How Many Tables

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 46694 Accepted Submission(s): 23319

題目鏈接：http://acm.hdu.edu.cn/showproblem.php?pid=1213

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

題意：

給出n個人，然後說明他們是否認識，並且這個關系能夠傳遞。問至少有多少個集合，在這個集合裏面的人互相認識。

題解：

由於這個關系可以傳遞，可以用並查集求解，這可以說是個並查集基礎題。

代碼如下：

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

const int N = 1005;
int t,n,m;
int f[N];
int find(int x){
    return x==f[x] ? f[x] :f[x]=find(f[x]);
}
int main(){
    scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n+1;i++) f[i]=i;
        for(int i=1,x,y;i<=m;i++){
            scanf("%d%d",&x,&y);
            int fx=find(x),fy=find(y);
            f[fx]=fy;
        }
        int ans = 0;
        for(int i=1;i<=n;i++){
            int fi = find(i);
            if(fi==i) ans++;
        }
        printf("%d\n",ans);
    }
    
    return 0;
}

HDU1213：How Many Tables（並查集）