-3</span>: <span class="number">#444</span>;</span><br><span class="line"> <span class="attr">--grey-4</span>: <span class="number">#666</span>;</span><br><span class="line"> <span class="attr">--grey-5</span>: <span class="number">#aaa</span>;</span><br><span class="line"> <span class="attr">--grey-6</span>: <span class="number">#ccc</span>;</span><br><span class="line"> <span class="attr">--grey-7</span>: <span class="number">#ddd</span>;</span><br><span class="line"> <span class="attr">--grey-8</span>: <span class="number">#eee</span>;</span><br><span class="line"> <span class="attr">--grey-9</span>: <span class="number">#f7f7f7</span>;</span><br><span class="line"> <span class="attr">--grey-1-a7</span>: <span class="built_in">rgba</span>(<span class="number">34</span>, <span class="number">34</span>, <span class="number">34</span>, .<span class="number">7</span>);</span><br><span class="line"> <span class="attr">--grey-1-a5</span>: <span class="built_in">rgba</span>(<span class="number">34</span>, <span class="number">34</span>, <span class="number">34</span>, .<span class="number">5</span>);</span><br><span class="line"> <span class="attr">--grey-1-a3</span>: <span class="built_in">rgba</span>(<span class="number">34</span>, <span class="number">34</span>, <span class="number">34</span>, .<span class="number">3</span>);</span><br><span class="line"> <span class="attr">--grey-1-a0</span>: <span class="built_in">rgba</span>(<span class="number">34</span>, <span class="number">34</span>, <span class="number">34</span>, <span class="number">0</span>);</span><br><span class="line"> <span class="attr">--grey-9-a1</span>: <span class="built_in">rgba</span>(<span class="number">51</span>, <span class="number">51</span>, <span class="number">51</span>, .<span class="number">1</span>);</span><br><span class="line"> <span class="attr">--grey-2-a0</span>: <span class="built_in">rgba</span>(<span class="number">54</span>, <span class="number">54</span>, <span class="number">54</span>, <span class="number">0</span>);</span><br><span class="line"> <span class="attr">--color-pink-light</span>: <span class="number">#322d31</span>;</span><br><span class="line"> <span class="attr">--color-cyan-light</span>: <span class="number">#2d3230</span>;</span><br><span class="line"> <span class="attr">--color-red</span>: <span class="built_in">rgba</span>(<span class="number">237</span>, <span class="number">118</span>, <span class="number">137</span>, .<span class="number">9</span>);</span><br><span class="line"> <span class="attr">--color-pink</span>: <span class="built_in">rgba</span>(<span class="number">241</span>, <span class="number">139</span>, <span class="number">179</span>, .<span class="number">8</span>);</span><br><span class="line"> <span class="attr">--color-orange</span>: <span class="built_in">rgba</span>(<span class="number">240</span>, <span class="number">163</span>, <span class="number">135</span>, .<span class="number">8</span>);</span><br><span class="line"> <span class="attr">--color-yellow</span>: <span class="number">#ffe175</span>;</span><br><span class="line"> <span class="attr">--color-green</span>: <span class="number">#86c59d</span>;</span><br><span class="line"> <span class="attr">--color-aqua</span>: <span class="number">#97d3d6</span>;</span><br><span class="line"> <span class="attr">--color-blue</span>: <span class="number">#9cd0ed</span>;</span><br><span class="line"> <span class="attr">--color-purple</span>: <span class="number">#cfacc5</span>;</span><br><span class="line"> <span class="attr">--color-grey</span>: <span class="number">#c3c8ca</span>;</span><br><span class="line"> <span class="attr">--body-bg-shadow</span>: <span class="number">#000</span>;</span><br><span class="line"> <span class="attr">--box-bg-shadow</span>: <span class="number">#000</span>;</span><br><span class="line"> <span class="attr">--text-color</span>: <span class="built_in">var</span>(--grey-<span class="number">5</span>);</span><br><span class="line"> <span class="attr">--header-text-color</span>: <span class="built_in">var</span>(--grey-<span class="number">9</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-page</span> {</span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">linear-gradient</span>(to top, <span class="built_in">var</span>(--body-bg-shadow) <span class="number">0</span>, <span class="built_in">var</span>(--grey-<span class="number">1</span>) <span class="number">20%</span>) no-repeat bottom;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-page</span> <span class="selector-class">.max-w-screen-md</span> {</span><br><span class="line"> <span class="attribute">max-width</span>: <span class="number">1000px</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-header</span> {</span><br><span class="line"> <span class="attribute">position</span>: sticky;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">400px</span>;</span><br><span class="line"> <span class="attribute">top</span>: -<span class="number">360px</span>;</span><br><span class="line"> <span class="attribute">z-index</span>: <span class="number">1</span>;</span><br><span class="line"> <span class="attribute">border</span>: none;</span><br><span class="line"> <span class="attribute">background-color</span>: <span class="built_in">var</span>(--grey-<span class="number">1</span>)</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-header</span> <span class="selector-class">.flex</span><span class="selector-class">.py-12</span><span class="selector-class">.w-full</span> {</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">80%</span>;</span><br><span class="line"> <span class="attribute">justify-content</span>: center;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-header</span> <span class="selector-class">.xlog-banner</span> {</span><br><span class="line"> <span class="attribute">height</span>: <span class="built_in">calc</span>(<span class="number">100%</span> - <span class="number">40px</span>)</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-header</span> <span class="selector-class">.xlog-banner</span> <span class="selector-tag">img</span><span class="selector-attr">[alt=banner]</span> {</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">max-width</span>: unset;</span><br><span class="line"> <span class="attribute">filter</span>: none <span class="comment">/*blur(5px) brightness(75%)*/</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">@media</span> (<span class="attribute">width</span> > <span class="number">1024px</span>) {</span><br><span class="line"> <span class="selector-class">.xlog-page-index</span> <span class="selector-class">.xlog-header</span> {</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">100vh</span>;</span><br><span class="line"> <span class="attribute">top</span>: <span class="built_in">calc</span>(<span class="number">40px</span> - <span class="number">100vh</span>);</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-page-index</span>,</span><br><span class="line"><span class="selector-class">.xlog-page-post</span> {</span><br><span class="line"> <span class="attribute">font-family</span>: <span class="string">"LXGW WenKai Screen R"</span>, sans-serif;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-tag">main</span> {</span><br><span class="line"> <span class="attribute">max-width</span>: <span class="number">1000px</span> <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">background</span>: none ;<span class="comment">/*linear-gradient(to top, var(--grey-0) 0, var(--grey-1) 20%) no-repeat top;*/</span></span><br><span class="line"> <span class="attribute">box-shadow</span>: none; <span class="comment">/*0 1.25rem 1rem 0.3125rem var(--body-bg-shadow);*/</span></span><br><span class="line"> <span class="attribute">padding-bottom</span>: <span class="number">2rem</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.xlog-header</span> <span class="selector-class">.text-gray-500</span> {</span><br><span class="line"> <span class="attribute">color</span>: white <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">text-shadow</span>: <span class="number">0</span> <span class="number">0.2rem</span> <span class="number">0.3rem</span> <span class="built_in">rgba</span>(<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, .<span class="number">5</span>);</span><br><span class="line">}</span><br><span class="line"><span class="comment">/**/</span></span><br><span class="line"><span class="comment">/* post */</span></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-pseudo">:not</span>(pre)><span class="selector-tag">code</span> {</span><br><span class="line"> <span class="attribute">color</span>: <span class="built_in">var</span>(--theme-color);</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0.3rem</span>;</span><br><span class="line"> <span class="attribute">border</span>: <span class="number">0.0625rem</span> solid <span class="built_in">rgba</span>(<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>,.<span class="number">1</span>);</span><br><span class="line"> <span class="attribute">background-color</span>: <span class="built_in">var</span>(--grey-<span class="number">0</span>);</span><br><span class="line"> <span class="attribute">padding</span>: <span class="number">0.2rem</span> <span class="number">0.3rem</span>;</span><br><span class="line"> <span class="attribute">overflow-wrap</span>: break-word;</span><br><span class="line"> <span class="attribute">word-wrap</span>: break-word;</span><br><span class="line">}</span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">blockquote</span> {</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0.1875rem</span>;</span><br><span class="line"> <span class="attribute">padding</span>: .<span class="number">625rem</span> <span class="number">1.25rem</span>;</span><br><span class="line"> <span class="attribute">border-left</span>: <span class="number">0.25rem</span> solid <span class="built_in">var</span>(--theme-color);</span><br><span class="line"> <span class="attribute">font-size</span>: <span class="number">90%</span>;</span><br><span class="line"> <span class="attribute">background-color</span>: <span class="built_in">var</span>(--grey-<span class="number">2</span>);</span><br><span class="line"> <span class="attribute">margin</span>: <span class="number">1.25rem</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">ol</span> {</span><br><span class="line"> <span class="attribute">counter-reset</span>: counter;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">li</span> {</span><br><span class="line"> <span class="attribute">list-style</span>: none;</span><br><span class="line"> <span class="attribute">position</span>: relative;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">ol</span> <span class="selector-tag">li</span><span class="selector-pseudo">:before</span> {</span><br><span class="line"> <span class="attribute">counter-increment</span>: counter;</span><br><span class="line"> <span class="attribute">content</span>: <span class="built_in">counter</span>(counter);</span><br><span class="line"> <span class="attribute">position</span>: absolute;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">1.4em</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">1.4em</span>;</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">50%</span>;</span><br><span class="line"> <span class="attribute">text-align</span>: center;</span><br><span class="line"> <span class="attribute">font-size</span>: .<span class="number">8em</span>;</span><br><span class="line"> <span class="attribute">line-height</span>: <span class="number">1.4</span>;</span><br><span class="line"> <span class="attribute">top</span>: <span class="number">0.5em</span>;</span><br><span class="line"> <span class="attribute">left</span>: -<span class="number">1.8em</span>;</span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">var</span>(--theme-color);</span><br><span class="line"> <span class="attribute">color</span>: <span class="built_in">rgba</span>(<span class="built_in">var</span>(--tw-colors-i-gray-<span class="number">100</span>), <span class="number">1</span>);</span><br><span class="line"> <span class="attribute">cursor</span>: pointer;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">ul</span> <span class="selector-tag">li</span><span class="selector-pseudo">:before</span> {</span><br><span class="line"> <span class="attribute">content</span>: <span class="string">""</span>;</span><br><span class="line"> <span class="attribute">position</span>: absolute;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">0.4em</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">0.4em</span>;</span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">var</span>(--theme-color);</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">50%</span>;</span><br><span class="line"> <span class="attribute">top</span>: <span class="number">0.85em</span>;</span><br><span class="line"> <span class="attribute">left</span>: -<span class="number">1em</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-class">.table-wrapper</span> {</span><br><span class="line"> <span class="attribute">border</span>: none <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0</span> <span class="meta">!important</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">table</span> {</span><br><span class="line"> <span class="attribute">border-collapse</span>: collapse;</span><br><span class="line"> <span class="attribute">border-spacing</span>: <span class="number">0</span>;</span><br><span class="line"> <span class="attribute">font-size</span>: .<span class="number">875em</span>;</span><br><span class="line"> <span class="attribute">margin</span>: <span class="number">0</span> <span class="number">0</span> <span class="number">1.25rem</span>;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">overflow</span>: auto;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">table</span> <span class="selector-tag">tbody</span> <span class="selector-tag">tr</span><span class="selector-pseudo">:nth-child</span>(<span class="number">2</span>n-<span class="number">1</span>) {</span><br><span class="line"> <span class="attribute">background</span>: none <span class="meta">!important</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">table</span> <span class="selector-tag">th</span>,</span><br><span class="line"><span class="selector-tag">td</span> {</span><br><span class="line"> <span class="attribute">border</span>: <span class="number">0.0625rem</span> solid <span class="built_in">var</span>(--border-color);</span><br><span class="line"> <span class="attribute">border-bottom</span>: <span class="number">0.1875rem</span> solid <span class="built_in">var</span>(--border-color);</span><br><span class="line"> <span class="attribute">padding</span>: <span class="number">0.5rem</span>;</span><br><span class="line"> <span class="attribute">padding-bottom</span>: <span class="number">0.625rem</span>;</span><br><span class="line"> <span class="attribute">text-align</span>: left;</span><br><span class="line"> <span class="attribute">vertical-align</span>: middle;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">table</span> <span class="selector-tag">th</span> {</span><br><span class="line"> <span class="attribute">font-weight</span>: <span class="number">700</span>;</span><br><span class="line"> <span class="attribute">text-align</span>: center;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.prose</span> <span class="selector-tag">table</span> <span class="selector-tag">td</span> {</span><br><span class="line"> <span class="attribute">border-bottom-width</span>: <span class="number">0.0625rem</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.spoiler</span> {</span><br><span class="line"> <span class="attribute">filter</span>: <span class="built_in">blur</span>(<span class="number">8px</span>);</span><br><span class="line"> <span class="attribute">transition</span>: filter .<span class="number">5s</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.spoiler</span><span class="selector-pseudo">:hover</span> {</span><br><span class="line"> <span class="attribute">filter</span>: <span class="built_in">blur</span>(<span class="number">0px</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dark</span> <span class="selector-class">.info</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="built_in">rgba</span>(<span class="number">85</span>, <span class="number">98</span>, <span class="number">132</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="built_in">rgba</span>(<span class="number">48</span>, <span class="number">49</span>, <span class="number">50</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="built_in">rgba</span>(<span class="number">109</span>, <span class="number">164</span>, <span class="number">219</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="built_in">rgba</span>(<span class="number">39</span>, <span class="number">127</span>, <span class="number">214</span>, <span class="number">0.8</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.info</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="number">#8fa4dc</span>;</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="number">#f1f9ff</span>;</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="number">#1d4974</span>;</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="number">#1d5fa0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.note</span> {</span><br><span class="line"> <span class="attribute">background</span>: <span class="built_in">var</span>(--note-bg, <span class="built_in">var</span>(--grey-<span class="number">2</span>));</span><br><span class="line"> <span class="attribute">color</span>: <span class="built_in">var</span>(--grey-<span class="number">6</span>);</span><br><span class="line"> <span class="attribute">border-left</span>: <span class="number">0.25rem</span> solid <span class="built_in">var</span>(--note-border, <span class="built_in">var</span>(--grey-<span class="number">4</span>));</span><br><span class="line"> <span class="attribute">font-size</span>: .<span class="number">875em</span>;</span><br><span class="line"> <span class="attr">--primary-color</span>: <span class="built_in">var</span>(--note-text);</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0.1875rem</span>;</span><br><span class="line"> <span class="attribute">margin</span>: <span class="number">1rem</span> <span class="number">0</span>;</span><br><span class="line"> <span class="attribute">padding</span>: <span class="number">1rem</span>;</span><br><span class="line"> <span class="attribute">position</span>: relative;</span><br><span class="line"> <span class="attribute">padding-left</span>: <span class="number">1rem</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dark</span> <span class="selector-class">.error</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="built_in">rgba</span>(<span class="number">146</span>, <span class="number">107</span>, <span class="number">115</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="built_in">rgba</span>(<span class="number">50</span>, <span class="number">48</span>, <span class="number">48</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="built_in">rgba</span>(<span class="number">239</span>, <span class="number">38</span>, <span class="number">79</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="built_in">rgba</span>(<span class="number">168</span>, <span class="number">49</span>, <span class="number">72</span>, <span class="number">0.8</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.error</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="number">#f4b3c1</span>;</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="number">#fff2f5</span>;</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="number">#cc0f35</span>;</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="number">#f14668</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.dark</span> <span class="selector-class">.success</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="built_in">rgba</span>(<span class="number">97</span>, <span class="number">116</span>, <span class="number">88</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="built_in">rgba</span>(<span class="number">50</span>, <span class="number">50</span>, <span class="number">48</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="built_in">rgba</span>(<span class="number">128</span>, <span class="number">200</span>, <span class="number">129</span>, <span class="number">0.8</span>);</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="built_in">rgba</span>(<span class="number">41</span>, <span class="number">95</span>, <span class="number">42</span>, <span class="number">0.8</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="selector-class">.success</span> {</span><br><span class="line"> <span class="attr">--note-border</span>: <span class="number">#a3c293</span>;</span><br><span class="line"> <span class="attr">--note-bg</span>: <span class="number">#fcfff5</span>;</span><br><span class="line"> <span class="attr">--note-text</span>: <span class="number">#2c662d</span>;</span><br><span class="line"> <span class="attr">--note-hover</span>: <span class="number">#3b883c</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">/* phone */</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">@media</span> (<span class="attribute">max-width</span>: <span class="number">767px</span>) {</span><br><span class="line"> <span class="selector-class">.xlog-post</span> {</span><br><span class="line"> <span class="attribute">flex-direction</span>: column-reverse <span class="meta">!important</span>;</span><br><span class="line"> <span class="attribute">height</span>: -webkit-fit-content;</span><br><span class="line"> <span class="attribute">height</span>: -moz-fit-content;</span><br><span class="line"> <span class="attribute">height</span>: fit-content;</span><br><span class="line"> <span class="attribute">max-height</span>: -webkit-fit-content;</span><br><span class="line"> <span class="attribute">max-height</span>: -moz-fit-content;</span><br><span class="line"> <span class="attribute">max-height</span>: fit-content;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="selector-class">.xlog-post</span> <span class="selector-class">.xlog-post-cover</span> {</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">14rem</span>;</span><br><span class="line"> <span class="attribute">margin</span>: auto;</span><br><span class="line"> -webkit-<span class="attribute">clip-path</span>: <span class="built_in">polygon</span>(<span class="number">0</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">92%</span>, <span class="number">0</span> <span class="number">100%</span>);</span><br><span class="line"> <span class="attribute">clip-path</span>: <span class="built_in">polygon</span>(<span class="number">0</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">92%</span>, <span class="number">0</span> <span class="number">100%</span>);</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0.625rem</span> <span class="number">0.625rem</span> <span class="number">0</span> <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="selector-class">.xlog-posts</span>><span class="selector-class">.xlog-post</span><span class="selector-pseudo">:nth-child</span>(even) <span class="selector-class">.xlog-post-cover</span> {</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">margin</span>: auto;</span><br><span class="line"> -webkit-<span class="attribute">clip-path</span>: <span class="built_in">polygon</span>(<span class="number">0</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">100%</span>, <span class="number">0</span> <span class="number">92%</span>);</span><br><span class="line"> <span class="attribute">clip-path</span>: <span class="built_in">polygon</span>(<span class="number">0</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">0</span>, <span class="number">100%</span> <span class="number">100%</span>, <span class="number">0</span> <span class="number">92%</span>);</span><br><span class="line"> <span class="attribute">border-radius</span>: <span class="number">0.625rem</span> <span class="number">0.625rem</span> <span class="number">0</span> <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="selector-class">.xlog-post</span>><span class="selector-tag">div</span><span class="selector-pseudo">:nth-of-type</span>(<span class="number">1</span>) {</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100%</span>;</span><br><span class="line"> <span class="attribute">padding</span>: <span class="number">10px</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="selector-tag">main</span> {</span><br><span class="line"> <span class="attribute">max-width</span>: <span class="number">500px</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">/**/</span></span><br><span class="line"></span><br><span class="line"><span class="selector-tag">body</span> {</span><br><span class="line"> <span class="attribute">cursor</span>:<span class="built_in">url</span>(<span class="string">https://raw.gitmirror.com/genkaim/blog_pic/main/data/noramal_bl.cur</span>),</span><br><span class="line"> default;</span><br><span class="line">}</span><br><span class="line"><span class="selector-tag">a</span>,</span><br><span class="line"><span class="selector-tag">img</span> {</span><br><span class="line"> <span class="attribute">cursor</span>:<span class="built_in">url</span>(<span class="string">https://raw.gitmirror.com/genkaim/blog_pic/main/data/choose_bl.cur</span>),</span><br><span class="line"> default; </span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> 教程 </tag>
</tags>
</entry>
<entry>
<title>十大排序算法之归并排序、快速排序、堆排序</title>
<link href="/posts/954ceb85.html"/>
<url>/posts/954ceb85.html</url>
<content type="html"><![CDATA[<p><img src="https://i.pinimg.com/originals/3d/d6/c5/3dd6c57a2974cd0706930dd41a419c81.jpg" class="lazy" data-srcset="https://i.pinimg.com/originals/3d/d6/c5/3dd6c57a2974cd0706930dd41a419c81.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141809567.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141809567.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="33238e2b7a5d476195dfc19af728bbaf" /></p><h2 id="归并排序"><a class="markdownIt-Anchor" href="#归并排序"></a> 归并排序</h2><h3 id="介绍"><a class="markdownIt-Anchor" href="#介绍"></a> 介绍</h3><p>归并排序 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>M</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mo>−</mo><mi>s</mi><mi>o</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(Merge-sort)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span> 是利用归并的思想实现的排序方法，该算法采用经典的分治 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>d</mi><mi>e</mi><mo>−</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo>−</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>q</mi><mi>u</mi><mi>e</mi><mi>r</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(divide-and-conquer)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord mathnormal">u</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">)</span></span></span></span> 策略。</p><p>如图，具体来说，归并排序在排序的时候，会把一段数组拆分成不同的小数组（临界时只有一个元素），并在合并时排序。</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141651494.jpeg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141651494.jpeg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="img" /></p><h3 id="复杂度稳定性"><a class="markdownIt-Anchor" href="#复杂度稳定性"></a> 复杂度/稳定性</h3><p><strong>时间复杂度</strong></p><p>以上图代码为例，此时 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">n = 8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span></span></span></span> ，可以看到，归并排序的分段是以下标二分的办法.</p><p>如下图，具体来看，对于分出的每两段数组合并的时候，每一层都会比较 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 次，总共有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi></mrow><annotation encoding="application/x-tex">log_2n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span></span></span></span> 层，时间复杂度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(nlog_2n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141815144.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308141815144.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230814181555918" /></p><p><strong>稳定性</strong></p><p>每两段数组都是相邻的，相同的数合并时相对位置不会变化，因此它是稳定的。</p><h3 id="代码实现"><a class="markdownIt-Anchor" href="#代码实现"></a> 代码实现</h3><p>以下是c++实现，请参考注释理解：</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1e4</span><span class="number">+5</span>;</span><br><span class="line"><span class="type">int</span> n, tmp[N], a[N];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">fsort</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r)</span></span>{</span><br><span class="line"> <span class="comment">//先进行递归分组</span></span><br><span class="line"> <span class="keyword">if</span>(l >= r) <span class="keyword">return</span> ;<span class="comment">//临界情况，分得的数组最小为1</span></span><br><span class="line"> <span class="type">int</span> mid = (l+r)/<span class="number">2</span>; <span class="comment">//取中间值</span></span><br><span class="line"> <span class="built_in">fsort</span>(l, mid); <span class="comment">//左边</span></span><br><span class="line"> <span class="built_in">fsort</span>(mid<span class="number">+1</span>, r); <span class="comment">//右边</span></span><br><span class="line"></span><br><span class="line"> <span class="comment">//回溯时进行合并，并排序，因为不能直接在原数组操作（），所以新定义tmp数组暂存合并结果</span></span><br><span class="line"> <span class="type">int</span> i = l, j = mid<span class="number">+1</span>, k = l;</span><br><span class="line"> <span class="keyword">while</span>(i <= mid && j <= r){ <span class="comment">//比较两个序列每个元素的大小并按次序存入暂存数组</span></span><br><span class="line"> <span class="keyword">if</span>(a[i] <= a[j]){</span><br><span class="line"> tmp[k] = a[i];<span class="comment">//左边区间的数小，放入</span></span><br><span class="line"> i++;</span><br><span class="line"> k++;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span>{</span><br><span class="line"> tmp[k] = a[j];<span class="comment">//右边区间的数小，放入</span></span><br><span class="line"> j++;</span><br><span class="line"> k++;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//还有可能其中一个数组有多出来的数，需要额外放置</span></span><br><span class="line"> <span class="keyword">while</span>(i<=mid){</span><br><span class="line"> tmp[k]=a[i];</span><br><span class="line"> i++;</span><br><span class="line"> k++;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(j<=r){</span><br><span class="line"> tmp[k]=a[j];</span><br><span class="line"> j++;</span><br><span class="line"> k++;</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//把暂存区的数存入原数组</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = l; i <= r; i++)</span><br><span class="line"> a[i] = tmp[i]; </span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="built_in">fsort</span>(<span class="number">1</span>, n);</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="快速排序"><a class="markdownIt-Anchor" href="#快速排序"></a> 快速排序</h2><h3 id="介绍-2"><a class="markdownIt-Anchor" href="#介绍-2"></a> 介绍</h3><p>快速排序 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>Q</mi><mi>u</mi><mi>i</mi><mi>c</mi><mi>k</mi><mo>−</mo><mi>s</mi><mi>o</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(Quick-sort)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">Q</span><span class="mord mathnormal">u</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span> 利用二分思想，完成数列的排序操作。</p><p>快速排序通过在待排序序列中选取基准值，再将数列调整为以基准值位置为界，一侧比基准值小，另一侧则比基准值大，然后递归两侧执行同样操作，即可完成排序。</p><p>如图1：</p><p><img src="https://raw.githubusercontent.com/Genkaim/blog_video/main/data/202308151543209.jpeg" class="lazy" data-srcset="https://raw.githubusercontent.com/Genkaim/blog_video/main/data/202308151543209.jpeg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="img" /></p><p>而具体到每次操作，可以参考下面这张图2：</p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308161700002.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308161700002.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="3" /></p><h3 id="复杂度稳定性分析"><a class="markdownIt-Anchor" href="#复杂度稳定性分析"></a> 复杂度/稳定性分析</h3><p><strong>时间复杂度</strong></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> 最好情况下，每次划分可以均衡，类比归并排序，每一层排 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个数，共有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi></mrow><annotation encoding="application/x-tex">log_2n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span></span></span></span> 层，时间复杂度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(nlog_2n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/></mrow><annotation encoding="application/x-tex">\qquad</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mspace" style="margin-right:2em;"></span></span></span></span> 最坏情况下：基准值选取最值，每次划分会出现空序列，需要划分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 次，即共有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 层，时间复杂度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p><p>同理，如果基准值失去随机性，快速排序的时间复杂度也会退化到 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p><p><strong>稳定性</strong></p><p>快速排序每次按照基准值分类的时候，如上图，若两个元素数值相等，在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span> 、 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span> 互换的过程中，相对位置会发生变化，所以不稳定。</p><h3 id="代码实现-2"><a class="markdownIt-Anchor" href="#代码实现-2"></a> 代码实现</h3><p>以下是c++实现，请参考注释理解：</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1e4</span><span class="number">+5</span>;</span><br><span class="line"><span class="type">int</span> n, a[N];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">quicksort</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r)</span></span>{<span class="comment">//参考上图2理解</span></span><br><span class="line"> <span class="keyword">if</span>(l >= r) <span class="keyword">return</span> ;<span class="comment">//不要越界</span></span><br><span class="line"> <span class="type">int</span> t = a[l]; <span class="comment">//选基准值，如上图，选第一个位置的</span></span><br><span class="line"> <span class="type">int</span> i = l, j = r;</span><br><span class="line"> <span class="keyword">while</span>(i < j){ <span class="comment">//i!=j时，进入循环</span></span><br><span class="line"> <span class="keyword">while</span>( a[j] > t ) j--; <span class="comment">//从后往前依次寻找比基准值小的</span></span><br><span class="line"> <span class="keyword">while</span>( a[i] <= t && i<j) i++;<span class="comment">//从前往后依次寻找比基准值大的</span></span><br><span class="line"> <span class="keyword">if</span>(i < j) <span class="built_in">swap</span>(a[i], a[j]);<span class="comment">//满足i < j才能交换，不能相同位置互换</span></span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">swap</span>(a[l],a[i]); <span class="comment">//把基准值放到合适的位置，此时i = j</span></span><br><span class="line"> <span class="built_in">quicksort</span>(l,i<span class="number">-1</span>);<span class="comment">//继续向下分</span></span><br><span class="line"> <span class="built_in">quicksort</span>(i<span class="number">+1</span>,r);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="built_in">quicksort</span>(<span class="number">1</span>, n);</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="堆排序"><a class="markdownIt-Anchor" href="#堆排序"></a> 堆排序</h2><p>堆排序 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>H</mi><mi>e</mi><mi>a</mi><mi>p</mi><mo>−</mo><mi>s</mi><mi>o</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(Heap-sort)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span> 是借助堆这种数据结构完成的排序，思路类似于选择排序。</p><p>它和选择排序最大的不同是使用了树这一数据结构，把选择排序效率低下的一个个元素遍历的查找改为在树中查找。</p><h3 id="前置芝士堆"><a class="markdownIt-Anchor" href="#前置芝士堆"></a> 前置芝士：堆</h3><p>如图，堆是一种特殊的完全二叉树，分为大顶堆与小顶堆两种：</p><ol><li>大顶堆： 完全二叉树中任一非叶子结点的值都大于等于其子结点的值。</li><li>小顶堆： 完全二叉树中任一非叶子结点的值都小于等于其子结点的值。</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308181121357.jpeg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308181121357.jpeg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="img" /></p><h3 id="介绍-3"><a class="markdownIt-Anchor" href="#介绍-3"></a> 介绍</h3><p>选择排序的原理还是很好懂的，所以跳过这一块（类比即可），着重讲如何用堆查找元素。</p><p>如果我们需要数组元素单调递减，需要最终形成一个大顶堆：从下往上倒序遍历非叶子结点（没有儿子节点的节点），通过交换方式依次调整父子结点顺序，直至符合大顶堆的规则。</p><p>举例：有如图的一个数组，需要这样操作便可得到一个有序的数组。</p><p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308181127112.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202308181127112.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230818112757861" /></p><h3 id="复杂度稳定性分析-2"><a class="markdownIt-Anchor" href="#复杂度稳定性分析-2"></a> 复杂度/稳定性分析</h3><p><strong>时间复杂度</strong></p><p>和选择排序类似，总共需要操作 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个数，不同的是，选择排序操作一个数需要 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> ，而堆排序查找一个数只需要 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi></mrow><annotation encoding="application/x-tex">log_2n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span></span></span></span> ，所以堆排序的时间复杂度是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>l</mi><mi>o</mi><msub><mi>g</mi><mn>2</mn></msub><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(nlog_2n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></p><p><strong>稳定性</strong></p><p>堆排序和选择排序类似，排序过程中相同元素位置发生改变，不稳定。</p><h3 id="代码实现-3"><a class="markdownIt-Anchor" href="#代码实现-3"></a> 代码实现</h3><p>以下是c++实现，请参考注释理解：</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1e4</span><span class="number">+5</span>;</span><br><span class="line"><span class="type">int</span> m, a[N]</span><br><span class="line"><span class="comment">//堆排序</span></span><br><span class="line"><span class="comment">//堆部分</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">adjust</span><span class="params">(<span class="type">int</span> i, <span class="type">int</span> parent)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> child = parent * <span class="number">2</span>;<span class="comment">//先判断儿子</span></span><br><span class="line"> <span class="comment">// 保证判断的范围不超过i</span></span><br><span class="line"> <span class="keyword">if</span>(child + <span class="number">1</span> <= i && a[child] < a[child + <span class="number">1</span>]){</span><br><span class="line"> child++;<span class="comment">//选择两个儿子中较大的那个往上传递（维护大顶堆）</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(a[child] > a[parent]){</span><br><span class="line"> <span class="built_in">swap</span>(a[child], a[parent]);<span class="comment">//如果儿子比较大，就往上交换</span></span><br><span class="line"> <span class="keyword">if</span>(child <= i / <span class="number">2</span>){<span class="comment">//不超过i的父节点</span></span><br><span class="line"> <span class="built_in">adjust</span>(i, child);<span class="comment">//如果当前节点更新，那么当前节点的子节点也需要更新</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="comment">//主体排序部分</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">heapSort</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = n; i > <span class="number">1</span>; i--){<span class="comment">//从右侧往左侧维护，注意不能从左往右，因为不能保证其子节点已经被维护过</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = i / <span class="number">2</span>; j >= <span class="number">1</span>; j--){<span class="comment">//从i节点的父节点开始维护</span></span><br><span class="line"> <span class="built_in">adjust</span>(i, j);<span class="comment">//以j号节点往根节点调整，传递的i辅助判断是否越界</span></span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">swap</span>(a[<span class="number">1</span>], a[i]);<span class="comment">//此时树根是下标[1, i]范围内最大的数，和当前位置交换（参考选择排序）</span></span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="built_in">heapSort</span>();</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> Coding </tag>
</tags>
</entry>
<entry>
<title>在博客里接入AI机器人(Chatgpt)，并且读取博客文章</title>
<link href="/posts/add30ed0.html"/>
<url>/posts/add30ed0.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092059559.jpg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092059559.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="起因"><a class="markdownIt-Anchor" href="#起因"></a> 起因</h2><p>我看到<a href="https://endercat.eu.org">endercat</a>的这篇<a href="https://endercat.ir/zai-bo-ke-shang-qian-ru-ke-yi-du-qu-wen-zhang-de-ChatGPT">文章</a>，起了往博客添加机器人的想法，但是期望是以悬浮窗的形式，就到处寻找，终于！！！找到了<br /><s>实际上是我太菜不会加悬浮窗（）</s></p><h2 id="创建机器人new-bot"><a class="markdownIt-Anchor" href="#创建机器人new-bot"></a> 😆创建机器人New bot</h2><p>这次借助的是<a href="https://chatthing.ai/">Chat Thing</a> 网站，免费版支持gpt-3</p><ol><li>进入后注册登录，然后会看到仪表盘。</li><li>创建机器人，注意免费版只能创建一个机器人。</li><li>设置机器人的基础信息，注意催眠的地方在<strong>Advanced settings</strong>中最下面</li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/image-20230809203623323.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/image-20230809203623323.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809203623323" /></p><h2 id="设置-data-source-数据来源"><a class="markdownIt-Anchor" href="#设置-data-source-数据来源"></a> 🫤设置 Data source 数据来源</h2><p><strong>注意免费版只能有一个数据来源</strong>，但一般也够了</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092140893.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092140893.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809214044613" /></p><p>有很多中不同方式，这里介绍两种方式：</p><ol><li>Website：（因为可以用sitemap）如图，输入网址即可</li></ol><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092043992.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092043992.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809204349728" width="50%" height="50%" /><ol start="2"><li><p>RSS订阅：点击你的xlog主页的RSS按钮，复制新打开网页的网址到下图位置即可即可</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100858296.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100858296.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810085810825" /></p></li></ol><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100859979.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100859979.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810085956865" /></p><p><big><strong>注意要保存并同步数据源</strong></big></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100901485.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100901485.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230810090147307" /></p><p>这样，数据源也设置好啦</p><h2 id="嵌入博客-embed-bot"><a class="markdownIt-Anchor" href="#嵌入博客-embed-bot"></a> 🥰嵌入博客 Embed Bot</h2><p>点开Embed Bot，参考下图翻译，选择你想要的方式插入就好了</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092045929.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092045929.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809204552761" width="50%" height="50%"><p>如果是插入文章/页面，那么很简单，直接在对应<code>.md</code>插入你看到的代码就好了。</p><p>如果想要全局小组件，直接在bottom引入：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><script src="https://chatthing.ai/chat-widget.js" type="text/javascript" id="<替换为你在小组件代码中看到的id(保留引号)>" async defer></script></span><br></pre></td></tr></table></figure><p>效果分别如图</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092105044.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092105044.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809210531921" width="30%" height="30%" /><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092053443.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308092053443.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230809205358309" width="80%" height="80%" /><p>这样就完成啦🥳</p><p>如有错误/改进，欢迎指正🥲</p>]]></content>
<tags>
<tag> AI </tag>
</tags>
</entry>
<entry>
<title>博客接入搜索引擎、百度统计</title>
<link href="/posts/72dcbf6a.html"/>
<url>/posts/72dcbf6a.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_img/main/data/202309230802993.jpg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_img/main/data/202309230802993.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="接入百度统计gridea"><a class="markdownIt-Anchor" href="#接入百度统计gridea"></a> 😉接入百度统计(Gridea)</h2><p>按图示操作</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459568.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459568.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_17-02-50" /></p><p>如果你的theme直接支持百度统计，那么只需要把图中圈出的部分复制进对应位置并保存就行了</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459861.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459861.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-54-20" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500037.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500037.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-53-04" /></p><p>如果theme不支持百度统计，那么还需要在前文提到的<code>head.ejs</code>加入百度提供的代码：</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500572.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500572.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-59-01" /></p><p>验证后出现图示就成功了🥳🥳🥳</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500857.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221500857.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_17-22-57" height="40%" width="40%" /><h2 id="搜索引擎索引"><a class="markdownIt-Anchor" href="#搜索引擎索引"></a> 搜索引擎索引</h2><h3 id="在bing-webmaster-tools加入自己的网站"><a class="markdownIt-Anchor" href="#在bing-webmaster-tools加入自己的网站"></a> 😶在Bing Webmaster Tools加入自己的网站</h3><p>进入网站：👉 <a href="https://www.bing.com/webmasters/">https://www.bing.com/webmasters/</a></p><p>你会看到如下页面：</p><p>键入自己的网址，通常是<code>https://<你的用户名>.github.io/</code></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221454530.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221454530.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="1" /></p><p>然后复制箭头所指的位置的<meta>标记，将它复制到站点原文件夹下的</p><p><code>./themes/<当前选择的主题>/templates/includes(或者_blocks)/head.ejs</code>文件内（如图）</p><p><small>只要在一坨<meta…>之间换行并复制就行了</small></p><p>最好顺便把这条也一并复制进去，利于让bing抓取。</p><p>//标记网站适用的语言</p><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="tag"><<span class="name">meta</span> <span class="attr">http-equiv</span>=<span class="string">'content-language'</span> <span class="attr">content</span>=<span class="string">'zh_cn'</span>></span></span><br></pre></td></tr></table></figure><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455655.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455655.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-10-21" /></p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455125.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455125.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="微信图片_20230617161808" /></p><p><strong>同步</strong>后确认，就验证成功啦</p><h3 id="创建网站地图"><a class="markdownIt-Anchor" href="#创建网站地图"></a> 😃创建网站地图</h3><p>一个网站有很多网页，我们不可能一个个的去申请抓取，这太烦了<s>悲</s></p><p>但是gridea本身并不支持生成网站地图，需要借助一个网页来完成：</p><p>👉<a href="https://www.xml-sitemaps.com/">https://www.xml-sitemaps.com/</a></p><p>输入网址后按图操作</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455877.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221455877.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-26-15" style="zoom:33%;" /><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456464.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456464.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-26-40" style="zoom:33%;" /><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456211.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456211.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-27-02" style="zoom: 33%;" /><p>接下来，将下载好的.xml文件放在 <code>./static</code> 下</p><h3 id="上传网站地图"><a class="markdownIt-Anchor" href="#上传网站地图"></a> 😊上传网站地图</h3><p>回到 👉<a href="https://www.bing.com/webmasters/">https://www.bing.com/webmasters/</a></p><p>在左侧侧边栏选择网站地图，并上传.xml文件</p><p>地址是<code>https://*<你的用户名>*.github.io/sitemap.xml</code></p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456991.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456991.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-30-53" height="40%" width="40%"/><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456386.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221456386.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-32-04" height="40%" width="40%" /><p>等待bing处理即可，如果你的网站符合要求就会被抓取（可能会有延时）</p><h3 id="查看是否被抓取"><a class="markdownIt-Anchor" href="#查看是否被抓取"></a> 🤔查看是否被抓取</h3><p>同样在侧边栏选择url检查，键入需要查询的地址就可以看到抓取状态</p><p>如果出现下图的状态，那么恭喜你，一次就成功了<s>虽然不太可能</s></p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221457615.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221457615.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="image-20230622145730437" style="zoom: 33%;" /><p>但如果出现下图的状态，需要点击实时url进一步查询</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459471.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221459471.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="微信图片_20230617164208" style="zoom: 25%;" /><p>在这个页面可以看到网站的SEO问题，点击问题后</p><p>大致如图</p><p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221458583.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202306221458583.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="Snipaste_2023-06-17_16-47-56" /></p><p>大部分问题代码在前文提到的<code>head.ejs</code>可以解决，按照说明添加/删除代码即可</p><p>如果仅仅是SEO<strong>提醒</strong>，那么不用太在意，并不会影响抓取（比如图像的alt属性）</p><p>完成这些后只需要等待就行了🤗</p><p>附：SEO问题严重程度</p><blockquote><p>错误：这些是我们在您的网站上发现的最关键的问题。您应优先解决这些问题，因为它们可能会影响您网站的可索引性。</p><p>警告：这些是中等严重性的问题，可能会影响您的SEO健康。</p><p>注意：这些是严重性最低的问题或建议，可以在解决所有错误和警告后进行调查。</p></blockquote>]]></content>
<tags>
<tag> 教程 </tag>
</tags>
</entry>
<entry>
<title>LCA|最近公共祖先 详解 </title>
<link href="/posts/90748940.html"/>
<url>/posts/90748940.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100919024.webp" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100919024.webp" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="lca介绍"><a class="markdownIt-Anchor" href="#lca介绍"></a> LCA介绍</h2><p>和它的全称一样，lca（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>o</mi><mi>w</mi><mi>e</mi><mi>s</mi><mi>t</mi><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>o</mi><mi>n</mi><mi>A</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mi>t</mi><mi>o</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">Lowest Common Ancestor</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">o</span><span class="mord mathnormal">m</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mord mathnormal">A</span><span class="mord mathnormal">n</span><span class="mord mathnormal">c</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span>）目的就是任意两个点最近的公共祖先在哪</p><h2 id="性质-small或许你不需要记这个small"><a class="markdownIt-Anchor" href="#性质-small或许你不需要记这个small"></a> 性质 <SMALL><s>（或许你不需要记这个）</s></SMALL></h2><blockquote><p>From <a href="https://oi-wiki.org/graph/lca/">OI-wiki</a></p></blockquote><p>为了方便，我们记某点集 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>=</mo><mrow><mo fence="true">{</mo><msub><mi>v</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>v</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mi>v</mi><mi>n</mi></msub><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">S = \left\{ v_1,v_2,...,v_n \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span> 的最近公共祖先为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>v</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mi>v</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(v_1,v_2,...,v_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 或 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(S)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mclose">)</span></span></span></span></p><ol><li><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mrow><mo fence="true">{</mo><mi>u</mi><mo fence="true">}</mo></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>u</mi></mrow><annotation encoding="application/x-tex">LCA(\left\{u\right\}) = u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal">u</span><span class="mclose delimcenter" style="top:0em;">}</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">u</span></span></span></span> ;</p></li><li><p>若 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">u</span></span></span></span> 是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span> 的祖先，当且仅当 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">)</mo><mo>=</mo><mi>u</mi></mrow><annotation encoding="application/x-tex">LCA(u, v) = u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">u</span></span></span></span> ;</p></li><li><p>如果 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">u</span></span></span></span> 不为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span> 的祖先，并且 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span> 不为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">u</span></span></span></span> 的祖先，那么 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi><mo separator="true">,</mo><mi>v</mi></mrow><annotation encoding="application/x-tex">u, v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span> 分别处于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(u, v)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">)</span></span></span></span> 的两颗不同子树中 ;</p></li><li><p>前序遍历中， <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(S)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mclose">)</span></span></span></span> 出现在所有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 元素之前，后续遍历中 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(S)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mclose">)</span></span></span></span> 则出现在所有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 元素之后 ;</p></li><li><p>两点集并的最近公共祖先为两点集分别的最近公共祖先，即<br /><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mspace width="2em"/><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\qquad LCA(A \cup B) = LCA(LCA(A), LCA(B))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mspace" style="margin-right:2em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mclose">)</span></span></span></span> ;</p></li><li><p>两点的最近公共祖先必定处在树上两点间的最短路上 ;</p></li><li><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">)</mo><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo>+</mo><mi>h</mi><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo><mo>−</mo><mn>2</mn><mo>×</mo><mi>h</mi><mo stretchy="false">(</mo><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">d(u, v) = h(u) + h(v) - 2 \times h(LCA(u, v))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">d</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">)</span><span class="mclose">)</span></span></span></span></span></p></li></ol><p>其中 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">d</span></span></span></span> 是树上两点间的距离， <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">h</span></span></span></span> 代表某点到树根的距离 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(dep)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span> ;</p><h2 id="朴素求法"><a class="markdownIt-Anchor" href="#朴素求法"></a> 朴素求法</h2><p>朴素求LCA的想法很简单，只要一层层往上走直到两个点相同即可（但是有很多小细节需要注意）。</p><p>1.计算每个点的父节点以及每个点的深度（到父节点的距离）显然，我们需要定义dep[N], root[N]两个数组来分别存储 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span> 点的深度和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span> 点的父节点，在求LCA需要先跑一遍dfs。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment">调用函数时，传入根节点，显然根节点并没有父节点，所以_root可以传入0 形如 init_root(1, 0);</span></span><br><span class="line"><span class="comment">之后在计算dep[N]数组的时候不用特判，直接在dep[0]的基础上加1，深度就是1（当然你的dep[0]需要初始化）</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init_root</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> _root)</span></span>{<span class="comment">//x代表当前节点，_root代表当前节点的父节点</span></span><br><span class="line"> root[x] = _root;<span class="comment">//存储x点的父节点</span></span><br><span class="line"> dep[x] = dep[_root]<span class="number">+1</span>;<span class="comment">//存储x点的深度</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < mp[x].<span class="built_in">size</span>(); ++i){<span class="comment">//dfs</span></span><br><span class="line"> <span class="type">int</span> y = mp[x][i];</span><br><span class="line"> <span class="keyword">if</span>(y == _root)<span class="keyword">continue</span>;<span class="comment">//不能往回走</span></span><br><span class="line"> <span class="built_in">init_root</span>(y, x);<span class="comment">//下一个点</span></span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>2.接下来就是LCA函数了，需要注意的是，对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>A</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LCA(x, y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span> 其中 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 的深度必须和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 相同才能一起往上走不然就会~~（爱人<sub>错过）</sub>，所以在网上走前需要把 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 的深度弄到相同。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">lca</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(dep[x] < dep[y])<span class="built_in">swap</span>(x, y);<span class="comment">//永远让dep[x] > dep[y]这样后面就不用判断力</span></span><br><span class="line"> <span class="keyword">while</span>(dep[x] != dep[y]){</span><br><span class="line"> x = root[x];<span class="comment">//让x 和 y深度相同</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(x != y){<span class="comment">//一起向上走</span></span><br><span class="line"> x = root[x];</span><br><span class="line"> y = root[y];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> x;<span class="comment">//此时x == y返回谁都行</span></span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="倍增求法"><a class="markdownIt-Anchor" href="#倍增求法"></a> 倍增求法</h2><p>和朴素的求法不同，倍增求法用st表进行预处理，可以减少向上走的次数，从而减少复杂度。</p><p>因为需要减少向上走的次数，对于 st [i] [j] 存储的是从i点出发，走了(1<<j)个点到的位置。</p><p>1.首先我们需要预处理。（dfs还是要跑的，但是在此处省略，和朴素LCA一样）</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">init_st</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i){</span><br><span class="line"> st[i][<span class="number">0</span>] = root[i];<span class="comment">//st表的初始状态：i走(1<<0)到的是i的父节点</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; (<span class="number">1</span><<j) <= n; ++j){<span class="comment">//因为状态由j-1推到j,所以要先循环j</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i){</span><br><span class="line"> st[i][j] = st[st[i][j<span class="number">-1</span>]][j<span class="number">-1</span>];</span><br><span class="line"> <span class="comment">/*</span></span><br><span class="line"><span class="comment"> 从i跳（1<<j）个点可以分解成先跳(1<<(j-1))个点，跳到st[i][j-1]，</span></span><br><span class="line"><span class="comment"> 再从st[i][j-1]跳(1<<(j-1))个点到st[i][j]</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>2.接下来写LCA函数：这里需要对两个部分分别修改。</p><p>2.1对于让 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 深度相同的部分，我们需要用到一些2进制的知识</p><p>对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> ，需要向上走到步数是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 的深度差。（向上走一步，深度-1）</p><p>所以记录下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>e</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">len</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span></span></span></span> 为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 的深度差。</p><p>我们需要知道的是，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>e</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">len</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span></span></span></span> 如何分解成 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span></span></span></span> 的次方相加（因为st表是以2的次方存储的）。</p><p><strong>举个栗子</strong></p><p>假设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>e</mi><mi>n</mi><mo>=</mo><mn>100</mn></mrow><annotation encoding="application/x-tex">len = 100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span></span>，转成二进制是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1100100</mn></mrow><annotation encoding="application/x-tex">1100100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span></span> ，显然，</p><p>只有对应位是1的位置才对总体的值有贡献，</p><p>所以我们当位置存在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> 时，向上走(1<<i)个点就行了（i指对应的位数）</p><p>这样，总共走的点数就会是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>e</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">len</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span></span></span></span> 。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">int</span> len = dep[x]-dep[y];</span><br><span class="line"><span class="type">int</span> i = <span class="number">0</span>;<span class="comment">//第几位</span></span><br><span class="line"><span class="keyword">while</span>(len != <span class="number">0</span>){<span class="comment">//使得x, y深度相同 建议脑子里换成二进制理解</span></span><br><span class="line"> <span class="keyword">if</span>(len%<span class="number">2</span> == <span class="number">1</span>){<span class="comment">//当前位置存在1</span></span><br><span class="line"> x = st[x][i];<span class="comment">//向上走</span></span><br><span class="line"> }</span><br><span class="line"> len /= <span class="number">2</span>;<span class="comment">//或者右移 (len>>1);</span></span><br><span class="line"> i++;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">if</span>(x == y)<span class="keyword">return</span> x;<span class="comment">//如果这个时候x == y就说明x和y在同一棵子树，没必要进行下一步了。</span></span><br></pre></td></tr></table></figure><p>2.2接下来需要 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 一起向上走。</p><p>这里用到二分的思想，但是写法和常规二分不太一样。</p><p>如果 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 一起跳了(1<<i)个点后，x == y了，说明跳过了</p><p>它们最近的公共祖先深度必然<=当前点的深度。</p><p>如图，对于5和4号点，显然跳过了它们的最近公共祖先</p><p>(顺手推荐下很方面画图的网站<a href="https://csacademy.com/app/graph_editor/">https://csacademy.com/app/graph_editor/</a>)</p><p>所以显然，我们需要在第一个 x’ != y’ 的地方更新x和y才能保证不走过。</p><p>(x’ 和 y’指在循环中走跳(1<<i)个点时到的点)</p><p>这样得到的点应该是在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> 的最近公共祖先的前一个点，所以需要返回root[x]。</p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308090851667.png" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308090851667.png" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" style="zoom:30%;" /><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//log2(n)函数在头文件cmath中，得以2为底n的对数</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="built_in">log2</span>(n); i >= <span class="number">0</span>; --i){</span><br><span class="line"> <span class="type">int</span> _x = st[x][i];<span class="comment">//在当前i下x和y跳到的位置</span></span><br><span class="line"> <span class="type">int</span> _y = st[y][i];</span><br><span class="line"> <span class="keyword">if</span>(_x == _y)<span class="keyword">continue</span>;<span class="comment">//当x和y跳到的位置相同，说明跳过了，x和y不更新</span></span><br><span class="line"> x = _x;<span class="comment">//更新以二分逼近x和y的最近公共祖先的子节点</span></span><br><span class="line"> y = _y;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> root[x];</span><br></pre></td></tr></table></figure><p>最后附上包含预处理的完整代码：</p><p><a href="https://www.luogu.com.cn/problem/P3379">洛谷</a>P3379 【模板】最近公共祖先（LCA）</p><p>模板题目也不能抄题解哦ヾ(•ω•`)o</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string"><vector></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string"><cstdio></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string"><cmath></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1e6</span>;</span><br><span class="line">vector<<span class="type">int</span>> mp[N];</span><br><span class="line"><span class="type">int</span> n, m;</span><br><span class="line"><span class="type">int</span> dep[N], root[N], st[N][<span class="number">20</span>];</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment">调用函数时，传入根节点，显然根节点并没有父节点，所以_root可以传入0 形如 init_root(1, 0);</span></span><br><span class="line"><span class="comment">之后在计算dep[N]数组的时候不用特判，直接在dep[0]的基础上加1，深度就是1（当然你的dep[0]需要初始化）</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init_root</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> _root)</span></span>{<span class="comment">//x代表当前节点，_root代表当前节点的父节点</span></span><br><span class="line"> root[x] = _root;<span class="comment">//存储x点的父节点</span></span><br><span class="line"> dep[x] = dep[_root]<span class="number">+1</span>;<span class="comment">//存储x点的深度</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < mp[x].<span class="built_in">size</span>(); ++i){<span class="comment">//dfs</span></span><br><span class="line"> <span class="type">int</span> y = mp[x][i];</span><br><span class="line"> <span class="keyword">if</span>(y == _root)<span class="keyword">continue</span>;<span class="comment">//不能往回走</span></span><br><span class="line"> <span class="built_in">init_root</span>(y, x);<span class="comment">//下一个点</span></span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init_st</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i){</span><br><span class="line"> st[i][<span class="number">0</span>] = root[i];<span class="comment">//st表的初始状态：i走(1<<0)到的是i的父节点</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; (<span class="number">1</span><<j) <= n; ++j){<span class="comment">//因为状态由j-1推到j,所以要先循环j</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i){</span><br><span class="line"> st[i][j] = st[st[i][j<span class="number">-1</span>]][j<span class="number">-1</span>];</span><br><span class="line"> <span class="comment">/*</span></span><br><span class="line"><span class="comment"> 从i跳（1<<j）个点可以分解成先跳(1<<(j-1))个点，跳到st[i][j-1]，</span></span><br><span class="line"><span class="comment"> 再从st[i][j-1]跳(1<<(j-1))个点到st[i][j]</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">lca</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(dep[x] < dep[y])<span class="built_in">swap</span>(x, y);</span><br><span class="line"> <span class="type">int</span> len = dep[x]-dep[y];<span class="comment">//按位取位权</span></span><br><span class="line"> <span class="type">int</span> i = <span class="number">0</span>;<span class="comment">//第几位</span></span><br><span class="line"> <span class="keyword">while</span>(len != <span class="number">0</span>){<span class="comment">//使得x, y深度相同 建议脑子里换成二进制理解</span></span><br><span class="line"> <span class="keyword">if</span>(len%<span class="number">2</span> == <span class="number">1</span>){<span class="comment">//当前位置存在1</span></span><br><span class="line"> x = st[x][i];<span class="comment">//向上走</span></span><br><span class="line"> }</span><br><span class="line"> len /= <span class="number">2</span>;<span class="comment">//或者右移 (len>>1);</span></span><br><span class="line"> i++;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(x == y)<span class="keyword">return</span> x;<span class="comment">//如果这个时候x == y就说明x和y在同一棵子树，没必要进行下一步了。</span></span><br><span class="line"> <span class="comment">//log2(n)函数在头文件cmath中，得以2为底n的对数</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="built_in">log2</span>(n); i >= <span class="number">0</span>; --i){</span><br><span class="line"> <span class="type">int</span> _x = st[x][i];<span class="comment">//在当前i下x和y跳到的位置</span></span><br><span class="line"> <span class="type">int</span> _y = st[y][i];</span><br><span class="line"> <span class="keyword">if</span>(_x == _y)<span class="keyword">continue</span>;<span class="comment">//当x和y跳到的位置相同，说明跳过了，x和y不更新</span></span><br><span class="line"> x = _x;<span class="comment">//更新以二分逼近x和y的最近公共祖先的子节点</span></span><br><span class="line"> y = _y;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> root[x];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> cin >> n >> m;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i){</span><br><span class="line"> <span class="type">int</span> x, y;</span><br><span class="line"> cin >> x >> y;</span><br><span class="line"> mp[x].<span class="built_in">push_back</span>(y);</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">init_root</span>(<span class="number">1</span>, <span class="number">0</span>);</span><br><span class="line"> <span class="built_in">init_st</span>();</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= m; ++i){</span><br><span class="line"> <span class="type">int</span> x, y;</span><br><span class="line"> cin >> x >> y;</span><br><span class="line"> cout << <span class="built_in">lca</span>(x, y) << endl;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="例题"><a class="markdownIt-Anchor" href="#例题"></a> 例题</h2><p><a href="https://www.luogu.com.cn/problem/P9432">洛谷</a>P9432 [NAPC-#1] rStage5 - Hard Conveyors</p><p>这里什么都没有捏😋</p>]]></content>
<tags>
<tag> Coding </tag>
</tags>
</entry>
<entry>
<title>素数筛法|欧拉函数|欧拉筛法 埃氏筛法 详解</title>
<link href="/posts/12100565.html"/>
<url>/posts/12100565.html</url>
<content type="html"><![CDATA[<p><img src="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100920077.jpg" class="lazy" data-srcset="https://raw.gitmirror.com/genkaim/blog_pic/main/data/202308100920077.jpg" srcset="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAABlBMVEXMzMyWlpYU2uzLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAACklEQVQImWNgAAAAAgAB9HFkpgAAAABJRU5ErkJggg==" alt="cover" /></p><h2 id="定义"><a class="markdownIt-Anchor" href="#定义"></a> 定义</h2><p>欧拉函数是由<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>指向小于等于<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>且与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>互质的正整数个数的函数，用<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>表示。</p><p><big><strong>example</strong></big></p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext>，（</mtext><mn>1</mn><mtext>）</mtext></mrow><annotation encoding="application/x-tex">phi(2) = 1，（1）</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">（</span><span class="mord">1</span><span class="mord cjk_fallback">）</span></span></span></span></span></p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mtext>，（</mtext><mn>1</mn><mtext>，</mtext><mn>2</mn><mtext>）</mtext></mrow><annotation encoding="application/x-tex">phi(3) = 2，（1，2） </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord">3</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">（</span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">2</span><span class="mord cjk_fallback">）</span></span></span></span></span></p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mtext>，（</mtext><mn>1</mn><mtext>，</mtext><mn>3</mn><mtext>）</mtext></mrow><annotation encoding="application/x-tex">phi(4) = 2，（1，3）</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord">4</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">（</span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">3</span><span class="mord cjk_fallback">）</span></span></span></span></span></p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo>=</mo><mn>4</mn><mtext>，（</mtext><mn>1</mn><mtext>，</mtext><mn>2</mn><mtext>，</mtext><mn>3</mn><mtext>，</mtext><mn>4</mn><mtext>）</mtext></mrow><annotation encoding="application/x-tex">phi(5) = 4，（1，2，3，4） </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">4</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">（</span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">2</span><span class="mord cjk_fallback">，</span><span class="mord">3</span><span class="mord cjk_fallback">，</span><span class="mord">4</span><span class="mord cjk_fallback">）</span></span></span></span></span></p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mtext>，（</mtext><mn>1</mn><mtext>，</mtext><mn>5</mn><mtext>）</mtext></mrow><annotation encoding="application/x-tex">phi(6) = 2，（1，5）</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord">6</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">（</span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">5</span><span class="mord cjk_fallback">）</span></span></span></span></span></p><h2 id="公式"><a class="markdownIt-Anchor" href="#公式"></a> 公式</h2><h3 id="结论"><a class="markdownIt-Anchor" href="#结论"></a> <strong>结论</strong></h3><p>假设n的质因数分解为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>p</mi><mn>1</mn><mi>a</mi></msubsup><mo>×</mo><msubsup><mi>p</mi><mn>2</mn><mi>b</mi></msubsup><mo>×</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>×</mo><msubsup><mi>p</mi><mi>m</mi><mi>k</mi></msubsup></mrow><annotation encoding="application/x-tex">p_1^a \times p_2^b \times ... \times p_m^k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9125em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">a</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.097216em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.096108em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span></span></span>（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>是质因数），则欧拉函数可以用公式求得：</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>1</mn></msub></mfrac><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>2</mn></msub></mfrac><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mi>m</mi></msub></mfrac><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(n) = n \times (1- \cfrac{1}{p_1} ) \times (1- \cfrac{1}{p_2} ) \times ... \times (1-\cfrac{1}{p_m})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span></span></p><h3 id="推导"><a class="markdownIt-Anchor" href="#推导"></a> <strong>推导</strong></h3><p>首先一个数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>互质，说明没有公共的质因子，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>不能有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">p_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">p_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、…<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">p_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>等质因子。<br />那么<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1...</mn><mi>n</mi></mrow><annotation encoding="application/x-tex">1...n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord mathnormal">n</span></span></span></span>中有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">p_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>质因子的个数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>n</mi><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\cfrac{n}{p_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span></span></span></span>。<br />同样，对质因子<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1...</mn><mi>n</mi></mrow><annotation encoding="application/x-tex">1...n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord mathnormal">n</span></span></span></span>中有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>n</mi><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\cfrac{n}{p_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span></span></span></span>个 数带<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>质因子。<br />显然，没有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的质因子的数量，就是要减去<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>n</mi><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\cfrac{n}{p_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span></span></span></span>，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>−</mo><mi>s</mi><mi>u</mi><mi>m</mi><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>n</mi><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">n-sum(\cfrac{n}{p_i})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">u</span><span class="mord mathnormal">m</span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span>。</p><p>加上重复减去的数，根据容斥原理就得到了：</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>−</mo><mi>s</mi><mi>u</mi><mi>m</mi><mo stretchy="false">(</mo><mfrac><mi>n</mi><msub><mi>p</mi><mi>i</mi></msub></mfrac><mo stretchy="false">)</mo><mo>+</mo><mi>s</mi><mi>u</mi><mi>m</mi><mo stretchy="false">(</mo><mfrac><mi>n</mi><mrow><msub><mi>p</mi><mi>i</mi></msub><mo>×</mo><msub><mi>p</mi><mi>j</mi></msub></mrow></mfrac><mo stretchy="false">)</mo><mo>−</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>+</mo><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mi>m</mi></msup><mo>×</mo><mfrac><mi>n</mi><mrow><msub><mi>p</mi><mn>1</mn></msub><mo>×</mo><msub><mi>p</mi><mn>2</mn></msub></mrow></mfrac><mo>×</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>×</mo><msub><mi>p</mi><mi>m</mi></msub><mo>=</mo><mi>n</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>1</mn></msub></mfrac><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>2</mn></msub></mfrac><mo stretchy="false">)</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mi>m</mi></msub></mfrac><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(n) = n - sum( \cfrac{n}{p_i} ) + sum( \cfrac{n}{p_i \times p_j} ) - ... + (-1)^m \times \cfrac{n}{p_1 \times p_2} \times ...\times p_m=n(1- \cfrac{1}{p_1}) \times (1-\cfrac{1}{p_2})...(1-\cfrac{1}{p_m})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">u</span><span class="mord mathnormal">m</span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.562108em;vertical-align:-0.972108em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">u</span><span class="mord mathnormal">m</span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">1</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span></span></p><h2 id="朴素算法"><a class="markdownIt-Anchor" href="#朴素算法"></a> 朴素算法</h2><h3 id="1"><a class="markdownIt-Anchor" href="#1"></a> 1</h3><p>根据定义，直接枚举<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1...</mn><mi>n</mi></mrow><annotation encoding="application/x-tex">1...n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord mathnormal">n</span></span></span></span>里与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>的最大公约数是1的个数。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>; i<=n; i++)</span><br><span class="line"> ans += <span class="built_in">gcd</span>(n, i)==<span class="number">1</span>;</span><br></pre></td></tr></table></figure><h3 id="2"><a class="markdownIt-Anchor" href="#2"></a> 2</h3><p>根据公式</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>1</mn></msub></mfrac><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mn>2</mn></msub></mfrac><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mi>m</mi></msub></mfrac><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(n) = n \times (1- \cfrac{1}{p_1} ) \times (1- \cfrac{1}{p_2} ) \times ... \times (1-\cfrac{1}{p_m})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span></span></p><p>循环求质因子，在过程中计算 ans=ans*(1-1/pi) ,即 ans-= ans/pi</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line">ans = n;</span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">2</span>; i*i<=n; i++) {</span><br><span class="line"> <span class="keyword">if</span>(n%i==<span class="number">0</span>) {</span><br><span class="line"> ans -= ans/i;</span><br><span class="line"> <span class="keyword">while</span>(n%i==<span class="number">0</span>) n/=i;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="keyword">if</span>(n><span class="number">1</span>) ans -= ans/n;</span><br></pre></td></tr></table></figure><h2 id="筛法解法"><a class="markdownIt-Anchor" href="#筛法解法"></a> 筛法解法</h2><h3 id="埃氏筛法"><a class="markdownIt-Anchor" href="#埃氏筛法"></a> 埃氏筛法</h3><p>根据欧拉函数的定义，</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>x</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><msub><mi>p</mi><mi>i</mi></msub></mfrac><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(x)=x \times (1- \cfrac{1}{p_i})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span></span></p><p>埃氏筛法的原理是用素数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 筛所有的倍数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">j \times p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，说明此时<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">j \times p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>有一个质因数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，因此可以用上面的公式进行递推。</p><ul><li>首先 phi[x] = x</li><li>对每个素数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的倍数 j , 有phi[j] *= (1-1/pi)，也即phi[j] -= phi[j]/pi<ul><li>如果对于某个i，其phi[i] != i，说明之前筛过，是合数</li></ul></li></ul><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">shai</span><span class="params">(<span class="type">int</span> mx)</span> </span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>; i<=mx; i++)</span><br><span class="line"> phi[i] = i;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">2</span>; i<=mx; i++) {</span><br><span class="line"> <span class="keyword">if</span>(phi[i] != i) <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j=i; j<=mx; j+=i)</span><br><span class="line"> phi[j] -= phi[j]/i;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="欧拉筛法"><a class="markdownIt-Anchor" href="#欧拉筛法"></a> 欧拉筛法</h3><p>对于某个质数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，分两种情况分析：</p><ol><li>如果是x的质因子，则对<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x \times p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 来说，pi已经在欧拉函数里计算了<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(1-\cfrac{1}{p_i})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span></span></span></span>，因此有：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">phi(x \times p_i) = phi(x) \times p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li><li>如果不是x的质因子，则对<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>×</mo><mi>p</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">x \times pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">i</span></span></span></span>来说又多了一个质因子，有：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>×</mo><msub><mi>p</mi><mi>i</mi></msub><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><msub><mi>p</mi><mi>i</mi></msub></mfrac></mstyle><mo stretchy="false">)</mo><mo>=</mo><mi>p</mi><mi>h</mi><mi>i</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><msub><mi>p</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">phi(x \times p_i) = phi(x) \times p_i \times (1- \cfrac{1}{p_i}) = phi(x) \times (p_i - 1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.47044em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5899999999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span></li></ol><p>结合欧拉筛法，就可以求phi[x]的代码。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">shai</span><span class="params">(<span class="type">int</span> mx)</span> </span>{</span><br><span class="line"> phi[<span class="number">1</span>] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">2</span>; i<=mx; i++) {</span><br><span class="line"> <span class="keyword">if</span>(!notPrime[i]) {</span><br><span class="line"> p[++last] = i;</span><br><span class="line"> phi[i] = i<span class="number">-1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">1</span>; j<=last; j++) {</span><br><span class="line"> <span class="type">int</span> t = i * p[j];</span><br><span class="line"> <span class="keyword">if</span>(t>=mx) <span class="keyword">break</span>;</span><br><span class="line"> notPrime[t] = <span class="literal">true</span>;</span><br><span class="line"> <span class="keyword">if</span>(i % p[j]==<span class="number">0</span>) {</span><br><span class="line"> phi[t] = phi[i] * p[j];</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> } <span class="keyword">else</span></span><br><span class="line"> phi[t]= phi[i] * (p[j]<span class="number">-1</span>);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> Coding </tag>
</tags>
</entry>
</search>