chore: import upstream snapshot with attribution

math/largest_power.cpp

@@ -0,0 +1,77 @@
+/**
+ * @file
+ * @brief Algorithm to find largest x such that p^x divides n! (factorial) using
+ * Legendre's Formula.
+ * @details Given an integer n and a prime number p, the task is to find the
+ * largest x such that p^x (p raised to power x) divides n! (factorial). This
+ * will be done using Legendre's formula: x = [n/(p^1)] + [n/(p^2)] + [n/(p^3)]
+ * + \ldots + 1
+ * @see more on
+ * https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n
+ * @author [uday6670](https://github.com/uday6670)
+ */
+
+#include <cassert>   /// for assert
+#include <cstdint>
+#include <iostream>  /// for std::cin and std::cout
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+
+/**
+ * @brief Function to calculate largest power
+ * @param n number
+ * @param p prime number
+ * @returns largest power
+ */
+uint64_t largestPower(uint32_t n, const uint16_t& p) {
+    // Initialize result
+    int x = 0;
+
+    // Calculate result
+    while (n) {
+        n /= p;
+        x += n;
+    }
+    return x;
+}
+
+}  // namespace math
+
+/**
+ * @brief Function for testing largestPower function.
+ * test cases and assert statement.
+ * @returns `void`
+ */
+static void test() {
+    uint8_t test_case_1 = math::largestPower(5, 2);
+    assert(test_case_1 == 3);
+    std::cout << "Test 1 Passed!" << std::endl;
+
+    uint16_t test_case_2 = math::largestPower(10, 3);
+    assert(test_case_2 == 4);
+    std::cout << "Test 2 Passed!" << std::endl;
+
+    uint32_t test_case_3 = math::largestPower(25, 5);
+    assert(test_case_3 == 6);
+    std::cout << "Test 3 Passed!" << std::endl;
+
+    uint32_t test_case_4 = math::largestPower(27, 2);
+    assert(test_case_4 == 23);
+    std::cout << "Test 4 Passed!" << std::endl;
+
+    uint16_t test_case_5 = math::largestPower(7, 3);
+    assert(test_case_5 == 2);
+    std::cout << "Test 5 Passed!" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // execute the tests
+    return 0;
+}