magic_number.cpp

/**
 * @file
 * @brief A simple program to check if the given number is a magic number or
 * not. A number is said to be a magic number, if the sum of its digits are
 * calculated till a single digit recursively by adding the sum of the digits
 * after every addition. If the single digit comes out to be 1,then the number
 * is a magic number.
 *
 * This is a shortcut method to verify Magic Number.
 * On dividing the input by 9, if the remainder is 1 then the number is a magic
 * number else not. The divisibility rule of 9 says that a number is divisible
 * by 9 if the sum of its digits are also divisible by 9. Therefore, if a number
 * is divisible by 9, then, recursively, all the digit sums are also divisible
 * by 9. The final digit sum is always 9. An increase of 1 in the original
 * number will increase the ultimate value by 1, making it 10 and the ultimate
 * sum will be 1, thus verifying that it is a magic number.
 * @author [Neha Hasija](https://github.com/neha-hasija17)
 */
#include <cassert>   /// for assert
#include <cstdint>
#include <iostream>  /// for io operations

/**
 * @namespace math
 * @brief Mathematical algorithms
 */
namespace math {
/**
 * Function to check if the given number is magic number or not.
 * @param n number to be checked.
 * @return if number is a magic number, returns true, else false.
 */
bool magic_number(const uint64_t &n) {
    if (n <= 0) {
        return false;
    }
    // result stores the modulus of @param n with 9
    uint64_t result = n % 9;
    // if result is 1 then the number is a magic number else not
    if (result == 1) {
        return true;
    } else {
        return false;
    }
}
}  // namespace math

/**
 * @brief Test function
 * @returns void
 */
static void tests() {
    std::cout << "Test 1:\t n=60\n";
    assert(math::magic_number(60) == false);
    std::cout << "passed\n";

    std::cout << "Test 2:\t n=730\n";
    assert(math::magic_number(730) == true);
    std::cout << "passed\n";

    std::cout << "Test 3:\t n=0\n";
    assert(math::magic_number(0) == false);
    std::cout << "passed\n";

    std::cout << "Test 4:\t n=479001600\n";
    assert(math::magic_number(479001600) == false);
    std::cout << "passed\n";

    std::cout << "Test 5:\t n=-35\n";
    assert(math::magic_number(-35) == false);
    std::cout << "passed\n";
}

/**
 * @brief Main function
 * @returns 0 on exit
 */
int main() {
    tests();  // execute the tests
    return 0;
}