Happy Numbers

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 which 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 reach 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 a number, we return false.

C++

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// 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;
}

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Java

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// 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 */

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C#

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// 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

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Output:

Yes

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++

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// 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;
}

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Java

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// 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.*/

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Python3

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# 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.

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C#

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// 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 

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PHP

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<?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
?>

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Output:

Yes

This article is contributed by ashish madaan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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