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 ).

Solution (Python):
import os
import sys
from io import BytesIO, IOBase



def main():
    n, m = getints()
    g = [0] * n
    for i in range(n):
        g[i] = i
    def find(u):
        if u == g[u]:
            return u
        else:
            g[u] = find(g[u])
            return g[u]
    def merge(u, v):
        g[find(u)] = find(v)
    for _ in range(m):
        a, b = getints()
        merge(a - 1, b - 1)
    cnt = 0
    for i in range(n):
        if i == g[i]:
            cnt += 1
    print(cnt - 1)





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)


def input(): return sys.stdin.readline().rstrip("\r\n")
def getint(): return int(input())
def getints(): return list(map(int, input().split()))
def getint1(): return list(map(lambda x: int(x) - 1, input().split()))





if __name__ == "__main__":
    main()

Solution (Python):
import sys
from collections import deque


N, M = map(int, input().split())
edge = [[] for _ in range(N)]
for s in sys.stdin.readlines():
    a, b = map(lambda x: int(x) - 1, s.split())
    edge[a].append(b)
    edge[b].append(a)

path = [-1] * N
cnt = 0
for i in range(N):
    if path[i] < 0:
        cnt += 1
        q = deque()
        path[i] = i
        q.append(i)
        while q:
            p = q.popleft()
            for np in edge[p]:
                if path[np] < 0:
                    path[np] = i
                    q.append(np)

print(cnt - 1)

Solution (Python):
from networkx import *
 
n,m = map(int, input().split())
G = Graph()
 
for i in range(m):
    a,b = map(int, input().split())
    G.add_edges_from([(a, b)])
 
m3 = list(connected_components(G))

count = 0
 
if len(max(connected_components(G), key=len)) == n:
    print(0)
    exit()
else:
    for i in m3:
        count += len(i)
 
sub = n - count
 
print((len(m3)-1)+sub)

Solution (Python):

import queue

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

road = [[] for i 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)
ans = 0

city = set(i for i in range(n))

while len(city):
  
  q = queue.Queue()
  
  q.put(city.pop())
  
  while not q.empty():
    x = q.get()
    for i in road[x]:
      
      if i in city:
        
        q.put(i)
        
        city.discard(i)
  
  if len(city):
    ans += 1
print(ans)

Solution (Python):
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)

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

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

Solution (Python):
import sys


class UnionFind():
    def __init__(self, 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


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

print(sum(p < 0 for p in uf.parents) - 1)

Solution (Python):
import sys


class UnionFind():
    def __init__(self, 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


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

print(sum(p < 0 for p in uf.parents) - 1)

Solution (Python):
class UnionFind:
    def __init__(self, n=1):
        self.parent = [i for i in range(n)]
        self.rank = [0] * n
    
    def find(self, x):
        if self.parent[x] == x:
            return x
        else:
            self.parent[x] = self.find(self.parent[x])
            return self.parent[x]
    
    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if x != y:
            if self.rank[x] < self.rank[y]:
                x, y = y, x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.parent[y] = x
    
    def is_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)

for i in range(N):
    uf.find(i)

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

Solution (Python):
class UnionFind():
    def __init__(self, n):
        self.parents = list(range(n))
        self.rank = [0] * n

    def find(self, x):
        if self.parents[x] == x:
            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.rank[x] < self.rank[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

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

uf = UnionFind(n)

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

for i in range(n):
    uf.find(i)

print(len(set(uf.parents))-1)

Solution (Python):
n,m = map(int,input().split())
par = [i for i in range(n+1)]
def find(x):
    if par[x] == x:
        return x
    else:
        par[x] = find(par[x]) 
        return par[x]
def same(x,y):
    return find(x) == find(y)
def unite(x,y):
    x = find(x)
    y = find(y)
    if x == y:
        return 0
    par[max(x,y)] = min(x,y)



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

tag=[0 for i in range(n+1)]
for i in range(1,n+1):
    tag[find(i)]=1
print(sum(tag)-1)

Solution (Python):
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)

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

Solution (Python):

class UnionFind():
    def __init__(self, n):
        self.r = [-1 for i in range(n)]
    
    
    def root(self, x):
        if self.r[x] < 0: 
            return x
        self.r[x] = self.root(self.r[x])
        return self.r[x]

    
    def add(self, x, y):
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return False
        self.r[x] += self.r[y]
        self.r[y] = x
        return True

n, m = map(int, input().split())
UF = UnionFind(n)
for i in range(m):
    a, b = map(lambda x: int(x)-1, input().split())
    UF.add(a, b)

ans = 0
for i in UF.r:
    if i < 0:
        ans += 1

print(ans-1)

Solution (Python):

import sys
sys.setrecursionlimit(10000)

class UnionFindTree:
	def __init__(self,size):
		"""
		size個の集合を作成
		負の値は、ルートで集合の個数
		正の値は、次の要素
		"""
		self.table=[-1 for _ in range(size)]

	def find(self,x):
		"""
		グループ番号を取得
		"""
		
		
		if self.table[x] < 0:
			
			return x
		else:
			
			self.table[x] = self.find(self.table[x])
			return self.table[x]
		return x

	
	def union(self,x,y):
		
		
		s1=self.find(x)
		s2=self.find(y)
		if s1!=s2:
			
			
			if self.table[s2]<=self.table[s1]:
				
				self.table[s1]+=self.table[s2]
				self.table[s2]=s1
			else:
				
				self.table[s2]+=self.table[s1]
				self.table[s1]=s2
			return True
		return False

	def groupCount(self):
		ret=0
		for i in range(len(self.table)):
			if self.table[i] < 0:
				ret+=1
		return ret

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

UF=UnionFindTree(N)

for _ in range(M):
	A,B=map(int,input().split())
	UF.union(A-1,B-1)


print(UF.groupCount()-1)

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


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

    def root(self,x):
        while self.par[x]!=x:
            self.par[x]=self.par[self.par[x]]
            x=self.par[x]
        return x

    def unite(self,x,y):
        x=self.root(x)
        y=self.root(y)
        if x==y:
            return False
        if self.siz[x]<self.siz[y]:
            x,y=y,x
        self.siz[x]+=self.siz[y]
        self.par[y]=x
        return True

    def is_same(self,x,y):
        return self.root(x)==self.root(y)

    def size(self,x):
        return self.siz[self.root(x)]

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

cnt = [0]*(n)
for i in range(n):
    cnt[uni.root(i)] = 1

print(sum(cnt)-1)

Solution (Python):
n,m=map(int,input().split())
par=[-1]*n


def find(x):
    global par
    if par[x]<0:
        return x
    else:
        par[x]=find(par[x])
        return par[x]
        
def unite(x,y):
    x,y=find(x),find(y)
    global par
    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)]
def same(x,y):
    return find(x)==find(y)

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

cnt=0
for i in par:
  if i<0:
    cnt+=1
print(cnt-1)

Solution (Python):
class Unionfind:
     
    def __init__(self,n):
        self.uf = [-1]*n
 
    def find(self,x):
        if self.uf[x] < 0:
            return x
        else:
            self.uf[x] = self.find(self.uf[x])
            return self.uf[x]
 
    def same(self,x,y):
        return self.find(x) == self.find(y)
 
    def union(self,x,y):
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return False
        if self.uf[x] > self.uf[y]:
            x,y = y,x
        self.uf[x] += self.uf[y]
        self.uf[y] = x
        return True
 
    def size(self,x):
        x = self.find(x)
        return -self.uf[x]

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

u = Unionfind(n)
count = 0
for i in range(m):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    u.union(a,b)

s = set()
for i in range(n):
    s.add(u.find(i))
print(len(s)-1)

Solution (Python):
class UnionFind:
    pairs = {}
    def __init__(self, n):
        for i in range(n):
            self.pairs[i] = i

    def set(self, s, t):
        if s in self.pairs and self.pairs[s] == s:
            self.pairs[s] = self.root(t)
        else:
            self.pairs[t] = self.root(s)

    def root(self, x):
        if self.pairs[x] == x:
            return x
        self.pairs[x] = self.root(self.pairs[x])
        return self.pairs[x]

    def unite(self, x, y):
        rx = self.root(x)
        ry = self.root(y)
        if rx == ry :
            return
        self.pairs[rx] = ry
    def same(self, x, y ):
        rx = self.root(x)
        ry = self.root(y)
        if rx == ry:
            return True
        else:
            return False
        
def main():
    n, m = map(int, input().split())

    uf = UnionFind(n)
    pairs =[]
    for i in range(m):
        s, t = map(int,input().split())
        if uf.same(s-1, t-1) == False:
            uf.unite(s-1,t-1)
        

    
    
    
    
    
    

    root = []
    for i in range(n):
        root.append(uf.root(i))
 
    single_root = set(root)

    print(len(single_root)-1)
main()

Solution (Python):
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 unite(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())

import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n,m=map(int,input().split())
u=UnionFind(n)
for i in range(m):
    a,b=map(int,input().split())
    a-=1
    b-=1
    u.unite(a,b)
ans=u.roots()
print(len(ans)-1)

Solution (Python):
import os
import sys
from io import BytesIO, IOBase



def main():
    sys.setrecursionlimit(10**6 + 10)
    n, m = getints()
    g = [0] * n
    for i in range(n):
        g[i] = i
    def find(u):
        if u == g[u]:
            return u
        else:
            g[u] = find(g[u])
            return g[u]
    def merge(u, v):
        g[find(u)] = find(v)
    for _ in range(m):
        a, b = getints()
        merge(a - 1, b - 1)
    cnt = 0
    for i in range(n):
        if i == g[i]:
            cnt += 1
    print(cnt - 1)





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)


def input(): return sys.stdin.readline().rstrip("\r\n")
def getint(): return int(input())
def getints(): return list(map(int, input().split()))
def getint1(): return list(map(lambda x: int(x) - 1, input().split()))





if __name__ == "__main__":
    main()

Solution (Python):
import sys

sys.setrecursionlimit(10**7)
def MI(): return map(int,sys.stdin.readline().rstrip().split())


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

    def unite(self,x,y):  
        x = self.find(x)
        y = self.find(y)
        if self.rank[x] < self.rank[y]:
            x,y = y,x
        if self.rank[x] == self.rank[y]:
            self.rank[x] += 1
        self.par[y] = x


N,M = MI()
UF = UnionFind(N)
for _ in range(M):
    a,b = MI()
    UF.unite(a,b)

A = UF.par
A = [UF.find(A[i]) for i in range(1,N+1)]

print(len(set(A))-1)

Solution (Python):
import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy

sys.setrecursionlimit(10**7)
inf=10**20
mod=10**9+7
dd=[(-1,0),(0,1),(1,0),(0,-1)]
ddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]

def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return input()


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

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

  def find(self,k):
    if self.data[k]<0:
      return k
    self.data[k]=self.find(self.data[k])
    return self.data[k]

  def size(self,k):
    return -self.data[self.find(k)]


def main():
  n,m=LI()
  uf=UnionFind(n)
  for _ in range(m):
    a,b=LI()
    a-=1
    b-=1
    uf.unite(a,b)
  
  d={}
  for i in range(n):
    d[uf.find(i)]=i

  return len(d)-1


print(main())

Solution (Python):
class UnionFind:
    def __init__(self, n):
        self.n = 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.par[x] = y
            self.size[y] += self.size[x]
        else:
            self.par[y] = x
            self.size[x] += self.size[y]
            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 members(self, x):
        root = self.find(x)
        return [i for i in range(1,self.n+1) if self.find(i) == root]

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

    
    def roots(self):
        return [i for i, x in enumerate(self.par) if x == i and i != 0]
    
    
    def group_count(self):
        return len(self.roots())
    
    
    def all_group_members(self):
        return {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.union(a,b)
print(len(uf.roots())-1)

Solution (Python):
class UnionFind():
    def __init__(self, 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


N,M=map(int,input().split())
A=[0]*M
B=[0]*M
for i in range(M):
    A[i],B[i]=map(int,input().split())

uf=UnionFind(N+1)
for i in range(M):
    uf.union(A[i],B[i])
a=[0]*(N+1)
con=0

for i in uf.parents:
    if(i<0):
        con=con+1

print(con-2)

Solution (Python):
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+1)
for ab in AB:
    uf.union(ab[0], ab[1])

print(uf.group_count() - 1 - 1)

Solution (Python):
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())

A = [0 for _ in range(M)]
B = [0 for _ in range(M)]
for i in range(M):
    A[i] , B[i] = map(int, input().split())
    A[i] -= 1
    B[i] -= 1






uf = UnionFind(N)
for i in range(M):
    uf.union(A[i], B[i])
print(uf.group_count()-1)

Solution (Python):
import collections
n, m = map(int, input().split())
linked = collections.defaultdict(list)
i2group = dict()

gid = n + 1
def get_root(i):
  if i not in linked:
    return i
  j = get_root(linked[i])
  linked[i] = j
  return j

def get_groups():
  return [get_root(i) for i in range(1, n + 1)]

for i in range(m):
  a, b = map(int, input().split())
  ra, rb = get_root(a), get_root(b)
  if ra == rb: continue
  linked[ra] = gid
  linked[rb] = gid
  gid += 1

g = get_groups()
print(len(set(g)) - 1)
exit()

n_connected = 0
n_group = 0
for s in linked.values():
  s = s[0]
  if s:
    n_group += 1
    n_connected += len(s)
    s.clear()
print((n - n_connected) + (n_group - 1))

Solution (Python):
from collections import deque

def bfs(s):
    visit[i] = 1
    q = deque()
    q.append(s)
    while q:
        p = q.popleft()
        for j in G[p]:
            if not visit[j]:
                visit[j] = 1
                q.append(j)
    return

n, m = map(int, input().split())
G = [[] for _ in range(n + 1)]
for _ in range(m):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
visit = [0] * (n + 1)
ans = -1
for i in range(1, n + 1):
    if not visit[i]:
        bfs(i)
        ans += 1
print(ans)

Solution (Python):
import sys
INF = 1 << 60
MOD = 10**9 + 7 
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()

class UnionFind(object):
    def __init__(self, n, recursion = False):
        self._par = list(range(n))
        self._size = [1] * n
        self._recursion = recursion

    def root(self, k):
        if self._recursion:
            if k == self._par[k]:
                return k
            self._par[k] = self.root(self._par[k])
            return self._par[k]
        else:
            root = k
            while root != self._par[root]: root = self._par[root]
            while k != root: k, self._par[k] = self._par[k], root
            return root

    def unite(self, i, j):
        i, j = self.root(i), self.root(j)
        if i == j: return False
        if self._size[i] < self._size[j]: i, j = j, i
        self._par[j] = i
        self._size[i] += self._size[j]
        return True

    def is_connected(self, i, j):
        return self.root(i) == self.root(j)

    def size(self, k):
        return self._size[self.root(k)]

def resolve():
    n, m = map(int, input().split())
    uf = UnionFind(n)
    for _ in range(m):
        u, v = map(int, input().split())
        u -= 1; v -= 1
        uf.unite(u, v)

    ans = len(set(uf.root(v) for v in range(n))) - 1
    print(ans)
resolve()

Solution (Python):
class UnionFind():
    def __init__(self,size):
        self.table = [-1 for _  in range(size)]
        self.member_num = [1 for _ in range(size)]

    
    def find(self,x):
        while self.table[x] >= 0:
            x = self.table[x]
        return x

    def union(self,x,y):
        s1 = self.find(x)
        s2 = self.find(y)
        m1=self.member_num[s1]
        m2=self.member_num[s2]
        if s1 != s2:
            if m1 != m2:
                if m1 < m2:
                    self.table[s1] = s2
                    self.member_num[s2]=m1+m2
                    return [m1,m2]
                else:
                    self.table[s2] = s1
                    self.member_num[s1]=m1+m2
                    return [m1,m2]
            else:
                self.table[s1] = -1
                self.table[s2] = s1
                self.member_num[s1] = m1+m2
                return [m1,m2]
        return [0,0]

N,M = list(map(int,input().split()))
uf = UnionFind(N)
count = 0
for i in range(M):
    A,B = list(map(int,input().split()))
    A,B = A-1,B-1
    if uf.find(A)!=uf.find(B):
        uf.union(A,B)
        count+=1

B = set()

for i in range(N):
    B.add(uf.find(i))

print(len(B)-1)