Problem:


Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3



Sample input:
5 3
1 2
3 4
5 1


Sample output:
3

Submission status: Accepted

Solution code:
from math import inf, log2


class SegmentTree:
    def __init__(self, array, func=max):
        self.n = len(array)
        self.size = 2**(int(log2(self.n-1))+1) if self.n != 1 else 1
        self.func = func
        self.default = 0 if self.func != min else inf
        self.data = [self.default] * (2 * self.size)
        self.process(array)

    def process(self, array):
        self.data[self.size : self.size+self.n] = array
        for i in range(self.size-1, -1, -1):
            self.data[i] = self.func(self.data[2*i], self.data[2*i+1])

    def query(self, alpha, omega):
        """Returns the result of function over the range (inclusive)!"""
        if alpha == omega:
            return self.data[alpha + self.size]
        res = self.default
        alpha += self.size
        omega += self.size + 1
        while alpha < omega:
            if alpha & 1:
                res = self.func(res, self.data[alpha])
                alpha += 1
            if omega & 1:
                omega -= 1
                res = self.func(res, self.data[omega])
            alpha >>= 1
            omega >>= 1
        return res

    def update(self, index, value):
        """Updates the element at index to given value!"""
        index += self.size
        self.data[index] = value
        index >>= 1
        while index:
            self.data[index] = self.func(self.data[2*index], self.data[2*index+1])
            index >>= 1


# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# ------------------- fast io --------------------
from math import gcd, ceil

def pre(s):
    n = len(s)
    pi = [0] * n
    for i in range(1, n):
        j = pi[i - 1]
        while j and s[i] != s[j]:
            j = pi[j - 1]
        if s[i] == s[j]:
            j += 1
        pi[i] = j
    return pi


def prod(a):
    ans = 1
    for each in a:
        ans = (ans * each)
    return ans

def lcm(a, b): return a * b // gcd(a, b)


def binary(x, length=16):
    y = bin(x)[2:]
    return y if len(y) >= length else "0" * (length - len(y)) + y

def connected_components(n, graph):
    components, visited = [], [False] * n

    def dfs(start):
        component, stack = [], [start]

        while stack:
            start = stack[-1]

            if visited[start]:
                stack.pop()
                continue
            else:
                visited[start] = True
                component.append(start)

            for i in graph[start]:
                if not visited[i]:
                    stack.append(i)

        return component

    for i in range(1,n):
        if not visited[i]:
            components.append(dfs(i))

    return components

for _ in range(int(input()) if not True else 1):
    #n = int(input())
    #d, t, s = map(int, input().split())
    n, m = map(int, input().split())
    #c, d = map(int, input().split())
    graph = [[] for _ in range(n+1)]
    for i in range(m):
        x, y=  map(int, input().split())
        graph[x] += [y]
        graph[y] += [x]
    c = connected_components(n+1, graph)
    ans = 0
    for i in c:ans = max(ans, len(i))
    print(ans)

Submission status: Accepted

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

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

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

        if x == y:
            return

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

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

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

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

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

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

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

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

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
N,M = map(int,input().split())
uf = UnionFind(N)
for i in range(M):
    A,B = map(int,input().split())
    uf.union(A-1,B-1)
ans = 0
for i in uf.roots():
    ans = max(uf.size(i),ans)
print(ans)

Submission status: Accepted

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

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

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

    if x == y:
      return

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

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

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

  def roots(self):
    return max([abs(x) 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)
for i in range(M):
  a,b = map(int, input().split())
  uf.union(a-1,b-1)
ans = uf.roots()
print(ans)

Submission status: Accepted

Solution code:
#!/usr/bin/env python
#pyrival orz
import os
import sys
from io import BytesIO, IOBase

"""
    for _ in range(int(input())):
    n,m=map(int,input().split())
    n=int(input())
    a = [int(x) for x in input().split()]
"""

class DisjointSetUnion:
    def __init__(self, n):
        self.parent = list(range(n))
        self.size = [1] * n
        self.num_sets = n

    def find(self, a):
        acopy = a
        while a != self.parent[a]:
            a = self.parent[a]
        while acopy != a:
            self.parent[acopy], acopy = a, self.parent[acopy]
        return a

    def union(self, a, b):
        a, b = self.find(a), self.find(b)
        if a != b:
            if self.size[a] < self.size[b]:
                a, b = b, a

            self.num_sets -= 1
            self.parent[b] = a
            self.size[a] += self.size[b]

    def set_size(self, a):
        return self.size[self.find(a)]

    def __len__(self):
        return self.num_sets

def main():
    n,m=map(int,input().split())
    a=DisjointSetUnion(n)
    for _ in range(m):
        u,v=map(int,input().split())
        a.union(u-1,v-1)
    ans=0
    for i in range(n):
        ans=max(ans,a.set_size(i))

    print(ans)

# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
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)

ans = 0
for i in range(N):
    ans = max(ans, uf.size(i))
print(ans)

Submission status: Accepted

Solution code:
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]

class UnionFind:
    def __init__(self, n):
        self.state = [-1] * n
        self.size_table = [1] * n
        # cntはグループ数
        # self.cnt = n

    def root(self, u):
        v = self.state[u]
        if v < 0: return u
        self.state[u] = res = self.root(v)
        return res

    def merge(self, u, v):
        ru = self.root(u)
        rv = self.root(v)
        if ru == rv: return
        du = self.state[ru]
        dv = self.state[rv]
        if du > dv: ru, rv = rv, ru
        if du == dv: self.state[ru] -= 1
        self.state[rv] = ru
        # self.cnt -= 1
        self.size_table[ru] += self.size_table[rv]
        return

    # グループの要素数
    def size(self, u):
        return self.size_table[self.root(u)]

n,m=MI()
uf=UnionFind(n)
for _ in range(m):
    a,b=MI1()
    uf.merge(a,b)
ans=1
print(max(uf.size_table))

Submission status: Accepted

Solution code:
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)

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

    # 併合
    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
            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

    # 同じ集合に属するか判定
    def same_check(self, x, y):
        return self.find(x) == self.find(y)


n, m = map(int, input().split())
uf = UnionFind(n)
for _ in range(m):
    a, b = map(int, input().split())
    uf.unite(a - 1, b - 1)
ans = 0
for i in range(n):
    ans = max(ans, uf.size[uf.find(i)])
print(ans)

Submission status: Accepted

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

class UnionFind():
    '''
    UnionFindでグラフの状態を管理する
    '''
    def __init__(self, n):
        self.n = n
        self.root = [-1]*(n+1)
        self.rnk = [0]*(n+1)

    def find_root(self, x):
        '''
        ルートのノードを見つける
        '''
        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):
        '''
        ノード同士を連結する
        '''
        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):
        '''
        同一のルーツを持つかどうか調査する
        '''
        return self.find_root(x) == self.find_root(y)

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

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

ans = 0
for i in range(N):
    ans = max(ans, uf.count(i))

print(ans)

Submission status: Accepted

Solution code:
import sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

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

#Union Find

#xの根を求める
def find(x):
    if par[x] < 0:
        return x
    else:
        par[x] = find(par[x])
        return par[x]
#xとyの属する集合の併合
def unite(x,y):
    x = find(x)
    y = find(y)

    if x == y:
        return False
    else:
        #sizeの大きいほうがx
        if par[x] > par[y]:
            x,y = y,x
        par[x] += par[y]
        par[y] = x
        return True

#xとyが同じ集合に属するかの判定
def same(x,y):
    return find(x) == find(y)

#xが属する集合の個数
def size(x):
    return -par[find(x)]

#初期化
#根なら-size,子なら親の頂点
par = [-1]*n

###具体例###
for _ in range(m):
    a, b = [int(x) for x in input().split()]
    unite(a - 1, b - 1)

ans = -float('inf')

for i in range(n):
    ans = max(ans, size(i))

print(ans)

Submission status: Accepted

Solution code:
import sys
input = lambda: sys.stdin.readline().rstrip()
N, M = map(int, input().split())
X = [[] for _ in range(N)]
for _ in range(M):
    a, b = map(int, input().split())
    X[a-1].append(b-1)
    X[b-1].append(a-1)

def col(n, E):
    C = [-1] * n
    c = 0
    for i in range(n):
        if C[i] >= 0: continue
        Q = [i]
        C[i] = c
        while Q:
            x = Q.pop()
            for y in E[x]:
                if C[y] == -1:
                    C[y] = C[x]
                    Q.append(y)
        c += 1
    return C

Y = [0] * N
for i in col(N, X):
    Y[i] += 1
print(max(Y))

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

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

# UnionFind

Group = [i for i in range(N)] # グループ分け
Nodes = [1]*N # 各グループのノードの数

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

from collections import Counter

print(max(Counter([find(x) for x in range(N)]).values()))

Submission status: Accepted

Solution code:
from collections import deque
def bfs(start):
    q=deque([start])
    vis[start]=1
    res=1
    while q:
        v=q.popleft()
        for to in g[v]:
            if not vis[to]:
                vis[to]=1
                q.append(to)
                res+=1
    return res
input=__import__('sys').stdin.readline
n,m=map(int,input().split())
g=[[]for _ in range(n+1)]
vis=[0]*(n+1)
for _ in range(m):
    a,b=map(int,input().split())
    g[a]+=b,
    g[b]+=a,
ans=0
for i in range(1,n+1):
    if not vis[i]:ans=max(ans,bfs(i))
print(ans)

Submission status: Accepted

Solution code:
import sys

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('.') for s in readline() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().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):
        ret = dict()
        for i in range(self.n):
            r = self.find(i)
            if r in ret:
                ret[r].append(i)
            else:
                ret[r] = [i]
        return ret

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


def main():

    N, M = in_nn()
    uni = UnionFind(N)

    for i in range(M):
        a, b = in_nn()
        a, b = a - 1, b - 1
        uni.union(a, b)

    roots = uni.roots()

    ans = 0
    for r in roots:
        ans = max(ans, uni.size(r))

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
def Find(x, par):
    if par[x] < 0:
        return x
    else:
        par[x] = Find(par[x], par)
        return par[x]

def Unite(x, y, par, rank):
    x = Find(x, par)
    y = Find(y, par)

    if x != y:
        if rank[x] < rank[y]:
            par[y] += par[x]
            par[x] = y
        else:
            par[x] += par[y]
            par[y] = x
            if rank[x] == rank[y]:
                rank[x] += 1

def Same(x, y, par):
    return Find(x, par) == Find(y, par)

def Size(x, par):
    return -par[Find(x, par)]

import sys
input = sys.stdin.readline

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

par = [-1]* n
rank = [0]*n

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

ans = 1
for i in range(n):
    if par[i] < 0:
        ans = max(ans, -par[i])
print(ans)

Submission status: Accepted

Solution code:
'''
自宅用PCでの解答
'''
import math
#import numpy as np
import itertools
import queue
import bisect
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)
mod = 10**9+7 #998244353
dir = [(-1,0),(0,-1),(1,0),(0,1)]
alp = "abcdefghijklmnopqrstuvwxyz"

#UnionFindのクラス,0-indexed
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,ipt().split())
    uf = UnionFind(n)
    for i in range(m):
        a,b = map(int,ipt().split())
        uf.union(a-1,b-1)

    rt = uf.roots()
    ma = 0
    for i in rt:
        sz = uf.size(i)
        if ma < sz:
            ma = sz

    print(ma)

    return None

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
# D - Friends

class UnionFind():
    
    # インデックスは0-start
    # 初期化
    def __init__(self, n):
        self.n = n
        self.parents = [-1]*n
        self.group = n
    
    # private function
    def root(self, x):
        if self.parents[x]<0:
            return x
        else:
            self.parents[x] = self.root(self.parents[x])
            return self.parents[x]
    
    # x,yが属するグループの結合
    def union(self, x, y):
        x = self.root(x)
        y = self.root(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
        self.group -= 1
    
    # x,yが同グループか判定
    def same(self, x, y):
        return self.root(x)==self.root(y)

    # xと同じグループの要素数を取得
    def size(self, x):
        return -self.parents[self.root(x)]

N,M = map(int,input().split())
friend = UnionFind(N)
for _ in range(M):
    x,y = map(int,input().split())
    friend.union(x-1,y-1)
ans = 0
for i in range(N):
    ans = max(ans,friend.size(i))
print(ans)

Submission status: Accepted

Solution code:
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)

M=0
V=U.roots()
for v in V:
    M=max(M,U.size(v))

print(M)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(300000)
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)
for i in range(m):
    a,b = map(int,input().split())
    a-=1;b-=1
    uf.merge(a,b)
ma = 0
for i in range(n):
    ma = max(ma, uf.getsize(i))
print(ma)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    ################
    class UnionFind():
        """
        parents : 親要素(findしない場合は根ではないことの注意)，根の場合は"-(要素数）"
        find(x):要素xの属するグループの根を返す
        size(x):要素xの属するグループの要素数を返す
        same(x,y):x,yが同じグループに属しているか返す
        重いかも！　　members(x):要素xが属するグループに属する要素をリストで返す
        roots():全ての根の要素を返す
        group_count():グループの数を返す
        重いかも！　all_group_members():{根要素：[そのグループに含まれる要素のリスト]}の辞書を返す
        """
        def __init__(self, n):
            self.n = n
            self.parents = [-1] * n

        def find(self, x):
            #根を探す&つなぎかえる
            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=MI()
    uf=UnionFind(N)
    
    for _ in range(M):
        a,b=MI()
        a-=1
        b-=1
        uf.union(a,b)
        
    ans=0
    
    from collections import defaultdict
    dd = defaultdict(int)
    
    for i in range(N):
        root=uf.find(i)
        dd[root]+=1
        
    for k,v in dd.items():
        s=uf.size(k)
        ans=max(ans,s)
        
    print(ans)
        
        
    

main()