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())
AB = [list(map(int, input().split())) 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())


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

print(u.group_count() - 1)

Submission status: Accepted

Solution code:
import sys
import math
import itertools
import bisect
from copy import copy,deepcopy
from collections import deque,Counter
from decimal import Decimal
def s(): return input()
def i(): return int(input())
def S(): return input().split()
def I(): return map(int,input().split())
def L(): return list(input().split())
def l(): return list(map(int,input().split()))
def lcm(a,b): return a*b//math.gcd(a,b)
sys.setrecursionlimit(10 ** 9)
INF = 10**9
mod = 10**9+7

class UnionFind:
  def __init__(self,n):
    self.n=[-1]*n
    self.r=[0]*n
  def find_root(self,x):
    if self.n[x]<0:
      return x
    else:
      self.n[x]=self.find_root(self.n[x])
      return self.n[x]
  def unite(self,x,y):
    x=self.find_root(x)
    y=self.find_root(y)
    if x==y:return
    elif self.r[x]>self.r[y]:
      self.n[x]+=self.n[y]
      self.n[y]=x
    else:
      self.n[y]+=self.n[x]
      self.n[x]=y
      if self.r[x]==self.r[y]:
        self.r[y]+=1
  def root_same(self,x,y):
    return self.find_root(x)==self.find_root(y)
  def count(self,x):
    return -self.n[self.find_root(x)]

N,M = I()
u = UnionFind(N)
for i in range(M):
    a,b = I()
    u.unite(a-1,b-1)
li = []
q = []
ans = 0
for i in range(N):
    num = u.count(i)
    if num not in li:
        li.append(num)
    q.append(num)
for i in li:
    ans += q.count(i)//i
print(ans-1)

Submission status: Accepted

Solution code:
from collections import deque

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

AB = [[] for _ in range(N)]

for _ in range(M):
    a,b = map(lambda x: int(x)-1, input().split())
    AB[a].append(b)
    AB[b].append(a)

visited = [0] * N
ans = []
for i in range(N):
    if visited[i]:
        continue
    group = [i]
    d = deque(AB[i])
    while d:
        s = d.popleft()
        if visited[s]:
            continue
        visited[s] = 1
        group.append(s)
        for k in AB[s]:
            d.append(k)
    ans.append(len(group))

print(len(ans)-1)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, n):
        self.par = [-1]*(n+1)  # 頂点番号とindexをそろえるためにn+1。idx0は使わない
        self.rank = [0]*(n+1)

    def find(self, x):
        if self.par[x] < 0:
            return x
        else:
            self.par[x] = self.find(self.par[x])  # 再帰で根までたどる.その過程で根とつなぎかえる
            return self.par[x]

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

        if x == y:
            return
        else:
            if self.rank[x] < self.rank[y]:
                self.par[y] += self.par[x]
                self.par[x] = y
            else:
                self.par[x] += self.par[y]
                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)  # 根同じならTrue違うならFalseを返す

    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())
    uf.union(a, b)
st = set()
for i in range(1, n+1):
    st.add(uf.find(i))
print(len(st)-1)

Submission status: Accepted

Solution code:
class path_compressed_quick_union:
    def __init__(self, n):
        self.n = n
        self.data = [i for i in range(n)]
        self.size = [1 for i in range(n)]

    def root(self, p):
        while p != self.data[p]:
            self.data[p] = self.data[self.data[p]]
            p = self.data[p]
        return p

    def connected(self, p, q):
        return self.root(p) == self.root(q)

    def union(self, p, q):
        proot = self.root(p)
        qroot = self.root(q)
        if self.size[proot] < self.size[qroot]:
            self.data[qroot] = proot
            self.size[qroot] += self.size[proot]
        else:
            self.data[proot] = qroot
            self.size[proot] += self.size[qroot]



N, M = map(int,input().split())
uf = path_compressed_quick_union(N)
for i in range(M):
    a,b=map(int,input().split())
    uf.union(a-1,b-1)
ans = []
for i in range(N):
    ans.append(uf.root(i))
print(len(set(ans))-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())
uf = UnionFind(N)

#H = list(map(int, input().split()))

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

#丸暗記。隣接リストの初期化
graph = [[] for _ in range(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 math
import collections
import itertools
import copy

def YesNo(Bool):
    if(Bool):
        print("YES")
    else:
        print("NO")
    return

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 resolve():

    N,M=map(int,input().split())
    A=[0]*M
    B=[0]*M

    uf = UnionFind(N)
    for i in range(M):
        A[i],B[i]=map(int,input().split())
        uf.union(A[i]-1, B[i]-1)
        
    # for i in range(N):
    #     uf.find(i)

    cnt=uf.group_count()

    print(cnt-1)

resolve()

Submission status: Accepted

Solution code:
n, m = map(int, input().split())
par = [i for i in range(n)]
import sys
sys.setrecursionlimit(1000000)

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

def unite(x, y):
    x = find(x, par)
    y = find(y, par)
    if x != y:
        par[x] = y

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

groups= 0
for i in range(n):
    if i == par[i]:
        groups +=1
print(groups-1)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Sep 26 17:37:27 2020

@author: divyarth
"""

import sys
import heapq
import math

#sys.setrecursionlimit(50000)
#input=sys.stdin.readline
#print=sys.stdout.write

from collections import deque
from collections import defaultdict
from collections import Counter

modH=int(10**9)+7

I=lambda : list(map(int,input().split(' ')))
def PRINT(lst,sep=' '): print(sep.join(map(str,lst)))

n,m=I()
edges=[I() for i in range(m)]
graph=[[] for i in range(n)]

for src,des in edges:
    graph[src-1].append(des-1)
    graph[des-1].append(src-1)

def bfs(node):
    queue=deque()
    queue.append(node)
    while queue:
        cur=queue.popleft()
        for w in graph[cur]:
            if visited[w]==None:
                queue.append(w)
                visited[w]=1

visited=[None]*n
cmp=0
for i in range(n):
    if visited[i]==None:
        bfs(i)
        cmp+=1

print(cmp-1)

Submission status: Accepted

Solution code:
from collections import Counter


def find(x):
    if par[x] < 0:
        return x
    else:
        par[x] = find(par[x])
        return par[x]


def unite(x, y):
    x = find(x)
    y = find(y)

    if x == y:
        return False
    else:

        if par[x] > par[y]:
            x, y = y, x
        par[x] += par[y]
        par[y] = x
        return True


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


N, M = map(int, input().split())
par = [-1]*N

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

count = 0
for i in par:
    count += i < 0

print(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())

def resolve():
    import sys

    input = sys.stdin.readline

    n, m = [int(x) for x in input().rstrip().split(" ")]

    uf = UnionFind(n)

    for i in range(m):
        a, b = [int(x) for x in input().rstrip().split(" ")]
        uf.union(a-1, b-1)

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


if __name__ == "__main__":
    resolve()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(2 * (10 ** 6))
n, m = map(int, input().split())
edges = [[] for i in range(n)]
visit = [False for i in range(n)]
def dfs(v):
    visit[v] = True
    for i in edges[v]:
        if not visit[i]:
            dfs(i)
for i in range(m):
    a, b = map(int, input().split())
    edges[a - 1].append(b - 1)
    edges[b - 1].append(a - 1)
cnt = 0
for i in range(n):
    if not visit[i]:
        dfs(i)
        cnt += 1
print(cnt - 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())
uf = UnionFind(N+1)
for _ in range(M):
    A, B = map(int, input().split())
    uf.union(A, B)

print(len(uf.roots()) - 2)

Submission status: Accepted

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

#素集合 無向グラフ
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 False

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

  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):
  x,y=map(int,input().split())
  uf.union(x-1,y-1)
print(uf.group_count()-1)

Submission status: Accepted

Solution code:
from collections import deque

n, m = map(int, input().split())
road = [[] for _ in range(n)]
flag = [-1 for _ in range(n)]

for i in range(m):
  a, b = map(int, input().split())
  road[a-1].append(b-1)
  road[b-1].append(a-1)

count = 0

for k in range(n):
  if(flag[k] != -1):
    continue
  
  count += 1
  queue = deque([k])
  while queue:
    now = queue.popleft()
    flag[now] = count
    for i in road[now]:
      if(flag[i] == -1):
        queue.append(i)
  
print(count-1)

Submission status: Accepted

Solution code:
import sys, bisect, math, itertools, string, queue, copy
import numpy as np
import scipy
from collections import Counter,defaultdict,deque
from itertools import permutations, combinations
from heapq import heappop, heappush
# input = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7
def inp(): return int(input())
def inpm(): return map(int,input().split())
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())
def inplm(n): return list(int(input()) for _ in range(n))
def inplL(n): return [list(input()) for _ in range(n)]
def inplT(n): return [tuple(input()) for _ in range(n)]
def inpll(n): return [list(map(int, input().split())) for _ in range(n)]
def inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]
def inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])

#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())

n,m = inpm()
AB = inplt(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:
class uft():
    def __init__(self,n):
        #pは代表元か-1
        self.p=[ -1 for i in range(n)]
        #ランク　木の深さ
        self.r=[ 1 for i in range(n)]
        #要素数
        self.e=[ 1 for i in range(n)]
        
    def find(self,x):
        if(self.p[x]==-1):
            return x
        else:
            self.p[x]=self.find(self.p[x])
            return self.find(self.p[x])
        
    def unite(self,x,y):
        x=self.find(x)
        y=self.find(y)
        if(x==y):
            return
        
        if(self.r[x]>self.r[y]):
            tmp=x
            x=y
            y=tmp
        
        if(self.r[x]==self.r[y]):
            self.r[y]+=1
        
        self.e[y]+=self.e[x]
            
        if(x!=y):
            self.p[x]=y
        return
    
    def tsize(self,x):
        return self.e[self.find(x)]
n,m=map(int,input().split())

uf=uft(n)
for i in range(m):
    x,y=map(int,input().split())
    x-=1
    y-=1
    uf.unite(x,y)
oya=0

for i in range(n):
    if(uf.p[i]==-1):
        oya+=1
print(oya-1)

Submission status: Accepted

Solution code:
import sys, re
from math import ceil, floor, sqrt, pi, factorial, gcd
from copy import deepcopy
from collections import Counter, deque
from heapq import heapify, heappop, heappush
from itertools import accumulate, product, combinations, combinations_with_replacement
from bisect import bisect, bisect_left, bisect_right
from functools import reduce
from decimal import Decimal, getcontext
# input = sys.stdin.readline 
def i_input(): return int(input())
def i_map(): return map(int, input().split())
def i_list(): return list(i_map())
def i_row(N): return [i_input() for _ in range(N)]
def i_row_list(N): return [i_list() for _ in range(N)]
def s_input(): return input()
def s_map(): return input().split()
def s_list(): return list(s_map())
def s_row(N): return [s_input for _ in range(N)]
def s_row_str(N): return [s_list() for _ in range(N)]
def s_row_list(N): return [list(s_input()) for _ in range(N)]
def lcm(a, b): return a * b // gcd(a, b)
sys.setrecursionlimit(10 ** 6)
INF = float('inf')
MOD = 10 ** 9 + 7
num_list = []
str_list = []

class UnionFind:
    # 作りたい要素数nで初期化
    # 使用するインスタンス変数の初期化
    def __init__(self, n):
        self.n = n
        # root[x]<0ならそのノードが根かつその値が木の要素数
        # rootノードでその木の要素数を記録する
        self.root = [-1]*(n+1)
        # 木をくっつける時にアンバランスにならないように調整する
        self.rank = [0]*(n+1)

    # ノードxのrootノードを見つける
    def findRoot(self, x):
        if(self.root[x] < 0): # 根
            return x
        else:
            # ここで代入しておくことで、後の繰り返しを避ける
            self.root[x] = self.findRoot(self.root[x])
            return self.root[x]

    # 木の併合、入力は併合したい各ノード
    def unite(self, x, y):
        # 入力ノードのrootノードを見つける
        x = self.findRoot(x)
        y = self.findRoot(y)

        # すでに同じ木に属していた場合
        if x == y:
            return 

        # 違う木に属していた場合rankを見てくっつける方を決める
        if 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
            # rnkが同じ（深さに差がない場合）は1増やす
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1

    # xとyが同じグループに属するか判断
    def isSameGroup(self, x, y):
        return self.findRoot(x) == self.findRoot(y)

    # ノードxが属する木のサイズを返す
    def count(self, x):
        return -self.root[self.findRoot(x)]

def main():
    n, m = i_map()

    uf = UnionFind(n)

    for _ in range(m):
        a, b = i_map()
        uf.unite(a, b)

    count = 0
    for i in range(2, n+1):
        if uf.isSameGroup(1, i):
            continue
        uf.unite(1, i)
        count += 1

    print(count)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
N,M=map(int, sys.stdin.readline().split())

par=[ i for i in range(N+1) ]
size=[ 1 for i in range(N+1) ]

#Union Find
def root(x):
    while par[x]!=x:
        x=par[x]
    return x

def same(x,y):
	return root(x)==root(y)

def unite(x,y):
    x=root(x)
    y=root(y)
    if x==y: return
    if size[y]<size[x]: x,y=y,x
    size[y]+=size[x]
    par[x]=y

def getsize(x):
	return size[root(x)]

for _ in range(M):
    a,b=map(int, sys.stdin.readline().split())
    unite(a,b)

s=set()
for i in range(1,N+1):
    s.add(root(i))

print len(s)-1

Submission status: Accepted

Solution code:
from collections import deque
def bfs(edges,start):
    waiting = deque()
    done[start] = 2
    c = 1
    for n in edges[start]:
        done[n] = 1
        waiting.append(n)
    while len(waiting):
        cur_node = waiting.popleft()
        if done[cur_node] != 2:
            done[cur_node] = 2
            c += 1
            for n in edges[cur_node]:
                if done[n] != 2:
                    done[n] = 1
                    waiting.append(n)
    #print(done,c)
    return c 
N,M = [int(a) for a in input().split()]
edge = [[] for _ in range(N)] 
for _ in range(M):
    a,b = [int(a) for a in input().split()]
    edge[a-1].append(b-1)
    edge[b-1].append(a-1)
done = [0]*N
ans = []
for i in range(N):
    if done[i]==0: ans.append(bfs(edge,i))
#print(ans)
print(len(ans)-1)

Submission status: Accepted

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

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+1)
A = [0]*m
B = [0]*m
for i in range(m):
    A[i], B[i] = sorted(map(int, input().split()))
    uf.union(A[i], B[i])
print(uf.group_count()-2)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)

def inp():
    return int(input())
def inps():
    return input().rstrip()
def inpl():
    return list(map(int, input().split()))
def inpls():
    return list(map(str, input().split()))
def _debug(obj):
    print(obj, file=sys.stderr)

# import decimal
# from decimal import Decimal
# decimal.getcontext().prec = 10

# from heapq import heappush, heappop, heapify
# import math
# from math import gcd
# import itertools as it
# import collections
# from collections import deque 

# ---------------------------------------
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 = inpl()
graph = [[] for i in range(N + 1)]
uf = UnionFind(N + 1)

for i in range(M):
    a, b = inpl()
    uf.union(a, b)

print(len(uf.roots()) - 2)

Submission status: Accepted

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# FileName: 	C
# CreatedDate:  2020-09-26 20:52:24 +0900
# LastModified: 2020-09-26 21:19:33 +0900
#


import os
import sys
sys.setrecursionlimit(2000000)
# import numpy as np
# import pandas as pd


def BFS(cnt, color, path, u):
    color[u] = cnt
    for v in path[u]:
        if color[v] == -1:
            BFS(cnt, color, path, v)


def main():
    N, M = map(int, input().split())
    path = [[] for _ in range(N+1)]
    for _ in range(M):
        A, B = map(int, input().split())
        path[A].append(B)
        path[B].append(A)
    color = [-1] * (N+1)
    cnt = 0
    for i in range(1, N+1):
        if color[i] == -1:
            BFS(cnt, color, path, i)
            cnt += 1
    print(max(color))


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())

    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 _ in range(m):
  a,b = map(int,input().split())
  uf.union(a-1,b-1)
root = [0]*n
for i in range(n):
  root[uf.find(i)] += 1
cnt = 0
for v in root:
  if v!=0:
    cnt += 1
print(cnt-1)

Submission status: Accepted

Solution code:
import collections

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

class UnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n)]
        self.rank = [0] * 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, x, y):
        x = self.find(x)
        y = self.find(y)
        
        if self.rank[x] < self.rank[y]:
            self.par[x] = y
        else:
            self.par[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1
                
UF = UnionFind(n)

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

for i in range(n):
    _ = UF.find(i)

c = collections.Counter(UF.par)
print(len(c.keys()) - 1)