Problem:


  MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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



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

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def assign_color():
    _id = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _id)
            _id += 1
    return None


def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color
    while vertices_stack:
        current_vertex = vertices_stack[-1]
        vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())

    relation_info = _input[1:relation_num + 1]

    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]

    adj_list = tuple([] for _ in range(vertices_num))
    vertices_status_list = [-1] * vertices_num

    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)

    assign_color()

    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def assign_color():
    _color = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _color)
            _color += 1
    return None


def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color
    while vertices_stack:
        current_vertex = vertices_stack[-1]
        vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())

    relation_info = _input[1:relation_num + 1]

    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]

    adj_list = [[] for _ in range(vertices_num)]
    vertices_status_list = [-1] * vertices_num

    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)

    assign_color()

    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def assign_color():
    _color = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _color)
            _color += 1
    return None


def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color
    while vertices_stack:
        current_vertex = vertices_stack[-1]
        vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())

    relation_info = _input[1:relation_num + 1]

    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]

    adj_list = tuple([[] for _ in range(vertices_num)])
    vertices_status_list = [-1] * vertices_num

    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)

    assign_color()

    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def assign_color():
    _color = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _color)
            _color += 1
    return None


def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color

    while vertices_stack:
        current_vertex = vertices_stack[-1]
        vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None


def solve():
    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)

    assign_color()

    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")
    return vertices_status_list


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())

    relation_info = _input[1:relation_num + 1]

    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]

    adj_list = tuple([[] for _ in range(vertices_num)])
    vertices_status_list = [-1] * vertices_num
    ans = solve()

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def assign_color():
    _color = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _color)
            _color += 1
    return None


def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color

    while vertices_stack:
        current_vertex = vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None


def solve():
    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)

    assign_color()

    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")
    return vertices_status_list


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())

    relation_info = _input[1:relation_num + 1]

    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]

    adj_list = tuple([[] for _ in range(vertices_num)])
    vertices_status_list = [-1] * vertices_num
    ans = solve()

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
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

output:
yes
yes
no

"""

import sys


def assign_color():
    current_color = 1
    for v in range(vertices):
        if color[v] == -1:
            graph_dfs(v, current_color)
            current_color += 1
    return None


def graph_dfs(vertex, current_color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    color[vertex] = current_color

    while vertices_stack:
        current_vertex = vertices_stack.pop()
        for v in adj_table[current_vertex]:
            if color[v] == -1:
                color[v] = current_color
                vertices_stack.append(v)
    return None


def solve():
    for relation in relation_info:
        key, value = map(int, relation)
        adj_table[key].append(value)
        adj_table[value].append(key)

    assign_color()

    # print(adj_list)
    for question in questions:
        source, target = map(int, question)
        if color[source] == color[target]:
            print("yes")
        else:
            print("no")
    return color


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices, relations = map(int, _input[0].split())

    relation_info = map(lambda x: x.split(), _input[1:relations + 1])

    q_num = int(_input[relations + 1])
    questions = map(lambda x: x.split(), _input[relations + 2:])

    adj_table = tuple([] for _ in range(vertices))
    color = [-1] * vertices
    ans = solve()

Submission status: Accepted

Solution code:
from collections import deque


def dfs(G, C, id, color):
    S = deque()
    S.append(id)
    C[id] = color

    while S:
        u = S.pop()
        #S = S[:-1]  # pop
        for i in range(len(G[u])):
            v = G[u][i]
            if C[v] == -1:
                C[v] = color
                S.append(v)


if __name__ == '__main__':
    # ??????????????\???
    num_of_users, num_of_links = [int(x) for x in input().split(' ')]
    links = []
    for _ in range(num_of_links):
        links.append(list(map(int, input().split(' '))))
    num_of_queries = int(input())
    queries = []
    for _ in range(num_of_queries):
        queries.append(list(map(int, input().split(' '))))

    # ???????????????
    G = [[] for _ in range(100000)]
    C = [-1] * 100000
    for f, t in links:
        G[f].append(t)
        G[t].append(f)

    color = 1
    for id in range(num_of_users):
        if C[id] == -1:
            dfs(G, C, id, color)
        color += 1

    # ???????????????
    for x, y in queries:
        if C[x] == C[y]:
            print('yes')
        else:
            print('no')

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
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

output:
yes
yes
no

"""

import sys


def assign_color():
    current_color = 1
    for v in range(v_num):
        if color[v] == -1:
            graph_dfs(v, current_color)
            current_color += 1
    return None


def graph_dfs(current, current_color):
    stack = list()
    stack.append(current)
    color[current] = current_color

    while stack:
        current = stack.pop()
        for v in adj_table[current]:
            if color[v] == -1:
                color[v] = current_color
                stack.append(v)
    return None


def solve():
    for edge in edges:
        source, target = map(int, edge)
        adj_table[source].append(target)
        adj_table[target].append(source)

    assign_color()

    for question in questions:
        q_source, q_target = map(int, question)
        if color[q_source] == color[q_target]:
            print("yes")
        else:
            print("no")
            
    return color


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    v_num, r_num = map(int, _input[0].split())

    edges = map(lambda x: x.split(), _input[1:r_num + 1])

    q_num = int(_input[r_num + 1])
    questions = map(lambda x: x.split(), _input[r_num + 2:])

    adj_table = tuple([] for _ in range(v_num))
    color = [-1] * v_num
    ans = solve()

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
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

output:
yes
yes
no

"""

import sys


def assign_color():
    v_color = 0
    for v in range(v_num):
        if color[v] == -1:
            graph_dfs(v, v_color)
            # use int as color to represent different connected groups
            v_color += 1
    return None


def graph_dfs(current, v_color):
    stack = list()
    stack.append(current)
    color[current] = v_color

    while stack:
        current = stack.pop()
        for adj in adj_table[current]:
            if color[adj] == -1:
                color[adj] = v_color
                stack.append(adj)
    return None


def solve():
    for edge in edges:
        source, target = map(int, edge)
        adj_table[source].append(target)
        adj_table[target].append(source)

    assign_color()

    for question in questions:
        q_source, q_target = map(int, question)
        if color[q_source] == color[q_target]:
            print("yes")
        else:
            print("no")

    return color


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    v_num, r_num = map(int, _input[0].split())

    edges = map(lambda x: x.split(), _input[1:r_num + 1])

    q_num = int(_input[r_num + 1])
    questions = map(lambda x: x.split(), _input[r_num + 2:])

    adj_table = tuple([] for _ in range(v_num))
    color = [-1] * v_num
    ans = solve()

Submission status: Accepted

Solution code:
import sys
from collections import deque

def debug(x, table):
    for name, val in table.items():
        if x is val:
            print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
            return None

def paint_col(adj, cols, i, col):
    nxt = deque([i])

    while nxt:
        u = nxt.popleft()
        cols[u] = col
        for child in adj[u]:
            if cols[child] == 0:
                nxt.append(child)

def solve():
    n, m = map(int, input().split())
    adj = [[] for i in range(n)]

    for i in range(m):
        s, t = map(int, input().split())
        adj[s].append(t)
        adj[t].append(s)

    cols = [0] * n
    col = 1

    for i in range(n):
        if cols[i] == 0:
            paint_col(adj, cols, i, col)
            col += 1

    q = int(input())

    for i in range(q):
        s, t = map(int, input().split())

        if cols[s] == cols[t]:
            ans = 'yes'
        else:
            ans = 'no'

        print(ans)

if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
import sys
from collections import deque

def debug(x, table):
    for name, val in table.items():
        if x is val:
            print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
            return None

def paint_col(adj, cols, i, col):
    nxt = deque([i])

    while nxt:
        u = nxt.popleft()
        cols[u] = col
        for child in adj[u]:
            if cols[child] == 0:
                nxt.append(child)

def solve():
    n, m = map(int, sys.stdin.readline().split())
    adj = [[] for i in range(n)]

    for i in range(m):
        s, t = map(int, sys.stdin.readline().split())
        adj[s].append(t)
        adj[t].append(s)

    cols = [0] * n
    col = 1

    for i in range(n):
        if cols[i] == 0:
            paint_col(adj, cols, i, col)
            col += 1

    q = int(sys.stdin.readline())

    for i in range(q):
        s, t = map(int, sys.stdin.readline().split())

        if cols[s] == cols[t]:
            ans = 'yes'
        else:
            ans = 'no'

        print(ans)

if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
import sys

def debug(x, table):
    for name, val in table.items():
        if x is val:
            print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
            return None

def paint_col(adj, cols, i, col):
    nxt = [i]

    while nxt:
        u = nxt[-1]
        try:
            v = next(adj[u])
            if cols[v] == 0:
                cols[v] = col
                nxt.append(v)
        except StopIteration:
            nxt.pop()
            cols[u] = col

def solve():
    n, m = map(int, sys.stdin.readline().split())
    adj = [[] for i in range(n)]

    for i in range(m):
        s, t = map(int, sys.stdin.readline().split())
        adj[s].append(t)
        adj[t].append(s)

    cols = [0] * n
    col = 1
    adj = list(map(iter, adj))

    for i in range(n):
        if cols[i] == 0:
            paint_col(adj, cols, i, col)
            col += 1

    # debug(cols, locals())

    q = int(sys.stdin.readline())

    for i in range(q):
        s, t = map(int, sys.stdin.readline().split())

        if cols[s] == cols[t]:
            ans = 'yes'
        else:
            ans = 'no'

        print(ans)

if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
from collections import deque


def bfs(root):
    global time
    Q = deque()
    distance[root] = 0
    Q.append(root)
    i = root
    while len(Q) > 0:
        i = Q.popleft()
        for v in adjDict[i]:
            if color[v] == 'white':
                Q.append(v)
                color[v] = 'gray'
                distance[v] = distance[i] + 1
        color[i] = 'black'
        label[i] = time


firstline = list(map(int, input().split()))

n = firstline[0]
adjDict = {i: [] for i in range(n)}
color = ['white'] * n
distance = [-1] * n
label = [-1] * n

m = firstline[1]
for _ in range(m):
    adj = list(map(int, input().split()))
    adjDict[adj[0]].append(adj[1])
    adjDict[adj[1]].append(adj[0])

time = 0
for i in range(n):
    if color[i] == 'white':
        bfs(i)
        time += 1

q = int(input())
for _ in range(q):
    question = list(map(int, input().split()))
    if label[question[0]] == label[question[1]]:
        print('yes')
    else:
        print('no')

Submission status: Accepted

Solution code:
import sys
import os
import pprint

#fd = os.open('ALDS1_11_D-3.txt', os.O_RDONLY)
#os.dup2(fd, sys.stdin.fileno())

"""connected components"""

l = list(map(int, input().split()))
DEBUG = False

# node num
n = l[0]

# relation num
m = l[1]

# each node color
colors = [None] * n

rel_list = []
for _ in range(n):
    rel_list.append([])
# relation
for _ in range(m):
    l = list(map(int, input().split()))
    s = l[0]
    t = l[1]
    rel_list[s].append(t)
    rel_list[t].append(s)

if DEBUG:
    print(rel_list)

# coloring by DFS or BFS
for node_index in range(n):

    stack = []
    if colors[node_index] is None:
        stack.append(node_index)
        while stack:
            # process top of stack
            top = stack.pop()
            colors[top] = node_index

            relations = rel_list[top]
            for relation in relations:
                if colors[relation] is None:
                    stack.append(relation)

if DEBUG:
    print(colors)

# question num
q = int(input())

for _ in range(q):
    l = list(map(int, input().split()))
    s = l[0]
    t = l[1]
    if colors[s] == colors[t]:
        print('yes')
    else:
        print('no')

Submission status: Accepted

Solution code:
def grouping(G):
  gid_list = [0] * len(G)

  gid = 1
  for i, _ in enumerate(G):
    if gid_list[i] > 0: continue
    q = [i]
    while len(q) > 0:
      v = q.pop(0)
      gid_list[v] = gid
      for v in sorted(G[v]):
        if gid_list[v] <= 0: q.append(v)
    gid += 1
  return gid_list

u, n = map(int, input().split())
G = [[] for _ in range(u)]
for _ in range(n):
  a, b = map(int, input().split())
  if b not in G[a]: G[a].append(b)
  if a not in G[b]: G[b].append(a)

gid_list = grouping(G)

q = int(input())
for _ in range(q):
  s, t = map(int, input().split())
  if gid_list[s] == gid_list[t]:
    print("yes")
  else:
    print("no")

Submission status: Accepted

Solution code:
n,m = map(int, input().split())
SNS = {i:[] for i in range(n)}
for i in range(m):
 s,t = map(int, input().split())
 SNS[s].append(t)
 SNS[t].append(s)

color = [None] * n
S = []
def dfs(r, c):
 S.append(r)
 color[r] = c
 while len(S) != 0:
  u = S.pop()
  for i in SNS[u]:
   if color[i] == None:
    color[i] = c
    S.append(i)
id = 0
for i in range(n):
 if color[i] == None:
  id += 1
  dfs(i, id)

q = int(input())
for i in range(q):
 s,t = map(int, input().split())
 if color[s] == color[t]:
  print("yes")
 else:
  print("no")

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor(G):
    n = len(G)
    C = [-1 for i in range(n)]
    for i in range(n):
        if C[i] == -1:
            C = BFS(G, i, C)
    return C

#@profile
def BFS(G, start, C):
    n = len(G)
    Q = []

    Q.append(start)
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
    
    return C

def main():
    
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]

    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)

    C = assignColor(G)
        
    q = int(input())
    
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")
            
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
 
import sys
 
 
def assign_color():
    _color = 1
    for m in range(vertices_num):
        if vertices_status_list[m] == -1:
            graph_dfs(m, _color)
            _color += 1
    return None
 
 
def graph_dfs(vertex, color):
    vertices_stack = list()
    vertices_stack.append(vertex)
    vertices_status_list[vertex] = color
 
    while vertices_stack:
        current_vertex = vertices_stack[-1]
        vertices_stack.pop()
        for v in adj_list[current_vertex]:
            if vertices_status_list[v] == -1:
                vertices_status_list[v] = color
                vertices_stack.append(v)
    return None
 
 
def solve():
    for relation in relation_info:
        key, value = map(int, relation.split())
        adj_list[key].append(value)
        adj_list[value].append(key)
 
    assign_color()
 
    # print(adj_list)
    for question in question_list:
        start, target = map(int, question.split())
        if vertices_status_list[start] == vertices_status_list[target]:
            print("yes")
        else:
            print("no")
    return vertices_status_list
 
 
if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices_num, relation_num = map(int, _input[0].split())
 
    relation_info = _input[1:relation_num + 1]
 
    question_num = int(_input[relation_num + 1])
    question_list = _input[relation_num + 2:]
 
    adj_list = tuple([[] for _ in range(vertices_num)])
    vertices_status_list = [-1] * vertices_num
    ans = solve()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor(G):
    n = len(G)
    C = [-1 for i in range(n)]
    for i in range(n):
        if C[i] == -1:
            C = BFS(G, i, C)
    return C

#@profile
def BFS(G, start, C):
    n = len(G)
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
    
    return C

def main():
    
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]

    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)

    C = assignColor(G)
        
    q = int(input())
    
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")
            
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor():
    C = [-1 for i in range(n)]
    for i in range(n):
        if C[i] == -1:
            C = BFS(G, i, C)
    return C

#@profile
def BFS(G, start, C):
    n = len(G)
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
    
    return C

def main():
    
    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)

    C = assignColor()
        
    q = int(input())
    
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")
            
if __name__ == "__main__":
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]

    main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor():
    C = [-1 for i in range(n)]
    for i in range(n):
        if C[i] == -1:
            C = BFS(i, C)
    return C

#@profile
def BFS(start, C):
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
    
    return C

def main():
    
    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)

    C = assignColor()
        
    q = int(input())
    
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")
            
if __name__ == "__main__":
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]

    main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor():
    global C
    for i in range(n):
        if C[i] == -1:
            C = BFS(i, C)

#@profile
def BFS(start, C):
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
    
    return C

if __name__ == "__main__":
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]
    C = [-1]*n
    
    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)
    assignColor()
    q = int(input())
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor():
    global C
    for i in range(n):
        if C[i] == -1:
            #BFS(i)
            DFS(i)
            
#@profile
def BFS(start):
    global C
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]

#@profile
def DFS(start):
    global C
    S = [start]
    C[start] = start
    while len(S) != 0:
        u = S.pop(0)
        for i in G[u]:
            if C[i] == -1:
                C[i] = start
                S.append(i)

if __name__ == "__main__":
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]
    C = [-1]*n
    
    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)
    assignColor()
    q = int(input())
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

def assignColor():
    for i in range(n):
        if C[i] == -1:
            #BFS(i)
            DFS(i)
            
#@profile
def BFS(start):
    global C
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]

#@profile
def DFS(start):
    S = [start]
    C[start] = start
    while len(S) != 0:
        u = S.pop(0)
        for i in G[u]:
            if C[i] == -1:
                C[i] = start
                S.append(i)

if __name__ == "__main__":
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]
    C = [-1]*n
    
    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)
    assignColor()
    q = int(input())
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys


def assignColor():
    for i in range(n):
        if C[i] == -1:
            #BFS(i)
            DFS(i)

def BFS(start):
    global C
    Q = [start]
    C[start] = start

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if C[i] == -1] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]

#@profile
def DFS(start):
    S = [start]
    C[start] = start
    while len(S) != 0:
        u = S.pop(0)
        for i in G[u]:
            if C[i] == -1:
                C[i] = start
                S.append(i)

if __name__ == "__main__":
    _input = sys.stdin.readlines()
    n, m = list(map(int, _input[0].split()))
    G = [[] for i in range(n)]
    C = [-1]*n
    
    for i in range(m):
        s, t = list(map(int, _input[i+1].split()))
        G[s].append(t)
        G[t].append(s)
    assignColor()
    q = int(_input[m+1])
    for i in range(q):
        s, t = list(map(int, _input[m+i+2].split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")