使用动态编程进行字符串操作

def lcs(X, Y):
    m = len(X)
    n = len(Y)
    dp = [[0] * (n + 1) for _ 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
            else:
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
    
    return dp[m][n]

# 使用示例
X = "ABCBDAB"
Y = "BDCAB"
print("最长公共子序列的长度是:", lcs(X, Y))  # 输出: 4

def lcs_optimized(X, Y):
    m = len(X)
    n = len(Y)
    if m < n:
        X, Y = Y, X
        m, n = n, m
    dp = [[0] * (n + 1) for _ in range(2)]
    
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if X[i - 1] == Y[j - 1]:
                dp[i % 2][j] = dp[(i - 1) % 2][j - 1] + 1
            else:
                dp[i % 2][j] = max(dp[(i - 1) % 2][j], dp[i % 2][j - 1])
    
    return dp[m % 2][n]

# 使用示例
X = "ABCBDAB"
Y = "BDCAB"
print("最长公共子序列的长度是:", lcs_optimized(X, Y))  # 输出: 4