【POJ】1611 The Suspects

本文探讨了在SARS疫情期间,Not-Spreading-Your-Sickness University (NSYSU)如何通过收集学生群体成员名单,并制定规则来有效识别和隔离疑似病例,以防止病毒传播的方法。主要介绍了并查集算法在该情境下的应用,包括输入处理、初始化、查找和合并操作,以及输出疑似病例数量的过程。

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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

分析:基础并查集。

解法一:

#include <iostream>
#include <vector>
using namespace std;
int N,M;
vector<int> par;
vector<int> rank;

void init(int n){
	par.clear();
	rank.clear();
	par.resize(n);
	rank.resize(n);
	for(int i=0; i<n; i++){
		par[i] = i;
		rank[i] = 0;
	}
}

int find(int x){
	if(par[x]==x){
		return x;
	}else{
		return par[x] = find(par[x]);
	}
}

void unite(int x, int y){
	x = find(x);
	y = find(y);
	if(x==y) return;
	if(rank[x] < rank[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if(rank[x]==rank[y])
			rank[x]++;
	}
}

bool same(int x, int y){
	return find(x)==find(y);
}

int main(){
	int i;
	while(scanf("%d%d",&N,&M)){
		if(N==0 && M==0) break;
		init(N);
		int num, t;	
		int first;
		for(int j=0; j<M; j++){
			scanf("%d",&num);
			for(i=0; i<num; i++){
				scanf("%d",&t);
				if(i==0){
					first = t;
				}
				unite(first,t);
			}
		}	
		int cnt = 0;
		for(i=0; i<N; i++){
			if(same(0,i)){
				cnt++;
			}
		}			
		printf("%d\n",cnt);
	}
	return 0;
}



解法二:

#include <iostream>
#include <vector>
using namespace std;
int N,M;
vector<int> par;
vector<int> num;

void init(int n){
	par.clear();
	num.clear();
	par.resize(n); 
	num.resize(n);
	for(int i=0; i<n; i++){
		par[i] = i;
		num[i] = 1;
	}
}

int find(int x){
	if(par[x]==x){
		return x;
	}else{
		return par[x] = find(par[x]);
	}
}

void unite(int x, int y){
	x = find(x);
	y = find(y);
	if(x==y) return;
	if(num[x] <= num[y]){
		par[x] = y;
		num[y] += num[x];
	}else if(num[x] > num[y]){
		par[y] = x;
		num[x] += num[y];
	}
}

bool same(int x, int y){
	return find(x)==find(y);
}

int main(){
	int i;
	while(scanf("%d%d",&N,&M)){
		if(N==0 && M==0) break;
		init(N);
		int cnt, t;	
		int first;
		for(int j=0; j<M; j++){
			scanf("%d",&cnt);
			for(i=0; i<cnt; i++){
				scanf("%d",&t);
				if(i==0){
					first = t;
				}
				unite(first,t);
			}
		}		 	
		printf("%d\n",num[find(0)]);
	}
	return 0;
}






内容概要:本文档为《400_IB Specification Vol 2-Release-2.0-Final-2025-07-31.pdf》,主要描述了InfiniBand架构2.0版本的物理层规范。文档详细规定了链路初始化、配置与训练流程,包括但不限于传输序列(TS1、TS2、TS3)、链路去偏斜、波特率、前向纠错(FEC)支持、链路速度协商及扩展速度选项等。此外,还介绍了链路状态机的不同状态(如禁用、轮询、配置等),以及各状态下应遵循的规则和命令。针对不同数据速率(从SDR到XDR)的链路格式化规则也有详细说明,确保数据包格式和控制符号在多条物理通道上的一致性和正确性。文档还涵盖了链路性能监控和错误检测机制。 适用人群:适用于从事网络硬件设计、开发及维护的技术人员,尤其是那些需要深入了解InfiniBand物理层细节的专业人士。 使用场景及目标:① 设计和实现支持多种数据速率和编码方式的InfiniBand设备;② 开发链路初始化和训练算法,确保链路两端设备能够正确配置并优化通信质量;③ 实现链路性能监控和错误检测,提高系统的可靠性和稳定性。 其他说明:本文档属于InfiniBand贸易协会所有,为专有信息,仅供内部参考和技术交流使用。文档内容详尽,对于理解和实施InfiniBand接口具有重要指导意义。读者应结合相关背景资料进行学习,以确保正确理解和应用规范中的各项技术要求。
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