Create a file factorial_top_down_dp to the dynamic programming directory

dynamic_programming/factorial_top_down_dp.cpp

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+/**
+ * @file
+ * @brief [Factorial calculation using recursion and memoization (dynamic programming)](https://en.wikipedia.org/wiki/Factorial)
+ * @details
+ * This program computes the factorial of a non-negative integer using recursion
+ * with memoization (top-down dynamic programming). It stores intermediate results
+ * to avoid redundant calculations for improved efficiency.
+ * 
+ * Time Complexity: O(n)
+ * Space Complexity: O(n)
+ @author [Vedant Mukhedkar](https://github.com/git5v)
+ */
+
+#include <iostream>
+#include <cassert>  // For test cases
+
+/// Array to store computed factorials for memoization
+long long memo[1000] = {0};
+
+/**
+ * @brief Computes the factorial of a non-negative integer using recursion and memoization.
+ * @param n The integer whose factorial is to be computed
+ * @returns The factorial of n
+ */
+long long fact_rec(int n) {
+    if (n == 0) return 1;        // Base case: 0! = 1
+    if (memo[n] != 0) return memo[n]; // Return already computed value
+    memo[n] = n * fact_rec(n - 1);    // Store and return the computed value
+    return memo[n];
+}
+
+/**
+ * @brief Self-test implementations for the fact_rec function.
+ * @returns void
+ */
+void test_fact_rec() {
+    // Test cases for factorial computation
+    assert(fact_rec(0) == 1);
+    assert(fact_rec(1) == 1);
+    assert(fact_rec(5) == 120);
+    assert(fact_rec(10) == 3628800);
+    std::cout << "All test cases passed!\n";
+}
+
+/**
+ * @brief Main function to run test cases and interact with the user.
+ * @returns 0 on program success
+ */
+int main() {
+    // Run test cases
+    test_fact_rec();
+
+    // User interaction loop
+    // int n;
+    // std::cout << "Enter a non-negative integer to compute factorial (0 to exit): ";
+    // std::cin >> n;
+    // if (n < 0) {
+    //     std::cout << "Please enter a non-negative integer only.\n";
+    //     return 0;
+    // }
+    // std::cout << "Factorial of " << n << " = " << fact_rec(n) << std::endl;
+
+    return 0;
+}