[pull] master from TheAlgorithms:master

math/factorial_memoization.cpp

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+/**
+ * @file
+ * @brief [Factorial](https://en.wikipedia.org/wiki/Factorial) calculation using recursion and [memoization](https://en.wikipedia.org/wiki/Memoization) 
+ * @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.
+ * 
+ * Memoization is a form of caching where the result to an expensive function call
+ * is stored and returned.
+ * Example:
+ * Input: n = 5
+ * Output: 120
+ * 
+ * Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120
+ * 
+ * The program uses a recursive function fact_recursion which caches computed 
+ * results in a memo array to avoid recalculating factorials for the same numbers.
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(n)
+ * @author [Vedant Mukhedkar](https://github.com/git5v)
+ */
+
+#include <iostream> // for std::cout
+#include <cassert>  // For test cases
+#include <array>    // For std::array
+#include <cstdint>  // For uint64_t
+
+/// Array to store computed factorials for memoization
+std::array<uint64_t, 1000> memo{0};
+
+/**
+ * @namespace math
+ * @brief Math algorithms
+ */
+namespace math {
+
+/**
+ * @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
+ */
+uint64_t fact_recursion(uint64_t 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_recursion(n - 1);    // Store and return the computed value
+    return memo[n];
+}
+
+} // namespace math
+/**
+ * @brief Self-test implementations for the fact_recursion function.
+ * @returns void
+ */
+void test_fact_recursion() {
+    // Test cases for factorial computation
+    assert(math::fact_recursion(0) == 1);
+    assert(math::fact_recursion(1) == 1);
+    assert(math::fact_recursion(5) == 120);
+    assert(math::fact_recursion(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_recursion();
+    return 0;
+}