# PAT B1019A1067 题解

1069 The Black Hole of Numbers （20 分）
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 (0,10
​4
​​ ).

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.

``````#includeiostream
#includecstdio
#includealgorithm
using namespace std;
bool cmp(int a,int b){
return ab;
}
int change_array(int a[]){
int num=0;
for(int i=0;i4;i++){
num=num*10+a[i];
}
return num;
}
int change_num(int a[],int n){
int count=0;
while(n!=0){
a[count++]=n%10;
n=n/10;
}
}
int main(){
int n,count=0,up=0,down=0;
int num;
cinn;
change_num(num,n);
sort(num,num+4);
up=change_array(num);
sort(num,num+4,cmp);
down=change_array(num);
while(true){
n=down-up;
printf("%04d - %04d = %04d\n",down,up,n);
change_num(num,n);
sort(num,num+4);
up=change_array(num);
sort(num,num+4,cmp);
down=change_array(num);
if(n==0||n==6174)
break;
}
return 0;
}
``````