PAT甲级 1132 Cut Integer (20 分)

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本文探讨一种数学性质：一个整数能否被其一半长度的两个数字相乘得到。通过实例展示如何切割并验证这种特性，并提供输入输出样例。主要关注的是编程实现，如C++代码检查整数是否满足此条件。

Cutting an integer means to cut a K digits lone integer Z into two integers of (K/2) digits long integers A and B. For example, after cutting Z = 167334, we have A = 167 and B = 334. It is interesting to see that Z can be devided by the product of A and B, as 167334 / (167 × 334) = 3. Given an integer Z, you are supposed to test if it is such an integer.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤ 20). Then N lines follow, each gives an integer Z (10 ≤ Z <2³¹). It is guaranteed that the number of digits of Z is an even number.

Output Specification:

For each case, print a single line if it is such a number, or if not.Yes``No

Sample Input:

Sample Output:

Yes
No
No

#include <iostream>

using namespace std;

int main() {
    int k;
    string s;
    int a, b, c;
    cin >> k;
    for (int i = 0; i < k; ++i) {
        cin >> s;
        a = stoi(s.substr(0, s.size() / 2));
        b = stoi(s.substr(s.size() / 2));
        c = stoi(s);
        if (a * b != 0 && c % (a * b) == 0)
            puts("Yes");
        else
            puts("No");
    }
}