一道并查集的水题

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.
题目链接 https://vjudge.net/contest/278632#problem/A
题目大意 一道并查集的板子题，首先给你数N，表示接下来多少个数据，然后给你的第i个数pi，表示i和pi是连同的，视为同一个集合，最后让你输出有多少个这样的集合。
数据范围 n (1 ≤ n ≤ 1e4)
解题思路 套模板就过了，当 k == 根节点的值 ，ans++；

这个英文题看的不是很懂，在网上找了一下大意，发现好像是并查集
之前学并查集的时候就没懂，就找同学要了板子是这样的

简单优化了一下，感觉这样好像更加简单一点
int a[MAX_N];
int fa[MAX_N];
int find (int x){
return fa[x]==x?x:fa[x]=find(fa[x]);
}
void combine(int x,int y)
{
if(find(x) != find(y)) fa[find(x)] = find(y);
}

解决代码

#include
int a[10005];
int fa[10005];
int find (int x){
return fa[x]==x?x:fa[x]=find(fa[x]);
}

void combine(int x,int y)
{
if(find(x) != find(y)) fa[find(x)] = find(y);
}
int main ()
{
int n;
int ans = 0;
scanf("%d",&n);
for(int i = 1;i<=n;i++)
	fa[i] = i;
    for (int i = 1;i <= n;i++)
    scanf("%d",&a[i]);
    for (int j = 1;j <= n;j++)
    	combine(a[j],j);

    for (int k = 1;k <= n;k++)
        if (find(k) == k)ans++;
    printf("%d",ans);
return 0;
}