YT14-HDU-满足(a^2+b^2 +m)/(ab)的（a,b)有多少

最新推荐文章于 2022-04-13 11:51:05 发布

SAP 皮德憨

最新推荐文章于 2022-04-13 11:51:05 发布

阅读量2.4k

点赞数 1

CC 4.0 BY-SA版权

文章标签： c++ iostream namespace 编程博客

本文链接：https://blog.youkuaiyun.com/Liuchang54/article/details/43936695

HDU 专栏收录该内容

48 篇文章

订阅专栏

本文介绍了一种算法，用于解决特定数学问题：给定两个整数n和m，计算满足条件0<a<b<n且(a^2+b^2+m)/(ab)为整数的整数对(a,b)的数量。该算法通过双重循环遍历所有可能的a和b值来解决问题，并提供了一个C++实现示例。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Problem Description

Given two integers n and m, count the number of pairs of integers (a,b) such that 0 < a < b < n and (a^2+b^2 +m)/(ab) is an integer.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

Input

You will be given a number of cases in the input. Each case is specified by a line containing the integers n and m. The end of input is indicated by a case in which n = m = 0. You may assume that 0 < n <= 100.

Output

For each case, print the case number as well as the number of pairs (a,b) satisfying the given property. Print the output for each case on one line in the format as shown below.

Sample Input

Sample Output

Case 1: 2
Case 2: 4
Case 3: 5

代码如下：

#include <iostream>
using namespace std;
int main()
{
    int T,n,m;
    int a,b;
    int k,num;
    cin>>T;
    while (T--)
    {
        k=1;
        while (cin>>n>>m)
        {
            num=0;
            if(n==0&&m==0)
                break;
            for (b=1; b<n; b++)
            {
                for (a=1; a<b; a++)
                {
                    if ((a*a+b*b+m)%(a*b)==0)          //判断是否为整数
                        num++;
                }
            }
            cout<<"Case "<<k<<": "<<num<<endl;
            k++;
        }
        if (T>0)                                     //题目要求，每个输出块之间有一个空白，但最后一个输出块后面没有
        cout<<endl;
    }
    return 0;
}

解题思路：

题目大意是输入N,M,求(a,b)(0<a<b<N)能满足(a^2+b^2 +M)/(ab)是一个整数的个数。这道题唯一的难点就是在于输出块之间的空白，再有就是输出格式问题，我又一次给大小写坑了。。