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# Kaprekar Constant

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` `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

 ``

## Javascript

 ``

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.
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