add python code

public/py/ch3/lcs/lcs.py

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+"""
+最长公共子序列 (LCS) — 动态规划
+比较两个序列的相似度
+"""
+
+def lcs_length(X, Y):
+    """计算 LCS 长度并返回 DP 表"""
+    m, n = len(X), 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], dp
+
+def lcs_backtrack(X, Y, dp):
+    """回溯找出 LCS 序列"""
+    i, j = len(X), len(Y)
+    result = []
+
+    while i > 0 and j > 0:
+        if X[i - 1] == Y[j - 1]:
+            result.append(X[i - 1])
+            i -= 1
+            j -= 1
+        elif dp[i - 1][j] > dp[i][j - 1]:
+            i -= 1
+        else:
+            j -= 1
+
+    return ''.join(reversed(result))
+
+if __name__ == "__main__":
+    X = "ABCBDAB"
+    Y = "BDCABB"
+
+    length, dp_table = lcs_length(X, Y)
+    lcs_str = lcs_backtrack(X, Y, dp_table)
+
+    print(f"序列 X: {X}")
+    print(f"序列 Y: {Y}")
+    print(f"LCS 长度: {length}")
+    print(f"LCS 序列: {lcs_str}")