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.

 

Solution:

Dynamic programming
Create a max array, store the max until that index
Update the max sum for return

class Solution {
    public int maxSubArray(int[] nums) {
        int n = nums.length;
        int maxSum = nums[0];
        
        for (int i = 1; i < n; i++) {
            if (nums[i - 1] > 0) {
                nums[i] += nums[i - 1];
            }
            maxSum = Math.max(maxSum, nums[i]);
        }
        
        return maxSum;
    }
}

Time complexity: O(n)

Space complexity: O(1)