Maximum Subarray

Question

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.

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

Tags

• Array
• Dynamic Programming

Thought

Reference: https://discuss.leetcode.com/topic/10722/a-python-solution

Use dynamic programming here. curSum represents the maximum sum of the substring which must includes the last item in the substring. maxSum represents the maximum sum of the substring which is allowed to ignore the last item in the substring.

Code

class Solution(object):
    def maxSubArray(self, A):
        """
        :type nums: List[int]
        :rtype: int
        """
        if not A:
            return 0

        curSum = maxSum = A[0]
        for num in A[1:]:
            curSum = max(num, curSum + num)
            maxSum = max(maxSum, curSum)

        return maxSum