largest_power.cpp

/**
 * @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;
}