Problem: An SNS has N users - User 1, User 2, \cdots, User N.  Between these N users, there are some relationships - M _friendships_ and K _blockships_.  For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.  For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i and User D_i.  We define User a to be a _friend candidate_ for User b when all of the following four conditions are satisfied:    * a \neq b.   * There is not a friendship between User a and User b.   * There is not a blockship between User a and User b.   * There exists a sequence c_0, c_1, c_2, \cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0, 1, \cdots, L - 1.  For each user i = 1, 2, ... N, how many friend candidates does it have?

Submission attempts (in order):
import sys
def input(): return sys.stdin.readline().strip()
N,M,K = map(int,input().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):
        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())
uni = UnionFind(N)
frd = [[] for i in range(N)]
bl = [[] for i in range(N)]
for i in range(M):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    uni.union(a,b)
    frd[a].append(b)
    frd[b].append(a)
for i in range(K):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    bl[a].append(b)
    bl[b].append(a)
ans = [0 for i in range(N)]
for i in range(N):
    a = set(uni.members(i)) - set(bl[i])
    print(len(a)-len(frd[i])-1,sep=' ')

import sys
def input(): return sys.stdin.readline().strip()
N,M,K = map(int,input().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):
        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())
uni = UnionFind(N)
frd = [0 for i in range(N)]
bl = [[] for i in range(N)]
for i in range(M):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    uni.union(a,b)
    frd[a] +=1
    frd[b] += 1
for i in range(K):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    bl[a].append(b)
    bl[b].append(a)
ans = [0 for i in range(N)]
for i in range(N):
    a = set(uni.members(i)) - set(bl[i])
    print(len(a)-frd[i]-1,end=' ')

import sys
def input(): return sys.stdin.readline().strip()
N,M,K = map(int,input().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):
        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())
uni = UnionFind(N)
fn = [0 for i in range(N)]
bl = [[] for i in range(N)]
bn = [0 for i in range(N)]
for i in range(M):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    uni.union(a,b)
    fn[a] +=1
    fn[b] += 1
for i in range(K):
    a,b= map(int,input().split())
    a -= 1
    b -= 1
    if uni.find(a) == uni.find(b):
        bn[a] += 1
        bn[b] += 1
ans = [0 for i in range(N)]
for i in range(N):
    ans[i] = uni.size(i) - bn[i] - fn[i] -1
print(' '.join([str(i) for i in ans]))

Verdicts: Time Limit Exceeded

Time Limit Exceeded

Accepted