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Kaprekar Constant

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  • Difficulty Level : Medium
  • Last Updated : 23 Nov, 2022
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6174 is the Kaprekar Constant. This number is special as we always get this number when following steps are followed for any four digit number such that all digits of number are not same, i.e., all four digit numbers excluding (0000, 1111, …)
 

  1. Sort four digits in ascending order and store result in a number “asc”.
  2. Sort four digits in descending order and store result in a number “desc”.
  3. Subtract number larger number from smaller number, i.e., abs(asc – desc).
  4. Repeat above three steps until the result of subtraction doesn’t become equal to the previous number.
  5. We always end up with 6174.

Below is the implementation of the above approach:

C++




// C++ program to demonstrate working of
// Kaprekar constant
#include<bits/stdc++.h>
using namespace std;
 
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant for
// any four digit number "n" such that all digits
// of n are not same.
int kaprekarRec(int n, int &prev)
{
    if (n == 0)
       return 0;
 
    // Store current n as previous number
    prev = n;
 
    // Get four digits of given number
    int digits[4];
    for (int i=0; i<4; i++)
    {
       digits[i] = n%10;
       n = n/10;
    }
 
    // Sort all four digits in ascending order
    // And giet in the form of number "asc"
    sort(digits, digits+4);
    int asc = 0;
    for (int i=0; i<4; i++)
       asc = asc*10 + digits[i];
 
    // Get all four digits in descending order
    // in the form of number "desc"
    sort(digits, digits+4, std::greater<int> ());
    int desc = 0;
    for (int i=0; i<4; i++)
       desc = desc*10 + digits[i];
 
    // Get the difference of two numbers
    int diff = abs(asc - desc);
 
    // If difference is same as previous, we have
    // reached kaprekar's constant
    if (diff == prev)
        return diff;
 
    // Else recur
    return kaprekarRec(diff, prev);
}
 
// A wrapper over kaprekarRec()
int kaprekar(int n)
{
    int prev = 0;
    return kaprekarRec(n, prev);
}
 
// Driver code
int main()
{
    // Trying few four digit numbers, we
    // always get 6174
    cout << kaprekar(1000) << endl;
    cout << kaprekar(1112) << endl;
    cout << kaprekar(9812) << endl;
    return 0;
}


Java




// Java program to demonstrate working of
// Kaprekar constant
import java.util.Arrays;
 
class GFG{
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant for
// any four digit number "n" such that all digits
// of n are not same.
static int kaprekarRec(int n, int prev)
{
    if (n == 0)
    return 0;
 
    // Store current n as previous number
    prev = n;
 
    // Get four digits of given number
    int[] digits=new int[4];
    for (int i=0; i<4; i++)
    {
    digits[i] = n%10;
    n = n/10;
    }
 
    // Sort all four digits in ascending order
    // And giet in the form of number "asc"
    Arrays.sort(digits);
    int asc = 0;
    for (int i=0; i<4; i++)
    asc = asc*10 + digits[i];
 
    // Get all four digits in descending order
    // in the form of number "desc"
    Arrays.sort(digits);
    int desc = 0;
    for (int i=3; i>=0; i--)
    desc = desc*10 + digits[i];
 
    // Get the difference of two numbers
    int diff = Math.abs(asc - desc);
 
    // If difference is same as previous, we have
    // reached kaprekar's constant
    if (diff == prev)
        return diff;
 
    // Else recur
    return kaprekarRec(diff, prev);
}
 
// A wrapper over kaprekarRec()
static int kaprekar(int n)
{
    int prev = 0;
    return kaprekarRec(n, prev);
}
 
// Driver code
public static void main(String[] args)
{
    // Trying few four digit numbers, we
    // always get 6174
    System.out.println(kaprekar(1000));
    System.out.println(kaprekar(1112));
    System.out.println(kaprekar(9812));
}
}
// This code is contributed by mits


Python3




# Python3 program to demonstrate
# working of Kaprekar constant
 
# This function checks validity of
# kaprekar's constant. It returns
# kaprekar's constant for any four
# digit number "n" such that all
# digits of n are not same.
def kaprekarRec(n, prev):
 
    if (n == 0):
        return 0;
 
    # Store current n as previous
    # number
    prev = n;
 
    # Get four digits of given number
    digits = [0] * 4;
    for i in range(4):
        digits[i] = n % 10;
        n = int(n / 10);
 
    # Sort all four digits in ascending order
    # And giet in the form of number "asc"
    digits.sort();
    asc = 0;
    for i in range(4):
        asc = asc * 10 + digits[i];
 
    # Get all four digits in descending order
    # in the form of number "desc"
    digits.sort();
    desc = 0;
    for i in range(3, -1, -1):
        desc = desc * 10 + digits[i];
 
    # Get the difference of two numbers
    diff = abs(asc - desc);
 
    # If difference is same as previous,
    # we have reached kaprekar's constant
    if (diff == prev):
        return diff;
 
    # Else recur
    return kaprekarRec(diff, prev);
 
# A wrapper over kaprekarRec()
def kaprekar(n):
 
    rev = 0;
    return kaprekarRec(n, rev);
 
# Driver code
 
# Trying few four digit numbers, 
# we always get 6174
print(kaprekar(1000));
print(kaprekar(1112));
print(kaprekar(9812));
 
# This code is contributed by mits.


C#




// C# program to demonstrate working of
// Kaprekar constant
using System;
 
class GFG{
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant for
// any four digit number "n" such that all digits
// of n are not same.
static int kaprekarRec(int n, int prev)
{
    if (n == 0)
    return 0;
 
    // Store current n as previous number
    prev = n;
 
    // Get four digits of given number
    int[] digits=new int[4];
    for (int i=0; i<4; i++)
    {
    digits[i] = n%10;
    n = n/10;
    }
 
    // Sort all four digits in ascending order
    // And giet in the form of number "asc"
    Array.Sort(digits);
    int asc = 0;
    for (int i=0; i<4; i++)
    asc = asc*10 + digits[i];
 
    // Get all four digits in descending order
    // in the form of number "desc"
    Array.Sort(digits);
    int desc = 0;
    for (int i=3; i>=0; i--)
    desc = desc*10 + digits[i];
 
    // Get the difference of two numbers
    int diff = Math.Abs(asc - desc);
 
    // If difference is same as previous, we have
    // reached kaprekar's constant
    if (diff == prev)
        return diff;
 
    // Else recur
    return kaprekarRec(diff, prev);
}
 
// A wrapper over kaprekarRec()
static int kaprekar(int n)
{
    int prev = 0;
    return kaprekarRec(n, prev);
}
 
// Driver code
public static void Main()
{
    // Trying few four digit numbers, we
    // always get 6174
    System.Console.WriteLine(kaprekar(1000));
    System.Console.WriteLine(kaprekar(1112));
    System.Console.WriteLine(kaprekar(9812));
}
}
// This code is contributed by mits


PHP




<?php
// PHP program to demonstrate working of
// Kaprekar constant
 
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant
// for any four digit number "n" such that
// all digits of n are not same.
function kaprekarRec($n, $prev)
{
    if ($n == 0)
    return 0;
 
    // Store current n as previous number
    $prev = $n;
 
    // Get four digits of given number
    $digits = array_fill(0, 4, 0);
    for ($i = 0; $i < 4; $i++)
    {
        $digits[$i] = $n % 10;
        $n = (int)($n / 10);
    }
 
    // Sort all four digits in ascending order
    // And giet in the form of number "asc"
    sort($digits);
    $asc = 0;
    for ($i = 0; $i < 4; $i++)
    $asc = $asc * 10 + $digits[$i];
 
    // Get all four digits in descending order
    // in the form of number "desc"
    rsort($digits);
    $desc = 0;
    for ($i = 0; $i < 4; $i++)
    $desc = $desc * 10 + $digits[$i];
 
    // Get the difference of two numbers
    $diff = abs($asc - $desc);
 
    // If difference is same as previous,
    // we have reached kaprekar's constant
    if ($diff == $prev)
        return $diff;
 
    // Else recur
    return kaprekarRec($diff, $prev);
}
 
// A wrapper over kaprekarRec()
function kaprekar($n)
{
    $rev = 0;
    return kaprekarRec($n, $rev);
}
 
// Driver code
 
// Trying few four digit numbers, we
// always get 6174
echo kaprekar(1000) . "\n";
echo kaprekar(1112) . "\n";
echo kaprekar(9812) . "\n";
 
// This code is contributed by mits.
?>


Javascript




<script>
 
// Javascript program to demonstrate working of
// Kaprekar constant
 
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant for
// any four digit number "n" such that all digits
// of n are not same.
function kaprekarRec(n , prev)
{
    if (n == 0)
    return 0;
 
    // Store current n as previous number
    prev = n;
 
    // Get four digits of given number
    var digits= Array.from({length: 4}, (_, i) => 0);
    for (i=0; i<4; i++)
    {
    digits[i] = n%10;
    n = parseInt(n/10);
    }
 
    // Sort all four digits in ascending order
    // And giet in the form of number "asc"
    digits.sort();
    var asc = 0;
    for (i=0; i<4; i++)
    asc = asc*10 + digits[i];
 
    // Get all four digits in descending order
    // in the form of number "desc"
    digits.sort();
    var desc = 0;
    for (i=3; i>=0; i--)
    desc = desc*10 + digits[i];
 
    // Get the difference of two numbers
    var diff = Math.abs(asc - desc);
 
    // If difference is same as previous, we have
    // reached kaprekar's constant
    if (diff == prev)
        return diff;
 
    // Else recur
    return kaprekarRec(diff, prev);
}
 
// A wrapper over kaprekarRec()
function kaprekar(n)
{
    var prev = 0;
    return kaprekarRec(n, prev);
}
 
// Driver code
 
//Trying few four digit numbers, we
// always get 6174
document.write(kaprekar(1000)+"<br>");
document.write(kaprekar(1112)+"<br>");
document.write(kaprekar(9812)+"<br>");
 
 
// This code contributed by Princi Singh
 
</script>


Output

6174
6174
6174

Illustration : 

n = 2324
1) asc  = 2234
2) desc = 4322
3) Difference = 2088 
4) Repeating above steps as difference is not same
as n

n = 2088
1) asc  = 0288
2) desc = 8820
3) Difference = 8532  
4) Repeating above steps as difference is not same
as n.

n = 8532
1) asc  = 2358
2) desc = 8532
3) Difference = 6174  
4) Repeating above steps as difference is not same
as n.

n = 6174
1) asc  = 1467
2) desc = 7641
3) Difference = 6174  
Stopping here as difference is same as n.

Time Complexity: O(n log n) where n is the number of digits.
Auxiliary Space: O(1)

Reference: 
https://en.wikipedia.org/wiki/6174_(number)
Related Article: 
Kaprekar Number
This article is contributed by Gaurav 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 review-team@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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