Add longest_common_subsequence algorithm to strings

strings/longest_common_subsequence.py

@@ -0,0 +1,51 @@
+def longest_common_subsequence(s1: str, s2: str) -> str:
+    """
+    Returns the Longest Common Subsequence (LCS) of two strings.
+
+    The LCS is the longest sequence of characters that appear in both strings in the
+    same relative order, but not necessarily contiguously.
+
+    Args:
+        s1: The first string.
+        s2: The second string.
+
+    Returns:
+        The longest common subsequence as a string.
+
+    Example:
+    >>> longest_common_subsequence("ABCBDAB", "BDCAB")
+    'BCAB'
+    >>> longest_common_subsequence("XMJYAUZ", "MZJAWXU")
+    'MJAU'
+    """
+    m, n = len(s1), len(s2)
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    # Fill DP table
+    for i in range(m):
+        for j in range(n):
+            if s1[i] == s2[j]:
+                dp[i + 1][j + 1] = dp[i][j] + 1
+            else:
+                dp[i + 1][j + 1] = max(dp[i][j + 1], dp[i + 1][j])
+
+    # Backtrack to get LCS string
+    i, j = m, n
+    lcs_chars = []
+    while i > 0 and j > 0:
+        if s1[i - 1] == s2[j - 1]:
+            lcs_chars.append(s1[i - 1])
+            i -= 1
+            j -= 1
+        elif dp[i - 1][j] >= dp[i][j - 1]:
+            i -= 1
+        else:
+            j -= 1
+
+    return "".join(reversed(lcs_chars))
+
+
+if __name__ == "__main__":
+    # Basic tests
+    print(longest_common_subsequence("ABCBDAB", "BDCAB"))  # BCAB
+    print(longest_common_subsequence("XMJYAUZ", "MZJAWXU"))  # MJAU