Problem:
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Connected Components

Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.

Input

In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0, 1, ..., n-1$.

In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).

In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.

Output

For each query, print "yes" if $t$ is reachable from $s$ through the social network, "no" otherwise.

Constraints

$2 \leq n \leq 100,000$

$0 \leq m \leq 100,000$

$1 \leq q \leq 10,000$

Sample Input

10 9
0 1
0 2
3 4
5 7
5 6
6 7
6 8
7 8
8 9
3
0 1
5 9
1 3

Sample Output

yes
yes
no

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var G = new UnionFindForest();
			for(int i = 0; i<N; i++) {
				G.Add(i);
			}
			var m = cin.ReadInt;
			for(int j = 0; j<m; j++) {
				var line = cin.ReadIntArray(2);
				G.Union(line[0], line[1]);
			}
			var qCount = cin.ReadInt;
			for(int j = 0; j<qCount; j++) {
				var q = cin.ReadIntArray(2);
				Console.WriteLine(G.Find(q[0], q[1]) ? "yes" : "no");
			}
		}

	}
	static class ExtendClass {
		public static void Swap<T>(this T[] A, int x, int y) {
			var tmp = A[x];
			A[x]=A[y];
			A[y]=tmp;
		}
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
		public static IEnumerable<int> Indices<T>(this T[] X) => Enumerable.Range(0, X.Length);
		public static IEnumerable<int> Indices<T>(this T[,] X, int dim)
			=> Enumerable.Range(0, X.GetLength(dim));
		//public static IEnumerable<(int i1, int i2)> Indices<T>(this T[,] X)
		//	=> X.Indices(0).SelectMany(i => X.Indices(1).Select((i, j) => (i, j)));
		public static string Join<T>(this T[,] X, string separatorD2 = ",", string separatorD1 = "\n")
			=> X.Indices(0).Select(
				i => X.Indices(1).Select(j => X[i, j]).Join(separatorD2)
			).Join(separatorD1);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}
	class UnionFindForest {
		public class Node {
			public int value { get; set; }
			public Node parent { get; set; }
			public Node root {
				get {
					var path = new Queue<Node>();
					var res = this;
					while(res.parent!=res) {
						path.Enqueue(res);
						res=res.parent;
					}
					while(path.Any())
						path.Dequeue().parent=res;
					return res;
				}
			}
			public int rank { get; private set; }    //meanful iff this is root
			public void rankIncrement() => rank++;
			public Node(int thisValue) {
				value=thisValue;
				parent=this;
				rank=1;
			}
		}

		private readonly Dictionary<int, Node> phoneBook = new Dictionary<int, Node>();
		public void Union(int x, int y) => Union(phoneBook[x], phoneBook[y]);
		public void Union(Node X, Node Y) {
			var RX = X.root;
			var RY = Y.root;
			switch(RX.rank.CompareTo(RY.rank)) {
				case 1:
					RY.parent=RX;
					break;
				case -1:
					RX.parent=RY;
					break;
				default:
					RX.parent=RY;
					RY.rankIncrement();
					break;
			}
		}
		public bool Find(int x, int y) => Find(phoneBook[x], phoneBook[y]);
		public bool Find(Node X, Node Y) => X.root==Y.root;
		public void Add(int id) {
			var N = new Node(id);
			phoneBook.Add(id, N);
		}
	}
}