lcs.py

''' mbinary
#########################################################################
# File : lcs.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-08-25  12:00
# Description:
#########################################################################
'''


def lcs(a, b):
    '''time: O(mn); space: O(mn)'''
    m, n = len(a), len(b)
    board = [[[] for i in range(n+1)] for i in range(m+1)]
    for i in range(m):
        for j in range(n):
            if a[i] == b[j]:
                board[i+1][j+1] = board[i][j]+[a[i]]
            elif len(board[i][j+1]) < len(board[i+1][j]):
                board[i+1][j+1] = board[i+1][j]
            else:
                board[i+1][j+1] = board[i][1+j]
    return board[m][n]


def lcs2(a, b):
    '''time: O(mn); space: O(m)'''
    m, n = len(a), len(b)
    board = [[] for i in range(n+1)]
    for i in range(m):
        upperLevel = board[0].copy()
        for j in range(n):
            tmp = board[j+1].copy()
            if a[i] == b[j]:
                board[j+1] = upperLevel+[a[i]]
            elif len(board[j+1]) < len(board[j]):
                board[j+1] = board[j].copy()  # copy is needed
            upperLevel = tmp
    return board[n]


if __name__ == '__main__':
    a = 'ABCBDAB'
    b = 'BDCABA'
    print('s1:', a)
    print('s2:', b)
    while 1:
        print('lcs:', lcs2(a, b))
        a = input('s1: ')
        b = input('s2: ')