Leetcode53.最大子序和（python3）

Leetcode53.最大子序和

题目描述：
给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。
实例：
输入: [-2,1,-3,4,-1,2,1,-5,4],
输出: 6
解释: 连续子数组 [4,-1,2,1] 的和最大，为 6。
解法1：（python）

class Solution(object):
    def maxSubArray(self, nums):
        sum=0
        real_max_sum=nums[0]
        for num in nums:
            sum+=num
            if sum>real_max_sum:
                real_max_sum=sum
            if sum<0:
                sum=0
        return real_max_sum

解法1的另一种表达：（python）

class Solution:
    def maxSubArray(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        res = 0
        max0 = nums[0]
        for i in nums:
            res = max(i,res+i)
            max0 = max(res,max0)
            if res < 0:
                res = 0
        return max0

解法2：分治法（python）

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

        left = 0
        right = len(nums)-1
        maxSum = self.divide(nums,left,right)
        return maxSum
        
    def divide(self,nums,left,right):
        if left==right:
            return nums[left]
        center = (left+right)//2
        leftMaxSum = self.divide(nums,left,center)
        rightMaxSum = self.divide(nums,center+1,right)
        leftBorderSum = nums[center]
        leftSum = nums[center]
        for i in range(center-1,left-1,-1):
            leftSum += nums[i]
            if leftSum>leftBorderSum:
                leftBorderSum = leftSum
        rightBorderSum = nums[center+1]
        rightSum = nums[center+1]
        for i in range(center+2,right+1):
            rightSum += nums[i]
            if rightSum>rightBorderSum:
                rightBorderSum = rightSum
        BorderSum = leftBorderSum + rightBorderSum        
        return max(leftMaxSum,rightMaxSum,BorderSum)