Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 859 ms):
import java.util.*;
import java.io.*;
import java.math.*;

public class sub {

	static int mod = 998244353;

	public static void main(String args[]) throws IOException {
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			ArrayList<ArrayList<Integer>> adj = new ArrayList();
			for(int i = 0;i<n;i++)adj.add(new ArrayList());
			int deg[] = new int[n];
			for(int i = 0;i<n-1;i++) {
				int u = sc.nextInt()-1;
				int v = sc.nextInt()-1;
				adj.get(u).add(v);
				adj.get(v).add(u);
				deg[u]++;
				deg[v]++;
			}
			TreeMap<Integer, Integer> tm = new TreeMap(Collections.reverseOrder());
			for(int i = 0;i<deg.length;i++) {
				tm.put(deg[i], tm.getOrDefault(deg[i], 0)+1);
			}
			int ans = 0;
			for(int i = 0;i<n;i++) {
				for(int j : adj.get(i)) {
					ans = Math.max(ans, deg[j]+deg[i]-2);
					tm.put(deg[j], tm.get(deg[j])-1);
					if(tm.get(deg[j])==0) {
						tm.remove(deg[j]);
					}
				}
				tm.put(deg[i], tm.get(deg[i])-1);
				if(tm.get(deg[i])==0) {
					tm.remove(deg[i]);
				}
				//out.println(pq);
				ans=Math.max(ans, deg[i]+(tm.isEmpty() ? 0: tm.firstKey())-1);
				for(int j : adj.get(i)) {
					tm.put(deg[j], tm.getOrDefault(deg[j], 0)+1);
				}
				tm.put(deg[i], tm.getOrDefault(deg[i],0)+1);
			}
			out.println(ans);
		}
		out.close();
	}

//	static long bincoef(int n, int k) {
//	    if (n < k) return 0L;
//	    return (p[n] * pow((p[n - k] * p[k]) % mod, mod - 2, mod)) % mod;
//	}
	


	static long pow(long a, long b, long mod) {
		if (b == 0) {
			return 1L;
		}
		long val = pow(a, b / 2, mod);
		if (b % 2 == 0) {
			return val * val % mod;
		}
		return val * val % mod * a % mod;
	}

	static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}

	static Kattio sc = new Kattio();
	static PrintWriter out = new PrintWriter(System.out);

	static class Kattio {

		static BufferedReader r;
		static StringTokenizer st;

		public Kattio() {
			r = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			try {
				while (st == null || !st.hasMoreTokens()) {
					st = new StringTokenizer(r.readLine());
				}
				return st.nextToken();
			} catch (Exception e) {
				return null;
			}
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}

Solution 2 (runtime: 1140 ms):

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class C {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(
                    new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                if (st.hasMoreTokens()) {
                    str = st.nextToken("\n");
                } else {
                    str = br.readLine();
                }
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public  static class Pair{
        int vtx;
        long deg;
        Pair(int vtx,long deg){
            this.vtx=vtx;
            this.deg=deg;
        }

        public long getDeg() {
            return this.deg;
        }
    }
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t != 0) {
            t--;
            int n = sc.nextInt();
            TreeSet<Integer>[] graph=new TreeSet[n+1];
            for (int i = 0; i <= n; i++) {
                graph[i]=new TreeSet<>();
            }

            for (int i = 1; i <=n-1 ; i++) {
                int u= sc.nextInt();
                int v= sc.nextInt();
                graph[u].add(v);
                graph[v].add(u);
            }
            Pair[] d=new Pair[n];
            for (int i = 0; i <n ; i++) {
                d[i]=new Pair(i+1,graph[i+1].size());
            }
            long ans=Long.MIN_VALUE;
//            long c=0;
            for (int i=1;i<=n;i++){
                for (int nbr:graph[i]){
                    ans=Math.max(ans,graph[i].size()+graph[nbr].size()-2);
//                    ++c;
                }
            }
//            System.out.println(ans);
            Arrays.sort(d, Comparator.comparing(Pair::getDeg).reversed());
//            for (Pair p:d) {
////                System.out.println(p.vtx+" "+p.deg);
//            }
            for (int i = 0; i <n ; i++) {
                int src=d[i].vtx;
//                System.out.print(src+" ");
                for (int j = i+1; j < n; j++) {
                    int nbr=d[j].vtx;
//                    System.out.print(nbr);
                    if (j!=i && !graph[src].contains(nbr)){
//                        System.out.println(src+" "+nbr);
                        ans=Math.max(ans,graph[src].size()+graph[nbr].size()-1);
                        break;
                    }
                }
//                System.out.println();
            }

            System.out.println(ans);

        }
    }
}