Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 905 ms):
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.List;
import java.util.Set;
import java.util.HashSet;

public class C {
	
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {
            int n = fs.nextInt();
            if (n == 1) {
                out.println(0);
                continue;
            }
            Set<Integer>[] adjList = new HashSet[n+1];
            for (int i = 0; i <= n; i++) {
                adjList[i] = new HashSet<>();
            }
            List<Integer> maxVertices = new ArrayList<>();
            int maxNeighbour = Integer.MIN_VALUE;
            for (int i = 0; i < n-1; i++) {
                int u = fs.nextInt(), v = fs.nextInt();
                adjList[u].add(v);
                adjList[v].add(u);
                boolean flagu = false;
                boolean flagv = false;
                if (maxNeighbour < adjList[u].size()) {
                    maxNeighbour = adjList[u].size();
                    maxVertices = new ArrayList<>();
                    maxVertices.add(u);
                    flagu = true;
                }
                if (maxNeighbour < adjList[v].size()) {
                    maxNeighbour = adjList[v].size();
                    maxVertices = new ArrayList<>();
                    maxVertices.add(v);
                    flagv = true;
                }
                if (!flagu && maxNeighbour == adjList[u].size()) {
                    maxVertices.add(u);
                }
                if (!flagv && maxNeighbour == adjList[v].size()) {
                    maxVertices.add(v);
                }
            }
            
            int ans = Integer.MIN_VALUE;

            for (int i = 0; i < Math.min(2,maxVertices.size()); i++) {
                int maxNode = maxVertices.get(i);
                Set<Integer> maxNodeNeigh = adjList[maxNode];
                
                for (int j = 1; j <= n; j++) {
                    if (j != maxNode) {
                        if (maxNodeNeigh.contains(j)) {
                            ans = Math.max(ans, maxNodeNeigh.size() + adjList[j].size() - 2);
                        }
                        else {
                            ans = Math.max(ans, maxNodeNeigh.size() + adjList[j].size() - 1);
                        }
                    } 
                    
                }
            }
            out.println(ans);
        }
		out.close();
	}

	public static long binpowmod(long a, long b, long m) {
		a %= m;
		long result = 1L;
		while (b > 0) {
			if ((b & 1) == 1) {
				result = (result * a) % m;
			}
			a = (a * a) % m;
			b >>= 1;
		}
		return result;
	}

    public static long hash(String s) {
        int MOD = (int) (1e9 + 7);
        long value = 0;
        for (char c : s.toCharArray()) {
            value = (value * 31 + (c - 'a' + 1)) % MOD;
        }
        return value;
    }

    // this is for FLOOR DIVISION with NEGATIVE numerator
    public static long fDiv(long x, long y) {
        if (x >= 0) {
            return x/y;
        }
        else {
            return (x-y+1)/y;
        }
    }

    // change long to int accordingly
    public static long binomialCoeff(int n, int k)
    {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate  value of Binomial
        // Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using
                // previously stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

	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());
		}
	}
	
	 // GCD - Euclid's Algo by Modulo
    // log max(a,b)
    /* 
    public static int gcd(int a, int b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }
    */
	
	// Sieve of Eratosthenes
	/*
	boolean[] array = new boolean[length + 1];
 
	for (int i = 2; i * 2 <= length; i++) {
		if (array[i] == false) {
			for (int j = i; j <= length;j+= i) {
				//out.println(j);
				array[j] = true;
			}
		}
	}*/

	// Next permutation
	/*
	public static boolean nextPermutation(int[] ordering) {
 
 
		// If the given ordering set is empty
        // or contains only one element
        // next_permutation is not possible
        if (ordering.length <= 1)
            return false;
 
        int last = ordering.length - 2;
 
        // find the longest non-increasing suffix
        // and find the pivot
        while (last >= 0) {
            if (ordering[last] < ordering[last + 1]) {
                break;
            }
            last--;
        }
 
        // If there is no increasing pair
        // there is no higher order permutation
        if (last < 0)
            return false;
 
        int nextGreater = ordering.length - 1;
 
        // Find the rightmost successor to the pivot
        for (int i = ordering.length - 1; i > last; i--) {
            if (ordering[i] > ordering[last]) {
                nextGreater = i;
                break;
            }
        }
 
        // Swap the successor and the pivot
        swap(ordering, nextGreater, last);
 
        // Reverse the suffix
        reverse(ordering, last + 1, ordering.length - 1);
 
        // Return true as the next_permutation is done
        return true;
	}
 
	public static int[] swap(int ordering[], int left, int right)
    {
 
        // Swap the ordering
        int temp = ordering[left];
        ordering[left] = ordering[right];
        ordering[right] = temp;
 
        // Return the updated array
        return ordering;
    }
 
    // Function to reverse the sub-array
    // starting from left to the right
    // both inclusive
    public static int[] reverse(int ordering[], int left, int right)
    {
 
        // Reverse the sub-array
        while (left < right) {
            int temp = ordering[left];
            ordering[left++] = ordering[right];
            ordering[right--] = temp;
        }
 
        // Return the updated array
        return ordering;
    } */

    // KMP Algorithm
    // Compute LPS array
    // 0 >= arr[i], arr[i] <= i (array is 0-indexed)
    public static int[] computeLPS(String s) {
        int n = s.length();
        int[] arr = new int[n];
        for (int i = 1; i < n; i++) {
            int j = arr[i-1]; 
            while (j > 0 && s.charAt(i) != s.charAt(j)) {
                j = arr[j-1];
            }
            if (s.charAt(i) == s.charAt(j)) {
                j++;
            }
            arr[i] = j;
        }
        return arr;
    }
}

Solution 2 (runtime: 796 ms):

import java.io.*;
import java.util.*;

public class CodeForces {
    public static final int MOD = 1_000_000_007;
    public static final int BUFFERSIZE = 512000;
    //    private static Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in), BUFFERSIZE));
    private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out, BUFFERSIZE));


    static class Pair<T, E> {
        private T first;
        private E second;

        public Pair(T key, E value) {
            this.first = key;
            this.second = value;
        }

    }

    public static int solve(int n, ArrayList<Integer> connections[]) throws Exception {
        for (int k = 0; k < 2; k++) {
            int maxConnections = Integer.MIN_VALUE;
            int maxVertex = -1;
            for (int i = 1; i <= n; i++) {
                if (connections[i] != null && connections[i].size() > maxConnections) {
                    maxVertex = i;
                    maxConnections = connections[i].size();
                }else{
                    if (connections[i] != null && connections[i].size() == maxConnections) {
                        boolean take = false;
                        for (int j = 0; j < connections[i].size(); j++) {
                            int connectedTo = connections[i].get(j);  // 1 5
                            for (int l = 0; l < connections[connectedTo].size(); l++) {
                                if(connections[connectedTo].get(l) == i) continue;
                                if(connections[connections[connectedTo].get(l)].size() >= maxConnections){
                                    take = true;
                                    maxVertex = i;
                                    break;
                                }
                            }
                            if(take){
                                break;
                            }
                        }
                    }
                }
            }
            for (int i = 0; i < connections[maxVertex].size(); i++) {
                int toRemove = connections[maxVertex].get(i);
                connections[toRemove].remove((Object) maxVertex);
            }
            connections[maxVertex]  = null;
        }
        int ans = 0;
        boolean marked[] = new boolean[n + 1];
        for (int i = 1; i <= n ; i++) {
            if(!marked[i] && connections[i] != null){
                dfs(connections, i, marked);
                ans++;
            }
        }
        return ans;
    }

    private static void dfs(ArrayList<Integer>[] connections, int vertex, boolean[] marked) {
        if(marked[vertex])
            return;
        marked[vertex] = true;
        for (int connectedVertex :connections[vertex]) {
            dfs(connections, connectedVertex, marked);
        }
    }


    public static void main(String args[]) throws Exception {
        in.init(System.in);
        Random random = new Random();
//        int totalTestCases = 10000;
        int totalTestCases = in.nextInt();
        for (int testCase = 0; testCase < totalTestCases; testCase++) {
            int n = in.nextInt();
            ArrayList<Integer> connections[] = new ArrayList[n + 1];
            for (int i = 1; i <= n; i++) {
                connections[i] = new ArrayList<>();
            }
            for (int i = 0; i < n - 1; i++) {
                int a = in.nextInt();
                int b = in.nextInt();
                connections[a].add(b);
                connections[b].add(a);
            }
            out.println(solve(n, connections));
//            long s2 = solve2(n, k, a, b);
//            if(s1 != s2){
//                System.out.println(n + " " + k);
//                System.out.println(Arrays.toString(a));
//                System.out.println(Arrays.toString(b));
//            }
//            long t2 = System.currentTimeMillis();
//            String solve2 = solve2(a);
//            long t3 = System.currentTimeMillis();
//            System.out.println(t3-t2);
//            System.out.println(t2-t1);
//            if(!solve1.equals(solve2)){
//                System.out.println(Arrays.toString(a));
//                System.out.println(solve1);
//                System.out.println(solve2);
//            }
        }
        out.close();
    }


    private static int lowerBound(int[] ar, int i) {
        int start = 0;
        int end = ar.length - 1;
        // 5, 7, 9
        int candidate = ar.length;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (ar[mid] >= i) {
                candidate = mid;
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        return candidate;
    }

//    public static void numberPrimeNumber() {
//        int nn = 12;
//        int arr[] = new int[nn + 1];
//        for (int i = 1; i <= nn; ++i) {
//            for (int j = 2 * i; j <= nn; j += i) {
//                if (arr[j] == arr[i]) {
//                    ++arr[j];
//                }
//            }
//        }
//    }


    public static List<Integer> calculatePrimes(int n) {
        List<Integer> primes = new ArrayList<>();

        boolean[] isPrime = new boolean[n + 1];

        for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        for (int i = 2; i * i <= n; i++) {
            if (isPrime[i]) {
                for (int j = i * i; j <= n; j += i) {
                    isPrime[j] = false;
                }
            }
        }

        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) {
                primes.add(i);
            }
        }

        return primes;
    }

    public static class in {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        static void init(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input), BUFFERSIZE);
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

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

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

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

    static {
        Bigmod.reset(false, 300300);
    }

    static class Bigmod {
        static long M9 = 998244353L, M1 = 1000_000_007L;
        static long M = 0;
        static int MAXN = -1;
        static long[] cacheStepmul;
        static long[] cacheStepmulInv;
        static long[] exp2;
        long num = 0;

        // TODO: reset this before anything.
        static void reset(boolean use998, int maxN) {
            // 300300
            M = use998 ? M9 : M1;
            MAXN = maxN;
            cacheStepmul = new long[MAXN];
            cacheStepmulInv = new long[MAXN];
            exp2 = new long[MAXN];
        }

        Bigmod(long num) {
            if (num >= 0) {
                this.num = num % M;
            } else {
                this.num = M - (-num) % M;
            }
        }

        static Bigmod valueOf(long num) {
            return new Bigmod(num);
        }

        @Override
        public String toString() {
            return Long.toString(num);
        }

        Bigmod add(long x) {
            if (x > 0) {
                num = (num + x % M) % M;
            } else if (x < 0) {
                num = (num - (-x) % M + M) % M;
            }
            return this;
        }

        Bigmod add(Bigmod bm) {
            return add(bm.num);
        }

        Bigmod sub(long x) {
            return add(-x);
        }

        Bigmod sub(Bigmod bm) {
            return add(-bm.num);
        }

        Bigmod mul(long x) {
            num = num * (x % M) % M;
            return this;
        }

        Bigmod mul(Bigmod bm) {
            return mul(bm.num);
        }

        Bigmod div(long x) {
            if (x == 0) throw new RuntimeException("cannot div 0.");
            return mul(exp(x, M - 2));
        }

        Bigmod div(Bigmod bm) {
            return div(bm.num);
        }

        Bigmod exp(long p) {
            long ret = 1L, baseLong = num % M;
            for (int i = 0; i <= 60 && p > 0; ++i) { //1<<30=1073741824
                if ((p & (1L << i)) > 0) {
                    ret = ret * baseLong % M;
                    p ^= (1L << i);
                }
                baseLong = baseLong * baseLong % M;
            }
            if (p != 0) throw new RuntimeException("p should reduced to 0 in exp.");
            num = ret;
            return this;
        }

        Bigmod exp(Bigmod bm) {
            return exp(bm.num);
        }

        static long exp(long x, long p) {
            return new Bigmod(x).exp(p).num;
        }

        static long exp2(long n) { // 2^n
            if (n >= exp2.length) throw new RuntimeException("overflow exp2 size. " + n + " >= " + exp2.length);
            if (exp2[0] == 0) {
                exp2[0] = 1;
                for (int i = 1; i < exp2.length; ++i)
                    exp2[i] = exp2[i - 1] * 2 % M;
            }
            return exp2[(int) n];
        }

        static long C(long n, long m) {
            if (n < 0 || m < 0) throw new RuntimeException("n/m cannot be negative in C(n,m).");
            if (n < m) throw new RuntimeException("n is less than m in C(n,m).");
            if (n == 0) return 1;
            if (m == 0 || m == n) return 1;
            return new Bigmod(P(n, m)).mul(stepmulInv(m)).num;
        }

        static long P(long n, long m) {
            if (n < 0 || m < 0) throw new RuntimeException("n/m cannot be negative in P(n,m).");
            if (n < m) throw new RuntimeException("n is less than m in P(n,m).");
            if (n == 0) return 1;
            if (n < cacheStepmul.length) {
                // P(n,m)=n!/(n-m)!
                return new Bigmod(stepmul(n)).mul(stepmulInv(n - m)).num;
            }
            // NOTE: O(m) complexity when n is large.
            Bigmod r = new Bigmod(1);
            long val = n;
            for (long i = 0; i < m; ++i) r.mul(val--);
            return r.num;
        }

        static long stepmul(long n) { // n!
            if (n >= cacheStepmul.length) throw new RuntimeException("overflow cacheSm size.");
            if (cacheStepmul[0] == 0) {
                cacheStepmul[0] = 1;
                cacheStepmulInv[0] = exp(cacheStepmul[0], M - 2);
                for (int i = 1; i < cacheStepmul.length; ++i) {
                    cacheStepmul[i] = cacheStepmul[i - 1] * i % M;
                    cacheStepmulInv[i] = exp(cacheStepmul[i], M - 2);
                }
            }
            return cacheStepmul[(int) n];
        }

        static long stepmulInv(long n) {
            if (cacheStepmulInv[1] == 0) stepmul(2);
            return cacheStepmulInv[(int) n];
        }


    }
}