53. Maximum Subarray

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

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

simple dp.

dp[i] --> maxSubString that ends at nums[i].

if dp[i-1] > 0 , which means dp[i] using the maxSubarray before will be greater than only nums[i].