最长公共子序列算法python

动态规划（空间优化）：

def LCS(a, b):
    """ 最长公共子序列 空间复杂度为O(min(a,b))+1  记录左上角值"""
    if len(a) < len(b):
        a, b = b, a
    print(a, b)
    list = [0 for i in range(len(b))]
    for i in range(len(a)):
        upperleft = 0
        for j in range(len(b)):
            if a[i] == b[j]:
                upperleft, list[j] = list[j], upperleft+1
                # 记住修改之前list[j]的值，为了下次作为左上角的值使用
            else:
                upperleft = list[j]
                # 记住修改之前list[j]的值，为了下次作为左上角的值使用
                list[j] = (max(list[j], list[j-1]) if j != 0 else list[j])
        print(list)
    return list[-1]


def main():
    # a="67824681"
    # b="123456789"
    a = input("Please input one string:")
    print("Your enter is : ", a)
    b = input("Please input another string:")
    print("Your enter is : ", b)
    print("The longth of the longest common subsequence is :", LCS(a, b))

  
if __name__ == '__main__':
    main()