算法导论之求解最大子数组问题python代码实现

算法导论之最大子数组问题

使用分治策略求解

基于python的源代码如下：

#求出跨越中点的最大子数组
def FIND_MAX_CROSSING_SUBARRARY(list,low,mid,high):
	left_max = -float("inf")
	right_max = -float("inf")
	left_sum = 0
	right_sum = 0
	left_index = mid
	right_index = mid
	for i in range(mid,low-1,-1):
		left_sum=left_sum+list[i]
		if left_sum>left_max:
			left_max=left_sum
			left_index=i
	for j in range(mid+1,high+1):
		right_sum=right_sum+list[j]
		if right_sum>right_max:
			right_max=right_sum
			right_index=j
	return (left_index,right_index,left_max+right_max)

def FIND_MAXIMUM_SUBARRARY(list,low,high):
	left_low,left_high,left_sum = 0,0,0
	right_low,right_high,right_sum = 0,0,0
	cross_low,cross_high,cross_sum = 0,0,0
	if high == low:
		return (low,high,list[low])
	else:
		mid = (low + high) // 2
		(left_low,left_high,left_sum)=FIND_MAXIMUM_SUBARRARY(list,low,mid)
		(right_low,right_high,right_sum)=FIND_MAXIMUM_SUBARRARY(list,mid+1,high)
		(cross_low,cross_high,cross_sum)=FIND_MAX_CROSSING_SUBARRARY(list,low,mid,high)
		if left_sum>=right_sum and left_sum>=cross_sum:
			return (left_low,left_high,left_sum)
		if right_sum>=left_sum and right_sum>=cross_sum:
			return (right_low,right_high,right_sum)
		else:
			return (cross_low,cross_high,cross_sum)