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+1)

    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 + 1) 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()}





N,M = list(map(int,input().split()))
G  = UnionFind(N)
for i in range(M):
    a,b = map(int,input().split())
    G.union(a,b)
print(G.group_count()-2)

Solution (Python):
N,M = map(int,input().split())
AB = [tuple(map(int,input().split())) for i in range(M)]

class UnionFind:
    def __init__(self,N):
        self.parent = [i for i in range(N)]
        self._size = [1] * N
        self.count = 0
    def root(self,a):
        if self.parent[a] == a:
            return a
        else:
            self.parent[a] = self.root(self.parent[a])
            return self.parent[a]
    def is_same(self,a,b):
        return self.root(a) == self.root(b)
    def unite(self,a,b):
        ra = self.root(a)
        rb = self.root(b)
        if ra == rb: return
        if self._size[ra] < self._size[rb]: ra,rb = rb,ra
        self._size[ra] += self._size[rb]
        self.parent[rb] = ra
        self.count += 1
    def size(self,a):
        return self._size[self.root(a)]

uf = UnionFind(N)
for a,b in AB:
    a,b = a-1,b-1
    if uf.is_same(a,b): continue
    uf.unite(a,b)
for i in range(N):
    uf.root(i)

st = set()
for i in range(N):
    st.add(uf.root(i))
print(len(st) - 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 roots(self):
    return [i for i, x in enumerate(self.parents) if x < 0]

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

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

  def num_members(self,x):
    return abs(self.parents[self.find(x)])

  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)
cnt = 0
for i in range(M):
  a,b = map(int, input().split())
  if not uf.same(a-1,b-1):
    cnt += 1
    uf.union(a-1,b-1)
print(N-1-cnt)

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
n, m = map(int, input().split())
G = [[] for _ in range(n)]
for _ in range(m):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    G[a].append(b)
    G[b].append(a)
seen = [False]*n
def dfs(v):
    seen[v] = True
    stack = [v]
    while stack:
        v = stack.pop()
        for nv in G[v]:
            if seen[nv]:
                continue
            seen[nv] = True
            stack.append(nv)
ans = 0
for i in range(n):
    if not seen[i]:
        ans += 1
        dfs(i)
ans -= 1
print(ans)

Solution (Python):
import sys
sys.setrecursionlimit(10**9)
N,M=map(int,input().split())

def get_par(x):
  if x == par_list[x]:
    return x
  else:
    par_list[x] = get_par(par_list[x])
    return par_list[x]
def merge(x,y):
  par_x = get_par(x)
  par_y = get_par(y)
  if par_x != par_y:
    par_list[par_y] = par_x
    siz_list[par_x]+= siz_list[par_y]
def is_same(x,y):
  return get_par(x) == get_par(y)

par_list = list(range(N+1))
siz_list = [1]*(N+1)

for _ in range(M):
  a,b=map(int,input().split())
  merge(a,b)
  
for i in range(1,N+1):
  par_list[i]=get_par(i)
  siz_list[i]=siz_list[par_list[i]]
  
set_comp=set()
for i in range(1,N+1):
  set_comp.add(par_list[i])
  
print(len(set_comp)-1)

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

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

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

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

def main():
    n, m = map(int, input().split())
    union = UnionFind(n)
    for i in range(m):
        a, b = map(int, input().split())
        union.union(a, b)
    
    ans = -1
    for j in range(1, n+1):
        if union.par[j] < 0:
            ans += 1

    print(ans)


    
if __name__ == "__main__":
    main()

Solution (Python):
class UnionFind():
    def __init__(self,n):
        self.n=n
        self.parents = [i for i in range(n+1)]
        self.size = [1]*(n+1)
    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 unite(self,x,y):
        xRoot = self.find(x)
        yRoot = self.find(y)
        if xRoot == yRoot:
            return
        if self.size[xRoot]>self.size[yRoot]:
            self.parents[yRoot] = xRoot
            self.size[xRoot] += self.size[yRoot]
            self.size[yRoot] = 0
        else:
            self.parents[xRoot] = yRoot
            self.size[yRoot] += self.size[xRoot]
            self.size[xRoot] = 0

N,M = map(int,input().split())
tree = UnionFind(N)
for _ in range(M):
    a,b = map(int,input().split())
    tree.unite(a,b)
cnt = 0
for i in range(1,N+1):
    if tree.size[i] > 0:
        cnt += 1
print(cnt-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())
group = UnionFind(N)

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

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

Solution (Python):
import sys
sys.setrecursionlimit(1000000)
class UnionFind(object):
    def __init__(self, N):
        self.parent = [i for i in range(N)]
        self.size = [1 for i in range(N)]
    
    def merge(self, a, b):
        if self.issame(a,b):
            return
        pa = self.root(a)
        pb = self.root(b)
        self.parent[pa] = pb
        self.size[pb] += self.size[pa]
    def root(self, x):
        p = self.parent[x]
        if p == x:
            return x
        else:
            r = self.root(p)
            self.parent[x] = r
            return r
    
    def issame(self, x, y):
        return self.root(x) == self.root(y)
    
    def getsize(self, x):
        return self.size[self.root(x)]
n,m = map(int,input().split())
uf=UnionFind(n)
ans = n-1
for i in range(m):
    a,b = map(int,input().split())
    a-=1;b-=1
    if uf.issame(a,b):continue
    uf.merge(a,b)
    ans-=1
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:
            st = []
            while self.parents[x] >= 0:
                st.append(x)
                x = self.parents[x]
            for y in st:
                self.parents[y] = x
            return 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())
        a -= 1
        b -= 1
        uf.union(a,b)
    print(uf.group_count() - 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 union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

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

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

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

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

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

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

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

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

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

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

uf = UnionFind(n)
for i, j in ab:
    uf.union(i-1, j-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):
        """ 根を見つける関数を定義（同時にxを直接根にくっつける操作も行う）"""
        tmp = []
        parents = self.parents
        while parents[x] >= 0:
            tmp.append(x)
            x = parents[x]
        for y in tmp:
            parents[y] = x
        return x

    def union(self, x, y):
        """ 二つの木をくっつける（子を多く持つ方を根とした親子関係）。これは破壊的操作を行う。"""
        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):
        """ xとyが同じ根の子かを判定 """
        return self.find(x) == self.find(y)

    def size(self, x):
        """ xの根のparent（= 要素数）を返す """
        return -self.parents[self.find(x)]

    def members(self, x):
        """ xが属するグループの要素をリストとして返す O(N)"""
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        """ 全ての根の要素をリストとして返す O(N)"""
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        """ グループの数を返す O(1)"""
        return len(self.roots())

    def size_list(self):
        """ 各グループの要素数のリストを返す(根の番号は返さない) O(N)"""
        return [-x for x in self.parents if x < 0]

    def all_group_members(self):
        """ {根:[根の子(根を含む)のリスト],...}を辞書で返す O(N)"""
        res = [[] for _ in range(self.n)]
        for i in range(self.n):
            x = self.find(i)
            res[x].append(i)
        return {r: res[r] for r in self.roots()}

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


import sys
input = sys.stdin.readline


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

print(U.group_count()-1)

Solution (Python):
class UnionFind(object):
    def __init__(self, n=1):
        self.par = [i for i in range(n)]
        self.rank = [0 for _ in range(n)]
        self.size = [1 for _ in range(n)]

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

    def union(self, 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.par[y] = x
            self.size[x] += self.size[y]

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

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


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

ans = 0
for i in range(1, N):
    if not uf.is_same(0, i):
        uf.union(0, i)
        ans += 1

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())

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

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

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


N, M = map(int, input().split())
class UnionFind:
    def __init__(self, n=0):
        self.d = [-1]*n
        self.u = n
    def root(self, x):
        if self.d[x] < 0:
            return x
        self.d[x] = self.root(self.d[x])
        return self.d[x]
    def unite(self, x, y):
        x, y = self.root(x), self.root(y)
        if x == y:
            return False
        if x > y:
            x, y = y, x
        self.d[x] += self.d[y]
        self.d[y] = x
        self.u -= 1
        return True
    def same(self, x, y):
        return self.root(x) == self.root(y)
    def size(self, x):
        return -self.d[self.root(x)]
    def num_union(self):
        return self.u

uf = UnionFind(N)
G = [[] for _ in [0]*N]
for _ in [0]*M:
    a, b = map(int, input().split())
    a -= 1; b -= 1
    uf.unite(a, b)

print(uf.num_union()-1)

Solution (Python):
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 unite(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
        else:
            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)


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)
d = [0] * n
ans = 0
for i in range(n):
    p = uf.find(i)
    if d[p] == 0:
        ans += 1
        d[p] = 1
print(ans - 1)

Solution (Python):
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


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, readline().split())

    uf = UnionFind(N)

    for _ in range(M):
        A, B = map(lambda x: int(x) - 1, readline().split())
        uf.union(A, B)

    print(uf.group_count() - 1)


if __name__ == '__main__':
    main()

Solution (Python):
mod = 1000000007
eps = 10**-9


def main():
    import sys
    from collections import deque
    input = sys.stdin.readline

    N, M = map(int, input().split())
    adj = [[] for _ in range(N+1)]
    for _ in range(M):
        a, b = map(int, input().split())
        adj[a].append(b)
        adj[b].append(a)

    seen = [0] * (N+1)
    num = 0
    for v0 in range(1, N+1):
        if seen[v0]:
            continue
        num += 1
        que = deque()
        que.append(v0)
        while que:
            v = que.popleft()
            for u in adj[v]:
                if seen[u] == 0:
                    seen[u] = 1
                    que.append(u)
    print(num - 1)


if __name__ == '__main__':
    main()

Solution (Python):
class UnionFind:
    def __init__(self, N):
        self.p = list(range(N))
        self.rank = [0] * N
        self.size = [1] * N

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

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

    def unite(self, x, y):
        u = self.root(x)
        v = self.root(y)
        if u == v:
            return False
        if self.rank[u] < self.rank[v]:
            self.p[u] = v
            self.size[v] += self.size[u]
            self.size[u] = 0
        else:
            self.p[v] = u
            self.size[u] += self.size[v]
            self.size[v] = 0
            if self.rank[u] == self.rank[v]:
                self.rank[u] += 1
        return True

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

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

Solution (Python):
N, M = map(int, input().split())

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

    def merge(self, a, b):
        
        
        x = self.leader(a)
        y = self.leader(b)
        if x == y: return x
        if -self.par_size[x] < -self.par_size[y]: x, y = y, x
        self.par_size[x] += self.par_size[y]
        self.par_size[y] = x
        return x

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

    def leader(self, a):
        
        x = a
        while self.par_size[x] >= 0:
            x = self.par_size[x]
        while self.par_size[a] >= 0:
            self.par_size[a] = x
            a = self.par_size[a]
        return x

    def size(self, a):
        
        return -self.par_size[self.leader(a)]

    def groups(self):
        leader_buf = [0] * self.n
        group_size = [0] * self.n
        res = [[] for _ in range(self.n)]
        for i in range(self.n):
            leader_buf[i] = self.leader(i)
            group_size[leader_buf[i]] += 1
        for i in range(self.n):
            res[leader_buf[i]].append(i)
        res = [res[i] for i in range(self.n) if res[i]]
        return res

uf = DisjointSetUnion(N)

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

l = len(uf.groups())
print(l - 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)
print(uf.group_count() - 1)

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

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

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

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

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

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

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

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

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

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


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

	
	for i in range(N):
		UF.par[i] = UF.find(i)

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

	print(res - 1)




if __name__ == '__main__':
	main()

Solution (Python):

import bisect
import heapq
import math
import random
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from fractions import Fraction
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations, accumulate
from operator import add, mul, sub, itemgetter, attrgetter


import sys


readline = sys.stdin.readline

INF = 1 << 60


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


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


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


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


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


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


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


def mt(f):
    import time

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

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

    return wrap


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

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

        return self.__table[x]

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

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

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

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

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



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

    return uf.num_of_group() - 1


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


if __name__ == '__main__':
    main()