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: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
#define N 100000
int *groupID;
int groupNum=0;//the number of groups
int n;//the number of users
void initGroupID(void);
void grouping(int,int);
int isGrouped(int,int);
void printGroup(void);//debugging
int main(void)
{
  int i;//counter
  int user1,user2;
  int num;//the number of relaions / questions
  scanf("%d",&n);
  groupID=(int*)malloc(sizeof(int)*n);
  initGroupID();
  scanf("%d",&num);
  for(i=0;i<num;i++)
    {
      scanf("%d%d",&user1,&user2);
      grouping(user1,user2);
    }
  //printGroup();
  scanf("%d",&num);
  for(i=0;i<num;i++)
    {
      scanf("%d%d",&user1,&user2);
      if(isGrouped(user1,user2)==1) printf("yes\n");
      else printf("no\n");
    }
  return 0;
}
void initGroupID(void)
{
  int i;//counter
  for(i=0;i<n;i++) groupID[i]=0;
}
void grouping(int user1,int user2)
{
  int i;//counter
  if(groupID[user1]==0&&groupID[user2]==0)
    {
      groupNum++;
      groupID[user1]=groupID[user2]=groupNum;
    }
  else if(groupID[user1]==0&&groupID[user2]!=0) groupID[user1]=groupID[user2];
  else if(groupID[user2]==0&&groupID[user1]!=0) groupID[user2]=groupID[user1];
  else if(groupID[user1]!=0&&groupID[user2]!=0&&groupID[user1]!=groupID[user2])
    {
      for(i=0;i<n;i++)
        {
          if(groupID[i]==groupID[user2]&&i!=user2) groupID[i]=groupID[user1];
        }
      groupID[user2]=groupID[user1];
    }
}
int isGrouped(int user1,int user2)
{
  if(groupID[user1]==groupID[user2]&&groupID[user1]!=0) return 1;
  else return 0;
}
void printGroup(void)
{
  int i;//counter
  for(i=0;i<n;i++)
    {
      printf("%d: Group %d\n",i,groupID[i]);
    }
}