Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (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());
		}
	}
}

Solution 2 (runtime: 968 ms):
import java.io.*;
import java.util.*;




public class HelpLancelot {
    


    static FastReader in = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static long mod = 1_000_000_007;
    
    static class Pair{
        int a, b;
        Pair(int a, int b){ this.a =a; this.b = b;}
    }
    
    static int[] isPerm(int a[]){
        int n = a.length;
        int pres[] = new int[n+1];
        Arrays.fill(pres, -1);
        pres[0] = 1;
        for(int i=0; i<n; i++) pres[a[i]] = i;
        
        for(int i=1; i<=n; i++) {
            if(pres[i] == -1) {
                pres[0] = -1;
                break;
            }
        }
        
        return pres;
    }

    public static void main(String[] args) {

        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            ArrayList<HashSet<Integer>> adj = new ArrayList<>();
            for(int i=0; i<n; i++){
                adj.add(new HashSet<>());
            }
            
            int deg[] = new int[n];
            for(int i=1; i<=n-1; i++){
                int u = in.nextInt(); int v = in.nextInt();
                u--; v--;
                deg[u]++; deg[v]++;
                adj.get(v).add(u);
                adj.get(u).add(v);
            }
            
            ArrayList<Pair> pair = new ArrayList<>();
            for(int i=0; i<n; i++) pair.add(new Pair(i, deg[i]));
            
            Collections.sort(pair, (p,q) -> q.b - p.b);
            
            if(n == 2) out.println(0);
            else {
                Pair pair1 = pair.get(0);
                Pair pair2 = pair.get(1);
                
                
                int ans = 0;
                if(adj.get(pair1.a).contains(pair2.a)) ans = Math.max(ans, pair1.b + pair2.b - 2);
                else ans = Math.max(ans, pair1.b + pair2.b - 1);
                
                for(int i=2; i<n; i++){
                    Pair pair3 = pair.get(i);
                    if(adj.get(pair3.a).contains(pair2.a)) ans = Math.max(ans, pair3.b + pair2.b - 2);
                    else ans = Math.max(ans, pair3.b + pair2.b - 1);
                    
                    if(adj.get(pair1.a).contains(pair3.a)) ans = Math.max(ans, pair1.b + pair3.b - 2);
                    else ans = Math.max(ans, pair1.b + pair3.b - 1);
                }
                out.println(ans);
            }
            
            
        }
        out.close();
    }

    static void inArr(int a[], int s, int e) {
        for (int i = s; i <= e; i++) {
            a[i] = in.nextInt();
        }
    }

    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 {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}