Longest_Increasing_Subsequence.cpp

/*
Given a sequence of integers, find the longest increasing subsequence (LIS).

You code should return the length of the LIS.

Example
For [5, 4, 1, 2, 3], the LIS  is [1, 2, 3], return 3

For [4, 2, 4, 5, 3, 7], the LIS is [4, 4, 5, 7], return 4

Challenge
Time complexity O(n^2) or O(nlogn)
*/
#include <vector>

using namespace std;

class Solution {
  public:
    /**
     * @param nums: The integer array
     * @return: The length of LIS (longest increasing subsequence)
     */
    int longestIncreasingSubsequence(vector<int> nums) {
        // write your code here
        if (nums.empty()) {
            return 0;
        }
        vector<int> dp(nums.size(), 1);
        for (int i = 1; i < nums.size(); i++) {
            for (int j = 0; j < i; j++) {
                if (nums[i] >= nums[j] && dp[i] < dp[j] + 1) {
                    dp[i] = dp[j] + 1;
                }
            }
        }
        int result = 1;
        for (int i = 0; i < dp.size(); i++) {
            result = max(result, dp[i]);
        }
        return result;
    }
};