最大子序列：
#! /usr/bin/env python
#coding=utf-8
def find_crossing_subarray（A,low,mid,high):
left_sum = float("-inf")
sum = 0
max_left = 0
max_right = 0
for i in range(mid,low-1,-1):
sum = sum + A[i]
if sum > lef_sum:
left_sum = sum
max_left = i
sum = 0
for j in range(mid+1,high+1,1):
sum = sum + A[j]
if sum > right_sum:
right_sum = sum
max_right = j
return [max_left,max_right,left_sum+right_sum]
import math
def find_maximum_subarray(A,low,high):
if high == low:
return (low,high,A[low])
else:
mid = math.floor((low+high)/2)
#递归部分
#最大子序列在左边
[left_low,left_high,left_sum] = find_maximum_subarray(A,low,mid)
#最大子序列在右边
[right_low,right_high,right_sum] = find_maximum_subarray(A,mid+1,high)
#最大子序列在中间
[cross_low,cross_high,cross_sum] = find_max_crossing_subarray(A,low,mid,high)
if left_sum >= right_sum and left_sum >= cross_sum:
return [left_low,left_high,left_sum]
elif right_sum >= left_sum and right_sum >= cross_sum:
return [right_low,right_high,right_sum]
else:return [cross_low,cross_high,cross_sum]
if __name__ == '__main__':
a=[-1,2,3,-4]
max = find_maximum_subarray(a, 0, len(a)-1)
print (max)
输出[1, 2, 5]
时间复杂度为nlgn，a[1]+a[2] = 5
当A[1,2，...n]为最大子序列，判断A[1，2,...n，n+1]的最大子序列：
#! /usr/bin/ python
#coding=utf-8
def j_subarry(A):
M = 0
M_high = len(A)-1
for j in range(0,len(A)-1):
M = M + A[j]
print(M)
print(A[len(A)-1])
if M+A[len(A)-1] > M:
M = M + A[len(A)-1]
M_high = M_high + 1
else:
M = M
M_high = M_high
return (M_high,M)
a = j_subarry([1,4,-2])
print(a)
时间复杂度为n
(2, 5)