ZOJ 2833 Friendship

ZOJ 2833 Friendship(并查集)

题目链接:https://zoj.pintia.cn/problem-sets/91827364500/problems/91827366332

Friendship

Time Limit: 3000 msMemory Limit: 32768 KB

A friend is like a flower,
a rose to be exact,
Or maybe like a brand new gate
that never comes unlatched.

A friend is like an owl,
both beautiful and wise.
Or perhaps a friend is like a ghost,
whose spirit never dies.

A friend is like a heart that goes
strong until the end.
Where would we be in this world
if we didn’t have a friend?

                   - By Emma Guest

Now you’ve grown up, it’s time to make friends. The friends you make in university are the friends you make for life. You will be proud if you have many friends.

Input

There are multiple test cases for this problem.

Each test case starts with a line containing two integers N, M (1 <= N <= 100’000, 1 <= M <= 200’000), representing that there are totally N persons (indexed from 1 to N) and M operations, then M lines with the form “M a b” (without quotation) or “Q a” (without quotation) follow. The operation “M a b” means that person a and b make friends with each other, though they may be already friends, while “Q a” means a query operation.

Friendship is transitivity, which means if a and b, b and c are friends then a and c are also friends. In the initial, you have no friends except yourself, when you are freshman, you know nobody, right? So in such case you have only one friend.

Output

For each test case, output “Case #:” first where “#” is the number of the case which starts from 1, then for each query operation “Q a”, output a single line with the number of person a’s friends.

Separate two consecutive test cases with a blank line, but Do NOT output an extra blank line after the last one.

Sample Input

3 5
M 1 2
Q 1
Q 3
M 2 3
Q 2
5 10
M 3 2
Q 4
M 1 2
Q 4
M 3 2
Q 1
M 3 1
Q 5
M 4 2
Q 4

Sample Output

Case 1:
2
1
3

Case 2:
1
1
3
1
4

Notes

This problem has huge input and output data, please use ‘scanf()’ and ‘printf()’ instead of ‘cin’ and ‘cout’ to avoid time limit exceed.

解题思路:
并查集模板题,加路径压缩即可.

代码如下:

#include <bits/stdc++.h>
using namespace std;
#define N 100005
int n,m,bin[N],sum[N];
inline int find(int a){return bin[a]==a?a:bin[a]=find(bin[a]);
}
inline void merge(int a,int b){int fa=find(a);int fb=find(b);if(fa!=fb){bin[fa]=fb;sum[fb]+=sum[fa];}
}
inline void init(){for(int i=1;i<=n;i++){bin[i]=i;sum[i]=1;}
}
int main(){int ans=1;while(scanf("%d %d",&n,&m)!=EOF){init();if(ans!=1)printf("\n");printf("Case %d:\n",ans++);for(int i=0;i<m;i++){getchar();char c;scanf("%c",&c);if(c=='M'){int a,b;scanf("%d %d",&a,&b);merge(a,b);}else{int a;scanf("%d",&a);printf("%d\n",sum[find(a)]);}}}return 0;
}