How Many Tables

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Problem Description

Today is Ignatius‘ birthday. He invites a lot of friends. Now it‘s dinner time. Ignatius wants to know how many tables he needs at least. You have to notice that not all the friends know each other, and all the friends do not want to stay with strangers.

One important rule for this problem is that if I tell you A knows B, and B knows C, that means A, B, C know each other, so they can stay in one table.

For example: If I tell you A knows B, B knows C, and D knows E, so A, B, C can stay in one table, and D, E have to stay in the other one. So Ignatius needs 2 tables at least.

Input

The input starts with an integer T(1<=T<=25) which indicate the number of test cases. Then T test cases follow. Each test case starts with two integers N and M(1<=N,M<=1000). N indicates the number of friends, the friends are marked from 1 to N. Then M lines
follow. Each line consists of two integers A and B(A!=B), that means friend A and friend B know each other. There will be a blank line between two cases.

Output

For each test case, just output how many tables Ignatius needs at least. Do NOT print any blanks.

Sample Input

2
5 3
1 2
2 3
4 5

5 1
2 5

Sample Output

2
4

Author

Ignatius.L

Source

杭电ACM省赛集训队选拔赛之热身赛

原题链接:http://acm.hdu.edu.cn/showproblem.php?pid=1213

题意:求连通分支的个数.

两种方式:

1.可以求出一共有多少个根节点（即fa[i]==-1的i个数）

2.可以用原始连通分量数n 减去 有效的合并次数。

即每次合并两个连通分量就会使得总的分量数目减少1.

AC代码1;

#include <iostream>
#include <cstring>
using namespace std;
const int maxn=1000+10;
int fa[maxn];
int Find(int x)
{
    if(fa[x]==-1)
        return x;
    return fa[x]=Find(fa[x]);
}
void mix(int x,int y)
{
    int fx=Find(x);
    int fy=Find(y);
    if(fx!=fy)
        fa[fx]=fy;
    //return ;
}
int main()
{
    int t,n,m,x,y;
    cin>>t;
    while(t--)
    {
        cin>>n>>m;
        memset(fa,-1,sizeof(fa));
        while(m--)
        {
            cin>>x>>y;
            mix(x,y);
        }
        int ans=0;
        for(int i=1;i<=n;i++)
        {
            if(fa[i]==-1)
                ans++;
        }
        cout<<ans<<endl;
    }
}

AC代码2:

#include <iostream>
#include <cstring>
using namespace std;
const int maxn=1000+5;
int fa[maxn];
int  Find(int x)
{
    if(fa[x]==-1)
        return x;
    return fa[x]=Find(fa[x]);
}
int mix(int x,int y)
{
    int fx=Find(x);
    int fy=Find(y);
    if(fx!=fy)
    {
        fa[fx]=fy;
        return 1;
    }
    return 0;
}
int main()
{
    int t,n,m,x,y;
    cin>>t;
    while(t--)
    {
        cin>>n>>m;
        memset(fa,-1,sizeof(fa));
        int ans=n;
        while(m--)
        {
            cin>>x>>y;
            ans-=mix(x,y);
        }
        cout<<ans<<endl;
    }
    return 0;
}