LEETCODE —— Maximum Subarray [一维DP]

Maximum Subarray

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.

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一维DP, O(n).
假设A(0, i)区间存在k，使得[k, i]区间是以i结尾区间的最大值， 定义为Max[i], 在这里，当求取Max[i+1]时，

if (Max[i] + A[i+1] >0)
　　Max[i+1] = Max[i] + A[i+1]

if(Max[i]+A[i+1] <0) #也就是要舍弃

　　Max[i+1] = 0

'''
Created on Nov 13, 2014
 
@author: ScottGu<gu.kai.66@gmail.com, 150316990@qq.com>
'''
class Solution:
    # @param A, a list of integers
    # @return an integer
    def maxSubArray(self, A):
        sum=0
        max=-655356
        for x in A:
            sum+=x
            if(sum>max):
                max=sum
            if(sum<0):
                sum=0
        return max