Happy Numbers

Last Updated : 12 Apr, 2024

A Happy Number n is defined by the following process. Starting with n, replace it with the sum of the squares of its digits, and repeat the process until n equals 1, or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are Happy Numbers, while those that do not end in 1 are unhappy numbers.

First few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100

Examples:

Input: 23
Output: Yes
Explanation :
First Iteration: 2² + 3² = 4 + 9 = 13
Second Iteration: 1² + 3² = 1 + 9 = 10
Third Iteration: 1² + 0² = 1 + 0 = 1. Since we reached 1, 23 is Happy.

The idea is simple, we repeated do sum of squares of digits. While doing so, we keep track of visited numbers using a hash. If we reach 1, we return true. Else if we reach a visited number, we return false.

Below is the implementation of the above approach:

C++

// CPP program to check if a number
// is happy number
#include <bits/stdc++.h>
using namespace std;

// Returns sum of squares of digits
// of a number n. For example for n = 12
// it returns 1 + 4 = 5
int sumDigitSquare(int n)
{
    int sq = 0;
    while (n) {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy number
// else returns false.
bool isHappy(int n)
{
    // A set to store numbers during
    // repeated square sum process
    set<int> s;
    s.insert(n);

    // Keep replacing n with sum of
    // squares of digits until we either
    // reach 1 or we endup in a cycle
    while (1) {

        // Number is Happy if we reach 1
        if (n == 1)
            return true;

        // Replace n with sum of squares
        // of digits
        n = sumDigitSquare(n);

        // If n is already visited, a cycle
        // is formed, means not Happy
        if (s.find(n) != s.end())
            return false;

        // Mark n as visited
        s.insert(n);
    }

    return false;
}

// Driver code
int main()
{
    int n = 23;
    if (isHappy(n))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}

Java

// Java program to check if a number
// is happy number
import java.util.*;

class GFG 
{

// Returns sum of squares of digits
// of a number n. For example for n = 12
// it returns 1 + 4 = 5
static int sumDigitSquare(int n)
{
    int sq = 0;
    while (n > 0) 
    {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy number
// else returns false.
static boolean isHappy(int n)
{
    // A set to store numbers during
    // repeated square sum process
    HashSet<Integer> s = new HashSet<Integer>();
    s.add(n);

    // Keep replacing n with sum of
    // squares of digits until we either
    // reach 1 or we endup in a cycle
    while (true) 
    {

        // Number is Happy if we reach 1
        if (n == 1)
            return true;

        // Replace n with sum of squares
        // of digits
        n = sumDigitSquare(n);

        // If n is already visited, a cycle
        // is formed, means not Happy
        
        if ((s.contains(n) && n != (int)s.toArray()[ s.size()-1 ] ))
            return false;

        // Mark n as visited
        s.add(n);
    }
}

// Driver code
public static void main(String[] args) 
{
    int n = 23;
    if (isHappy(n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}

/* This code contributed by PrinciRaj1992 */

Python 3

# python program to check if a number
# is happy number


# Returns sum of squares of digits
# of a number n. For example for n = 12
# it returns 1 + 4 = 5
def sumDigitSquare( n):
    sq = 0;
    while (n!=0):
        digit = n % 10
        sq += digit * digit
        n = n // 10
        
    return sq;


# Returns true if n is Happy number
# else returns false.
def isHappy(n):
    # A set to store numbers during
    # repeated square sum process
    s=set()
    s.add(n)

    # Keep replacing n with sum of
    # squares of digits until we either
    # reach 1 or we endup in a cycle
    while (True):

        # Number is Happy if we reach 1
        if (n == 1):
            return True;

        # Replace n with sum of squares
        # of digits
        n = sumDigitSquare(n)

        # If n is already visited, a cycle
        # is formed, means not Happy
        if n in s:
            return False

        # Mark n as visited
        s.add(n)

    return false;


# Driver code

n = 23
if (isHappy(n)):
    print("Yes") 
else:
    print("No")

// C# program to check if a number
// is happy number
using System; 
using System.Collections.Generic; 

class GFG 
{

// Returns sum of squares of digits
// of a number n. For example for n = 12
// it returns 1 + 4 = 5
static int sumDigitSquare(int n)
{
    int sq = 0;
    while (n > 0) 
    {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy number
// else returns false.
static bool isHappy(int n)
{
    // A set to store numbers during
    // repeated square sum process
    HashSet<int> s = new HashSet<int>();
    s.Add(n);

    // Keep replacing n with sum of
    // squares of digits until we either
    // reach 1 or we endup in a cycle
    while (true) 
    {

        // Number is Happy if we reach 1
        if (n == 1)
            return true;

        // Replace n with sum of squares
        // of digits
        n = sumDigitSquare(n);

        // If n is already visited, a cycle
        // is formed, means not Happy
        if (s.Contains(n))
            return false;

        // Mark n as visited
        s.Add(n);
    }
}

// Driver code
public static void Main() 
{
    int n = 23;
    if (isHappy(n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}

// This code contributed by Rajput-Ji

Javascript

// JavaScript program to check if a number
// is happy number

// Returns sum of squares of digits
// of a number n. For example for n = 12
// it returns 1 + 4 = 5
function sumDigitSquare(n)
{
    let sq = 0;
    while (n > 0)
    {
        var digit = n % 10
        sq += digit * digit;
        n = Math.floor(n / 10);
    }
        
    return sq;
}

// Returns true if n is Happy number
// else returns false.
function isHappy(n)
{
    // A set to store numbers during
    // repeated square sum process
    let s = [];
    s.push(n);

    // Keep replacing n with sum of
    // squares of digits until we either
    // reach 1 or we endup in a cycle
    while (true)
    {
        // Number is Happy if we reach 1
        if (n == 1)
            return true;

        // Replace n with sum of squares
        // of digits
        n = sumDigitSquare(n)
        
        
        // If n is already visited, a cycle
        // is formed, means not Happy
        if (s.includes(n))
            return false
    
        // Mark n as visited
        s.push(n)
    }
    return false;
}

/// Driver code
let n = 23
if (isHappy(n))
    console.log("Yes") 
else
    console.log("No")

// This code is contributed by phasing17

Output

Yes

Output:

Yes

Time complexity: O(log n) for a given number n
Auxiliary Space: O(n)

One important observation is, the cycle always contains 4. So we don’t need to keep track of all numbers. We can simply check for 4.

C++

// A space optimized CPP program to check if a number is
// happy number
#include <bits/stdc++.h>
using namespace std;

// Returns sum of squares of digits of a number n.
// For example for n = 12 it returns 1 + 4 = 5
int sumDigitSquare(int n)
{
    int sq = 0;
    while (n) {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy number else returns false.
bool isHappy(int n)
{
    // Keep replacing n with sum of squares of digits until
    // we either reach 1 or we end up in a cycle
    while (1) {
        // Number is Happy if we reach 1
        if (n == 1)
            return true;
        // Replace n with sum of squares of digits
        n = sumDigitSquare(n);
        // Number is not Happy if we reach 4
        if (n == 4)
            return false;
    }
    return false;
}

// Driver code
int main()
{
    int n = 23;
    if (isHappy(n))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}

// This code is contributed by Sania Kumari Gupta (kriSania804)

// A space optimized C program to check if a number is happy
// number
#include <stdbool.h>
#include <stdio.h>

// Returns sum of squares of digits of a number n.
// For example for n = 12 it returns 1 + 4 = 5
int sumDigitSquare(int n)
{
    int sq = 0;
    while (n) {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy number else returns false.
bool isHappy(int n)
{
    // Keep replacing n with sum of squares of digits until
    // we either reach 1 or we end up in a cycle
    while (1) {
        // Number is Happy if we reach 1
        if (n == 1)
            return true;
        // Replace n with sum of squares of digits
        n = sumDigitSquare(n);
        // Number is not Happy if we reach 4
        if (n == 4)
            return false;
    }
    return false;
}

// Driver code
int main()
{
    int n = 23;
    if (isHappy(n))
        printf("Yes\n");
    else
        printf("No\n");
    return 0;
}

// This code is contributed by Sania Kumari Gupta (kriSania804)

Java

// A space optimized Java 
// program to check if a
// number is happy number
import java.io.*;

class GFG {
    
    // Returns sum of squares of 
    // digits of a number n. For 
    // example for n = 12 it 
    // returns 1 + 4 = 5
    static int sumDigitSquare(int n)
    {
        int sq = 0;
        while (n != 0) 
        {
            int digit = n % 10;
            sq += digit * digit;
            n = n / 10;
        }
        return sq;
    }
    
    // Returns true if n is Happy 
    // number else returns false.
    static boolean isHappy(int n)
    {
        // Keep replacing n with 
        // sum of squares of digits 
        // until we either reach 1 
        // or we end up in a cycle
        while (true) 
        {
    
            // Number is Happy if 
            // we reach 1
            if (n == 1)
                return true;
    
            // Replace n with sum 
            // of squares of digits
            n = sumDigitSquare(n);
    
            // Number is not Happy 
            // if we reach 4
            if (n == 4)
                return false;
        }
    
    }
    
    // Driver code
    public static void main(String args[])
    {
        int n = 23;
        if (isHappy(n))
            System.out.println("Yes");
        else
            System.out.println("No" );
    }
}

/*This code is contributed by Nikita tiwari.*/

Python3

# A space optimized Python3 program to 
# check  if a number is happy number


# Returns sum of squares of 
# digits of a number n. For 
# example for n = 12 it 
# returns 1 + 4 = 5
def sumDigitSquare(n) :
    sq = 0
    while (n) :
        digit = n % 10
        sq = sq + digit * digit
        n = n // 10
    
    return sq


# Returns true if n 
# is Happy number else 
# returns false.
def isHappy(n) :

    # Keep replacing n with 
    # sum of squares of digits
    # until we either reach 1 
    # or we end up in a cycle
    while (1) :

        # Number is Happy if 
        # we reach 1
        if (n == 1) :
            return True

        # Replace n with sum of 
        # squares of digits
        n = sumDigitSquare(n)

        # Number is not Happy 
        # if we reach 4
        if (n == 4) :
            return False
    
    return False

# Driver code
n = 23
if (isHappy(n)) :
    print("Yes")
else :
    print("No")
    

# This code is contributed 
# by Nikita tiwari.

// A space optimized C# 
// program to check if a
// number is happy number
using System;

class GFG
{
    
// Returns sum of squares of 
// digits of a number n. For 
// example for n = 12 it 
// returns 1 + 4 = 5
static int sumDigitSquare(int n)
{
    int sq = 0;
    while (n != 0) 
    {
        int digit = n % 10;
        sq += digit * digit;
        n = n / 10;
    }
    return sq;
}

// Returns true if n is Happy 
// number else returns false.
static bool isHappy(int n)
{
    // Keep replacing n with 
    // sum of squares of digits 
    // until we either reach 1 
    // or we end up in a cycle
    while (true) 
    {

        // Number is Happy if 
        // we reach 1
        if (n == 1)
            return true;

        // Replace n with sum 
        // of squares of digits
        n = sumDigitSquare(n);

        // Number is not Happy 
        // if we reach 4
        if (n == 4)
            return false;
    }

}

// Driver code
static public void Main ()
{
    int n = 23;
    if (isHappy(n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No" );
}
}

// This code is contributed by ajit

Javascript

<script>

    // A space optimized Javascript 
    // program to check if a
    // number is happy number
    
    // Returns sum of squares of 
    // digits of a number n. For 
    // example for n = 12 it 
    // returns 1 + 4 = 5
    function sumDigitSquare(n)
    {
        let sq = 0;
        while (n != 0) 
        {
            let digit = n % 10;
            sq += digit * digit;
            n = parseInt(n / 10, 10);
        }
        return sq;
    }

    // Returns true if n is Happy 
    // number else returns false.
    function isHappy(n)
    {
        // Keep replacing n with 
        // sum of squares of digits 
        // until we either reach 1 
        // or we end up in a cycle
        while (true) 
        {

            // Number is Happy if 
            // we reach 1
            if (n == 1)
                return true;

            // Replace n with sum 
            // of squares of digits
            n = sumDigitSquare(n);

            // Number is not Happy 
            // if we reach 4
            if (n == 4)
                return false;
        }

    }
    
    let n = 23;
    if (isHappy(n))
        document.write("Yes");
    else
        document.write("No" );

</script>

PHP

<?php
// A space optimized PHP 
// program to check if a
// number is happy number

// Returns sum of squares 
// of digits of a number 
// n. For example for n = 12
// it returns 1 + 4 = 5
function sumDigitSquare($n)
{
    $sq = 0;
    while ($n) 
    {
        $digit = $n % 10;
        $sq += $digit * $digit;
        $n = $n / 10;
    }
    return $sq;
}

// Returns true if n 
// is Happy number
// else returns false.
function isHappy($n)
{
    // Keep replacing n with 
    // sum of squares of digits 
    // until we either reach 1
    // or we end up in a cycle
    while (1)
    {

        // Number is Happy
        // if we reach 1
        if ($n == 1)
            return true;

        // Replace n with sum 
        // of squares of digits
        $n = sumDigitSquare($n);

        // Number is not Happy 
        // if we reach 4
        if ($n == 4)
            return false;
    }

    return false;
}

// Driver code
$n = 23;
if (isHappy($n))
    echo "Yes";
else
    echo "No";

// This code is contributed by mits
?>