Revert "fix: remove potential segmentation fault from factorial_memoization.cpp (TheAlgorithms#2994)"

This reverts commit 1426fa4.

Author: realstealthninja

math/factorial_memoization.cpp

@@ -1,65 +1,73 @@
 /**
  * @file
- * @brief [Factorial](https://en.wikipedia.org/wiki/Factorial) calculation using
- * recursion and [memoization](https://en.wikipedia.org/wiki/Memoization)
+ * @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
- *
+ * 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 which caches computed
- * results in a memo array to avoid recalculating factorials for the same
- * numbers.
+ * 
+ * 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
-#include <vector>   // For std::vector
 
-class MemorisedFactorial {
-    std::vector<std::uint64_t> known_values = {1};
+/// Array to store computed factorials for memoization
+std::array<uint64_t, 1000> memo{0};
 
- public:
-    /**
-     * @note This function was intentionally written as recursive
-     * and it does not handle overflows.
-     * @returns factorial of n
-     */
-    std::uint64_t operator()(std::uint64_t n) {
-        if (n >= this->known_values.size()) {
-            this->known_values.push_back(n * this->operator()(n - 1));
-        }
-        return this->known_values.at(n);
-    }
-};
+/**
+ * @namespace math
+ * @brief Math algorithms
+ */
+namespace math {
 
-void test_MemorisedFactorial_in_order() {
-    auto factorial = MemorisedFactorial();
-    assert(factorial(0) == 1);
-    assert(factorial(1) == 1);
-    assert(factorial(5) == 120);
-    assert(factorial(10) == 3628800);
+/**
+ * @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];
 }
 
-void test_MemorisedFactorial_no_order() {
-    auto factorial = MemorisedFactorial();
-    assert(factorial(10) == 3628800);
+} // 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 tests
+ * @brief Main function to run test cases and interact with the user.
  * @returns 0 on program success
  */
 int main() {
-    test_MemorisedFactorial_in_order();
-    test_MemorisedFactorial_no_order();
+    // Run test cases
+    test_fact_recursion();
     return 0;
 }