LCS contraction addition in dynamic programming

src/DynamicProgramming/LCS.sol

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+// SPDX-License-Identifier: MIT
+
+pragma solidity  ^0.8.0;
+
+/**
+ * @title longest common subsequence (LCS) problem
+ * @author [Priyda](https://github.com/priyda)
+ */
+
+contract LCS {
+    // We use a mapping to store the results of each subproblem
+    mapping(uint => mapping(uint => uint)) public cache;
+
+    function lcs(string memory a, string memory b, uint m, uint n) public view returns (uint) {
+        // Check if the result is already stored in the cache
+        if (cache[m][n] != 0) {
+            return cache[m][n];
+        }
+        // If either string is empty, the LCS is 0
+        if (m == 0 || n == 0) {
+            return 0;
+        }
+        // If the last characters of the strings match, add 1 to the LCS
+        // of the strings without the last character
+        if (a[m - 1] == b[n - 1]) {
+            uint result = 1 + lcs(a, b, m - 1, n - 1);
+            // Store the result in the cache
+            cache[m][n] = result;
+            return result;
+        }
+        // Otherwise, the LCS is the maximum of the LCS of the strings
+        // without the last character of each string
+        uint result = max(lcs(a, b, m, n - 1), lcs(a, b, m - 1, n));
+        // Store the result in the cache
+        cache[m][n] = result;
+        return result;
+    }
+
+    // Helper function to find the maximum of two unsigned integers
+    function max(uint a, uint b) private view returns (uint) {
+        return a > b ? a : b;
+    }
+}