Create lcs_algorithm.py

lcs_algorithm.py

@@ -0,0 +1,47 @@
+def longest_common_subsequence(X, Y):
+    """
+    Find the longest common subsequence (LCS) between two strings.
+
+    Args:
+        X (str): First string
+        Y (str): Second string
+
+    Returns:
+        str: The longest common subsequence
+    """
+    m = len(X)
+    n = len(Y)
+
+    # Create a 2D array to store the lengths of common subsequences
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    # Fill the 2D array using dynamic programming
+    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])
+
+    # Reconstruct the LCS from the 2D array
+    lcs = []
+    i, j = m, n
+    while i > 0 and j > 0:
+        if X[i - 1] == Y[j - 1]:
+            lcs.append(X[i - 1])
+            i -= 1
+            j -= 1
+        elif dp[i - 1][j] > dp[i][j - 1]:
+            i -= 1
+        else:
+            j -= 1
+
+    # Return the LCS in the correct order
+    return "".join(reversed(lcs))
+
+
+# Example usage:
+X = "AGGTAB"
+Y = "GXTXAYB"
+lcs = longest_common_subsequence(X, Y)
+print(f"The longest common subsequence is: {lcs}")