[LeetCode] 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?

O(n^2): dp

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