1069. The Black Hole of Numbers (20)

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:
6767
Sample Output 1:
7766 - 6677 = 1089
9810 - 0189 = 9621
9621 - 1269 = 8352
8532 - 2358 = 6174
Sample Input 2:
2222
Sample Output 2:
2222 - 2222 = 0000

#include<cstdio>#include<algorithm>using namespace std;bool cmp(int a,int b){    return a>b;}void toArray(int a,int b[]){    int mask=1000;    for(int i=0;i<4;i++){        b[i]=a/mask;        a%=mask;        mask/=10;    }}int toNum(int a[]){    int ans=0;      for(int i=0;i<4;i++){        ans=ans*10+a[i];    }    return ans;}int main(){    int a;    scanf("%d",&a);    int num[5],min,max;    do{        toArray(a,num);        sort(num,num+4);        min=toNum(num);        sort(num,num+4,cmp);        max=toNum(num);        a=max-min;        printf("%04d - %04d = %04d\n",max,min,a);    }while(a!=0&&a!=6174);    return 0;}