Problem:


Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).



Sample input:
3 1
1 2


Sample output:
1

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
P = [-1 for i in range(N)]
def par(a):
    L = []
    while P[a] >= 0:
        L.append(a)
        a = P[a]
    for l in L:
        P[l] = a
    return a
def unite(a, b):
    if par(a) != par(b):
        if P[par(b)] >= P[par(a)]:
            if P[par(b)] == P[par(a)]: P[par(a)] -= 1
            P[par(b)] = par(a)
        else:
            P[par(a)] = par(b)

ans = N - 1
for _ in range(M):
    a, b = map(int, input().split())
    a, b = a-1, b-1
    if par(a) == par(b): continue
    unite(a, b)
    ans -= 1
print(ans)

Submission status: Accepted

Solution code:
import sys; input = sys.stdin.buffer.readline
sys.setrecursionlimit(10**7)
from collections import defaultdict
mod = 10 ** 9 + 7; INF = float("inf")

def getlist():
	return list(map(int, input().split()))

class UnionFind:
	def __init__(self, n):
		self.par = [i for i in range(n + 1)]
		self.rank = [0] * (n + 1)
		self.size = [1] * (n + 1)

	def find(self, x):
		if self.par[x] == x:
			return x
		else:
			self.par[x] = self.find(self.par[x])
			return self.par[x]

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

		if self.rank[x] < self.rank[y]:
			self.size[y] += self.size[x]
			self.size[x] = 0
			self.par[x] = y
		else:
			self.size[x] += self.size[y]
			self.size[y] = 0
			self.par[y] = x
			if self.rank[x] == self.rank[y]:
				self.rank[x] += 1

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

	def getsize(self, x):
		x = self.find(x)
		return self.size[x]


def main():
	N, M = getlist()
	UF = UnionFind(N)
	for i in range(M):
		a, b = getlist()
		a -= 1; b -= 1
		UF.union(a, b)

	#最後に根更新
	for i in range(N):
		UF.par[i] = UF.find(i)

	res = 0
	for i in range(N):
		if UF.size[i] != 0:
			res += 1

	print(res - 1)




if __name__ == '__main__':
	main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from fractions import Fraction
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations, accumulate
from operator import add, mul, sub, itemgetter, attrgetter


import sys
# sys.setrecursionlimit(10**6)
# readline = sys.stdin.buffer.readline
readline = sys.stdin.readline

INF = 1 << 60


def read_int():
    return int(readline())


def read_int_n():
    return list(map(int, readline().split()))


def read_float():
    return float(readline())


def read_float_n():
    return list(map(float, readline().split()))


def read_str():
    return readline().strip()


def read_str_n():
    return readline().strip().split()


def ep(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.perf_counter()
        ret = f(*args, **kwargs)
        e = time.perf_counter()

        ep(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)
        self.__rank = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
            return x
        else:
            a = x
            ul = []
            while a != self.__table[a]:
                ul.append(a)
                a = self.__table[a]
            for u in ul:
                self.__table[u] = a

        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x == y:
            return False

        if self.__rank[x] < self.__rank[y]:
            self.__table[x] = y
            self.__size[y] += self.__size[x]
        else:
            self.__table[y] = x
            self.__size[x] += self.__size[y]
            if self.__rank[x] == self.__rank[y]:
                self.__rank[x] += 1
        return True

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g



@mt
def slv(N, M, AB):
    uf = UnionFind()
    for i in range(1, N+1):
        uf.union(i, i)
    for a, b in AB:
        uf.union(a, b)

    return uf.num_of_group() - 1


def main():
    N, M = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    print(slv(N, M, AB))


if __name__ == '__main__':
    main()

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())

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

    def get_all_members(self):
        pare_d = {}
        for i in range(self.n):
            parent = self.find(i)
            pare_d.setdefault(parent,[])
            pare_d[parent].append(i)
        return list(pare_d.values())

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


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

for _ in range(m):
    a,b = map(int, input().split())
    a-=1
    b-=1
    uf.union(a,b)

cnt = uf.group_count()
ans = max(cnt-1,0)
print(ans)

Submission status: Accepted

Solution code:
'''
自宅用PCでの解答
'''
import math
#import numpy as np
import itertools
import queue
import bisect
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)
mod = 10**9+7
# mod = 998244353
dir = [(-1,0),(0,-1),(1,0),(0,1)]
alp = "abcdefghijklmnopqrstuvwxyz"
INF = 1<<32-1
# INF = 10**18

#UnionFindのクラス,0-indexed
class UnionFind():
    def __init__(self, n):
        self.n = n
        # parents = [-1,0,-4,1,1,1]のように、親の添字かマイナス要素数を表す
        self.parents = [-1] * n

    def find(self, x): # find: xの親がすべてrootになる。これにより計算量削減(O(N) for all (not each))
        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())


def main():
    n,m = map(int,ipt().split())
    uf = UnionFind(n)
    for i in range(m):
        a,b = map(int,ipt().split())
        uf.union(a-1,b-1)
    k = uf.roots()
    print(len(k)-1)

    return None

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n, m = map(int, input().split())


class UnionFind:
    def __init__(self, n):
        self.parent = [-1] * n
        self.rank = [1] * n
        self.count = [1] * n

    def get_root(self, i):
        while self.parent[i] != -1:
            i = self.parent[i]
        return i

    def is_same_tree(self, i, j):
        return self.get_root(i) == self.get_root(j)

    def merge(self, i, j):
        i = self.get_root(i)
        j = self.get_root(j)
        if i == j:
            return

        if self.rank[i] > self.rank[j]:
            self.parent[j] = i
            self.rank[i] = max(self.rank[i], self.rank[j] + 1)
            self.count[i] += self.count[j]
        else:
            self.parent[i] = j
            self.rank[j] = max(self.rank[j], self.rank[i] + 1)
            self.count[j] += self.count[i]


uf = UnionFind(n)
for _ in range(m):
    a, b = map(int, input().split())
    uf.merge(a-1, b-1)
print(uf.parent.count(-1)-1)

Submission status: Accepted

Solution code:
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 [group for group in res if group]


n, m = map(int, input().split())
info = [list(map(int, input().split())) for i in range(m)]

uf = UnionFind(n)
for a, b in info:
    a -= 1
    b -= 1
    uf.merge(a, b)
print(uf.count() - 1)

Submission status: Accepted

Solution code:
import sys, math
from itertools import accumulate
sys.setrecursionlimit(10**9)

def input():
    return sys.stdin.readline()[:-1]

def mi():
    return map(int, input().split())

def ii():
    return int(input())

def i2(n):
    tmp = [list(mi()) for i in range(n)]
    return [list(i) for i in zip(*tmp)]

# unionfind
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())

def main():
    N, M = mi()
    A, B = i2(M)
    
    uf = UnionFind(N)
    for i in range(M):
        uf.union(A[i]-1, B[i]-1)

    print(uf.group_count()-1)

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
class UF():
  def __init__(self, N):
    self._parent=[n for n in range(0, N)]
    self._size=[1] * N

  def find_root(self, x):
    if self._parent[x]==x:return x
    self._parent[x]=self.find_root(self._parent[x])
    return self._parent[x]

  def unite(self, x, y):
    gx=self.find_root(x)
    gy=self.find_root(y)
    if gx==gy:return

    if self._size[gx]<self._size[gy]:
      self._parent[gx]=gy
      self._size[gy]+=self._size[gx]
    else:
      self._parent[gy]=gx
      self._size[gx]+=self._size[gy]

  def size(self, x):
    return self._size[self.find_root(x)]

  def samegroup(self, x, y):
    return self.find_root(x)==self.find_root(y)

  def groupnum(self):
    N=len(self._parent)
    ans=0
    for i in range(N):
      if self.find_root(i)==i:
        ans+=1
    return ans

n,m=map(int,input().split())
UFa=UF(n)
for i in range(m):
  x,y=map(int,input().split())
  UFa.unite(x-1,y-1)
print(UFa.groupnum()-1)

Submission status: Accepted

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

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

    def unite(self, x, y): #和集合の生成
        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): #所属する集合の大きさ
        return -self.parents[self.find(x)]

    def same(self, x, y): #同じ集合に属しているか判定
        return self.find(x) == self.find(y)

    def members(self, x): #同じ集合に属する要素全列挙
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self): #集合のリーダー全列挙
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self): #集合の数
        return len(self.roots())

    def all_group_members(self): #辞書型,{(リーダーの番号):(その集合の要素全列挙)}
        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,m=map(int,input().split())
uf=UnionFind(n)
for i in range(m):
    a,b=map(int,input().split())
    uf.unite(a-1,b-1)
print(uf.group_count()-1)

Submission status: Accepted

Solution code:
class UnionFind():
    n=1
    par=[0]
    rnk=[0]
    def __init__(self,size):
        self.n=size
        self.par=[i for i in range(self.n)]
        self.rnk=[0 for i in range(self.n)]
    def find(self,vertex1):
        if self.par[vertex1]==vertex1:
            return vertex1
        else:
            self.par[vertex1]=self.find(self.par[vertex1])
            return self.par[vertex1]
    def unite(self,vertex1,vertex2):
        vertex1=self.find(vertex1)
        vertex2=self.find(vertex2)
        if vertex1==vertex2:
            return
        if (self.rnk[vertex1]<self.rnk[vertex2]):
            self.par[vertex1]=vertex2
        else:
            self.par[vertex2]=vertex1
            if(self.rnk[vertex1]==self.rnk[vertex2]):
                self.rnk[vertex1]+=1
    def same(self,vetrex1,vertex2):
        return self.find(vetrex1)==self.find(vertex2)

N,M=map(int,input().split())
G=UnionFind(N)
for i in range(M):
    a,b=map(int,input().split())
    G.unite(a-1,b-1)

X=[G.find(i) for i in range(N)]
print(len(set(X))-1)

Submission status: Accepted

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


class UnionFind:
    def __init__(self, N):
        self.par = [-1] * N

    def find(self, x):
        r = x
        while self.par[r] >= 0:
            r = self.par[r]
        while x != r:
            tmp = self.par[x]
            self.par[x] = r
            x = tmp
        return r

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

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

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

N, M = map(int, input().split())
uf = UnionFind(N)
for _ in range(M):
    A, B = map(int, input().split())
    A -= 1
    B -= 1
    uf.unite(A, B)
ans = len(set([uf.find(i) for i in range(N)])) - 1
print(ans)

Submission status: Accepted

Solution code:
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# ------------------- fast io --------------------
from math import gcd, ceil

def pre(s):
    n = len(s)
    pi = [0] * n
    for i in range(1, n):
        j = pi[i - 1]
        while j and s[i] != s[j]:
            j = pi[j - 1]
        if s[i] == s[j]:
            j += 1
        pi[i] = j
    return pi


def prod(a):
    ans = 1
    for each in a:
        ans = (ans * each)
    return ans

def lcm(a, b): return a * b // gcd(a, b)


def binary(x, length=16):
    y = bin(x)[2:]
    return y if len(y) >= length else "0" * (length - len(y)) + y

def getOverlap(a, b):
    return max(0, min(a[1], b[1]) - max(a[0], b[0]) + 1)

def connected_components(n, graph):
    components, visited = [], [False] * n

    def dfs(start):
        component, stack = [], [start]

        while stack:
            start = stack[-1]

            if visited[start]:
                stack.pop()
                continue
            else:
                visited[start] = True
                component.append(start)

            for i in graph[start]:
                if not visited[i]:
                    stack.append(i)

        return component

    for i in range(n):
        if not visited[i]:
            components.append(dfs(i))

    return components

for _ in range(int(input()) if not True else 1):
    #n = int(input())
    n, m = map(int, input().split())
    graph = [[] for _ in range(n+1)]
    for __ in range(m):
        x, y = map(int, input().split())
        graph[x] += [y]
        graph[y] += [x]
    cmp = connected_components(n+1, graph)
    print(len(cmp) - 2)

Submission status: Accepted

Solution code:
n, m = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(m)]


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

    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):  # all_group_members O(N)かかるので注意
        return {r: self.members(r) for r in self.roots()}


adlist = UnionFind(n+1)
for i in range(m):
    a = ab[i][0]
    b = ab[i][1]
    if adlist.same(a, b) == False:
        adlist.union(a, b)
print(adlist.group_count()-2)

Submission status: Accepted

Solution code:

def uf_find(n,p):

    ufl = []

    while p[n] != n:
        ufl.append(n)
        n = p[n]

    for i in ufl:
        p[i] = n

    return n


def uf_union(a,b,p,rank):

    ap = uf_find(a,p)
    bp = uf_find(b,p)

    if ap == bp:
        return True
    else:

        if rank[ap] > rank[bp]:
            p[bp] = ap
        elif rank[ap] < rank[bp]:
            p[ap] = bp
        else:
            p[bp] = ap
            rank[ap] += 1

        return False

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

p = [i for i in range(N)]
rank = [0] * N

for i in range(M):

    A,B = map(int,input().split())
    A -= 1
    B -= 1
    uf_union(A,B,p,rank)

ans = 0
for i in range(N):
    if uf_find(i,p) == i:
        ans += 1
print (ans-1)

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for _ in range(n)]
def LIR(n):
    return [LI() for _ in range(n)]
def SR(n):
    return [S() for _ in range(n)]
def LSR(n):
    return [LS() for _ in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    def root(x):
        if x == par[x]:
            return x
        par[x] = root(par[x])
        return par[x]

    def unite(x,y):
        x = root(x)
        y = root(y)
        if rank[x] < rank[y]:
            par[x] = y
        else:
            par[y] = x
            if rank[x] == rank[y]:
                rank[x] += 1

    n,m = LI()
    par = list(range(n))
    rank = [0]*n
    s = n-1
    for _ in range(m):
        a,b = LI()
        a -= 1
        b -= 1
        if root(a) != root(b):
            s -= 1
            unite(a,b)
    print(s)
    return

#Solve
if __name__ == "__main__":
    solve()

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self,N):
        self.par=[i for i in range(N)]
        self.siz=[1 for _ in range(N)]
        self.rank=[0 for _ in range(N)]
    def find(self,x):
        if self.par[x]==x:
            return x
        else:
            self.par[x]=self.find(self.par[x])
            return self.par[x]
    def union(self,a,b):
        a=self.find(a)
        b=self.find(b)
        if a==b:
            return 0
        else:
            if self.rank[a]>self.rank[b]:
                self.par[b]=a
                self.siz[a]+=self.siz[b]
            else:
                self.par[a]=b
                self.siz[b]+=self.siz[a]
                if self.rank[a]==self.rank[b]:
                    self.rank[b]+=1
    def size(self,a):
        return self.siz[self.find(a)]
    def same(self,a,b):
        return self.find(a)==self.find(b)

N,M=map(int,input().split())
DSU=UnionFind(N)
for _ in range(M):
    A,B=map(lambda x:int(x)-1,input().split())
    DSU.union(A,B)
s=set([DSU.find(i) for i in range(N)])
print(len(s)-1)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, n):
        self.parent = list(range(n)) #親ノード
        self.size = [1]*n #グループの要素数
 
    def root(self, x): #root(x): xの根ノードを返す．
        while self.parent[x] != x:
            self.parent[x] = self.parent[self.parent[x]]
            x = self.parent[x]
        return x 
 
    def merge(self, x, y): #merge(x,y): xのいる組とyのいる組をまとめる
        x, y = self.root(x), self.root(y)
        if x == y: return False
        if self.size[x] < self.size[y]: x,y=y,x #xの要素数が大きいように
        self.size[x] += self.size[y] #xの要素数を更新
        self.parent[y] = x #yをxにつなぐ
        return True
 
    def issame(self, x, y): #same(x,y): xとyが同じ組ならTrue
        return self.root(x) == self.root(y)
        
    def getsize(self,x): #size(x): xのいるグループの要素数を返す
        return self.size[self.root(x)]

# coding: utf-8
# Your code here!
import sys
readline = sys.stdin.readline
read = sys.stdin.read

n,m = map(int,readline().split())

UF = UnionFind(n)

ans = n-1
for i in range(m):
    a,b = map(int,readline().split())
    if UF.merge(a-1,b-1):
        ans -= 1

print(ans)

Submission status: Accepted

Solution code:
n,m=map(int,input().split())

class UnionFind():
    def __init__(self,num):
        self.n = num         #class内変数nに、外部から入力した値numを代入
        self.parents = [-1 for i in range(self.n)]
          #parentsは要素の親(1こ上のやつ)番号0~n-1を格納、自分が最親なら-(要素数)を格納(初期値は-1)

    #xの最親は誰？
    def find(self,x):
        if self.parents[x]<0:
            return x
        else:
            self.parents[x]=self.find(self.parents[x]) #再帰して1番上までいってる
                #調べながらparentsの値を更新してる！（経路圧縮）
            return self.parents[x]

    #結合せよ
    #xの親とyの親をくっつける
    def union(self,x,y):
        xx=self.find(x)  #xxはxの最親
        yy=self.find(y)  #yyはyの最親
        if xx==yy:
            return     #同じ屋根の下にあった場合は何もしない
        else:
            size_xx=abs(self.parents[xx]) #xが含まれる木のサイズ
            size_yy=abs(self.parents[yy]) #yが含まれる木のサイズ
            if size_xx>size_yy:
                xx,yy=yy,xx  #yyの方が大きい木、ってことにする

            self.parents[yy]+=self.parents[xx] #大きい木のサイズ更新
            self.parents[xx]=yy   #サイズが小さい木を大きい木に接ぐ

    #xの属する木の大きさ（まあunionでも使ったけど）
    def size(self,x):
        xx=self.find(x)
        return abs(self.parents[xx])

    #xとyはこの空の続く場所にいますか　いつものように笑顔でいてくれますか　今はただそれを願い続ける
    def same(self,x,y):
        return 1 if self.find(x)==self.find(y) else 0

    #xと　同じ木にいる　メンバーは？
    def members(self,x):
        xx=self.find(x)
        return [i for i in range(self.n) if self.find(i)==xx]
             #ifの条件式に漏れたら無視

    #最親だけを並べあげる
    def roots(self):
        return [i for i,x in enumerate(self.parents) if x < 0]
        #いやこれは天才すぎる、basisのenumerate.py参照

    #すべての最親について、メンバーを辞書で
    def all_group_members(self):
        return {r:self.members(r) for r in self.roots()}

    #グループ分けどうなりましたか、２重リストで
    def state_grouping(self):
        return list(self.all_group_members().values())

uf=UnionFind(n)
for i in range(m):
    a,b=map(int,input().split())
    a-=1;b-=1
    uf.union(a,b)

print(len(uf.roots())-1)

Submission status: Accepted

Solution code:
N,M=map(int,input().split())
belong=list()
group=list()

def init(X):
  global belong
  global group
  belong=list(range(X))
  group=[[i] for i in range(X)]

def unite(x,y):
  if len(group[belong[x]])<len(group[belong[y]]):
    x,y=y,x
  if belong[x]==belong[y]:
    return True
  z=belong[y]
  for i in range(len(group[z])):
    belong[group[z][-1]]=belong[x]
    group[belong[x]].append(group[z][-1])
    del group[z][-1]
  return False

init(N)
a,b=0,0
for i in range(M):
  a,b=map(int,input().split())
  unite(a-1,b-1)
P=0
for i in range(N):
  if len(group[i]):
    P+=1
print(P-1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
n, m = map(int,input().split())
C = [list(map(int,input().split())) for i in range(m)]
for i in range(m):
    for j in range(2):
        C[i][j] -= 1

class UnionFind():  # DSU（disjoint set union, 素集合データ構造）と同じ
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def leader(self, x):  # xが属する連結成分の代表元
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.leader(self.parents[x])
            return self.parents[x]

    def size(self, x):  # xが属する連結成分のサイズ
        return -self.parents[self.leader(x)]

    def merge(self, x, y):  # xとyを辺でつなぐ
        x = self.leader(x)
        y = self.leader(y)
        if x == y:
            return x
        if self.parents[x] > self.parents[y]:
            x, y = y, x
        self.parents[x] += self.parents[y]
        self.parents[y] = x
        return x

    def same(self, x, y):  # xとyが連結かどうか
        return self.leader(x) == self.leader(y)

    def groups(self):  # 連結成分ごとの頂点リスト
        n = self.n
        leader_index = [-1] * n
        ind = 0
        for i in range(n):
            if self.parents[i] < 0:
                leader_index[i] = ind
                ind += 1
        ANS = [[] for i in range(ind)]
        for i in range(n):
            ld = self.leader(i)
            ANS[leader_index[ld]].append(i)
        return ANS

    def n_cc(self):  # グラフ全体の連結成分の数
        A = [i for i in self.parents if i < 0]
        return len(A)

U = UnionFind(n)
for i in range(m):
    U.merge(C[i][0],C[i][1])
print(U.n_cc()-1)