Check if a number is magic (Recursive sum of digits is 1) - GeeksforGeeks

14 Jul, 2021
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. 
For example- Number= 50113 => 5+0+1+1+3=10 => 1+0=1 This is a Magic Number 
For example- Number= 1234 => 1+2+3+4=10 => 1+0=1 This is a Magic Number
Examples : 
 Input : 1234
Output : Magic Number

Input  : 12345
Output : Not a magic Number
The approach used brute force. The function keeps adding digits until a single digit sum is reached. To understand how i am calculating the sum upto a single digit view this page- Finding sum of digits of a number until sum becomes single digit
C++
Java
Python3
C#
PHP
Javascript
// CPP program to check if a number is Magic// number.#include<iostream>using namespace std; bool isMagic(int n){    int sum = 0;         // Note that the loop continues    // if n is 0 and sum is non-zero.    // It stops when n becomes 0 and    // sum becomes single digit.    while (n > 0 || sum > 9)    {        if (n == 0)        {            n = sum;            sum = 0;        }        sum += n % 10;        n /= 10;    }         // Return true if sum becomes 1.    return (sum == 1);}  // Driver codeint main(){    int n = 1234;    if (isMagic(n))        cout << "Magic Number";    else        cout << "Not a magic Number";    return 0;}
// Java program to check if// a number is Magic number.class GFG{   public static boolean isMagic(int n)   {       int sum = 0;             // Note that the loop continues       // if n is 0 and sum is non-zero.       // It stops when n becomes 0 and       // sum becomes single digit.       while (n > 0 || sum > 9)       {           if (n == 0)           {               n = sum;               sum = 0;           }           sum += n % 10;           n /= 10;       }             // Return true if sum becomes 1.       return (sum == 1);   }      // Driver code   public static void main(String args[])    {     int n = 1234;     if (isMagic(n))        System.out.println("Magic Number");               else        System.out.println("Not a magic Number");    }} // This code is contributed by Anshika Goyal.
# Python3 program to check# if a number is Magic# number. def isMagic(n):    sum = 0;         # Note that the loop    # continues if n is 0    # and sum is non-zero.    # It stops when n becomes    # 0 and sum becomes single    # digit.    while (n > 0 or sum > 9):        if (n == 0):            n = sum;            sum = 0;        sum = sum + n % 10;        n = int(n / 10);             # Return true if    # sum becomes 1.    return True if (sum == 1) else False; # Driver coden = 1234;if (isMagic(n)):    print("Magic Number");else:    print("Not a magic Number");     # This code is contributed# by mits.
// C# program to check if// a number is Magic number.using System; class GFG{    public static bool isMagic(int n)    {        int sum = 0;                 // Note that the loop continues        // if n is 0 and sum is non-zero.        // It stops when n becomes 0 and        // sum becomes single digit.        while (n > 0 || sum > 9)        {            if (n == 0)            {                n = sum;                sum = 0;            }            sum += n % 10;            n /= 10;        }                 // Return true if sum becomes 1.        return (sum == 1);    }         // Driver code    public static void Main()    {        int n = 1234;        if (isMagic(n))            Console.WriteLine("Magic Number");                     else            Console.WriteLine("Not a magic Number");    }} // This code is contributed by vt_m.
<?php// PHP program to check if// a number is Magic number.function isMagic($n){    $sum = 0;         // Note that the loop    // continues if n is 0    // and sum is non-zero.    // It stops when n becomes    // 0 and sum becomes single    // digit.    while ($n > 0 || $sum > 9)    {        if ($n == 0)        {            $n = $sum;            $sum = 0;        }        $sum += $n % 10;        $n /= 10;    }         // Return true if    // sum becomes 1.    return ($sum == 1);} // Driver code$n = 1234;if (isMagic($n))    echo"Magic Number";else    echo "Not a magic Number"; // This code is contributed// by nitin mittal.?>
<script> // JavaScript program to check if// a number is Magic number.function isMagic( n)   {       var sum = 0;             // Note that the loop continues       // if n is 0 and sum is non-zero.       // It stops when n becomes 0 and       // sum becomes single digit.       while (n > 0 || sum > 9)       {           if (n = 0)           {               n = sum;               sum = 0;           }           sum += n % 10;           n /= 10;       }             // Return true if sum becomes 1.       return (sum = 1);   }      // Driver code    var n = 1234;    if (isMagic(n))    document.write("Magic Number");              else        document.write("Not a magic Number");     // This code is contributed by shivanisinghss2110 </script>
Magic Number
 
Efficient Approach(Shortcut): There is also a shortcut method to verify Magic Number. The function will determine if the remainder on dividing the input by 9 is 1 or not. If it is 1, then the number is a magic number. 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. 
C++
C
Java
Python3
C#
Javascript
// C++ program to check// Whether the number is Magic or not.#include <iostream>using namespace std; int main() {    // Accepting sample input    int x = 1234;         // Condition to check Magic number    if(x%9==1)        cout << ("Magic Number");    else        cout << ("Not a Magic Number");         return 0;}
// C program to check// Whether the number is Magic or not.#include <stdio.h> int main() {         // Accepting sample input    int x = 1234;         // Condition to check Magic number    if(x%9==1)        printf("Magic Number");    else        printf("Not a Magic Number");           return 0;}
// Java program to check// Whether the number is Magic or not.class GFG{     public static void main(String[] args){         // Accepting sample input    int x = 1234;     // Condition to check Magic number    if (x % 9 == 1)        System.out.printf("Magic Number");    else        System.out.printf("Not a Magic Number");}} // This code is contributed by Amit Katiyar
# Python3 program to check# Whether the number is Magic or not. # Accepting sample inputx = 1234 # Condition to check Magic numberif (x % 9 == 1):    print("Magic Number")else:    print("Not a Magic Number") # This code is contributed by kirti
// C# program to check// Whether the number is Magic or not.using System;using System.Collections.Generic; class GFG{     public static void Main(String[] args){         // Accepting sample input    int x = 1234;     // Condition to check Magic number    if (x % 9 == 1)        Console.Write("Magic Number");    else        Console.Write("Not a Magic Number");}} // This code is contributed by Princi Singh
<script> // JavaScript program to check// Whether the number is Magic or not. // Accepting sample inputvar x = 1234; // Condition to check Magic numberif (x % 9 == 1)    document.write("Magic Number");else    document.write("Not a Magic Number"); // This code is contributed by shivanisinghss2110 </script>
Magic Number
 
This article is contributed by Ayush Saxena. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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