1. 并查集

#include<iostream>
#include<cstdio>
using namespace std;
const int N=2e5+10;
int find(int x);

int T;
int n;
int p[N], cnt[N];

signed main()
{
    cin>>T;

    while(T--)
    {
        scanf("%d", &n);
        for(int i=1;i<=n;i++) p[i]=i, cnt[i]=1;

        for(int i=1;i<=n;i++)
        {
            int j;
            scanf("%d", &j);

            int a=find(i), b=find(j);
            if(a!=b)
            {
                cnt[b]+=cnt[a];
                p[a]=b;
            }
        }

        for(int i=1;i<=n;i++) printf("%d ", cnt[find(i)]);
        puts("");
    }
}

int find(int x)
{
    if(p[x]!=x) p[x]=find(p[x]);
    return p[x];
}

2. dfs

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int N=2e5+10;
int find(int x);
int dfs(int now, int num, int root);

int T;
int n;
int p[N];
int cnt[N];

signed main()
{
    cin>>T;

    while(T--)
    {
        memset(cnt, 0, sizeof cnt);

        scanf("%d", &n);
        for(int i=1;i<=n;i++) scanf("%d", &p[i]);

        for(int i=1;i<=n;i++)
            if(cnt[i]) printf("%d ", cnt[i]);
            else printf("%d ", dfs(p[i], 1, i));
        puts("");
    }
}

int dfs(int now, int num, int root)
{
    if(now==root)
    {
        cnt[root]=num;
        return num;
    }

    cnt[now]=dfs(p[now], num+1, root);
    return cnt[now];
}