Maximum continuous subarray sum (maximum field sum)

Maximum continuous sub-array:

problem:

Given a sequence of n integers (possibly negative) a [1], a [2], a [3], ..., a [n], find the sequence as a [i] + a [i + 1] +… + The maximum value of the sum of subsections of a [j]. When the given integers are all negative, the sub-segment sum is defined as 0. According to this definition, the optimal value is: Max {0, a [i] + a [i + 1] +… + a [j]} , 1 <= i <= j <= n

For example, when (a [1], a [2], a [3], a [4], a [5], a [6]) = (-2,11, -4,13, -5,- 2), the maximum sub-segment sum is 20.

Divide and conquer:

def Max_cross_sum(list1,left,mid,right):
    left_sum = 0
    right_sum = 0
    temp = 0
    mid_1 = mid
    while mid_1>=left:
        temp += list1[mid_1]
        left_sum = max(left_sum,temp)
        mid_1 -= 1
    temp = 0
    mid_1 = mid + 1
    while mid_1<=right:
        temp += list1[mid_1]
        right_sum = max(right_sum,temp)
        mid_1 += 1
    return left_sum+right_sum
def Max_sum(list1,left,right):
    if left == right:
        return list1[left]
    mid = (left+right)//2
    left_sum = Max_sum(list1,left,mid)
    right_sum = Max_sum(list1,mid+1,right)
    cross_sum = Max_cross_sum(list1,left,mid,right)
    return max(left_sum,max(right_sum,cross_sum))    
list1 = [-2,1,-3,4,-10,2,10,-5,6]
Max_sum(list1,0,len(list1)-1)

Dynamic programming method:

def Max_sum(lis1):
    temp = 0
    max_sum = 0
    for cnt in list1:
        temp = max(temp+cnt,cnt)
        max_sum = max(max_sum,temp)
    return max_sum
list1 = [-2,1,-3,4,-1,2,10,-5,1]
Max_sum(list1)