Problem #
Source: PAT 1069{target="_blank"}
Description #
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 in the range .
Output Specification #
If all the 4 digits of 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 #
6767Sample Output 1 #
7766 - 6677 = 1089
9810 - 0189 = 9621
9621 - 1269 = 8352
8532 - 2358 = 6174Sample Input 2 #
2222Sample Output 2 #
2222 - 2222 = 0000Solution #
Code #
#include <iostream>
#include <algorithm>
#include <string>
#include <string.h>
using namespace std;
int up[4],down[4];
bool cmp(int a, int b) {
return a > b;
}
int toInt(int ans[]) {
return ans[0] * 1000 + ans[1] * 100 + ans[2] * 10 + ans[3];
}
int getup(int a) {
up[3] = a % 10;
up[2] = a / 10 % 10;
up[1] = a / 100 % 10;
up[0] = a / 1000;
sort(up, up + 4);
for (int i = 0; i < 4; i++) {
cout << up[i];
}
cout << " = ";
return toInt(up);
}
int getdown(int a) {
down[3] = a % 10;
down[2] = a / 10 % 10;
down[1] = a / 100 % 10;
down[0] = a / 1000;
sort(down, down + 4, cmp);
for (int i = 0; i < 4; i++) {
cout << down[i];
}
cout << " - ";
return toInt(down);
}
int subscribe(int n) {
int a = getdown(n),b = getup(n);
int temp = a - b;
up[3] = temp % 10;
up[2] = temp / 10 % 10;
up[1] = temp / 100 % 10;
up[0] = temp / 1000;
for (int i = 0; i < 4; i++) {
cout << up[i];
}
cout << endl;
return temp;
}
bool check(int a) {
up[3] = a % 10;
up[2] = a / 10 % 10;
up[1] = a / 100 % 10;
up[0] = a / 1000;
if (up[0] == up[1] && up[1] == up[2]&& up[2] == up[3]){
cout << a << " - " << a << " = " << "0000" << endl;
return true;
}
return false;
}
int main()
{
int n;
while (cin>>n) {
bool index = true;
if (check(n)) {
index = false;
}
while (index) {
n = subscribe(n);
if (n == 6174)
break;
}
}
return 0;
}
