From c836257d6f5155b83137b48dece10899f478734d Mon Sep 17 00:00:00 2001
From: chenzhengwei <chenzhengwei@baidu.com>
Date: Thu, 16 Feb 2017 14:55:45 +0800
Subject: [PATCH] m416

---
 Solution/401-450/416.md | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/Solution/401-450/416.md b/Solution/401-450/416.md
index 1940fad..738e96a 100644
--- a/Solution/401-450/416.md
+++ b/Solution/401-450/416.md
@@ -43,4 +43,45 @@ public class Solution {
         return dp[len][target];
     }
 }
+```
+另外一个降低了空间复杂度的01背包方案
+```java
+public class Solution {
+    /*
+        转化为01背包问题
+     */
+    public boolean canPartition(int[] nums) {
+        // 首先判断一些特殊情况
+        int sum = 0;
+        for (int i = 0; i < nums.length; i++) {
+            sum += nums[i];
+        }
+        if (sum % 2 == 1) {
+            return false;
+        }
+        int target = sum / 2;
+        for (int i = 0; i < nums.length; i++) {
+            if (nums[i] > target) {
+                return false;
+            } else if (nums[i] == target) {
+                return true;
+            }
+        }
+
+        // 如果仍无法判断，转化为01背包问题
+        int len = nums.length;
+        boolean[] dp = new boolean[target + 1];
+        Arrays.fill(dp, false);
+        dp[0] = true;
+        for (int i = 1; i < len + 1; i++) {
+            // 注意这里的方向是从后向前
+            for (int j = target; j > 0; j--) {
+                if (j >= nums[i - 1]) {
+                    dp[j] = dp[j] || dp[j - nums[i - 1]];
+                }
+            }
+        }
+        return dp[target];
+    }
+}
 ```
\ No newline at end of file