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  • 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<iostream>
    #include<algorithm>
    #include<cstring>
    #include<cstdio>
    using namespace std;
    int a[5],val;
    bool cmp(int a,int b){
    	return a>b;
    }
    int main(){
    	scanf("%d",&val);
    	int tmp = val;
    	while(1){
    		a[0]=val/1000;
    		val=val-a[0]*1000;
    		a[1]=val/100;
    		val=val-a[1]*100;
    		a[2]=val/10;
    		a[3]=val-a[2]*10;
    		if(a[0]==a[1]&&a[1]==a[2]&&a[2]==a[3]){
    			printf("%04d - %04d = 0000
    ",tmp,tmp);
    			return 0;
    		}
    		sort(a,a+4,cmp);
    		int val1=0;
    		int val2=0;
    		for(int i=3;i>=0;i--){
    			val1=val1*10+a[i];
    			val2=val2*10+a[3-i];
    		}
    		val=val2-val1;
    		printf("%04d - %04d = %04d
    ",val2,val1,val);
    		if(val==6174){
    			break;
    		}
    	}
    	return 0;
    } 
    

      



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  • 原文地址:https://www.cnblogs.com/grglym/p/7846631.html
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