Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 1296 ms):
import java.io.*;
import java.util.*;

public class RemoveExactlyTwo {

    static int mod = 1000000007;

    public static void main(String[] args) throws IOException {

        FastReader reader = new FastReader();
        FastWriter writer = new FastWriter();

        int numTests = reader.readSingleInt();
        for (int t = 0; t < numTests; t++) {
            int n = reader.readSingleInt();

            Node[] nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node(i);
            }

            for (int i = 0; i < n - 1; i++) {
                int[] uv = reader.readIntArray(2);
                int u = uv[0] - 1;
                int v = uv[1] - 1;
                nodes[u].children.add(nodes[v]);
                nodes[v].children.add(nodes[u]);
            }

            var largest = new HashSet<Node>();
            int max = 0;
            for (int i = 0; i < n; i++) {
                if (max == nodes[i].children.size()) {
                    largest.add(nodes[i]);
                } else if (max < nodes[i].children.size()) {
                    largest.clear();
                    largest.add(nodes[i]);
                    max = nodes[i].children.size();
                }
            }

            var toppers = new ArrayList<>(largest);
            var top = toppers.get(0);

            boolean allChildren = true;
            for (int i = 1; i < toppers.size(); i++) {
                if (!top.children.contains(toppers.get(i))) {
                    allChildren = false;
                    break;
                }
            }
            if (allChildren && toppers.size() > 1) {
                top = toppers.get(1);
            }


            for (var child : top.children) {
                child.children.remove(top);
            }
            top.children.clear();

            max = 0;
            for (int i = 0; i < n; i++) {
                if (nodes[max].children.size() < nodes[i].children.size()) {
                    max = i;
                }
            }

            for (var child : nodes[max].children) {
                child.children.remove(nodes[max]);
            }
            nodes[max].children.clear();

            var count = 0;
            var seen = new HashSet<Node>();
            for (int i = 0; i < n; i++) {
                if (seen.contains(nodes[i])) {
                    continue;
                }

                count++;

                seen.add(nodes[i]);
                var stack = new Stack<Node>();

                stack.push(nodes[i]);
                while (!stack.isEmpty()) {
                    top = stack.pop();
                    for (var child : top.children) {
                        if (seen.contains(child)) {
                            continue;
                        }
                        seen.add(child);
                        stack.push(child);
                    }
                }
            }

            writer.writeSingleInteger(count - 2);
        }
    }

    public static class Node {
        int id;
        Set<Node> children = new HashSet<>();

        Node(int id) {
            this.id = id;
        }
    }


    public static void mergeSort(int[] a, int n) {
        if (n < 2) {
            return;
        }
        int mid = n / 2;
        int[] l = new int[mid];
        int[] r = new int[n - mid];

        for (int i = 0; i < mid; i++) {
            l[i] = a[i];
        }
        for (int i = mid; i < n; i++) {
            r[i - mid] = a[i];
        }

        mergeSort(l, mid);
        mergeSort(r, n - mid);

        merge(a, l, r, mid, n - mid);
    }


    public static void merge(int[] a, int[] l, int[] r, int left, int right) {

        int i = 0, j = 0, k = 0;
        while (i < left && j < right) {
            if (l[i] <= r[j]) {
                a[k++] = l[i++];
            } else {
                a[k++] = r[j++];
            }
        }
        while (i < left) {
            a[k++] = l[i++];
        }
        while (j < right) {
            a[k++] = r[j++];
        }
    }


    public static class FastReader {

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer tokenizer;


        public int readSingleInt() throws IOException {
            return Integer.parseInt(reader.readLine());
        }

        public int[] readIntArray(int numInts) throws IOException {
            int[] nums = new int[numInts];
            tokenizer = new StringTokenizer(reader.readLine());
            for (int i = 0; i < numInts; i++) {
                nums[i] = Integer.parseInt(tokenizer.nextToken());
            }
            return nums;
        }

        public long[] readLongArray(int numInts) throws IOException {
            long[] nums = new long[numInts];
            tokenizer = new StringTokenizer(reader.readLine());
            for (int i = 0; i < numInts; i++) {
                nums[i] = Long.parseLong(tokenizer.nextToken());
            }
            return nums;
        }

        public String readString() throws IOException {
            return reader.readLine();
        }

    }


    public static class FastWriter {

        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));


        public void writeSingleInteger(int i) throws IOException {
            writer.write(Integer.toString(i));
            writer.newLine();
            writer.flush();
        }

        public void writeSingleLong(long i) throws IOException {
            writer.write(Long.toString(i));
            writer.newLine();
            writer.flush();
        }

        public void writeIntArrayWithSpaces(int[] nums) throws IOException {
            for (int i = 0; i < nums.length; i++) {
                writer.write(nums[i] + " ");
            }
            writer.newLine();
            writer.flush();
        }

        public void writeLongArrayWithSpaces(long[] nums) throws IOException {
            for (int i = 0; i < nums.length; i++) {
                writer.write(nums[i] + " ");
            }
            writer.newLine();
            writer.flush();
        }

        public void writeIntArrayListWithSpaces(ArrayList<Integer> nums) throws IOException {
            for (int i = 0; i < nums.size(); i++) {
                writer.write(nums.get(i) + " ");
            }
            writer.newLine();
            writer.flush();
        }

        public void writeIntArrayWithoutSpaces(int[] nums) throws IOException {
            for (int i = 0; i < nums.length; i++) {
                writer.write(Integer.toString(nums[i]));
            }
            writer.newLine();
            writer.flush();
        }

        public void writeString(String s) throws IOException {
            writer.write(s);
            writer.newLine();
            writer.flush();
        }

    }


}


Solution 2 (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);

        }
    }
}