Problem statement:

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [-2,1,-3,4,-1,2,1,-5,4],
the contiguous subarray [4,-1,2,1] has the largest sum = 6.

Solution:

The problem wants the max sum of a subarray. The basic idea is to drop the array if its sum is negative.

There two variables: one is the current sum, another is the max sum. The idea is similar with 300. Longest Increasing Subsequence.

Time complexity is O(n).

class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int cur_sum = 0;
        int max_sum = INT_MIN;
        
 
for(auto num : nums){
            if(cur_sum < 0){
                // cur_sum < 0, drop off it and make cur_sum = num
                cur_sum = num;
            } else {
                // if cur_sum >= 0, add num to cur_sum
                cur_sum += num;
            }
            // update the max sum for each element
 

            max_sum = max(max_sum, cur_sum);
        }
        return max_sum;
    }
};

53. Maximum Subarray