02: religious beliefs 02: religious beliefs

02: religious beliefs 02: religious beliefs

Total time limit:

5000 ms

 

Memory limit:

65536kB

Description

There are many religions in the world. You are interested in the number of religions your school students believe. Your school has n students (0 <n <= 50000). You are unlikely to ask everyone about their religious beliefs because they are reluctant to disclose their beliefs. But when you find two students at the same time, they are willing to tell you if they believe in the same religion. You can estimate the upper limit of the number of religions in the school by asking a lot like this. You can think that each student only believes in one of the most religions.

 

Input

The input includes multiple groups of data.
The first row of each group of data includes n and m, 0 <= m <= n (n-1)/2, and the next m row contains two numbers, I and j, indicates that student I and student j share the same religion and the student ID is 1 to n. The input end with a row of n = m = 0.

Output

For each group of data, first output its number (starting from 1), and then output the maximum number of different religions of students' beliefs.

Sample Input

10 91 21 31 41 51 61 71 81 91 1010 42 34 54 85 80 0

Sample output

Case 1: 1 Case 2: 7

First glance: Tarjan
Second eye: just blind, and check the collection to take away

 1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int MAXN=50001; 7 void read(int &n) 8 { 9     char c='+';int x=0;bool flag=0;10     while(c<'0'||c>'9'){c=getchar();if(c=='-')flag=1;}11     while(c>='0'&&c<='9')12     x=(x<<1)+(x<<3)+c-48,c=getchar();13     flag==1?n=-x:n=x;14 }15 int n,m;16 int fa[MAXN];17 bool vis[MAXN];18 int find(int x)19 {20     if(fa[x]==x)21         return fa[x];22     return fa[x]=find(fa[x]);23 }24 void unionn(int x,int y)25 {26     int fx=find(x);27     int fy=find(y);28     fa[fx]=fy;29 }30 int tot=0;31 int main()32 {33     while(scanf("%d%d",&n,&m))34     {35         if(n==0&&m==0)break;36         for(int i=1;i<=n;i++)37             fa[i]=i;38         memset(vis,0,sizeof(vis));39         40         for(int i=1;i<=m;i++)41         {42             int x,y;43             read(x);read(y);44             if(find(x)!=find(y))45                 unionn(x,y);46         }47         int ans=0;48         for(int i=1;i<=n;i++)49         {50             if(vis[find(i)]==0)51             {52                 vis[find(i)]=1;53                 ans++;54             }55         }56         printf("Case %d: %d\n",++tot,ans);57     }58     return 0;59 }