文章标题 coderforces 755C ： PolandBall and Forest（并查集）

PolandBall and Forest

PolandBall lives in a forest with his family. There are some trees in the forest. Trees are undirected acyclic graphs with k vertices and k - 1 edges, where k is some integer. Note that one vertex is a valid tree.

There is exactly one relative living in each vertex of each tree, they have unique ids from 1 to n. For each Ball i we know the id of its most distant relative living on the same tree. If there are several such vertices, we only know the value of the one with smallest id among those.

How many trees are there in the forest?

Input
The first line contains single integer n (1 ≤ n ≤ 104) — the number of Balls living in the forest.

The second line contains a sequence p1, p2, …, pn of length n, where (1 ≤ pi ≤ n) holds and pi denotes the most distant from Ball i relative living on the same tree. If there are several most distant relatives living on the same tree, pi is the id of one with the smallest id.

It’s guaranteed that the sequence p corresponds to some valid forest.

Hacking: To hack someone, you should provide a correct forest as a test. The sequence p will be calculated according to the forest and given to the solution you try to hack as input. Use the following format:

In the first line, output the integer n (1 ≤ n ≤ 104) — the number of Balls and the integer m (0 ≤ m < n) — the total number of edges in the forest. Then m lines should follow. The i-th of them should contain two integers ai and bi and represent an edge between vertices in which relatives ai and bi live. For example, the first sample is written as follows:

5 3
1 2
3 4
4 5
Output
You should output the number of trees in the forest where PolandBall lives.

Interaction
From the technical side, this problem is interactive. However, it should not affect you (except hacking) since there is no interaction.

Examples
input
5
2 1 5 3 3
output
2
input
1
1
output
1
Note
In the first sample testcase, possible forest is: 1-2 3-4-5.

There are 2 trees overall.

In the second sample testcase, the only possible graph is one vertex and no edges. Therefore, there is only one tree.
题意：有n个点，从1~n，先将每个点与其距离最远的点的标号给出，然后要我们求出这n个点有多少棵树形成的，比如第一个例子，1-2，3-4-5有两棵树。
分析：可以用并查集，每一个点与其相距最远的点一定在同一个树上，所以只要将这n个点将同一个树上的点指向同一个根节点就行，最后有多少个点其父节点是其自己说明就有几棵树。
代码：

#include<iostream>
#include<string>
#include<cstdio>
#include<cstring>
#include<vector>
#include<math.h>
#include<map>
#include<queue> 
#include<algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
int n;
int a[10005];
int fa[10005]; 
int find (int x){
    return fa[x]==x?x:fa[x]=find(fa[x]);
}
int main ()
{
    while (cin>>n){
        for (int i=1;i<=n;i++) fa[i]=i;//初始化 
        for (int i=1;i<=n;i++){
            cin>>a[i];
        }
        for (int i=1;i<=n;i++){
            int fu=find(i);//找父节点 
            int fv=find(a[i]);
            if (fu!=fv)fa[fu]=fv;//如果还没合并则合并 
        }
        int ans=0;
        for (int i=1;i<=n;i++){//遍历一遍看有多少棵树 
            if (fa[i]==i)ans++;
        }
        cout<<ans<<endl;
    }       
    return 0;
}