Problem:


Score : 100 points

Problem Statement

You are given an undirected graph with N vertices and 0 edges. Process Q queries of the following types.

0 u v: Add an edge (u, v).

1 u v: Print 1 if u and v are in the same connected component, 0 otherwise.

Constraints

1 \leq N \leq 200,000

1 \leq Q \leq 200,000

0 \leq u_i, v_i \lt N

Input

Input is given from Standard Input in the following format:

N Q
t_1 u_1 v_1
t_2 u_2 v_2
:
t_Q u_Q v_Q

出力

For each query of the latter type, print the answer.

Sample Input 1

4 7
1 0 1
0 0 1
0 2 3
1 0 1
1 1 2
0 0 2
1 1 3

Sample Output 1

0
1
0
1



Sample input:
4 7
1 0 1
0 0 1
0 2 3
1 0 1
1 1 2
0 0 2
1 1 3


Sample output:
0
1
0
1

Submission status: Accepted

Solution code:
class UnionFind:
    __slots__ = ["N", "root", "rank"]

    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        while self.root[x] >= 0:
            x = self.root[x]
        return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}


import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
class UnionFind:
    __slots__ = ["N", "root", "rank"]

    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        if self.root[x] < 0:
            return x
        else:
            while self.root[x] >= 0:
                x = self.root[x]
            return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}


import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
class UnionFind:
    __slots__ = ["N", "root", "rank"]

    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        if self.root[x] < 0:
            return x
        while self.root[x] >= 0:
            x = self.root[x]
        return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}


import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        if self.root[x] < 0:
            return x
        else:
            while self.root[x] >= 0:
                x = self.root[x]
            return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}




import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        if self.root[x] < 0:
            return x
        while self.root[x] >= 0:
            x = self.root[x]
        return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}





import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, N):
        """
        N:要素数
        root:各要素の親要素の番号を格納するリスト.
             ただし, root[x] < 0 ならその頂点が根で-root[x]が木の要素数.
        rank:ランク
        """
        self.N = N
        self.root = [-1] * N
        self.rank = [0] * N

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

    def find(self, x):
        """頂点xの根を見つける"""
        while self.root[x] >= 0:
            x = self.root[x]
        return x

    def union(self, x, y):
        """x,yが属する木をunion"""
        # 根を比較する
        # すでに同じ木に属していた場合は何もしない.
        # 違う木に属していた場合はrankを見てくっつける方を決める.
        # rankが同じ時はrankを1増やす
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        elif self.rank[x] > self.rank[y]:
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    def same(self, x, y):
        """xとyが同じグループに属するかどうか"""
        return self.find(x) == self.find(y)

    def count(self, x):
        """頂点xが属する木のサイズを返す"""
        return - self.root[self.find(x)]

    def members(self, x):
        """xが属する木の要素を列挙"""
        _root = self.find(x)
        return [i for i in range(self.N) if self.find == _root]

    def roots(self):
        """森の根を列挙"""
        return [i for i, x in enumerate(self.root) if x < 0]

    def group_count(self):
        """連結成分の数"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す"""
        return {r: self.members(r) for r in self.roots()}


import sys
input = sys.stdin.readline
n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
    t, u, v = map(int, input().split())
    if t:
        print(int(uf.same(u, v)))
    else:
        uf.union(u, v)

Submission status: Accepted

Solution code:
### https://note.nkmk.me/python-union-find/
# 例題
#https://atcoder.jp/contests/practice2/tasks/practice2_a
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.parents = [-1] * n 
    # 各要素の親要素の番号を格納するリスト 
    # 要素が根（ルート）の場合は-(そのグループの要素数)を格納する

  def find(self, x): # 要素xが属するグループの根を返す
    if self.parents[x] < 0:
      return x
    else:
      self.parents[x] = self.find(self.parents[x])
      return self.parents[x]

  def union(self, x, y): # 要素xが属するグループと要素yが属するグループとを併合する
    x = self.find(x)
    y = self.find(y)

    if x == y:
      return

    if self.parents[x] > self.parents[y]:
      x, y = y, x

    self.parents[x] += self.parents[y]
    self.parents[y] = x

  def size(self, x): # 要素xが属するグループのサイズ（要素数）を返す
    return -self.parents[self.find(x)]

  def same(self, x, y): # 要素x, yが同じグループに属するかどうかを返す
    return self.find(x) == self.find(y)

  def members(self, x): # 要素xが属するグループに属する要素をリストで返す
    root = self.find(x)
    return [i for i in range(self.n) if self.find(i) == root]

  def roots(self): # すべての根の要素をリストで返す
    return [i for i, x in enumerate(self.parents) if x < 0]

  def group_count(self): #グループの数を返す
    return len(self.roots())

  def all_group_members(self): #{ルート要素: [そのグループに含まれる要素のリスト], ...}の辞書を返す
    return {r: self.members(r) for r in self.roots()}

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
    #print()での表示用
    #ルート要素: [そのグループに含まれる要素のリスト]を文字列で返す

N, Q = map(int, input().split())
UF = UnionFind(N)
while Q:
  Q -= 1
  t, u, v = input().split()
  u = int(u)
  v = int(v)
  if t == '0':
    UF.union(u, v)
  else:
    if UF.same(u, v):
      print(1)
    else:
      print(0)

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
from libcpp cimport *
from libcpp.vector cimport vector


cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder":
    cdef cppclass dsu:
        dsu()
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

import sys
input = sys.stdin.buffer.readline

N, Q = map(int, input().split())
cdef dsu uf = dsu(N)
for _ in range(Q):
    t, u, v = map(int, input().split())
    if t == 0:
        uf.merge(u, v)
    else:
        if uf.same(u, v):
            print(1)
        else:
            print(0)

"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b solve.pyx')
import solve

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
from libcpp cimport *
from libcpp.vector cimport vector


cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder":
    cdef cppclass dsu:
        dsu()
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()


N, Q = map(int, input().split())
cdef dsu uf = dsu(N)
for _ in range(Q):
    t, u, v = map(int, input().split())
    if t == 0:
        uf.merge(u, v)
    else:
        if uf.same(u, v):
            print(1)
        else:
            print(0)

"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b solve.pyx')
import solve

Submission status: Accepted

Solution code:
# ref https://atcoder.jp/contests/practice2/submissions/16604990
# ref https://aotamasaki.hatenablog.com/entry/2020/09/09/Cython_in_AtCoder

mycode = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
# cython: language_level=3, boundscheck=False, wraparound=False, cdivision=True
from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder":
    cdef cppclass dsu:
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

from libc.stdio cimport scanf, printf
cdef int i
cdef int N, Q
cdef int t, u, v
scanf("%d%d", &N, &Q)
cdef dsu *d = new dsu(N)
for i in range(Q):
    scanf("%d%d%d", &t, &u, &v)
    if t == 0:
        d.merge(u, v)
    else:
        printf("%d\n", d.same(u, v))
"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    with open('solve.pyx', 'w') as f:
        f.write(mycode)
    os.system('cythonize -i -3 solve.pyx')
import solve

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
# cython: language_level=3, boundscheck=False, wraparound=False, cdivision=True
from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder":
    cdef cppclass dsu:
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

from libc.stdio cimport scanf, printf
cdef int i
cdef int N, Q
cdef int t, u, v
scanf("%d%d", &N, &Q)
cdef dsu *d = new dsu(N)
for i in range(Q):
    scanf("%d%d%d", &t, &u, &v)
    if t == 0:
        d.merge(u, v)
    else:
        printf("%d\n", d.same(u, v))
"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b solve.pyx')
import solve

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder":
    cdef cppclass dsu:
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

from libc.stdio cimport scanf, printf
cdef int i
cdef int N, Q
cdef int t, u, v
scanf("%d%d", &N, &Q)
cdef dsu *d = new dsu(N)
for i in range(Q):
    scanf("%d%d%d", &t, &u, &v)
    if t == 0:
        d.merge(u, v)
    else:
        printf("%d\n", d.same(u, v))

"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b solve.pyx')
import solve

Submission status: Accepted

Solution code:
class DisjointSets:#Union-Find
    def __init__(self, n):
        self.nodes = [-1] * n #根にサイズを負の値で格納する。
    def find(self, i):
        if self.nodes[i] < 0: #値が負の場合は根
            return i
        else:
            self.nodes[i] = self.find(self.nodes[i]) #縮約
            return self.nodes[i]
    def unite(self, i, j):
        i = self.find(i)
        j = self.find(j)
        if i == j:
            return
        if self.nodes[i] > self.nodes[j]: #サイズ比較してiの方がサイズが大きいようにする
            i, j = j, i
        self.nodes[i] += self.nodes[j] #大きい方に小さい方を統合しサイズを登録する。
        self.nodes[j] = i # jの親はi
    
    def size(self, i): # 所属する集合の大きさを返す
        i = self.find(i)
        return -self.nodes[i]

n, q = map(int, input().split())
ds = DisjointSets(n)
ans = []
for _ in range(q):
    t, u, v = map(int, input().split())
    if t == 0:
        ds.unite(u, v)
    else:
        ans.append(1 if ds.find(u) == ds.find(v) else 0)
for x in ans:
    print(x)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.buffer.readline


class UnionFind:
    """素集合を木構造として管理する。"""
    def __init__(self, n):
        self.parent = [-1] * n
        self.n = n
        self.cnt = n

    def root(self, x):
        """要素xの代表元を求める。O(α(N))"""
        if self.parent[x] < 0:
            return x
        else:
            self.parent[x] = self.root(self.parent[x])
            return self.parent[x]

    def merge(self, x, y):
        """要素xを含む集合と要素yを含む集合を併合する。O(α(N))"""
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return False
        if self.parent[x] > self.parent[y]:
            x, y = y, x
        self.parent[x] += self.parent[y]
        self.parent[y] = x
        self.cnt -= 1
        return True

    def is_same(self, x, y):
        """要素x, yが同じ集合に属するかどうかを求める。O(α(N))"""
        return self.root(x) == self.root(y)

    def size(self, x):
        """要素xを含む集合の要素数を求める。O(α(N))"""
        return -self.parent[self.root(x)]

    def count(self):
        """集合の個数を求める。O(1)"""
        return self.cnt

    def groups(self):
        """集合を列挙する。list[list[int]]で返す。O(N)"""
        res = [[] for _ in range(self.n)]
        for i in range(self.n):
            res[self.root(i)].append(i)
        return [grp for grp in res if grp]


n, q = map(int, input().split())
queries = [list(map(int, input().split())) for _ in range(q)]


uf = UnionFind(n)
for flag, u, v in queries:
    if flag:
        print(int(uf.is_same(u, v)))
    else:
        uf.merge(u, v)

Submission status: Accepted

Solution code:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

N,Q=map(int,input().split())

uf=UnionFind(N)
for i in range(Q):
    t,u,v=map(int,input().split())

    if t==0:
        uf.union(u,v)
    else:
        if uf.find(u)==uf.find(v):
            print(1)
        else:
            print(0)

Submission status: Accepted

Solution code:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

n, q = map(int, input().split())
uf = UnionFind(n)

for _ in range(q):
    t, u, v = list(map(int, input().split()))
    if t == 0:
        uf.union(u, v)
    if t == 1:
        print(1 if uf.same(u, v) else 0)

Submission status: Accepted

Solution code:
import typing


class DSU:
    '''
    Implement (union by size) + (path compression)
    Reference:
    Zvi Galil and Giuseppe F. Italiano,
    Data structures and algorithms for disjoint set union problems
    '''

    def __init__(self, n: int = 0):
        self._n = n
        self.parent_or_size = [-1] * n

    def merge(self, a: int, b: int) -> int:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        x = self.leader(a)
        y = self.leader(b)

        if x == y:
            return x

        if -self.parent_or_size[x] < -self.parent_or_size[y]:
            x, y = y, x

        self.parent_or_size[x] += self.parent_or_size[y]
        self.parent_or_size[y] = x

        return x

    def same(self, a: int, b: int) -> bool:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        return self.leader(a) == self.leader(b)

    def leader(self, a: int) -> int:
        assert 0 <= a < self._n

        if self.parent_or_size[a] < 0:
            return a

        self.parent_or_size[a] = self.leader(self.parent_or_size[a])
        return self.parent_or_size[a]

    def size(self, a: int) -> int:
        assert 0 <= a < self._n

        return -self.parent_or_size[self.leader(a)]

    def groups(self) -> typing.List[typing.List[int]]:
        leader_buf = [self.leader(i) for i in range(self._n)]

        result = [[] for _ in range(self._n)]
        for i in range(self._n):
            result[leader_buf[i]].append(i)

        return list(filter(lambda r: r, result))


# https://atcoder.jp/contests/practice2/tasks/practice2_a
def main() -> None:
    import sys

    n, q = map(int, sys.stdin.readline().split())
    dsu = DSU(n)

    for _ in range(q):
        t, u, v = map(int, sys.stdin.readline().split())
        if t == 0:
            dsu.merge(u, v)
        if t == 1:
            if dsu.same(u, v):
                print(1)
            else:
                print(0)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
# cython: boundscheck=False
# cython: wraparound=False
from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder" nogil:
    cdef cppclass dsu:
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

from cython.parallel cimport prange
from libc.stdio cimport scanf, printf
cdef int i
cdef int N, Q
cdef int t, u, v
scanf("%d%d", &N, &Q)
cdef dsu *d = new dsu(N)
for i in prange(Q, nogil=1):
    scanf("%d%d%d", &t, &u, &v)
    if t == 0:
        d.merge(u, v)
    else:
        printf("%d\n", d.same(u, v))
"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b -j 36 solve.pyx')
import solve

Submission status: Accepted

Solution code:
code = r"""
# distutils: language=c++
# distutils: include_dirs=/home/contestant/.local/lib/python3.8/site-packages/numpy/core/include
# cython: boundscheck=False
# cython: wraparound=False
from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "/opt/atcoder-stl/atcoder/dsu.hpp" namespace "atcoder" nogil:
    cdef cppclass dsu:
        dsu(int n)
        int merge(int a, int b)
        bool same(int a, int b)
        int leader(int a)
        int size(int a)
        vector[vector[int]] groups()

from cython.parallel cimport prange
from libc.stdio cimport scanf, printf
cdef int i
cdef int N, Q
cdef int t, u, v
scanf("%d%d", &N, &Q)
cdef dsu *d = new dsu(N)
for i in prange(Q, nogil=1):
    scanf("%d%d%d", &t, &u, &v)
    if t == 0:
        d.merge(u, v)
    else:
        printf("%d\n", d.same(u, v))
"""
import os
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    open('solve.pyx', 'w').write(code)
    os.system('cythonize -i -3 -b -j 18 solve.pyx')
import solve

Submission status: Accepted

Solution code:
class UnionFind():
    def __init__(self, n=0):
        self.d = [-1]*n
    
    def find(self, x):
        if self.d[x] < 0: return x
        self.d[x] = self.find(self.d[x])
        return self.d[x]

    def unite(self, x, y):
        x,y=self.find(x),self.find(y)
        if x==y:return False
        if self.d[x] > self.d[y]: x,y=y,x
        self.d[x] += self.d[y]
        self.d[y] = x
        return True

    def same(self, x,y): return self.find(x)==self.find(y)
    def size(self,x): return -self.d[self.find(x)]
    
def main():
  N,Q=map(int,input().split())
  uf = UnionFind(N)
  for i in range(Q):
    t,u,v=map(int,input().split())
    if t:
      print(+(uf.same(u,v)))
    else:
      uf.unite(u,v)
      
if __name__=="__main__":
  main()