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: 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;
        }
    }
}