Leetcode 300. Longest Increasing Subsequence

題目：

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that 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?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.

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思路：

使用動態規劃來做，
dp[i]表示到位置i爲止，最長遞增子序列長度爲多少，
那麼dp[i] = max（dp[i] ,dp[j]+1）對於所有j( 0< j

代碼：

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        int size = nums.size();
        if(size == 0) return 0;
        vector<int> dp(size, 1);
        int res = 1;
        for(int i = 1; i < size; ++i) {
            for(int j = 0; j < i; ++ j) {
                if(nums[i] > nums[j])
                    dp[i] = max(dp[i], dp[j] + 1);
            }
            res = max(res, dp[i]);
        }
        return res;
    }
};