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: 1843 ms):
// https://codeforces.com/problemset/problem/2063/C

import java.util.*;

public class Main
{
    private static void dfs_dp (int v, int p, final ArrayList<Integer>[] tree, int[] dp)
    {
        for (int to : tree[v])
        if (to != p)
        {
            dfs_dp(to, v, tree, dp);

            dp[v] = Math.max(dp[v], Math.max(dp[to], tree[to].size()));
        }
    }

    private static int dfs_ans (int v, int p, final ArrayList<Integer>[] tree, final int[] dp)
    {
        int ans = 0;

        for (int to : tree[v])
        if (to != p)
            ans = Math.max(ans, dfs_ans(to, v, tree, dp));

        for (int to : tree[v])
        if (to != p)
            ans = Math.max(ans, tree[v].size()-1 + Math.max(tree[to].size() - 1, dp[to]));
        
        int maxi = -1;

        for (int to : tree[v])
        if (to != p)
        {
            int cur = Math.max(tree[to].size(), dp[to]);

            if (maxi != -1)
                ans = Math.max(ans, maxi + cur - 1);
            
            maxi = Math.max(maxi, cur);
        }

        return ans;
    }
    
    private static void solve (Scanner in)
    {
        int n = in.nextInt();

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

        for (int i = 0; i < n; i++)
            tree[i] = new ArrayList<Integer>();

        for (int i = 1; i < n; i++)
        {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;

            tree[u].add(v);
            tree[v].add(u);
        }

        int[] dp = new int[n];

        for (int i = 0; i < n; i++)
            dp[i] = 0;

        dfs_dp(0, -1, tree, dp);
        
        int ans = dfs_ans(0, -1, tree, dp);

        System.out.println(ans);
    }

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

        int t = in.nextInt();

        for (int test = 0; test < t; test++)
            solve(in);

        in.close();
    }
}