A **happy number** is a number that reaches 1 after a sequence of steps. In each step, the number is replaced by the sum of its squared digits.



Let's test if 19 is a happy number or not:​

$1^2$ + $9^2$ = $82$

$8^2$ + $2^2$ = $68$

$6^2$ + $8^2$ = $100$

$1^2$ + $0^2$ + $0^2$ = $1$

Since we reached 1, 19 is a Happy Number.

## Implementation

The following codes test if a number is a happy or not:

#include <iostream> 
using namespace std; 

// Utility method to return sum of square of 
int numSquareSum(int n) 
{ 
	int squareSum = 0; 
	while (n) 
	{ 
		squareSum += (n % 10) * (n % 10); 
		n /= 10; 
	} 
	return squareSum; 
} 

// method return true if n is Happy number 
bool isHappynumber(int n) 
{ 
	int slow, fast; 

	// initialize slow and fast by n 
	slow = fast = n; 
	do
	{ 
		// move slow number by one iteration 
		slow = numSquareSum(slow); 

		// move fast number by two iteration 
		fast = numSquareSum(numSquareSum(fast)); 

	} 
	while (slow != fast); 

	// if both number meet at 1, then return true 
	return (slow == 1); 
} 

// Driver code to test above methods 
int main() 
{ 
	int n = 19; 
	if (isHappynumber(n)) 
		cout << n << " is a Happy number\n"; 
	else
		cout << n << " is not a Happy number\n"; 
} 


class example { 
   
// Utility method to return sum of square of 
// digit of n 
static int numSquareSum(int n) 
{ 
    int squareSum = 0; 
    while (n!= 0) 
    { 
        squareSum += (n % 10) * (n % 10); 
        n /= 10; 
    } 
    return squareSum; 
} 
   
//  method return true if n is Happy number 
static boolean isHappynumber(int n) 
{ 
    int slow, fast; 
   
    //  initialize slow and fast by n 
    slow = fast = n; 
    do
    { 
        //  move slow number 
        // by one iteration 
        slow = numSquareSum(slow); 
   
        //  move fast number 
        // by two iteration 
        fast = numSquareSum(numSquareSum(fast)); 
   
    } 
    while (slow != fast); 
   
    //  if both number meet at 1, 
    // then return true 
    return (slow == 1); 
} 
   
//  Driver code to test above methods 
public static void main(String[] args) 
{ 
    int n = 19; 
    if (isHappynumber(n)) 
        System.out.println(n +  
        " is a Happy number"); 
    else
        System.out.println(n +  
        " is not a Happy number"); 
} 
} 

Java

def numSquareSum(n): 
    squareSum = 0; 
    while(n): 
        squareSum += (n % 10) * (n % 10); 
        n = int(n / 10); 
    return squareSum; 
  
# method return true if n is Happy number 
def isHappynumber(n): 
  
    # initialize slow and fast by n 
    slow = n; 
    fast = n; 
    while(True): 
          
        # move slow number by one iteration 
        slow = numSquareSum(slow); 
  
        # move fast number by two iteration 
        fast = numSquareSum(numSquareSum(fast)); 
        if(slow != fast): 
            continue; 
        else: 
            break; 
  
    # if both number meet at 1, then return true 
    return (slow == 1); 
  
# Driver Code 
n = 19; 
if (isHappynumber(n)): 
    print(n , "is a Happy number"); 
else: 
    print(n , "is not a Happy number"); 

How to check if a number is a happy number

Implementation