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:

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

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

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


def main():
    N, M = map(int, input().split())

    uf = UnionFind(N)

    for m in range(M):
        A, B = map(int, input().split())
        A, B = A-1, B-1
        uf.union(A, B)
    
    print(uf.group_count() - 1)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
# import sys
# import math #sqrt,gcd,pi
# import decimal
import queue # queue
import bisect
# import heapq # priolity-queue
# from time import time
# from itertools import product,permutations,\
    # combinations,combinations_with_replacement
# 重複あり順列、順列、組み合わせ、重複あり組み合わせ
# import collections # deque
# from operator import itemgetter,mul
# from fractions import Fraction
# from functools import reduce

mod = int(1e9+7)
# mod = 998244353
INF = 1<<50

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

def main():
    n,m = readInt()
    road = [[] for i in range(n)]
    for i in range(m):
        a,b = readInt()
        road[a-1].append(b-1)
        road[b-1].append(a-1)
    ans = 0
    city = set(i for i in range(n))
    while len(city):
        q = queue.Queue()
        q.put(city.pop())
        visit = set()
        while not q.empty():
            x = q.get()
            visit.add(x)
            for i in road[x]:
                if i not in visit:
                    q.put(i)
                    city.discard(i)
        if len(city):
            ans += 1
    print(ans)
    return

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 same(self, x, y):
        return self.find(x) == self.find(y)
    
N,M=map(int,input().split())
uf=UnionFind(N)
for i in range(M):
    a,b=map(int,input().split(' '))
    uf.union(a-1,b-1)

ans=sum([1 for i in uf.parents if i<0])-1
print(ans)

Submission status: Accepted

Solution code:

N,M = map(int, input().split())
A = [-1 for i in range(M)]
B = [-1 for i in range(M)]
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())

for i in range(M):
    A[i],B[i] = map(int, input().split())

uf = UnionFind(N)

for i in range(M):
    uf.union(A[i]-1,B[i]-1)

print(uf.group_count()-1)

Submission status: Accepted

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

class UnionFindVerSize():
    def __init__(self, N):
        """ N個のノードのUnion-Find木を作成する """
        # 親の番号を格納する。自分が親だった場合は、自分の番号になり、それがそのグループの番号になる
        self._parent = [n for n in range(0, N)]
        # グループのサイズ（個数）
        self._size = [1] * N

    def find_root(self, x):
        """ xの木の根(xがどのグループか)を求める """
        if self._parent[x] == x: return x
        self._parent[x] = self.find_root(self._parent[x]) # 縮約
        return self._parent[x]

    def unite(self, x, y):
        """ xとyの属するグループを併合する """
        gx = self.find_root(x)
        gy = self.find_root(y)
        if gx == gy: return

        # 小さい方を大きい方に併合させる（木の偏りが減るので）
        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 get_size(self, x):
        """ xが属するグループのサイズ（個数）を返す """
        return self._size[self.find_root(x)]

    def is_same_group(self, x, y):
        """ xとyが同じ集合に属するか否か """
        return self.find_root(x) == self.find_root(y)

    def calc_group_num(self):
        """ グループ数を計算して返す """
        N = len(self._parent)
        ans = 0
        for i in range(N):
            if self.find_root(i) == i:
                ans += 1
        return ans
      
uf = UnionFindVerSize(n)

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

a = uf.calc_group_num()
print(a-1)

Submission status: Accepted

Solution code:
from sys import setrecursionlimit

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

    def union(self, a, b):
        assert 0 <= a < self._n
        assert 0 <= b < self._n
        x, y = self.find(a), self.find(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, b):
        assert 0 <= a < self._n
        assert 0 <= b < self._n
        return self.find(a) == self.find(b)

    def find(self, a):
        assert 0 <= a < self._n
        if self.parent_or_size[a] < 0: return a
        self.parent_or_size[a] = self.find(self.parent_or_size[a])
        return self.parent_or_size[a]

    def size(self, a):
        assert 0 <= a < self._n
        return -self.parent_or_size[self.find(a)]

    def groups(self):
        find_buf = [self.find(i) for i in range(self._n)]
        result = [[] for _ in range(self._n)]
        for i in range(self._n): result[find_buf[i]].append(i)
        return [r for r in result if r != []]

N, M = map(int,input().split())
uf = UnionFind(N)
setrecursionlimit(10**9+7)

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

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

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,M=map(int,input().split())
AB=[list(map(int,input().split())) for i in range(M)]

uf = UnionFind(N)
for a,b in AB:
    uf.union(a-1,b-1)

print(uf.group_count() - 1)

Submission status: Accepted

Solution code:
## necessary imports
import sys
input = sys.stdin.readline
# biesect_left is essentially an equivalent of lower_bound function in
# cpp and returns the first index not smaller than x.
from bisect import bisect_left;
from bisect import bisect_right;
from math import ceil, factorial;

def ceil(x):
    if x != int(x):
        x = int(x) + 1;
    return x;
    
# swap_array function
def swaparr(arr, a,b):
    temp = arr[a];
    arr[a] = arr[b];
    arr[b] = temp;

## gcd function
def gcd(a,b):
    if b == 0:
        return a;
    return gcd(b, a % b);

## nCr function efficient using Binomial Cofficient
def nCr(n, k, modulus = 1): 
    if(k > n - k): 
        k = n - k; 
    res = 1;
    for i in range(k): 
        res = res * (n - i);
        res = res / (i + 1);
        res %= modulus; 
    return int(res);

## prime factorization
def primefs(n):
    ## if n == 1    ## calculating primes
    primes = {}
    while(n%2 == 0 and n > 0):
        primes[2] = primes.get(2, 0) + 1
        n = n//2
    for i in range(3, int(n**0.5)+2, 2):
        while(n%i == 0 and n > 0):
            primes[i] = primes.get(i, 0) + 1
            n = n//i
    if n > 2:
        primes[n] = primes.get(n, 0) + 1
    ## prime factoriazation of n is stored in dictionary
    ## primes and can be accesed. O(sqrt n)
    return primes

## MODULAR EXPONENTIATION FUNCTION
def power(x, y, p): 
    res = 1
    x = x % p  
    if (x == 0) : 
        return 0
    while (y > 0) : 
        if ((y & 1) == 1) : 
            res = (res * x) % p 
        y = y >> 1      
        x = (x * x) % p 
    return res 

## DISJOINT SET UNINON FUNCTIONS
def swap(a,b):
    temp = a
    a = b
    b = temp
    return a,b;

# find function with path compression included (recursive)
# def find(x, link):
#     if link[x] == x:
#         return x
#     link[x] = find(link[x], link);
#     return link[x];

# find function with path compression (ITERATIVE)
def find(x, link):
    p = x;
    while( p != link[p]):
        p = link[p];
    
    while( x != p):
        nex = link[x];
        link[x] = p;
        x = nex;
    return p;


# the union function which makes union(x,y)
# of two nodes x and y
def union(x, y, link, size):
    x = find(x, link)
    y = find(y, link)
    if size[x] < size[y]:
        x,y = swap(x,y)
    if x != y:
        size[x] += size[y]
        link[y] = x

## returns an array of boolean if primes or not USING SIEVE OF ERATOSTHANES
def sieve(n): 
    prime = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1
    return prime

#### PRIME FACTORIZATION IN O(log n) using Sieve ####
MAXN = int(1e6 + 5)
def spf_sieve():
    spf[1] = 1;
    for i in range(2, MAXN):
        spf[i] = i;
    for i in range(4, MAXN, 2):
        spf[i] = 2;
    for i in range(3, ceil(MAXN ** 0.5), 2):
        if spf[i] == i:
            for j in range(i*i, MAXN, i):
                if spf[j] == j:
                    spf[j] = i;
    ## function for storing smallest prime factors (spf) in the array

################## un-comment below 2 lines when using factorization #################
# spf = [0 for i in range(MAXN)]
# spf_sieve();
def factoriazation(x):
    ret = {};
    while x != 1:
        ret[spf[x]] = ret.get(spf[x], 0) + 1;
        x = x//spf[x]
    return ret;
    ## this function is useful for multiple queries only, o/w use
    ## primefs function above. complexity O(log n)

## taking integer array input
def int_array():
    return list(map(int, input().strip().split()));

def float_array():
    return list(map(float, input().strip().split()));

## taking string array input
def str_array():
    return input().strip().split();

#defining a couple constants
MOD = int(1e9)+7;
CMOD = 998244353;
INF = float('inf'); NINF = -float('inf');

################### ---------------- TEMPLATE ENDS HERE ---------------- ###################

n, m = int_array();
link = [i for i in range(n + 1)];
size = [1 for i in range(n + 1)];
for _ in range(m):
    a, b = int_array();
    union(a, b, link, size);
ans = set();
for i in range(1, len(link)):
    ans.add(find(link[i], link));
print(len(ans) - 1);

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
ab = [0] * M
for i in range(M):
    ab[i] = list(map(int, input().split()))

import sys
sys.setrecursionlimit(100500)

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())

uf = UnionFind(N)

for i in range(M):
    uf.union(ab[i][0]-1, ab[i][1]-1)

print(uf.group_count() - 1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

n, m = map(int, input().split())
graph = [0] + [[] for _ in range(n)]
for _ in range(m):
    n1, n2 = map(int, input().split())
    graph[n1].append(n2)
    graph[n2].append(n1)

from collections import deque

def bfs(graph, queue, dist):
    while queue:
        current = queue.popleft()

        for _next in graph[current]:
            if dist[_next] != -1:
                continue
            else:
                dist[_next] = dist[current] + 1
                queue.append(_next)

dist = [0] + [-1] * n
part = 0
for i in range(1, n + 1):
    if dist[i] != -1:
        continue
    else:
        queue = deque([i])
        dist[i] = 0
        bfs(graph, queue, dist)
        part += 1
print(part - 1)

Submission status: Accepted

Solution code:
import math

# UnionFind、0-indexであることに注意
#############################################################
class UnionFind:

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

    def find(self, v):  # vが属する集合の根を返す
        if self.parents[v] < 0:
            return v
        else:
            self.parents[v] = self.find(self.parents[v])
            return self.parents[v]

    def unite(self, u, v):  # 「uが属する集合」と「vが属する集合」を併合（根同士を結ぶ）
        u = self.find(u)
        v = self.find(v)
        if u == v:
            return
        if self.parents[u] > self.parents[v]:  # u < v に統一する
            u, v = v, u
        self.parents[u] += self.parents[v]
        self.parents[v] = u

    def size(self, v):  # vが属する集合の要素数
        return -self.parents[self.find(v)]

    def same(self, u, v):  # uとvが同じ集合に属するか否か
        return self.find(u) == self.find(v)
#############################################################

# 普通のcombination
#############################################################


def comb(n, r):  # 普通のcombination計算
    if r < 0 or r > n:
        return 0
    else:
        n1 = math.factorial(n)
        n21 = math.factorial(n - r)
        n22 = math.factorial(r)
        ans = n1 // (n21 * n22)
        return ans
#############################################################

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)

root_list = []
for i in range(N):
    r = uf.find(i)
    root_list.append(r)

root_list = list(set(root_list))
num = len(root_list)

ans = num - 1
print(ans)

Submission status: Accepted

Solution code:
# import sys
# sys.setrecursionlimit(10 ** 6)
# import bisect
# from collections import deque

class UnionFind():
    """
    下記から拝借
    https://note.nkmk.me/python-union-find/
    """

    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())


# from decorator import stop_watch
# 
# 
# @stop_watch
def solve(N, M, AB):
    nf = UnionFind(N)
    for a, b in AB:
        nf.union(a - 1, b - 1)
    print(nf.group_count() - 1)


if __name__ == '__main__':
    # S = input()
    # N = int(input())
    N, M = map(int, input().split())
    # A = [int(i) for i in input().split()]
    # B = [int(i) for i in input().split()]
    AB = [[int(i) for i in input().split()] for _ in range(M)]
    solve(N, M, AB)

    # # test
    # from random import randint
    # from func import random_str
    # solve()

Submission status: Accepted

Solution code:
import bisect,collections,copy,itertools,math,string
import sys
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def main():
    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, m = LI()
    uf = UnionFind(n)

    for i in range(m):
        a, b = LI()
        a -= 1
        b -= 1
        uf.union(a, b)

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


main()

Submission status: Accepted

Solution code:
class unionfind():
    def __init__(self, n):
        self.parents = [-1 for i in range(n)]

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

    def union(self, x, y):
        x, y = self.find(x), self.find(y)
        if x == y:
            return
        if x < y:
            x, y = y, x
        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self):
        return len(list(filter(lambda x: x < 0, self.parents))) - 1

n, m = map(int, input().split())
uf = unionfind(n)
for i in range(m):
    tmp = list(map(int, input().split()))
    uf.union(tmp[0] - 1, tmp[1] - 1)

print(uf.size())

Submission status: Accepted

Solution code:
def resolve():
    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, m = map(int, input().split())
    UF = UnionFind(n)
    for i in range(m):

        a, b = map(int, input().split())
        a -= 1
        b -= 1
        UF.union(a,b)
    grp = UF.group_count()
    if grp == 1:
        print(0)
    else:
        print(grp-1)

resolve()

Submission status: Accepted

Solution code:
N,M = map(int,input().split())
AB = [list(map(int,input().split())) for x in range(M)]

group = 0
parents = [-1]*N

def find(x):#xの根を返す
    global parents
    if parents[x] < 0:
        return x
    else:
        parents[x] = find(parents[x])
        return parents[x]

def union(x,y):
    global parents
    X = find(x)
    Y = find(y)

    if X==Y:
        return

    if parents[X] > parents[Y]:
        X,Y = Y,X

    parents[X] += parents[Y]
    parents[Y] = X

for q in range(M):
    union(AB[q][0]-1,AB[q][1]-1)

for p in range(N):
    if parents[p] < 0:
        group += 1

print(group-1)

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

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

g = [[]*(n+1) for _ in range(n+1)]

uf = UnionFind(n)

# 友人関係のみ UnionFind でまとまる
# グラフに友人関係追加
for i in range(m):
    a,b = map(int,input().split())
    uf.union(a-1,b-1)

print(uf.group_count()-1)

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, m = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(m)]
uf = UnionFind(n)
for i in range(m):
    x, y = ab[i][0], ab[i][1]
    x -= 1
    y -= 1
    uf.union(x, y)
print(uf.group_count()-1)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**9)
n, m = map(int, input().split())

root = [-1]*n

def find(n):
    if root[n] < 0:
        return n
    else:
        root[n] = find(root[n])
        return root[n]

def unite(x, y):
    x = find(x)
    y = find(y)
    if x == y:
        return
    else:
        root[x] += root[y]
        root[y] = x

for i in range(m):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    unite(a, b)

ans = -1
for i in root:
    if i < 0:
        ans += 1

print(ans)

Submission status: Accepted

Solution code:
import sys

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())

input = sys.stdin.readline
N, M = map(int, input().split())
uf = UnionFind(N)
for _ in range(M):
    a, b = map(int, input().split())
    uf.union(a-1, b-1)

print(uf.group_count() - 1)

Submission status: Accepted

Solution code:
import sys


class UnionFind:
    def __init__(self, N):
        self.N = N  # ノード数
        # 親ノードを示す。負は自身が親ということ。親だった場合は−(その集合のサイズ)
        self.parent = [-1] * N

    def root(self, A):
        # Aがどのグループに属しているか調べる
        # ノード番号を受けとって一番上の親ノードの番号を返す
        # print(A)
        if self.parent[A] < 0:
            return A
        self.parent[A] = self.root(self.parent[A])
        return self.parent[A]

    def size(self, A):
        # 自分のいるグループの頂点数を調べる
        return -self.parent[self.root(A)]

    def unite(self, A, B):
        # AとBをくっつける
        # AとBを直接つなぐのではなく、root(A)にroot(B)をくっつける
        A = self.root(A)
        B = self.root(B)

        if A == B:
            return False  # すでにくっついてるからくっつけない

        if self.size(A) < self.size(B):
            # 大きい方(A)に小さいほう(B)をくっ付けたい
            # 大小が逆だったらひっくり返しちゃう。
            A, B = B, A

        # Aのサイズを更新する
        self.parent[A] += self.parent[B]
        # Bの親をAに変更する
        self.parent[B] = A

        return True

    def same(self, A, B):
        return self.root(A) == self.root(B)



input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)


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

    group = set()
    for i in range(N):
        # print(uf.root(i))
        group.add(uf.root(i))
    # print(group)
    ans = len(group) - 1
    print(ans)


if __name__ == "__main__":
    main()