05-树8 File Transfer（25 分）

题目来源：中国大学MOOC-陈越、何钦铭-数据结构-2018春
作者: 陈越
单位: 浙江大学
问题描述：
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≤N≤$10^4$
), 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
S
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:
5
C 3 2
I 3 2
C 1 5
I 4 5
I 2 4
C 3 5
S
Sample Output 1:
no
no
yes
There are 2 components.
Sample Input 2:
5
C 3 2
I 3 2
C 1 5
I 4 5
I 2 4
C 3 5
I 1 3
C 1 5
S
Sample Output 2:
no
no
yes
yes
The network is connected.

解答：
并差集的应用，需要进行路径压缩，用负数表示并差集中的元素个数。

#include <iostream>
#include <algorithm>
using namespace std;

const int maxn=10001;
int N;
int UnionSet[maxn];
int findfather(int x)
{
    int p=x,t;
    while(UnionSet[p]>0)
    {
        p=UnionSet[p];
    }
    while(x!=p)
    {
        t=UnionSet[x];
        UnionSet[x]=p;
        x=t;
    }
    return p;
}
void join(int c1,int c2)
{
    c1=findfather(c1);
    c2=findfather(c2);
    if(c1<c2)
    {
        UnionSet[c1]+=UnionSet[c2];
        UnionSet[c2]=c1;
    }
    else
    {
        UnionSet[c2]+=UnionSet[c1];
        UnionSet[c1]=c2;
    }
}
bool check(int c1,int c2)
{
    if(findfather(c1)==findfather(c2))
        return true;
    else
        return false;
}
int main()
{
    cin>>N;
    char input;
    fill(UnionSet,UnionSet+N+1,-1);
    while(cin>>input)
    {
        int c1,c2;
        if(input=='C')
        {
            cin>>c1>>c2;
            if(check(c1,c2))
                cout<<"yes"<<endl;
            else
                cout<<"no"<<endl;
        }
        else if(input=='I')
        {
            cin>>c1>>c2;
            join(c1,c2);
        }
        else
            break;
    }
    int num=0;
    for(int i=1;i<=N;i++)
    {
        if(UnionSet[i]<0)
            num++;
    }
    if(num==1)
        cout<<"The network is connected.";
    else
        cout<<"There are "<<num<<" components.";
    return 0;
}