Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (runtime: 1515 ms):
import java.util.*;
import java.lang.*;
import java.io.*;
public class Codechef
    {
	static FastScanner fs = null;
	static int res;
	static ArrayList<Set<Integer>> list;
	static int co[];
	static Map<Integer,Integer> map;
	static TreeSet<Integer> ts;
	static int inf = (int)1e8;
	static boolean vis[];
	public static void main(String[] args) {
		fs = new FastScanner();

		PrintWriter out = new PrintWriter(System.out);
		int t = fs.nextInt();
        while(t-->0){
            list = new ArrayList<>();
            int n = fs.nextInt();
            co = new int[n+1];
            ts = new TreeSet<>();
            map = new HashMap<>();
            vis = new boolean[n+1];
            Arrays.fill(vis,false);
            for(int i = 0;i<=n;i++){
                Set<Integer> se = new HashSet<>();
                list.add(se);
            }
            for(int i = 1;i<n;i++){
                int u = fs.nextInt();
                int v = fs.nextInt();
                list.get(u).add(v);
                list.get(v).add(u);
                co[u]+=1;
                co[v]+=1;
            }
            for(int i = 1;i<=n;i++){
                int num = co[i];
                ts.add(num);
                if(map.get(num)==null){
                    map.put(num,1);
                }
                else{
                    map.replace(num,1+map.get(num));
                }
            }
            res = 0;
            //System.out.println("---------");
            dfs(1,-1);
            //out.println(res+" ------ ");
            dfs2(1);
           // res = Math.min(res,n-2);
            out.println(res);
        }
		out.close();
	}
	static void dfs2(int node){
	    vis[node] = true;
	    int ans1 = co[node];
	        map.replace(ans1,-1+map.get(ans1));
	        if(map.get(ans1)==0){
	            ts.remove(ans1);
	        }
	    for(Integer p:list.get(node)){
	        int nu = co[p];
	        //System.out.println(p+" -- "+node+" -- "+nu+" --- "+map.get(nu));
	        
	        map.replace(nu,-1+map.get(nu));
	        if(map.get(nu)==0){
	            ts.remove(nu);
	        }
	    }
	    int re = ans1;
	    if(ts.floor(inf)!=null){
	        re+=ts.floor(inf);
	    }
	   // else{
	   //     re-=1;
	   // }
	   
	   
	   map.replace(ans1,+1+map.get(ans1));
	        ts.add(ans1);
	    for(Integer p:list.get(node)){
	        int nu = co[p];
	        map.replace(nu,+1+map.get(nu));
	        ts.add(nu);
	    }
	    //System.out.println(node+" --- "+re+" -- "+ans1);
	    res = Math.max(res,re-1);
	    for(Integer p:list.get(node)){
	        if(!vis[p]){
	            dfs2(p);
	        }
	    }
	     
	}
	static int dfs(int node,int par){
	    for(Integer p:list.get(node)){
	        if(p==par)
	        continue;
	        dfs(p,node);
	        if(par!=-1){
	            res = Math.max(res,co[node]+co[par]-2); 
	        }
	    }
	    
	    //System.out.println(d1+" -- "+d2+" --- "+node+" -- "+par+" -- "+sz);
	    return 0;
	}
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}

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;
        }
    }
}