7-1 File Transfer（25 分）

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本文探讨了一个计算机网络中文件传输的问题，通过输入连接信息判断任意两台计算机间是否能进行文件传输，并采用并查集算法来解决该问题。最终确定整个网络是否完全连通或存在多个独立组件。

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7-1 File Transfer（25 分）

We have a network of computers and a list of bi-directional connections. Each of these connections allows a file transfer from one computer to another. Is it possible to send a file from any computer on the network to any other?

Input Specification:

Each input file contains one test case. For each test case, the first line contains $N$ ( $2 \leq N \leq 1 0^{ 4 }$ ), the total number of computers in a network. Each computer in the network is then represented by a positive integer between 1 and $N$ . Then in the following lines, the input is given in the format:

I c1 c2

where I stands for inputting a connection between c1 and c2; or

C c1 c2

where C stands for checking if it is possible to transfer files between c1 and c2; or

where S stands for stopping this case.

Output Specification:

For each C case, print in one line the word "yes" or "no" if it is possible or impossible to transfer files between c1 and c2, respectively. At the end of each case, print in one line "The network is connected." if there is a path between any pair of computers; or "There are k components." where k is the number of connected components in this network.

Sample Input 1:

Sample Output 1:

no
no
yes
There are 2 components.

Sample Input 2:

Sample Output 2:

no
no
yes
yes
The network is connected.

思路:很明显的并查集

代码如下:

#include<iostream>
#include<set>
using namespace std;
int k[10005];
char p;
int find(int x){
	int a=x;
	while(k[x]!=x) x=k[x];
	while(a!=k[a]){
		int z=a;
		a=k[a];
		k[z]=x;
	}
	return x;
}
void union1(int a,int b){
	int fa=find(a);
	int fb=find(b);
	if(fa!=fb) k[fa]=fb;
}
int main()
{
	set<int>st;
	int n,a,b;
	scanf("%d",&n);
	for(int i=1;i<=n;i++) k[i]=i;
	while(cin>>p,p!='S'){
		cin>>a>>b;
		if(p=='I'){
			union1(a,b);
		}
		else{
			if(k[find(a)]!=k[find(b)]) cout<<"no"<<endl;
			else cout<<"yes"<<endl;
		}
	}
	for(int i=1;i<=n;i++){
		//cout<<i<<k[find(i)]<<endl;
		st.insert(k[find(i)]);
	}
	if(st.size()==1) cout<<"The network is connected."<<endl;
	else cout<<"There are "<<st.size()<<" "<<"components."<<endl;
}