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 = 10899810 - 0189 = 96219621 - 1269 = 83528532 - 2358 = 6174

Sample Input 2:

2222

Sample Output 2:

2222 - 2222 = 0000

注意本身有可能就是6174

#include<cstdio>#include<cmath>#include<algorithm>#include<iostream>using namespace std;int tomax(int a[]){int sum=0;for(int i=3;i>=0;i--){sum=sum*10+a[i];}return sum;}int tomin(int a[]){int sum=0;for(int i=0;i<=3;i++){sum=sum*10+a[i];}return sum;}int main() {int n;cin>>n;do{int fz=n;int a[10]={0},cnt=0;while(fz){a[cnt++]=fz%10;fz/=10;}sort(a,a+4);int maxn=tomax(a);int minn=tomin(a);n=maxn-minn;printf("%04d - %04d = %04d\n",maxn,minn,n);}while(n!=6174&&n!=0);    return 0;}