Problem: 2063C - Remove Exactly Two
Language: java

Solution 1 (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();
    }
}

Solution 2 (runtime: 905 ms):
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.List;
import java.util.Set;
import java.util.HashSet;

public class C {
	
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {
            int n = fs.nextInt();
            if (n == 1) {
                out.println(0);
                continue;
            }
            Set<Integer>[] adjList = new HashSet[n+1];
            for (int i = 0; i <= n; i++) {
                adjList[i] = new HashSet<>();
            }
            List<Integer> maxVertices = new ArrayList<>();
            int maxNeighbour = Integer.MIN_VALUE;
            for (int i = 0; i < n-1; i++) {
                int u = fs.nextInt(), v = fs.nextInt();
                adjList[u].add(v);
                adjList[v].add(u);
                boolean flagu = false;
                boolean flagv = false;
                if (maxNeighbour < adjList[u].size()) {
                    maxNeighbour = adjList[u].size();
                    maxVertices = new ArrayList<>();
                    maxVertices.add(u);
                    flagu = true;
                }
                if (maxNeighbour < adjList[v].size()) {
                    maxNeighbour = adjList[v].size();
                    maxVertices = new ArrayList<>();
                    maxVertices.add(v);
                    flagv = true;
                }
                if (!flagu && maxNeighbour == adjList[u].size()) {
                    maxVertices.add(u);
                }
                if (!flagv && maxNeighbour == adjList[v].size()) {
                    maxVertices.add(v);
                }
            }
            
            int ans = Integer.MIN_VALUE;

            for (int i = 0; i < Math.min(2,maxVertices.size()); i++) {
                int maxNode = maxVertices.get(i);
                Set<Integer> maxNodeNeigh = adjList[maxNode];
                
                for (int j = 1; j <= n; j++) {
                    if (j != maxNode) {
                        if (maxNodeNeigh.contains(j)) {
                            ans = Math.max(ans, maxNodeNeigh.size() + adjList[j].size() - 2);
                        }
                        else {
                            ans = Math.max(ans, maxNodeNeigh.size() + adjList[j].size() - 1);
                        }
                    } 
                    
                }
            }
            out.println(ans);
        }
		out.close();
	}

	public static long binpowmod(long a, long b, long m) {
		a %= m;
		long result = 1L;
		while (b > 0) {
			if ((b & 1) == 1) {
				result = (result * a) % m;
			}
			a = (a * a) % m;
			b >>= 1;
		}
		return result;
	}

    public static long hash(String s) {
        int MOD = (int) (1e9 + 7);
        long value = 0;
        for (char c : s.toCharArray()) {
            value = (value * 31 + (c - 'a' + 1)) % MOD;
        }
        return value;
    }

    // this is for FLOOR DIVISION with NEGATIVE numerator
    public static long fDiv(long x, long y) {
        if (x >= 0) {
            return x/y;
        }
        else {
            return (x-y+1)/y;
        }
    }

    // change long to int accordingly
    public static long binomialCoeff(int n, int k)
    {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate  value of Binomial
        // Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using
                // previously stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

	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());
		}
	}
	
	 // GCD - Euclid's Algo by Modulo
    // log max(a,b)
    /* 
    public static int gcd(int a, int b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }
    */
	
	// Sieve of Eratosthenes
	/*
	boolean[] array = new boolean[length + 1];
 
	for (int i = 2; i * 2 <= length; i++) {
		if (array[i] == false) {
			for (int j = i; j <= length;j+= i) {
				//out.println(j);
				array[j] = true;
			}
		}
	}*/

	// Next permutation
	/*
	public static boolean nextPermutation(int[] ordering) {
 
 
		// If the given ordering set is empty
        // or contains only one element
        // next_permutation is not possible
        if (ordering.length <= 1)
            return false;
 
        int last = ordering.length - 2;
 
        // find the longest non-increasing suffix
        // and find the pivot
        while (last >= 0) {
            if (ordering[last] < ordering[last + 1]) {
                break;
            }
            last--;
        }
 
        // If there is no increasing pair
        // there is no higher order permutation
        if (last < 0)
            return false;
 
        int nextGreater = ordering.length - 1;
 
        // Find the rightmost successor to the pivot
        for (int i = ordering.length - 1; i > last; i--) {
            if (ordering[i] > ordering[last]) {
                nextGreater = i;
                break;
            }
        }
 
        // Swap the successor and the pivot
        swap(ordering, nextGreater, last);
 
        // Reverse the suffix
        reverse(ordering, last + 1, ordering.length - 1);
 
        // Return true as the next_permutation is done
        return true;
	}
 
	public static int[] swap(int ordering[], int left, int right)
    {
 
        // Swap the ordering
        int temp = ordering[left];
        ordering[left] = ordering[right];
        ordering[right] = temp;
 
        // Return the updated array
        return ordering;
    }
 
    // Function to reverse the sub-array
    // starting from left to the right
    // both inclusive
    public static int[] reverse(int ordering[], int left, int right)
    {
 
        // Reverse the sub-array
        while (left < right) {
            int temp = ordering[left];
            ordering[left++] = ordering[right];
            ordering[right--] = temp;
        }
 
        // Return the updated array
        return ordering;
    } */

    // KMP Algorithm
    // Compute LPS array
    // 0 >= arr[i], arr[i] <= i (array is 0-indexed)
    public static int[] computeLPS(String s) {
        int n = s.length();
        int[] arr = new int[n];
        for (int i = 1; i < n; i++) {
            int j = arr[i-1]; 
            while (j > 0 && s.charAt(i) != s.charAt(j)) {
                j = arr[j-1];
            }
            if (s.charAt(i) == s.charAt(j)) {
                j++;
            }
            arr[i] = j;
        }
        return arr;
    }
}