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)

// 連結成分
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<stack>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<vector>

#include<queue>
#include<stack>

using namespace std;

#define MAX_N 100000

// 値の定義
const int INV = -1;

// 友達関係を保持する配列
vector<int> v_Link[MAX_N + 1];

// 接続情報を保持する配列
int ary_connection[MAX_N + 1];

void search_relation(int u_ID, int id);

int main(void)
{
    int n, m, q, s, t;

    for(int i = 0; i < MAX_N + 1; i++)
    {
        // 配列の初期化
        ary_connection[i] = INV;
    }

    cin >> n >> m;

    for(int i = 0; i < m; i++)
    {
        cin >> s >> t;

        // 友達関係を双方向に設定する
        v_Link[s].push_back(t);
        v_Link[t].push_back(s);
    }

    int id = 1;

    for(int u = 0; u < n; u++)
    {
        if( ary_connection[u] == INV )
        {
            // 友達関係の検索を実施
            search_relation(u, id++);
        }
    }

    cin >> q;

    for(int i = 0; i < q; i++)
    {
        cin >> s >> t;

        // 質問の結果を表示する
        if( ary_connection[s] == ary_connection[t] )
        {
            // 友達関係が存在する
            printf("yes\n");
        }
        else
        {
            printf("no\n");
        }
    }

    return 0;
}

// 友達関係を検索するための関数
// u_ID : 友達関係を検索する最初のユーザーID
// id   : ary_connection[]に設定するID値
void search_relation(int u_ID, int id)
{

    int user_id;

    queue<int> Q;

    // 開始点をキューにプッシュして, 友達関係を保存する
    Q.push(u_ID);
    ary_connection[u_ID] = id;

    while( !Q.empty() )
    {
        // キューの先頭要素を取得して, 削除する
        // ( 各ユーザーの巡回は1回だけ )
        int u = Q.front();
        Q.pop();

        for(int v = 0; v < v_Link[u].size(); v++)
        {
            // 接続関係にあるユーザーの検索
            user_id = v_Link[u][v];

            if( ary_connection[user_id] == INV )
            {
                // ----- 繋がっている頂点が見つかった -----

                // 接続関係を保存する
                ary_connection[user_id] = id;

                // キューにプッシュして, 検索を継続する
                Q.push(user_id);
            }
        }
    }

    return;
}