Added Python solution for Longest Common Subsequence

Author: jaimin45-art

strings/longest_common_subsequence.py

@@ -0,0 +1,47 @@
+# longest_common_subsequence.py
+# This program finds the Longest Common Subsequence (LCS) between two strings
+# using Dynamic Programming and also prints the actual LCS string.
+
+def longest_common_subsequence(x: str, y: str):
+    m, n = len(x), len(y)
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    # Fill the dp table
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            if x[i - 1] == y[j - 1]:
+                dp[i][j] = 1 + dp[i - 1][j - 1]
+            else:
+                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+
+    # Reconstruct the LCS string
+    i, j = m, n
+    lcs = []
+    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
+
+    lcs.reverse()
+    lcs_str = ''.join(lcs)
+
+    # Print DP table (for visualization)
+    print("DP Table:")
+    for row in dp:
+        print(row)
+
+    print(f"\nLength of LCS: {dp[m][n]}")
+    print(f"LCS String: {lcs_str}")
+
+    return dp[m][n], lcs_str
+
+
+if __name__ == "__main__":
+    s1 = input("Enter first string: ")
+    s2 = input("Enter second string: ")
+    longest_common_subsequence(s1, s2)