DP way (space O(N)): key point here is keep recording local max subarray sum while updating global max subarray sum

class Solution:
    def maxSubArray(self, A: List[int]) -> int:
        """ tc O(N) sc O(N)
        dp[i]: max sub array sum ending with A[i]
        use a global res to cache local subarary sum at each iteration 
        """
        n = len(A)
        dp =[0]*n
        dp[0] = A[0]
        res = dp[0]
        for i in range(1,n):
            dp[i] = A[i] + (dp[i-1] if dp[i-1]> 0  else 0 )
            res = max(res,dp[i])
        return res

Kadane’s algo: main idea– if sum of subarray is positive, it’s possible to make next value bigger. So keep adding until subarray sum is negtive

class Solution:
    def maxSubArray(self, A: List[int]) -> int:
        """ tc O(N) sc O(1)
        """
        n = len(A)
        sums = A[0]
        res = A[0]
        for i in range(1,n):
            if sums > 0:
                sums += A[i]
            else:
                sums = A[i]
            res = max(res,sums)
        return res