## C++, math, 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 <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;
}
``````