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 UnionFindTree():
    def __init__(self, num_leaves):
        #self.num_leaves = num_leaves
        self.root = [i for i in range(num_leaves+1)]
        
    def find(self, leaf):
        if self.root[leaf] == leaf:
            return self.root[leaf]
        else:
            self.root[leaf] = self.find(self.root[leaf])
            return self.root[leaf]
        
    def union(self, leaf_a, leaf_b):
      	# find roots
        root_a = self.find(leaf_a)
        root_b = self.find(leaf_b)
        if root_a != root_b:
            # then union roots
            self.root[leaf_b] = root_a
            
        
N, M = map(int, input().split())
uft = UnionFindTree(N)
for m in range(M):
  a, b = map(int, input().split())
  uft.union(a, b)
  
max_size = max([[uft.find(n) for n in range(N)].count(n) for n in range(N+1)])
print(max_size)

class UnionFindTree():
    def __init__(self, num_leaves):
        #self.num_leaves = num_leaves
        self.root = [i for i in range(num_leaves+1)]
        
    def find(self, leaf):
        if self.root[leaf] == leaf:
            return self.root[leaf]
        else:
            self.root[leaf] = self.find(self.root[leaf])
            return self.root[leaf]
        
    def union(self, leaf_a, leaf_b):
      	# find roots
        root_a = self.find(leaf_a)
        root_b = self.find(leaf_b)
        if root_a != root_b:
            # then union roots
            self.root[leaf_b] = root_a
            
        
N, M = map(int, input().split())
uft = UnionFindTree(N)
for m in range(M):
  a, b = map(int, input().split())
  uft.union(a, b)
  

for n in range(N):
  uft.find(n)
  
num_group = len(set(uft.root))-1
print(num_group)

class UnionFindTree():
    def __init__(self, num_leaves):
        #self.num_leaves = num_leaves
        self.root = [i for i in range(num_leaves+1)]
        
    def find(self, leaf):
        if self.root[leaf] == leaf:
            return self.root[leaf]
        else:
            self.root[leaf] = self.find(self.root[leaf])
            return self.root[leaf]
        
    def union(self, leaf_a, leaf_b):
      	# find roots
        root_a = self.find(leaf_a)
        root_b = self.find(leaf_b)
        if root_a != root_b:
            # then union roots
            self.root[leaf_b] = root_a
            
        
N, M = map(int, input().split())
uft = UnionFindTree(N)
for m in range(M):
  a, b = map(int, input().split())
  uft.union(a, b)
  

for n in range(N):
  uft.find(n)
  
max_size = [uft.root.count(n) for n in range(N)].max()
print(num_group)

class UnionFindTree():
    def __init__(self, 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 main():
  N, M = map(int, input().split())
  uft = UnionFindTree(N)
  
  for m in range(M):
    a, b = map(lambda x: int(x)-1, input().split())
    uft.union(a, b)
    
  print(-min(uft.parents))
  
  
  
if __name__ == "__main__":
  main()

Verdicts: Wrong Answer

Wrong Answer

Runtime Error

Accepted