leetcode 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.

贪心：

class Solution(object):
    def maxSubArray(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """

        ans = s = nums[0]
        for i in xrange(1, len(nums)):
            if s > 0:
                s = nums[i]+s                
            else:
                s = nums[i]
            ans = max(s, ans)
        return ans

DP解法：//dp[i] means the maximum subarray ending with A[i];

class Solution(object):
    def maxSubArray(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        dp = [0]*len(nums)
        ans = dp[0] = nums[0]
        for i in xrange(1, len(nums)):
            dp[i] = max(dp[i-1]+nums[i], nums[i])
            ans = max(ans, dp[i])
        return ans

递归解法：

TODO