Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 1968 ms):
import java.util.*;

public class RemoveExactlyTwo
{
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int t = in.nextInt();

        while (t-- > 0) {
            int n = in.nextInt();


            ArrayList<Integer>[] arr = new ArrayList[n];

            HashSet<Integer>[] s = new HashSet[n];

            for (int i = 0; i < n-1; i++) {
                int x = in.nextInt()-1;
                int y = in.nextInt()-1;

                if(arr[x] == null) {arr[x] = new ArrayList<>(); s[x] = new HashSet<>();}
                if(arr[y] == null) {arr[y] = new ArrayList<>(); s[y] = new HashSet<>();}

                arr[x].add(y); arr[y].add(x);
                s[x].add(y); s[y].add(x);
            }

            Comparator<int[]> comparator = (a, b) -> Integer.compare(b[0], a[0]);

            PriorityQueue<int[]> pq = new PriorityQueue<>(comparator);

//            pq.add(new int[]{n,0});

            HashSet<Integer> vis = new HashSet<>();

            int ans = dfs(pq, 0, vis, s, arr);

            System.out.println(ans);

        }



    }

    public static int dfs(PriorityQueue<int[]> pq, int m, HashSet<Integer> vis, HashSet<Integer>[] s, ArrayList<Integer>[] arr)
    {
        vis.add(m);
        int v = s[m].size();

        int max = 0;

        if(pq.isEmpty()){
            max = 0;
        }
        else if(s[m].contains(pq.peek()[1])) {
            int[] a = pq.poll();
            max = v + a[0] - 2;
            if(!pq.isEmpty()) max = Math.max( v + a[0] - 2, v + pq.peek()[0] - 1);
            pq.add(a);
        }
        else if(!s[m].contains(pq.peek()[1]))
        {
            max = Math.max(max, v + pq.peek()[0] - 1);
        }

        pq.add(new int[]{v, m});

        for (int i = 0; i < arr[m].size(); i++) {
            if(vis.contains(arr[m].get(i))) continue;
            max = Math.max(max, dfs(pq,arr[m].get(i), vis, s, arr));
        }

        return max;

    }



    /*          ─────────▄▄───────────────────▄▄──
                ──────────▀█───────────────────▀█─
                ──────────▄█───────────────────▄█─
                ──█████████▀───────────█████████▀─
                ───▄██████▄─────────────▄██████▄──
                ─▄██▀────▀██▄─────────▄██▀────▀██▄
                ─██────────██─────────██────────██
                ─██───██───██─────────██───██───██
                ─██────────██─────────██────────██
                ──██▄────▄██───────────██▄────▄██─
                ───▀██████▀─────────────▀██████▀──
                ──────────────────────────────────
                   ────────────────────────────
                    ─────────────────────────
                     ──────█████████████───
                     ──────────────────────
                     ──────────────────────
     */
}


Solution 2 (runtime: 1515 ms):
import java.util.*;
import java.lang.*;
import java.io.*;
public class Codechef
    {
	static FastScanner fs = null;
	static int res;
	static ArrayList<Set<Integer>> list;
	static int co[];
	static Map<Integer,Integer> map;
	static TreeSet<Integer> ts;
	static int inf = (int)1e8;
	static boolean vis[];
	public static void main(String[] args) {
		fs = new FastScanner();

		PrintWriter out = new PrintWriter(System.out);
		int t = fs.nextInt();
        while(t-->0){
            list = new ArrayList<>();
            int n = fs.nextInt();
            co = new int[n+1];
            ts = new TreeSet<>();
            map = new HashMap<>();
            vis = new boolean[n+1];
            Arrays.fill(vis,false);
            for(int i = 0;i<=n;i++){
                Set<Integer> se = new HashSet<>();
                list.add(se);
            }
            for(int i = 1;i<n;i++){
                int u = fs.nextInt();
                int v = fs.nextInt();
                list.get(u).add(v);
                list.get(v).add(u);
                co[u]+=1;
                co[v]+=1;
            }
            for(int i = 1;i<=n;i++){
                int num = co[i];
                ts.add(num);
                if(map.get(num)==null){
                    map.put(num,1);
                }
                else{
                    map.replace(num,1+map.get(num));
                }
            }
            res = 0;
            //System.out.println("---------");
            dfs(1,-1);
            //out.println(res+" ------ ");
            dfs2(1);
           // res = Math.min(res,n-2);
            out.println(res);
        }
		out.close();
	}
	static void dfs2(int node){
	    vis[node] = true;
	    int ans1 = co[node];
	        map.replace(ans1,-1+map.get(ans1));
	        if(map.get(ans1)==0){
	            ts.remove(ans1);
	        }
	    for(Integer p:list.get(node)){
	        int nu = co[p];
	        //System.out.println(p+" -- "+node+" -- "+nu+" --- "+map.get(nu));
	        
	        map.replace(nu,-1+map.get(nu));
	        if(map.get(nu)==0){
	            ts.remove(nu);
	        }
	    }
	    int re = ans1;
	    if(ts.floor(inf)!=null){
	        re+=ts.floor(inf);
	    }
	   // else{
	   //     re-=1;
	   // }
	   
	   
	   map.replace(ans1,+1+map.get(ans1));
	        ts.add(ans1);
	    for(Integer p:list.get(node)){
	        int nu = co[p];
	        map.replace(nu,+1+map.get(nu));
	        ts.add(nu);
	    }
	    //System.out.println(node+" --- "+re+" -- "+ans1);
	    res = Math.max(res,re-1);
	    for(Integer p:list.get(node)){
	        if(!vis[p]){
	            dfs2(p);
	        }
	    }
	     
	}
	static int dfs(int node,int par){
	    for(Integer p:list.get(node)){
	        if(p==par)
	        continue;
	        dfs(p,node);
	        if(par!=-1){
	            res = Math.max(res,co[node]+co[par]-2); 
	        }
	    }
	    
	    //System.out.println(d1+" -- "+d2+" --- "+node+" -- "+par+" -- "+sz);
	    return 0;
	}
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}