Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 1421 ms):
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class RemoveExactlyTwo {

    public static int[][] dfs(int src, int par, List<List<Integer>> arr) {

        int[][] new_components = new int[3][2];

        int first_max = 0, second_max = 0;

        for (int v : arr.get(src)) {
            if (par == v) continue;

            int[][] components = dfs(v, src, arr);

            new_components[0][0] = Math.max(new_components[0][0], components[0][0]);
            new_components[0][1] = Math.max(new_components[0][1], components[0][1]);

            new_components[1][0] = Math.max(new_components[1][0], Math.max(components[1][0], components[1][1]));
            new_components[1][1] = Math.max(new_components[1][1], components[0][0] + arr.get(src).size());
            new_components[1][1] = Math.max(new_components[1][1], components[0][1] + arr.get(src).size() - 1);
            
            new_components[2][0] = Math.max(new_components[2][0], Math.max(components[2][0], components[2][1]));
            new_components[2][1] = Math.max(new_components[2][1], components[1][0] + arr.get(src).size());
            new_components[2][1] = Math.max(new_components[2][1], components[1][1] + arr.get(src).size() - 1);

            if (first_max < components[1][0] || first_max < components[1][1]) {
                second_max = first_max;
                first_max = Math.max(components[1][0], components[1][1]);
            } else if (second_max < components[1][0] || second_max < components[1][1]) {
                second_max = Math.max(components[1][0], components[1][1]);
            }
        }

        if (arr.get(src).isEmpty()) {

            new_components[0][0] = 1;
            new_components[0][1] = Integer.MIN_VALUE/2;

            new_components[1][0] = Integer.MIN_VALUE/2;
            new_components[1][1] = 0;

            new_components[2][0] = Integer.MIN_VALUE/2;
            new_components[2][1] = Integer.MIN_VALUE/2;
            
        } else {
            new_components[2][0] = Math.max(first_max + second_max, new_components[2][0]);
        }

        return new_components;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t =  Integer.parseInt(br.readLine());

        while(t-- > 0) {

           int n = Integer.parseInt(br.readLine());
           
           int edges = n - 1;

           List<List<Integer>> arr = new ArrayList<>();

           for (int i = 0; i < n; i++) arr.add(new ArrayList<>());

           while (edges-- > 0) {
                int[] e = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();

                arr.get(e[0] - 1).add(e[1] - 1);
                arr.get(e[1] - 1).add(e[0] - 1);
           }

           int[][] components = dfs(0, -1, arr);

           System.out.println(Math.max(components[2][0], components[2][1]) - 1);

        }
    }
}

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];
        }


    }
}