The Suspects||POJ1611

本文提供了一道名为“The Suspects”的POJ 1611题目解答,采用并查集算法来解决学生群体中疑似病例的追踪问题。通过输入学生群体信息,程序能够快速识别所有潜在的接触者。

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题目链接:http://poj.org/problem?id=1611
The Suspects

Time Limit: 1000MS      Memory Limit: 20000K
Total Submissions: 40525        Accepted: 19575

Description

Severe acute respiratory syndrome (SARS), an atypical pneumonia of unknown aetiology, was recognized as a global threat in mid-March 2003. To minimize transmission to others, the best strategy is to separate the suspects from others.
In the Not-Spreading-Your-Sickness University (NSYSU), there are many student groups. Students in the same group intercommunicate with each other frequently, and a student may join several groups. To prevent the possible transmissions of SARS, the NSYSU collects the member lists of all student groups, and makes the following rule in their standard operation procedure (SOP).
Once a member in a group is a suspect, all members in the group are suspects.
However, they find that it is not easy to identify all the suspects when a student is recognized as a suspect. Your job is to write a program which finds all the suspects.

Input

The input file contains several cases. Each test case begins with two integers n and m in a line, where n is the number of students, and m is the number of groups. You may assume that 0 < n <= 30000 and 0 <= m <= 500. Every student is numbered by a unique integer between 0 and n−1, and initially student 0 is recognized as a suspect in all the cases. This line is followed by m member lists of the groups, one line per group. Each line begins with an integer k by itself representing the number of members in the group. Following the number of members, there are k integers representing the students in this group. All the integers in a line are separated by at least one space.
A case with n = 0 and m = 0 indicates the end of the input, and need not be processed.

Output

For each case, output the number of suspects in one line.

Sample Input

100 4
2 1 2
5 10 13 11 12 14
2 0 1
2 99 2
200 2
1 5
5 1 2 3 4 5
1 0
0 0

Sample Output

4
1
1

题解:简单的并查集运用

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int par[30003],num[30003];
void initial(int n)//初始化,每个人的父节点是自己,每棵树大小都为1 
{
    int i;
    for(i=0;i<n;i++)
    {
        par[i]=i;
        num[i]=1;
    }
}
int find(int x)//找祖宗 
{
    if(x!=par[x])
      par[x]=find(par[x]);
    return par[x];
}
void unite(int x,int y)//合并 
{
    int fx=find(x);
    int fy=find(y);
    if(fx==fy)//祖宗相同跳出 
      return ;
    if(num[fx]>=num[fy])//孩子多的是爸爸 
    {
        par[fy]=fx;
        num[fx]+=num[fy];
    }
    else
    {
        par[fx]=fy;
        num[fy]+=num[fx];
    }
}
int main()
{
    int n,m,k,a,b,i,j;
    while(cin>>n>>m)
    {
        if(n==0&&m==0) break;
        initial(n);
        for(i=0;i<m;i++)
        {
            scanf("%d%d",&k,&a);
            for(j=1;j<k;j++)
            {
                scanf("%d",&b);
                unite(a,b);
            }
        }
        printf("%d\n",num[par[0]]);//par【0】,是0的父节点,可能是0本身,然后num【par【0】】其实就是0所在这棵树的大小 
    }
return 0;
}
分数阶傅里叶变换(Fractional Fourier Transform, FRFT)是对传统傅里叶变换的拓展,它通过非整数阶的变换方式,能够更有效地处理非线性信号以及涉及时频局部化的问题。在信号处理领域,FRFT尤其适用于分析非平稳信号,例如在雷达、声纳和通信系统中,对线性调频(Linear Frequency Modulation, LFM)信号的分析具有显著优势。LFM信号是一种频率随时间线性变化的信号,因其具有宽频带和良好的时频分辨率,被广泛应用于雷达和通信系统。FRFT能够更精准地捕捉LFM信号的时间和频率信息,相比普通傅里叶变换,其性能更为出色。 MATLAB是一种强大的数值计算和科学计算工具,拥有丰富的函数库和用户友好的界面。在MATLAB中实现FRFT,通常需要编写自定义函数或利用信号处理工具箱中的相关函数。例如,一个名为“frft”的文件可能是用于执行分数阶傅里叶变换的MATLAB脚本或函数,并展示其在信号处理中的应用。FRFT的正确性验证通常通过对比变换前后信号的特性来完成,比如评估信号的重构质量、信噪比等。具体而言,可以通过计算原始信号与经过FRFT处理后的信号之间的相似度,或者对比LFM信号的关键参数(如初始频率、扫频率和持续时间)是否在变换后得到准确恢复。 在MATLAB代码实现中,通常包含以下步骤:首先,生成LFM信号模型,设定其初始频率、扫频率、持续时间和采样率等参数;其次,利用自定义的frft函数对LFM信号进行分数阶傅里叶变换;接着,使用MATLAB的可视化工具(如plot或imagesc)展示原始信号的时域和频域表示,以及FRFT后的结果,以便直观对比;最后,通过计算均方误差、峰值信噪比等指标来评估FRFT的性能。深入理解FRFT的数学原理并结合MATLAB编程技巧,可以实现对LFM信号的有效分析和处理。这个代码示例不仅展示了理论知识在
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