1069. The Black Hole of Numbers (20)-PAT甲级真题

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

分析：有一个测试用例注意点，如果当输入N值为6174的时候，依旧要进行下面的步骤，直到差值为6174才可以～所以用do while语句，无论是什么值总是要执行一遍while语句，直到遇到差值是0000或6174～

s.insert(0, 4 – s.length(), ‘0’);用来给不足4位的时候前面补0～

#include <iostream>
#include <algorithm>
using namespace std;
bool cmp(char a, char b) {return a > b;}
int main() {
    string s;
    cin >> s;
    s.insert(0, 4 - s.length(), '0');
    do {
        string a = s, b = s;
        sort(a.begin(), a.end(), cmp);
        sort(b.begin(), b.end());
        int result = stoi(a) - stoi(b);
        s = to_string(result);
        s.insert(0, 4 - s.length(), '0');
        cout << a << " - " << b << " = " << s << endl;
    } while (s != "6174" && s != "0000");
    return 0;
}

#include <iostream>

#include <algorithm>

using namespace std;

bool cmp(char a, char b) {return a > b;}

int main() {

string s;

cin >> s;

s.insert(0, 4 - s.length(), '0');

do {

string a = s, b = s;

sort(a.begin(), a.end(), cmp);

sort(b.begin(), b.end());

int result = stoi(a) - stoi(b);

s = to_string(result);

s.insert(0, 4 - s.length(), '0');

cout << a << " - " << b << " = " << s << endl;

} while (s != "6174" && s != "0000");

return 0;

}

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