leetcode 300. Longest Increasing Subsequence

Given an unsorted array of integers, find the length of longest increasing subsequence.
Example:
Input: [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
Note:
There may be more than one LIS combination, it is only necessary for you to return the length.
Your algorithm should run in O(n2) complexity.
Follow up: Could you improve it to O(n log n) time complexity?

方法：
见到求字符串极值或子串（子数组）的题目，先考虑动态规划。
其中**dp[i]的意思是以第i个元素结尾（不是指前i个元素）**的最长子序列长度

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> dp(nums.size(), 1);
        int res = 0;
        for (int i = 0; i < nums.size(); ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[i] > nums[j]) { //说明nums[i]可以放在nums[j]后面
                    dp[i] = max(dp[i], dp[j] + 1);
                }
            }
            res = max(res, dp[i]);  //更新res，保留每次最长的
        }
        return res;
    }
};