From 73a212ebd5b4a73f4b33ac1c5089ce67f1a7497e Mon Sep 17 00:00:00 2001
From: Anushka Gupta <100286919+Anushkagpt@users.noreply.github.com>
Date: Tue, 8 Oct 2024 20:02:27 +0530
Subject: [PATCH 1/2] Create lcs_algorithm.py

---
 lcs_algorithm.py | 46 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)
 create mode 100644 lcs_algorithm.py

diff --git a/lcs_algorithm.py b/lcs_algorithm.py
new file mode 100644
index 000000000000..0d224f40dbd3
--- /dev/null
+++ b/lcs_algorithm.py
@@ -0,0 +1,46 @@
+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}")

From 72535a17acb7f8a70be0e3a02b7258c6143ddb42 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 8 Oct 2024 14:33:12 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lcs_algorithm.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lcs_algorithm.py b/lcs_algorithm.py
index 0d224f40dbd3..2ac4f6e5db6c 100644
--- a/lcs_algorithm.py
+++ b/lcs_algorithm.py
@@ -39,6 +39,7 @@ def longest_common_subsequence(X, Y):
     # Return the LCS in the correct order
     return "".join(reversed(lcs))
 
+
 # Example usage:
 X = "AGGTAB"
 Y = "GXTXAYB"