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

Solution (Python):
n,m=[int(i) for i in raw_input().split()]
l=[i for i in range(n)]
r=[0 for i in range(n)]
def find(x):
    if l[x]==x:
        return l[x]
    return find(l[x])
for _ in range(m):
    u,v=[int(i)-1 for i in raw_input().split()]
    px=find(u)
    py=find(v)
    if r[px]<r[py]:
            l[px]=py
    elif r[px]==r[py]:
            l[py]=px
            r[px]+=1
    else:
            l[py]=px
ct=0
for i in range(n):
    if find(i)==i:
        ct+=1
print ct-1

Solution (Python):
import sys
input = sys.stdin.readline
I=lambda:int(input())
MI=lambda:map(int,input().split())
LI=lambda:list(map(int,input().split()))

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.root = [-1]*(n+1)
        self.rnk = [0]*(n+1)

    def find_root(self, x):
        if(self.root[x] < 0):
            return x
        else:
            self.root[x] = self.find_root(self.root[x])
            return self.root[x]
        
    def unite(self, x, y):
        x = self.find_root(x)
        y = self.find_root(y)
        if(x == y):
            return 
        elif(self.rnk[x] > self.rnk[y]):
            self.root[x] += self.root[y]
            self.root[y] = x
        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            if(self.rnk[x] == self.rnk[y]):
                self.rnk[y] += 1
                
    def is_same_group(self, x, y):
        return self.find_root(x) == self.find_root(y)

    def count(self, x):
        return -self.root[self.find_root(x)]
    
N,M=MI()
uf=UnionFind(N)
for _ in [0]*M:
    a,b=MI()
    uf.unite(a,b)
    
print(sum([uf.find_root(i+1)==i+1 for i in range(N)])-1)

Solution (Python):
from collections import defaultdict
from collections import deque
from collections import Counter
import math
import itertools

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

n,m = readInts()
u = UnionFind(n)
for i in range(m):
	a,b = readInts()
	u.union(a-1,b-1)

print(u.group_count()-1)

Solution (Python):
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10

class UnionFind:
    """ Union-Find木 """

    def __init__(self, n):
        self.n = n
        self.par = [i for i in range(n)]
        self.rank = [0] * n
        self.size = [1] * n
        self.tree = [True] * n
        self.grpcnt = n

    def find(self, x):
        """ 根の検索(グループ番号の取得) """
        t = []
        while self.par[x] != x:
            t.append(x)
            x = self.par[x]
        for i in t:
            self.par[i] = x
        return self.par[x]

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

        if x == y:
            self.tree[x] = False
            return
        if not self.tree[x] or not self.tree[y]:
            self.tree[x] = self.tree[y] = False

        self.grpcnt -= 1
        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 is_same(self, x, y):
        """ 同じ集合に属するか判定 """
        return self.find(x) == self.find(y)

    def get_size(self, x=None):
        if x is not None:
            """ あるノードの属する集合のノード数 """
            return self.size[self.find(x)]
        else:
            """ 集合の数 """
            return self.grpcnt
    
    def is_tree(self, x):
        """ 木かどうかの判定 """
        return self.tree[self.find(x)]

N, M = MAP()
uf = UnionFind(N)
for i in range(M):
    a, b = MAP()
    a -= 1; b -= 1
    uf.union(a, b)

ans = uf.get_size() - 1
print(ans)

Solution (Python):
from sys import stdin
nii=lambda:map(int,stdin.readline().split())
lnii=lambda:list(map(int,stdin.readline().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 same(self, x, y):
        return self.find(x) == self.find(y)

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

    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=nii()
l=[lnii() for i in range(m)]

uf=UnionFind(n)
for a,b, in l:
  a-=1
  b-=1
  uf.union(a,b)

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

Solution (Python):

class UnionFind():
    
    
    def __init__(self, n):
        self.n = n
        
        
        self.root = [-1]*(n+1)
        
        self.rnk = [0]*(n+1)

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

    
    def Unite(self, x, y):
        
        x = self.Find_Root(x)
        y = self.Find_Root(y)
        
        if (x == y):
            return 
        
        
        elif (self.rnk[x] > self.rnk[y]):
            self.root[x] += self.root[y]
            self.root[y] = x

        else:
            self.root[y] += self.root[x]
            self.root[x] = y
        
        if(self.rnk[x] == self.rnk[y]):
            self.rnk[y] += 1

    
    def isSameGroup(self, x, y):
        return self.Find_Root(x) == self.Find_Root(y)

    
    def Count(self, x):
        return -self.root[self.Find_Root(x)]

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

L=[]

for i in range(N):
    root = uni.Find_Root(i)
    L.append(root)

print(len(set(L))-1)

Solution (Python):
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())
AB  = [list(map(int, input().split())) for _ in range(M)]
uf = UnionFind(N)
for a, b in AB:
    a -= 1
    b -= 1
    uf.union(a, b)
print(uf.group_count()-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 i in range(m):
    a,b=map(int,input().split())
    uf.union(a-1,b-1)

print(uf.group_count()-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())


def main():
    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)


if __name__ == "__main__":
    main()

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

import sys
sys.setrecursionlimit(10**9) 

root=[i for i in range(n+1)] 

def r(x):   
    if root[x]==x:
        return x
    else:
        root[x]=r(root[x])
        return root[x]

def unite(x,y):
    x=r(x)
    y=r(y)
    if x==y:
        return
    if x>y:
        x,y=y,x
    root[y]=x

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

ans=0
for i in range(1,n+1):
    if root[i]==i:
        ans+=1
print(ans-1)

Solution (Python):
class Union_Find():
    def __init__(self,N):
        """0,1,...,n-1を要素として初期化する.

        n:要素数
        """
        self.n=N
        self.parents=[-1]*N
        self.rank=[0]*N

    def find(self, x):
        """要素xの属している族を調べる.

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

    def union(self, x, y):
        """要素x,yを同一視する.

        x,y:要素
        """
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.rank[x]>self.rank[y]:
            self.parents[x] += self.parents[y]
            self.parents[y] = x
        else:
            self.parents[y] += self.parents[x]
            self.parents[x] = y

            if self.rank[x]==self.rank[y]:
                self.rank[y]+=1

    def size(self, x):
        """要素xの属している要素の数.

        x:要素
        """
        return -self.parents[self.find(x)]

    def same(self, x, y):
        """要素x,yは同一視されているか?

        x,y:要素
        """
        return self.find(x) == self.find(y)

    def members(self, x):
        """要素xが属している族の要素.
        ※族の要素の個数が欲しいときはsizeを使うこと!!

        x:要素
        """
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        """族の名前のリスト
        """
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        """族の個数
        """
        return len(self.roots())

    def all_group_members(self):
        """全ての族の出力
        """
        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())
U=Union_Find(N)

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

print(U.group_count()-1)

Solution (Python):
import math
from functools import reduce
from collections import deque
import sys
sys.setrecursionlimit(10**7)

def input():
    return sys.stdin.readline().strip()


def get_nums_l():
    return [ int(s) for s in input().split(" ")]


def get_all_int():
    return map(int, open(0).read().split())

def log(*args):
    print("DEBUG:", *args, file=sys.stderr)

class union_find():
    def __init__(self, n):
        self.nodes = n
        self.node_groups = [ i for i in range(n)]
        self.group_sizes = [ 1 for _ in range(n)]
        self.group_ranks = [ 0 for _ in range(n)]

    def root(self, i):
        if self.node_groups[i] == i:
            return i
        else:
            self.node_groups[i] = self.root(self.node_groups[i])
            return self.node_groups[i]

    def same(self, a, b):
        return self.root(a) == self.root(b)

    def size(self, i):
        return self.group_sizes[self.root(i)]

    def unite(self, a, b):
        a = self.root(a)
        b = self.root(b)

        if a == b:
            return

        if self.group_ranks[a] < self.group_ranks[b]:
            self.group_sizes[b] += self.size(a)
            self.node_groups[a] = b
        else:
            self.group_sizes[a] += self.size(b)
            self.node_groups[b] = a
            if self.group_ranks[a] == self.group_ranks[b]:
                self.group_ranks[a] += 1


def main():
    INF = 999999999999999999999999
    MOD = 10**9+7

    n,m = get_nums_l()

    uf = union_find(n)

    for i in range(m):
        a,b = get_nums_l()
        a-=1
        b-=1
        uf.unite(a,b)
    
    groups = len(set([ uf.root(i) for i in range(n) ]))

    print(groups-1)

main()

Solution (Python):
import sys
import math
from collections import deque

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()


def make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]


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

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

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

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

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

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

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

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


def main():
    N, M = NMI()
    uf = UnionFind(N)
    for i in range(M):
        a, b = NMI()
        a, b = a-1, b-1
        uf.unite(a, b)
    print(uf.group_count() - 1)


if __name__ == "__main__":
    main()

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

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

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

print(uf.group_count() - 1)

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())
    a -= 1
    b -= 1
    uf.union(a, b)
print(uf.group_count() - 1)

Solution (Python):
import sys
input = sys.stdin.readline

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



Group = [i for i in range(N)] 
Nodes = [1]*(N) 

def find(x):
    while Group[x] != x:
        x=Group[x]
    return x

def Union(x,y):
    if find(x) != find(y):
        if Nodes[find(x)] < Nodes[find(y)]:
            
            Nodes[find(y)] += Nodes[find(x)]
            Nodes[find(x)] = 0
            Group[find(x)] = find(y)
            
        else:
            Nodes[find(x)] += Nodes[find(y)]
            Nodes[find(y)] = 0
            Group[find(y)] = find(x)

for i in range(M):
    A,B=map(int,input().split())
    Union(A-1,B-1)

X=len(set([find(i) for i in range(N)]))

print(X-1)

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

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

    def same(self, x,y): return self.find(x)==self.find(y)
    def size(self,x): return -self.d[self.find(x)]
    
N,M=map(int,input().split())
uf = UnionFind(N)
for i in range(M):
  a,b=map(int,input().split())
  uf.unite(a-1,b-1)
  
ans = 0
for v in range(N):
  if uf.d[v]<0: ans += 1
    
print(ans-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 same(self,x,y):
        return self.find(x)==self.find(y)

    
    def size(self,x):
        return self.parents[self.find(x)]*(-1)

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

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

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

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

    
    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):
    x,y=map(int,input().split())
    x,y=x-1,y-1
    UF.union(x,y)

ans=UF.group_count()-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())
  a,b=a-1,b-1
  uf.union(a,b)
print(uf.group_count()-1)

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())
    
    

town = UnionFind(N)
for k in range(M):
  A, B = map(int, input().split())
  town.union(A-1, B-1)
print(town.group_count()-1)

Solution (Python):
import sys

sys.setrecursionlimit(10**6)
int1 = lambda x: int(x)-1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def MI1(): return map(int1, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

n,m=MI()
to=[[] for _ in range(n)]
for _ in range(m):
    u,v=MI1()
    to[u].append(v)
    to[v].append(u)

cnt=0
fin=[False]*n
for u in range(n):
    if fin[u]:continue
    fin[u]=True
    cnt+=1
    stack=[u]
    while stack:
        u=stack.pop()
        for v in to[u]:
            if fin[v]:continue
            fin[v]=True
            stack.append(v)

print(cnt-1)

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

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

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

        if x == y:
            return False
        else:
            if self.v[x] > self.v[y]:
                x, y = y, x
            self.v[x] += self.v[y]
            self.v[y] = x
            return True

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

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


def main():
    import sys
    input = sys.stdin.readline
    N, M = map(int, input().split())

    uf = UnionFind(N)
    for _ in range(M):
        a, b = (int(x) - 1 for x in input().split())
        uf.unite(a, b)

    cnt = 0
    for v in range(N):
        if uf.find(v) == v:
            cnt += 1

    print(cnt - 1)


if __name__ == '__main__':
    main()

Solution (Python):
n,m = map(int,input().split())
peer = [[] for _ in range(n)]
for _ in range(m):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  peer[a].append(b)
  peer[b].append(a)
seen = [0 for _ in range(n)]
ans = -1
for i in range(n):
  if seen[i]:
    continue
  ans += 1
  now = [i]
  while now:
    last = now
    now = []
    for x in last:
      for y in peer[x]:
        if not seen[y]:
          seen[y] = 1
          now.append(y)
print(ans)

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