题目

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 ``````

分析

printf("%04d - %04d = %04d\n",a,b,a=a-b);

• %md 对不足m位的整数以m位进行右对齐输出，即前面补空格
• %0md 不足m位的时候前面补0
• %.mf 以精确到小数点后m位输出，四舍六入五成双的规则，若要四舍五入要用round。

代码

 `````` 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 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 `````` ``````#include #include #include using namespace std; void itoArray(int n,int (&C)[4]) { for(int i=3;i>=0;i--) { C[i] = n%10; n /= 10; } } void reverseArray(int *A,int (&B)[4]) { for(int i=0;i<4;i++) B[i]=A[3-i]; } void arraytoInt(int *C,int &n) { n = 0; for(int i=0;i<4;i++) { n *= 10; n +=C[i]; } } bool cmp(int a,int b) { //使sort函数从大到小排序 return a>b; } int main() { int A[4]; int B[4]; int a,b; scanf("%d",&a); itoArray(a,A); sort(A,A+4,cmp); arraytoInt(A,a); reverseArray(A,B); arraytoInt(B,b); while(true) { printf("%.4d - %.4d = %.4d\n",a,b,a-b); if((a=a-b)==0||a==6174) break; itoArray(a,A); sort(A,A+4,cmp); arraytoInt(A,a); reverseArray(A,B); arraytoInt(B,b); } return 0; } ``````
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