卡普雷卡·康斯坦斯

6174是Kaprekar常数。此数字很特殊，因为对于任何四位数的数字，按照以下步骤进行操作时，我们总是会得到此数字，以使数字的所有数字都不相同，即，所有四位数的数字除外(0000、1111，…)

1. 按升序对四位数进行排序，并将结果存储在数字“ asc”中。
2. 按降序对四位数字进行排序，并将结果存储在数字“ desc”中。
3. 用较小的数字减去较大的数字，即abs(asc – desc)。
4. 重复以上三个步骤，直到减法的结果不等于前一个数字。

我们总是以6174结尾。
以下是演示相同程序。

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 dgits 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 dgits in descending order
    // in the form of number "desc"
    sort(digits, digits+4, std::greater ());
    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 dgits 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 dgits 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 dgits 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 dgits 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 dgits 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 dgits 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

Javascript

 
// 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 dgits 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 dgits 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
 

输出 ：

6174
6174
6174

插图 ：

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.