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:
|
1 |
6767 |
Sample Output 1:
|
1 2 3 4 |
7766 - 6677 = 1089 9810 - 0189 = 9621 9621 - 1269 = 8352 8532 - 2358 = 6174 |
Sample Input 2:
|
1 |
2222 |
Sample Output 2:
|
1 |
2222 - 2222 = 0000 |
PAT-Basic-1019. 数字黑洞的英文版。
代码如下：
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 |
#include<stdio.h> int compare(const void *a,const void *b) { return *((char *)a)-*((char *)b); } int rcompare(const void *a,const void *b) { return *((char *)b)-*((char *)a); } int main() { char buf[5]="0000"; int i,num,rnum,result; scanf("%s",buf); for(i=0;i<4;i++) { if(buf[i]=='\0') buf[i]='0'; } do { qsort(buf,4,sizeof(char),compare); sscanf(buf,"%d",&num); qsort(buf,4,sizeof(char),rcompare); sscanf(buf,"%d",&rnum); result=rnum-num; printf("%04d - %04d = %04d\n",rnum,num,result); if(result==0) { break; } sprintf(buf,"%04d",result); }while(result!=6174); return 0; } |