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)