300. Longest Increasing Subsequence

https://leetcode.com/problems/longest-increasing-subsequence/

Problem

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?

Solution

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

• #binarysearch

• #dp

• #veryimportant