扫描算法求解连续子向量的最大和问题（Python）

上篇用有限状态机来求解，其实也是进行了一遍扫描，只是我把问题考虑的复杂了。

对于扫描，我以为首先要问本身3个问题：

1. 如何扫描 （这里是遍历数组元素）

2. 每次扫描会改变什么 （这里的算法会改变maxendinghere，前一篇的算法是改变状态）

3. 改变的东西会对结果有影响么 （maxendinghere若是大于maxsofar，那么maxsofar就被赋值为maxendinghere）

不一样的考虑问题的方式引入不一样的解决方案，其中的差距太大了！！前一篇我太关注正负号了，致使我采用了序列分段，状态转移的方式去解决问题；这里的解法关注最大和，以及有可能影响最大和的因素，maxsofar和maxendinghere的相对大小。虽然时间复杂度都是O(n)，可是，高下立现！

代码以下（python）：

 

#!/usr/bin/python                                                                                                                                                      

def scan(vector):               # return (maxsofar, low, high)                                                                                                         
    length = len(vector)
    maxsofar = 0
    maxendinghere = 0
    low = 0
    high = 0
    low2 = 0
    high2 = 0
    for i in range(0, length):
        if maxendinghere + vector[i] > 0:
            maxendinghere = maxendinghere + vector[i]
            high2 = i+1
        else:
            maxendinghere = 0
            low2 = i+1
        if maxsofar >= maxendinghere:
            high = high
            low = low
            maxsofar = maxsofar
        else:
            high = high2
            low = low2
            maxsofar = maxendinghere
    return (maxsofar, low, high)

def test():
    vector = [-1, -1, -1, -1]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

    vector = [1, -1, -1, -1]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

    vector = [-1, -1, -1, 1]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

    vector = [-1, 2, 3, -4]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

    vector = [1, 2, 3, 4]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

    vector = [31, -41, 59, 26, -53, 58, 97, -93, -23, 84]
    (maxsofar, low, high) = scan(vector)
    print vector
    print maxsofar, low, high
    print

def main():
    test()

if __name__ == '__main__':
    main()

运行结果：

root@localhost :/home/James/mypro/Python# ./scan.py
[-1, -1, -1, -1]
0 0 0

[1, -1, -1, -1]
1 0 1

[-1, -1, -1, 1]
1 3 4

[-1, 2, 3, -4]
5 1 3

[1, 2, 3, 4]
10 0 4

[31, -41, 59, 26, -53, 58, 97, -93, -23, 84]
187 2 7

root@localhost :/home/James/mypro/Python#

 

后记：感受python真的很适合写这种小demo，又快又方便。