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: 702 ms):
import javax.swing.tree.TreeNode;
import java.io.*;
import java.util.*;

/**
 * @Author: _Djhhh
 * @Introduction：
 */

public class Main {
    static FastReader fr = new FastReader();
    static FastWriter fw = new FastWriter();

    public static void solve() {
        int n=fr.nextInt();
        int[] in = new int[n];
        ArrayList<ArrayList<Integer>> to = new ArrayList<>();
        for(int i=0;i<n;i++){
            to.add(new ArrayList<>());
        }
        for(int i=0;i<n-1;i++){
            int x=fr.nextInt()-1;
            int y=fr.nextInt()-1;
            in[x]++;
            in[y]++;
            to.get(x).add(y);
            to.get(y).add(x);
        }
        int mx=0;
        int id1=0;
        for(int i=0;i<n;i++){
            if(in[i]>=mx){
                mx=in[i];
                int cnt=0;
                for(var y:to.get(i)){
                    if(in[y]==mx)cnt++;
                }
                if(cnt>=2)continue;
                id1=i;
            }
        }
        for(var y:to.get(id1)){
            in[y]--;
        }
        in[id1]=0;
        int mn=0;
        for(int i=0;i<n;i++){
            if(in[i]>=mn&&i!=id1){
                mn=in[i];
            }
        }
        fw.println((mx+mn-1));
    }

    public static void main(String[] args) {
        int t = 1;
        t = fr.nextInt();
        while (t-- > 0) solve();
    }
}

class DSU {
    int n;
    int[] fa;
    int[] dep;
    int[] siz;
    int[] edges;
    boolean[] v;
    DSU(int n) {
        fa = new int[n];
        dep = new int[n];
        siz = new int[n];
        edges = new int[n];
        v = new boolean[n];
        for (int i = 0; i < n; i++) {
            fa[i] = i;
            dep[i] = 0;
            siz[i] = 1;
            edges[i] = 0;
            v[i]=false;
        }
    }
    int look(int x) {
        if (fa[x] == x) return x;
        else return fa[x] = look(fa[x]);
    }
    void merge(int x, int y) {
        v[x]=v[y]=true;
        int xx = look(x);
        int yy = look(y);
        if (xx == yy) return;
        edges[xx] += edges[yy] + 1;
        siz[xx] += siz[yy];
        if (dep[xx] < dep[yy]) {
            fa[xx] = yy;
        } else {
            fa[yy] = xx;
        }

        if (dep[xx] == dep[yy]) dep[xx]++;
    }
    boolean isMerge(int x, int y) {
        return look(x) == look(y);
    }
    int getSize(int x) {
        return siz[look(x)];
    }
    int getEdges(int x) {
        return edges[look(x)];
    }
}
class Pair<T1, T2> {
    private T1 first;
    private T2 second;

    public Pair(T1 first, T2 second) {
        this.first = first;
        this.second = second;
    }
    public void setFirst(T1 first) {
        this.first=first;
    }

    public void setSecond(T2 second) {
        this.second=second;
    }
    public T1 getFirst() {
        return first;
    }

    public T2 getSecond() {
        return second;
    }
}
class Algorithm {
    /**
     * 查找第一个大于等于 x 的位置
     * @param arr 查找数组
     * @param x 值
     * @param L 左边界
     * @param R 右边界
     * @return 第一个大于等于 x 的位置
     */
    public static int lowBs(int[] arr, long x, int L, int R){
        int l = L;
        int r = R;
        int res = R + 1;
        while(l <= r){
            int mid = l+r>>1;
            if(arr[mid] >= x){
                res = mid;
                r = mid - 1;
            }
            else{
                l = mid + 1;
            }
        }
        return res;
    }

    /**
     * 查找第一个大于 x 的位置
     * @param arr 查找数组
     * @param x 值
     * @param L 左边界
     * @param R 右边界
     * @return 第一个大于 x 的位置
     */
    public static int highBs(int[] arr, long x, int L, int R) {
        int l = L;
        int r = R;
        int res = R + 1;
        while(l <= r){
            int mid = l+r>>1;
            if(arr[mid] > x){
                res = mid;
                r = mid -1;
            }
            else{
                l = mid +1;
            }
        }
        return res;
    }
}
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;
    }

    int[] nextIntArray() {
        String line = nextLine();
        String[] strNums = line.split("\\s+");
        int[] arr = new int[strNums.length];
        for (int i = 0; i < strNums.length; i++) {
            arr[i] = Integer.parseInt(strNums[i]);
        }
        return arr;
    }

    long[] nextLongArray() {
        String line = nextLine();
        String[] strNums = line.split("\\s+");
        long[] arr = new long[strNums.length];
        for (int i = 0; i < strNums.length; i++) {
            arr[i] = Long.parseLong(strNums[i]);
        }
        return arr;
    }

    char[] nextCharArray() {
        String line = nextLine();
        String[] strNums = line.split("\\s+");
        char[] arr = new char[strNums.length];
        for (int i = 0; i < strNums.length; i++) {
            arr[i] = strNums[i].charAt(0);
        }
        return arr;
    }

    char[] StringtoChar() {
        String line = nextLine();
        return line.toCharArray();
    }
}
class FastWriter {
    private final PrintWriter writer;

    public FastWriter() {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), true);
    }

    public void print(Object object) {
        writer.print(object);
    }

    public void println(Object object) {
        writer.println(object);
    }

    public void flush() {
        writer.flush();
    }
}