Problem: 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?

Submission attempts (in order):
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())

union = UnionFind(N)

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

ans = 0

for i in range(N):
    ans = max(union.size(i))

print(ans)

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())
    
    
    # exp. {0: [0, 1, 4], 2: [2, 3]}
    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())

union = UnionFind(N)

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

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

print(ans)

Verdicts: Runtime Error

Accepted