算法导论 第三章 and 第四章 python

import decimal

def FIND_MAX_CROSSING_SUBARRAY(A,low,mid,high):
    left_sum =  decimal.MIN_EMIN
    sum = 0
    for i in range(mid,low - 1,-1):
        sum = sum + A[i]
        if sum > left_sum:
            left_sum = sum
            max_left = i
    right_sum = decimal.MIN_EMIN
    sum = 0
    for i in range(mid + 1,high+1):
        sum = sum + A[i]
        if sum > right_sum:
            right_sum = sum
            m   ax_right = i
    return (max_left,max_right,left_sum + right_sum)    


def FIND_MAXIMUM_SUBARRAY(A,low,high):
    if high == low:
        return (low,high,A[low])
    else:
        mid = (low + high) //2
        (left_low,left_high,left_sum) = FIND_MAXIMUM_SUBARRAY(A,low,mid)
        (right_low,right_high,right_sum) = FIND_MAXIMUM_SUBARRAY(A,mid+1,high)
        (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 = [13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7]
    temp = FIND_MAXIMUM_SUBARRAY(A,0,len(A)-1)
    print(temp)
‘‘‘
========= RESTART: F:/python/algorithms/4_1_find_maximum_subarray.py =========
(7, 10, 43)

O（n*n）
python 3.5.1
win7
和伪代码几乎一模一样 - -！
唯一要注意的问题还是 python 从0开始
‘‘‘

def FindGreatestSumOfSubArray(A):
        if A :
                nCurSum = nGreatestSum = 0
                #nCurSum 保存现在和 nCreatestSum 保存最大的
                curStart = curEnd = 0
                start = end = 0
                for i in range(len(A)): #遍历A
                        nCurSum += A[i]
                        curEnd = i
                        if nCurSum < 0: #为负数摒弃 加一个正数=把正数减
小
                                nCurSum = 0
                                curStart = curEnd = i + 1
                        if nCurSum > nGreatestSum: #刷新最大数组
                                nGreatestSum = nCurSum
                                start = curStart
                                end = curEnd
                #都是负数 遍历找最大负数
                if nGreatestSum == 0:
                        nGreatestSum = A[0]
                        start = end = 0
                        for i in range(1,len(A)):
                                if A[i] > nGreatestSum:
                                        nGreatestSum = A[i]
                                        start = end = i
                return [start,end,nGreatestSum]
        else:
                return []
if __name__ =="__main__":
        A =  [13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7]
        temp = FindGreatestSumOfSubArray(A)
        print(temp)
‘‘‘
$ python3 4_1_5_find_maximum_subarray.py 
[7, 10, 43]

O（n）
Python 3.4.3+
Ubuntu 15.10

‘‘‘