magic_number.cpp File Reference

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. More...

#include <cassert>
#include <cstdint>
#include <iostream>

Include dependency graph for magic_number.cpp:

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Namespaces
namespace	math
	for assert

Functions
bool	math::magic_number (const uint64_t &n)
static void	tests ()
	Test function.
int	main ()
	Main function.

Detailed Description

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

Definition in file magic_number.cpp.

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

Definition at line 78 of file magic_number.cpp.

           {
    tests();  // execute the tests
    return 0;
}

tests()

void tests ( )

static

Test function.

Returns

void

Definition at line 52 of file magic_number.cpp.

                    {
    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";
}