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):
n,m=map(int,input().split())
g=[[] for i in range(n)]
for i in range(m):
	u,v=map(int,input().split())
	u-=1
	v-=1
	g[u].append(v)
	g[v].append(u)

vis=[False]*n
stk=[]

cnt=0
tt=0
for i in range(n):
	if not vis[i]:
		cnt+=1
		stk.append(i)
	while len(stk)!=0:
		u=stk[-1]
		stk.pop()
		if vis[u]:
			continue
		vis[u]=True
		for v in g[u]:
			tt+=1
			if not vis[v]:
				stk.append(v)
print(cnt-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[x] = y

ans = 0
for i in range(m):
    a,b = map(int,input().split())
    unite(a,b)

for i in range(n):
    find(i+1)
par = par[1:]
ans = 0
from collections import Counter
t = Counter(par)
print(len(t)-1)

Solution (Python):
class UnionFind():
    """unionFindツリー
    FindとUnionがきも
    https://note.nkmk.me/python-union-find/
    """
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

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

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

        if x == y:
            return

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

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

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

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

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

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

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

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

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

N,M = map(int, input().split())
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):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        """要素xが属するグループの根を返す"""
        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が属するグループと要素yが属するグループを併合"""
        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):
        """要素xが属するグループのサイズを返す"""
        return -self.parents[self.find(x)]

    def same(self, x, y):
        """要素x, yが同じグループかどうか"""
        return self.find(x) == self.find(y)

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

    def roots(self):
        """すべての根の要素をリストで返す"""
        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"""
        return len(self.roots())

    def all_group_members(self):
        """{ルート要素: [そのグループの要素, ...], ...}を返す"""
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        """print()での表示用"""
        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())
    a, b = a - 1, b - 1
    uf.union(a, b)

print(uf.group_count() - 1)

Solution (Python):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from itertools import accumulate, permutations, combinations, product, groupby, combinations_with_replacement
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

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()

uf = UnionFind(N)

for _ in range(M):
    A, B = MAP()
    uf.union(A-1, B-1)

print(uf.group_count()-1)

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product, combinations_with_replacement 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    def permutations_count(n, r, MOD=None):
        ans = 1
        if MOD:            
            for i in range(r):
                ans = (ans * (n-i))%MOD
        else:
            for i in range(r):
                ans = (ans * (n-i))
        return ans
    from copy import deepcopy, copy 
    import operator
    
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd
    def gcd(a,b):
        
        
        if a<b:
            a, b = b, a
        while a%b !=0 :
            a, b = b, a%b
        return b

    
    
    
    
    
    

    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)

    
    def sieve_of_eratosthenes(end, typecode="L"):
        
        

        
        import array
        import textwrap
        assert end > 1
        
        
        
        is_prime = array.array("B", (True for i in range(end)))
        
        is_prime[0] = False
        is_prime[1] = False
        
        primes = array.array(typecode)
        
        for i in range(2, end):
            if is_prime[i]:
                primes.append(i)
                for j in range(2 * i, end, i):
                    is_prime[j] = False  
        return primes

    class PrimeFactorization:
        '''初期化にO(NloglogN)/ 因数分解クエリをO(log(k))/ 素数判定クエリをO(1)
        >>> pf = PrimeFactorization(100)
        >>> pf.query(100)
        ((2, 2), (5, 2))
        
        '''
        
        
        
        
        
        
        
        def __init__(self, Num=10**6):
            from collections import defaultdict
            from math import floor
            self.Num = Num
            self.D = [-1] * (Num+1)
            for i in range(2, Num+1):
                if self.D[i] != -1:
                    continue
                self.D[i] = i
                for j in range(1, floor(Num/i)+1):
                    if self.D[j*i] != -1:
                        continue
                    else:
                        self.D[j*i] = i
        
        def query(self, k):
            ans = defaultdict(int)
            tmp = k
            while self.D[tmp] != -1:
                div = self.D[tmp]
                ans[div] += 1
                tmp = tmp//div
            return tuple(ans.items())
        
        def is_prime(self, k):
            return k == self.D[k]

    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrstuvwxyz') 
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    
    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something like:
        >>      pass
        >>  else:
        >>      do something like:
        >>      L[find_root(a)] = L[find_root(a)] + L[find_root(b)]
        >>      L[find_root(b)] = L[find_root(a)]
        >>      
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        
        操作	    segfunc	        単位元
        最小値	    min(x, y)	    float('inf')
        最大値	    max(x, y)	    -float('inf')
        区間和	    x + y	        0
        区間積	    x * y	        1
        最大公約数	math.gcd(x, y)	0
        
        >>  seg = SegTree([14, 5, 9, 13], min, float('inf'))
        >>  seg.update(k, x) 
        >>  seg.query(l, r) 
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    
    
    
    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        
        
        
        
        
        
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
    
    
    import random
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    N, M = R()
    AB = [R() for _ in range(M)]
    uf = UnionFindTree(N)
    for a, b in AB:
        a -= 1
        b -= 1
        if uf.find_root(a) == uf.find_root(b):
            pass
        else:
            uf.unite(a, b)
    cnt = 0
    for i in range(1, N):
        if uf.find_root(0) != uf.find_root(i):
            cnt += 1
            uf.unite(0, i)
    print(cnt)
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    https://atcoder.jp/contests/abc173/submissions/14966961
    for i in range(1<<h):
	    if (i >> x) & 1:
            hoge
    (1 >> x) & 1 でNビット目のビット値を取得している
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    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 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())
un = UnionFind(n)
for _ in range(m):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    un.union(a, b)
print(un.group_count() - 1)

Solution (Python):
import sys
if sys.argv[-1] == 'ONLINE_JUDGE':
    import os
    import re
    with open(__file__) as f:
        source = f.read().split('
    for s in source[1:]:
        s = re.sub("'''.*", '', s)
        sp = s.split(maxsplit=1)
        if os.path.dirname(sp[0]):
            os.makedirs(os.path.dirname(sp[0]), exist_ok=True)
        with open(sp[0], 'w') as f:
            f.write(sp[1])
    from nbmodule import cc
    cc.compile()
import numpy as np
from numpy import int64
from nbmodule import solve


f = open(0)
N, M = [int(x) for x in f.readline().split()]
AB = np.fromstring(f.read(), dtype=int64, sep=' ').reshape((-1, 2))
ans = solve(N, AB)
print(ans)

'''

import numpy as np
from numpy import int64
from numba import njit
from numba.types import i8
from numba.pycc import CC
import nbacl.dsu as dsu
cc = CC('nbmodule')


@cc.export('solve', (i8, i8[:, ::1]))
def solve(N, AB):
    t = np.full(N, -1, dtype=int64)
    for i in range(AB.shape[0]):
        dsu.merge(t, AB[i, 0] - 1, AB[i, 1] - 1)
    ret = 0
    for _ in dsu.groups(t):
        ret += 1
    return ret - 1

if __name__ == '__main__':
    cc.compile()


import numpy as np
from numpy import int64
from numba import njit


@njit
def dsu(t):
    t = -1


@njit
def merge(t, x, y):
    u = leader(t, x)
    v = leader(t, y)

    if u == v:
        return u

    if -t[u] < -t[v]:
        u, v = v, u

    t[u] += t[v]
    t[v] = u

    return u


@njit
def same(t, x, y):
    return leader(t, x) == leader(t, y)


@njit
def leader(t, x):
    if t[x] < 0:
        return x
    t[x] = leader(t, t[x])
    return t[x]


@njit
def size(t, x):
    return -t[leader(t, x)]


@njit
def groups(t):
    for i in range(t.shape[0]):
        if t[i] < 0:
            yield i

'''

Solution (Python):
from sys import setrecursionlimit, stdin
import numpy as np

readline = stdin.readline
setrecursionlimit(10 ** 6)

def find(parent, i):
    t = parent[i]
    if t < 0:
        return i
    t = find(parent, t)
    parent[i] = t
    return t
  
def unite(parent, i, j):
    i = find(parent, i)
    j = find(parent, j)
    if i == j:
        return
    parent[j] += parent[i]
    parent[i] = j

N,M = map(int,readline().split())
parent = - np.ones(N,int)

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

ans = 0
for i in range(N):
    if parent[i] < 0:
        ans += 1
print(ans-1)

Solution (Python):


















class UnionFind:
    
    def __init__(s, n):
        s.n_ = n
        s.ngroups_ = n
        s.parent_  = [i for i in range(n+1)]
          

    
    def n(s):
        return s.n_

    
    def ngroups(s):
        return s.ngroups_

    
    
    def find(s, i):
        x = i
        while True:
            y = s.parent_[x]
            if x == y:
                
                s.parent_[i] = x
                return x
            else:
                x = y

    
    def same_group(s, i, j):
        return s.find(i) == s.find(j)

    
    def items(s):
        return ((i, s.find(i)) for i in range(1, s.n_ + 1))

    
    
    def union(s, i, j):
        x, y = s.find(i), s.find(j)
        if x == y:
            
            return False
        else:
            s.parent_[x] = y
            s.parent_[i] = y
            s.ngroups_ -= 1
            return True


N, M = [int(x) for x in input().split()]

U = UnionFind(N)


for _ in range(M):
    a, b = [int(x) for x in input().split()]
    U.union(a, b)


answer = U.ngroups() - 1
print(answer)

Solution (Python):
import sys
def input():
    return sys.stdin.readline()[:-1]
N,M=map(int,input().split())
sys.setrecursionlimit(200000)
class uf:
    def __init__(self,n):
        self.n=n
        self.l=[-1]*n
    def ro(self,n):         
        if self.l[n]<0:
            return n
        r=self.ro(self.l[n])
        self.l[n]=r
        return r
    def me(self,a,b):       
        ra=self.ro(a)
        rb=self.ro(b)
        if self.l[ra]>self.l[rb]:
            ra,rb=rb,ra
        if ra!=rb:
            self.l[ra]+=self.l[rb]
            self.l[rb]=ra
    def size(self,n):
        return -self.l[self.ro(n)]
    def sa(self,a,b):       
        return self.ro(a)==self.ro(b)
    def rl(self):           
        return [i for i,v in enumerate(self.l) if v<0]
    
    def len(self):          
        return len(self.rl())
    def ul(self):
        d={n:i for i,n in enumerate(self.rl())}
        m=[[]for i in range(self.len())]
        for i in range(self.n):
            m[d[self.ro(i)]].append(i)
        return m
    def __str__(self):
        return f"{self.ul()}"
    def __setitem__(self,i,v):
        self.l[i]=v
u=uf(N)
for i in range(M):
    u.me(*map(lambda x: int(x)-1,input().split()))
print(u.len()-1)