chore: import upstream snapshot with attribution

math/check_factorial.cpp

@@ -0,0 +1,74 @@
+/**
+ * @file
+ * @brief A simple program to check if the given number is a
+ * [factorial](https://en.wikipedia.org/wiki/Factorial) of some number or not.
+ *
+ * @details A factorial number is the sum of k! where any value of k is a
+ * positive integer. https://www.mathsisfun.com/numbers/factorial.html
+ *
+ * @author [Divyajyoti Ukirde](https://github.com/divyajyotiuk)
+ * @author [ewd00010](https://github.com/ewd00010)
+ */
+#include <cassert>   /// for assert
+#include <cstdint>
+#include <iostream>  /// for cout
+
+/**
+ * @namespace
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * @brief Function to check if the given number is factorial of some number or
+ * not.
+ * @param n number to be checked.
+ * @return true if number is a factorial returns true
+ * @return false if number is not a factorial
+ */
+bool is_factorial(uint64_t n) {
+    if (n <= 0) {  // factorial numbers are only ever positive Integers
+        return false;
+    }
+
+    /*!
+     * this loop is basically a reverse factorial calculation, where instead
+     * of multiplying we are dividing. We start at i = 2 since i = 1 has
+     * no impact division wise
+     */
+    int i = 2;
+    while (n % i == 0) {
+        n = n / i;
+        i++;
+    }
+
+    /*!
+     * if n was the sum of a factorial then it should be divided until it
+     * becomes 1
+     */
+    return (n == 1);
+}
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void tests() {
+    assert(math::is_factorial(50) == false);
+    assert(math::is_factorial(720) == true);
+    assert(math::is_factorial(0) == false);
+    assert(math::is_factorial(1) == true);
+    assert(math::is_factorial(479001600) == true);
+    assert(math::is_factorial(-24) == false);
+
+    std::cout << "All tests have successfully passed!" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    tests();  // run self-test implementations
+    return 0;
+}