Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())

from collections import defaultdict

# union find
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

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

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

        if x == y:
            return

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

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

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

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

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

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

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

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

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

uf = UnionFind(N)
REL = defaultdict(set)

for _ in range(M):
    a, b = map(int, input().split())
    # REL[a].add(b)
    # REL[b].add(a)
    a -= 1
    b -= 1
    if a > b:
        c = b
        b = a
        a = c

    uf.union(a, b)

mm = 0
for root in uf.roots():
    mm = max(mm, len(uf.members(root)))

ic = 0
for m in range(N):
    if uf.members(m) == 0:
        ic += 1

# for r, g in uf.all_group_members():
#     if len(g) == 1:
#         ic += 1
#     else:
#         mm = max(mm, len(g))

if mm < ic:
    mm += 1

print(mm)

Fixed submission:
N, M = map(int, input().split())

from collections import defaultdict

# union find
class UnionFind:
    def __init__(self, n):
        self.table = [-1] * n
 
    def _root(self, x):
        stack = []
        tbl = self.table
        while tbl[x] >= 0:
            stack.append(x)
            x = tbl[x]
        for y in stack:
            tbl[y] = x
        return x
 
    def find(self, x, y):
        return self._root(x) == self._root(y)
 
    def union(self, x, y):
        r1 = self._root(x)
        r2 = self._root(y)
        if r1 == r2:
            return
        d1 = self.table[r1]
        d2 = self.table[r2]
        if d1 <= d2:
            self.table[r2] = r1
            self.table[r1] += d2
        else:
            self.table[r1] = r2
            self.table[r2] += d1

uf = UnionFind(N)

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

    uf.union(a, b)

# member = defaultdict(int)
r = min(uf.table)
if r != -1:
    mm = abs(r)
    # ic = 0
    # for n in uf.table:
    #     if n == -1:
    #         ic += 1

    # if ic%mm != 0:
    #     mm += 1
else:
    mm = 1

print(mm)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())

from collections import defaultdict

# union find
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

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

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

        if x == y:
            return

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

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

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

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

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

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

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

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

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

uf = UnionFind(N)
REL = defaultdict(set)

for _ in range(M):
    a, b = map(int, input().split())
    # REL[a].add(b)
    # REL[b].add(a)
    a -= 1
    b -= 1
    if a > b:
        c = b
        b = a
        a = c

    uf.union(a, b)

mm = 0
for root in uf.roots():
    mm = max(mm, len(uf.members(root)))

ic = 0
for m in range(N):
    if uf.members(m) == 0:
        ic += 1

if mm < ic:
    mm += 1

print(mm)

Fixed submission:
N, M = map(int, input().split())

from collections import defaultdict

# union find
class UnionFind:
    def __init__(self, n):
        self.table = [-1] * n
 
    def _root(self, x):
        stack = []
        tbl = self.table
        while tbl[x] >= 0:
            stack.append(x)
            x = tbl[x]
        for y in stack:
            tbl[y] = x
        return x
 
    def find(self, x, y):
        return self._root(x) == self._root(y)
 
    def union(self, x, y):
        r1 = self._root(x)
        r2 = self._root(y)
        if r1 == r2:
            return
        d1 = self.table[r1]
        d2 = self.table[r2]
        if d1 <= d2:
            self.table[r2] = r1
            self.table[r1] += d2
        else:
            self.table[r1] = r2
            self.table[r2] += d1

uf = UnionFind(N)

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

    uf.union(a, b)

# member = defaultdict(int)
r = min(uf.table)
if r != -1:
    mm = abs(r)
    # ic = 0
    # for n in uf.table:
    #     if n == -1:
    #         ic += 1

    # if ic%mm != 0:
    #     mm += 1
else:
    mm = 1

print(mm)