LCS 最长公共子序列

区别最长公共子串（连续）

'''
LCS 最长公共子序列
'''


def LCS_len(x, y):
    m = len(x)
    n = len(y)
    dp = [[0] * (n + 1) for i in range(m + 1)]
    B = [[' '] * (n + 1) for i in range(m + 1)]
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if x[i - 1] == y[j - 1]:
                dp[i][j] = dp[i - 1][j - 1] + 1
                B[i][j] = 'X'
            elif dp[i - 1][j] > dp[i][j - 1]:
                dp[i][j] = dp[i - 1][j]
                B[i][j] = 'L'
            else:
                dp[i][j] = dp[i][j - 1]
                B[i][j] = 'T'
    print(dp)
    return dp, B


def LCS_str(B, x, i, j):
    if i == 0 or j == 0:
        return
    if B[i][j] == 'X':
        print(x[i - 1])
        LCS_str(B, x, i - 1, j - 1)

    elif B[i][j] == 'L':
        LCS_str(B, x, i - 1, j)
    else:
        LCS_str(B, x, i, j - 1)


def main():
    x = 'ABDC'
    y = 'AFBC'
    dp, B = LCS_len(x, y)
    LCS_str(B, x, len(x), len(y))
main()