1069. The Black Hole of Numbers (20)

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本文介绍了一个有趣的数学现象——通过特定操作使任意四位数（不全相同）最终都会收敛到6174这个被称为Kaprekar常数的黑洞数。并提供了一段C++代码来演示这一过程。

For any 4-digit integer except the ones with all the digits being the same, if we sort the digits in non-increasing order first, and then in non-decreasing order, a new number can be obtained by taking the second number from the first one. Repeat in this manner we will soon end up at the number 6174 -- the "black hole" of 4-digit numbers. This number is named Kaprekar Constant.

For example, start from 6767, we'll get:

7766 - 6677 = 1089
9810 - 0189 = 9621
9621 - 1269 = 8352
8532 - 2358 = 6174
7641 - 1467 = 6174
... ...

Given any 4-digit number, you are supposed to illustrate the way it gets into the black hole.

Input Specification:

Each input file contains one test case which gives a positive integer N in the range (0, 10000).

Output Specification:

If all the 4 digits of N are the same, print in one line the equation "N - N = 0000". Else print each step of calculation in a line until 6174 comes out as the difference. All the numbers must be printed as 4-digit numbers.

Sample Input 1:

Sample Output 1:

7766 - 6677 = 1089
9810 - 0189 = 9621
9621 - 1269 = 8352
8532 - 2358 = 6174

Sample Input 2:

Sample Output 2:

2222 - 2222 = 0000

代码实现

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
using namespace std;

bool cmp(int a,int b)
{
    return a>b;
}
void to_arry(int n,int num[])
{
    for(int i=0;i<4;i++)
    {
        num[i]=n%10;
        n/=10;
    }
}
int to_number(int num[])
{
    int sum=0;
    for(int i=0;i<4;i++)
    {
        sum=sum*10+num[i];
    }
    return sum;
}
int main()
{
    int n,min,max;
    cin>>n;
    int num[4];
    while(1)
    {
        to_arry(n,num);
        sort(num,num+4);
        min=to_number(num);
        sort(num,num+4,cmp);
        max=to_number(num);
        n=max-min;
        printf("%04d - %04d = %04d\n",max,min,n);
        if(n==0 || n== 6174) break;
    }
    return 0;
}