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):
def root(x):
  if par[x] == x:
    return x
  par[x] = 1
  return par[x]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0
    
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 1)]
for i in range(1, n + 1):
  countpar[root(par[i])] += 1
print(max(countpar))


def root(i):
  if par[i] == i:
    return i
  par[i] = root(par[i])
  return par[i]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[ry] = rx

def same(x, y):
  return par[x] == par[y]

n,m = map(int, input().split(" "))
p = [0] + list(map(int, input().split(" ")))
a = [(list(map(int, input().split(" ")))) for i in range(m)]
par = list(range(n + 1))
count = 0
for i, j in a:
  union(i, j)
  #print(par)
#print(p)
for i in range(1, n):
  if same(root(par[p[i]]), root(par[i])):
    count += 1
print(count)

def root(x):
  if par[x] == x:
    return x
  par[x] = root(par[x])
  return 1

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0
    
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 1)]
for i in range(1, n + 1):
  countpar[root(par[i])] += 1
print(max(countpar))


def root(i):
  if par[i] == i:
    return i
  par[i] = root(par[i])
  return par[i]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[ry] = rx

def same(x, y):
  return par[x] == par[y]

n,m = map(int, input().split(" "))
p = [0] + list(map(int, input().split(" ")))
a = [(list(map(int, input().split(" ")))) for i in range(m)]
par = list(range(n + 1))
count = 0
for i, j in a:
  union(i, j)
  #print(par)
#print(p)
for i in range(1, n + 1):
  if same(root(par[p[i]]), root(par[i])):
    count += 1
print(count)

def root(x):
  if par[x] == x:
    return x
  par[x] = root(par[x])
  return par[x]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0
    
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 3)]
for i in range(1, n + 1):
  countpar[i] += 1
print(max(countpar))


def root(x):
  if par[x] == x:
    return x
  par[x] = root(par[x])
  return par[x]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0
    
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 1)]
for i in range(1, n + 1):
  print(i)
print(max(countpar))


def root(x):
  return 1
  if par[x] == x:
    return x
  par[x] = root(par[x])
  return par[x]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0
    
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 1)]
for i in range(1, n + 1):
  countpar[root(par[i])] += 1
print(max(countpar))


def root(i):
  if par[i] == i:
    return i
  par[i] = root(par[i])
  return par[i]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[ry] = rx

def same(x, y):
  return par[x] == par[y]

n,m = map(int, input().split(" "))
p = [0] + list(map(int, input().split(" ")))
a = [(list(map(int, input().split(" ")))) for i in range(m)]
par = list(range(n + 1))
count = 0
for i, j in a:
  union(i, j)
  #print(par)
#print(p)
for i in range(1, n + 5):
  if same(root(par[p[i]]), root(par[i])):
    count += 1
print(count)

import sys
import resource

def root(x):
  if par[x] == x:
    return x
  par[x] = root(par[x])
  return par[x]

def union(x, y):
  rx = root(x)
  ry = root(y)
  if rx != ry:
    par[rx] = ry
  return 0

sys.setrecursionlimit(10 ** 6)
n, m=map(int, input().split(" "))
par = list(range(n + 1))
for i in range(m):
  a, b = map(int, input().split(" "))
  union(a, b)
#print(par)
maxi = 0
count = 1
#print(par)
countpar = [0 for i in range(n + 1)]

for i in range(1, n + 1):
  countpar[root(par[i])] += 1
print(max(countpar))
#print(countpar, par)


Verdicts: Wrong Answer

Runtime Error

Runtime Error

Runtime Error

Wrong Answer

Wrong Answer

Wrong Answer

Runtime Error

Accepted