HDU 5019 Revenge of GCD（数学）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5019

Problem Description

In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), highest common factor (hcf), or greatest common measure (gcm), of two or more integers (when at least one of them is not zero), is the largest positive integer that divides the numbers without a remainder.
---Wikipedia

Today, GCD takes revenge on you. You have to figure out the k-th GCD of X and Y.

 

Input

The first line contains a single integer T, indicating the number of test cases. 

Each test case only contains three integers X, Y and K.

[Technical Specification]
1. 1 <= T <= 100
2. 1 <= X, Y, K <= 1 000 000 000 000

 

Output

For each test case, output the k-th GCD of X and Y. If no such integer exists, output -1.

 

Sample Input

   
   
   
   

    
    
    
    3
2 3 1
2 3 2
8 16 3
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    1
-1
2
   
   
   
   

 

Source

BestCoder Round #10

官方题解：

代码如下：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
typedef __int64 LL;
vector<LL>v;
LL GCD(LL a, LL b)
{
    if(b == 0)
        return a;
    return GCD(b,a%b);
}

int main()
{
    int t;
    LL x, y, k;
    scanf("%d",&t);
    while(t--)
    {
        v.clear();
        scanf("%I64d%I64d%I64d",&x,&y,&k);
        LL tt = GCD(x,y);
        // printf("%I64d\n",tt);
        for(LL i = 1; i*i <= tt; i++)
        {
            if(tt%i == 0)
            {
                v.push_back(i);
                if(i*i != tt)//防止放入两个i
                    v.push_back(tt/i);
            }
        }
        sort(v.begin(), v.end());
        if(k > v.size())
            printf("-1\n");
        else
            printf("%I64d\n",v[v.size()-k]);
    }
    return 0;
}