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: 905 ms):

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    static int m = 1000000007, M = 998244353;
    static long inf = (long) 1e18;

    static long timer = 0, max = -1;

    public static void main(String[] args) {
        FastReader next = new FastReader();
        int t = next.nextInt();
        l1:
        while (t-- > 0) {
            int n = next.nextInt();

            ArrayList<ArrayList<Integer>> lists = new ArrayList<>();
            int[] subTreeSize = new int[n + 1];
            int[] inTime = new int[n + 1], outTime = new int[n + 1];

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

            int[] neighbours = new int[n + 1];

            int p = 1;
            for (int i = 1; i < n; i++) {
                int v = next.nextInt();
                int u = next.nextInt();
                lists.get(v).add(u);
                lists.get(u).add(v);
            }
            int res = 0;
            int first = 0, second = 0;
            for (int i = 1; i <= n; i++) {
                if (lists.get(i).size() >= lists.get(first).size()) {
                    second = first;
                    first = i;
                } else {
                    if (lists.get(i).size() >= lists.get(second).size()) {
                        second = i;
                    }
                }
            }
//            System.out.println(lists);
            int max1= lists.get(first).size();
            int max2 = lists.get(second).size();
//            System.out.println(first  +" "+ second);
            ArrayList<ArrayList<Integer>> tem = deepCopy(lists);
            removeNodeEdges(tem, first);
//            System.out.println(tem);
            int f1 = findMaxDegree(tem);
            tem = deepCopy(lists);
            removeNodeEdges(tem, second);
//            System.out.println(tem);
            int f2 = findMaxDegree(tem);
//            ArrayList<Integer> first = lists.get(0), sec = lists.get(1);

            System.out.println(Math.max(max1 + f1 - 1, max2 + f2 - 1));
        }
    }

    private static ArrayList<ArrayList<Integer>> deepCopy(ArrayList<ArrayList<Integer>> original) {
        ArrayList<ArrayList<Integer>> copy = new ArrayList<>();
        for (ArrayList<Integer> list : original) {
            copy.add(new ArrayList<>(list));
        }
        return copy;
    }

    // Remove all edges connected to the given node
    private static void removeNodeEdges(ArrayList<ArrayList<Integer>> adjList, int node) {
        int ct = 0;
        for (ArrayList<Integer> neighbors : adjList) {
            if (ct == node){
                neighbors.clear();
                ct++;
                continue;
            }
            neighbors.removeIf(e -> e == node);
            ct++;
        }
    }

    // Find the maximum degree of any node in the adjacency list
    private static int findMaxDegree(ArrayList<ArrayList<Integer>> adjList) {
        int maxDegree = 0;
        for (ArrayList<Integer> neighbors : adjList) {
            maxDegree = Math.max(maxDegree, neighbors.size());
        }
        return maxDegree;
    }
    // Depth-First Search to count valid paths
    public static void dfs(int currentNode, int parent, ArrayList<ArrayList<Integer>> adjacencyList, int[] size, int[] in, int[] out) {
        size[currentNode] = 1;
        // Flag to check if current node is a leaf
        boolean isLeaf = true;

        // Traverse all connected nodes
        for (int neighbor : adjacencyList.get(currentNode)) {
            if (neighbor != parent) {
                isLeaf = false; // Not a leaf as it has a child
                dfs(neighbor, currentNode, adjacencyList, size, in, out);
                size[currentNode] += size[neighbor];
            }
        }
    }

    public static int[] shortestDistanceToLeaf(int n, ArrayList<ArrayList<Integer>> adj) {
        int[] dist = new int[n + 1];
        Arrays.fill(dist, -1);  // -1 indicates that the vertex has not been visited.
        Queue<Integer> queue = new LinkedList<>();

        // Special case: if the tree contains only one node, it is itself a leaf.
        if (n == 1) {
            dist[1] = 0;
            return dist;
        }

        // Identify all leaf nodes.
        // A vertex is a leaf if it has 0 or 1 neighbor.
        // (Typically, in a connected tree, leaves will have exactly 1 neighbor.)
        for (int i = 1; i <= n; i++) {
            if (adj.get(i).size() <= 1) {
                dist[i] = 0;
                queue.offer(i);
            }
        }

        // Multi-source BFS: propagate distances from all leaves simultaneously.
        while (!queue.isEmpty()) {
            int current = queue.poll();
            for (int neighbor : adj.get(current)) {
                if (dist[neighbor] == -1) {  // Not visited yet.
                    dist[neighbor] = dist[current] + 1;
                    queue.offer(neighbor);
                }
            }
        }
        return dist;
    }

    static void printTreeLevels(ArrayList<ArrayList<Integer>> graph, int root, int n) {
        Queue<Integer> queue = new LinkedList<>();
        boolean[] visited = new boolean[n];

        queue.add(root);
        visited[root] = true;

        int level = 0;
        while (!queue.isEmpty()) {
            int size = queue.size();
            System.out.print("Level " + level + ": ");

            for (int i = 0; i < size; i++) {
                int node = queue.poll();
                System.out.print(node + " ");

                for (int neighbor : graph.get(node)) {
                    if (!visited[neighbor]) {
                        visited[neighbor] = true;
                        queue.add(neighbor);
                    }
                }
            }
            System.out.println();
            level++;
        }
    }

    private static boolean isAncestor(int x, int y, int[] in, int[] out) {
        return in[x] <= in[y] && out[x] >= out[y];
    }


    public static int lowerBound(ArrayList<Integer> arr, long target, int start, int end) {
        int left = start, right = end;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (arr.get(mid) < target) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return left;
    }

    public 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 {
                if (st.hasMoreTokens()) {
                    str = st.nextToken("\n");
                } else {
                    str = br.readLine();
                }
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}