MAXIMUM SUBSEQUENCE SUM PROBLEM

排除不合理的项(负值), 设定一个标杆sum, 往后扫描看是否有比sum好的情况.

We should ensure the following conditions:

　　1. The result must be the max sum.

　　2.* If more than one sum is max(same max value), choose the longer sequence.

　　3.* If more than one sum is max & same length, choose the former sequence.

 

#!/usr/bin/python2.7
#File: maxChildSum.py
#Author: lxw
#Time: 2014-08-22
#Usage: Find the max sum of a sub-sequence in a sequence.
#NOTE:      @1: first, must be the max sum.
#           @2: if more than one sum is max(same max value), choose the longer sequence.

def main():
    #arr = [-12, 0, -14, -14, -13, -14, -2]  #"zero" test.
    #arr = [0, -14, -14, -13, -14, -2]  #another "zero" test.
    arr = [-100, -14, -14, -13, -14, -2]  #"all negtive" test.
    #arr = [-12, 10, 2, -14, -14, 13, -2]  #"longer sequence but not equal sum" test.
    #arr = [-12, 0, 10, -14, -14, -2]  #"as long as better" test.
    #arr = [-12, 0, 10, -14, -14, 3, 7, -2]  #"same sum & same length" test.
    #arr = [-12, 10, -14, -14, 3, 7, -2]  #"same sum but longer sequence" test.

    index = 0
    length = len(arr)
    while arr[index] < 0:
        index += 1
        if index == length:
            break

    if index < length:
        sum = -1    #This initial value is important.
        start = index
        temp_sum = 0    #sum
        temp_start = index
        end = 0

        while index < length:
            temp_sum += arr[index]
            if temp_sum >= 0:
                if temp_sum > sum:
                    sum = temp_sum
                    start = temp_start
                    end = index
                elif temp_sum == sum:
                    if start == temp_start:
                        end = index
                    elif index - temp_start > end - start:
                        start = temp_start
                        end = index
            else:
                temp_sum = 0
                temp_start = index + 1
            index += 1
        print "max sum:{0:<4}start:{1:<4}end:{2:<4}max length:{3:<4}".format(sum, start, end, end-start+1)
    else:
        #All the numbers are negative.
        print "max sum:{0:<4}start:{1:<4}end:{2:<4}max length:{3:<4}".format(0, 0, 0, 0)


if __name__ == '__main__':
    main()
else:
    print "Being imported as a module."