chore: import upstream snapshot with attribution

math/factorial_memoization.cpp

@@ -0,0 +1,65 @@
+/**
+ * @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 which caches computed
+ * results in a memo array to avoid recalculating factorials for the same
+ * numbers.
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(n)
+ */
+
+#include <cassert>  // For test cases
+#include <cstdint>  // For uint64_t
+#include <vector>   // For std::vector
+
+class MemorisedFactorial {
+    std::vector<std::uint64_t> known_values = {1};
+
+ 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);
+    }
+};
+
+void test_MemorisedFactorial_in_order() {
+    auto factorial = MemorisedFactorial();
+    assert(factorial(0) == 1);
+    assert(factorial(1) == 1);
+    assert(factorial(5) == 120);
+    assert(factorial(10) == 3628800);
+}
+
+void test_MemorisedFactorial_no_order() {
+    auto factorial = MemorisedFactorial();
+    assert(factorial(10) == 3628800);
+}
+
+/**
+ * @brief Main function to run tests
+ * @returns 0 on program success
+ */
+int main() {
+    test_MemorisedFactorial_in_order();
+    test_MemorisedFactorial_no_order();
+    return 0;
+}