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):
#!/usr/bin/env python3
import sys
from collections import defaultdict

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
        self.ranks = [0] * 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.ranks[x] < self.ranks[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.ranks[x] == self.ranks[y]:
                self.ranks[x]+=1

        # if self.parents[x] > self.parents[y]:
        

        # 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())

def tup(a,b):
    return (min(a,b),max(a,b))

def solve(N: int, M: int, K: int, A: "List[int]", B: "List[int]", C: "List[int]", D: "List[int]"):
    friends = set()
    group = UnionFind(N)
    for i in range(M):
        friends.add(tup(A[i]-1,B[i]-1))
        group.union(A[i]-1,B[i]-1)
    for i in range(K):
        friends.add(tup(C[i]-1,D[i]-1))
    result = ""
    isFirst = True
    roots = group.roots()
    rootSets = {r: [] for r in roots }
    for i in range(N):
        r = group.find(i)
        rootSets[r].append(i)
    for i in range(N):
        c = 0
        r = group.find(i)
        # for g in rootSets[r]:
        #     if g != i and tup(i,g) not in friends:
        #         c+= 1
        if not isFirst:
            result+=" "
        else:
            isFirst = False
        result+=str(c)
    print(result)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    A = [int()] * (M)  # type: "List[int]"
    B = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    C = [int()] * (K)  # type: "List[int]"
    D = [int()] * (K)  # type: "List[int]"
    for i in range(K):
        C[i] = int(next(tokens))
        D[i] = int(next(tokens))
    solve(N, M, K, A, B, C, D)

if __name__ == '__main__':
    main()


#!/usr/bin/env python3
import sys
from collections import defaultdict

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
        self.ranks = [0] * 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.ranks[x] < self.ranks[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.ranks[x] == self.ranks[y]:
                self.ranks[x]+=1

        # if self.parents[x] > self.parents[y]:
        

        # 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())

def tup(a,b):
    return (min(a,b),max(a,b))

def solve(N: int, M: int, K: int, A: "List[int]", B: "List[int]", C: "List[int]", D: "List[int]"):
    friends = defaultdict(bool)
    group = UnionFind(N)
    for i in range(M):
        friends[tup(A[i]-1,B[i]-1)] = True
        group.union(A[i]-1,B[i]-1)
    for i in range(K):
        friends[tup(C[i]-1,D[i]-1)] = True
    result = ""
    isFirst = True
    roots = group.roots()
    rootSets = {r: set() for r in roots }
    for i in range(N):
        r = group.find(i)
        rootSets[r].add(i)
    
    #     c = 0
    #     r = group.find(i)
    #     for g in rootSets[r]:
    #         if g != i and not friends[tup(i,g)]:
    #             c+= 1
    #     if not isFirst:
    #         result+=" "
    #     else:
    #         isFirst = False
    #     result+=str(c)
    print(result)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    A = [int()] * (M)  # type: "List[int]"
    B = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    C = [int()] * (K)  # type: "List[int]"
    D = [int()] * (K)  # type: "List[int]"
    for i in range(K):
        C[i] = int(next(tokens))
        D[i] = int(next(tokens))
    solve(N, M, K, A, B, C, D)

if __name__ == '__main__':
    main()


#!/usr/bin/env python3
import sys
from collections import defaultdict

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
        self.ranks = [0] * 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.ranks[x] < self.ranks[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.ranks[x] == self.ranks[y]:
                self.ranks[x]+=1

        # if self.parents[x] > self.parents[y]:
        

        # 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())

def tup(a,b):
    return (min(a,b),max(a,b))

def solve(N: int, M: int, K: int, A: "List[int]", B: "List[int]", C: "List[int]", D: "List[int]"):
    friends = set()
    fc = [0 for i in range(N)]
    group = UnionFind(N)
    for i in range(M):
        friends.add(tup(A[i]-1,B[i]-1))
        group.union(A[i]-1,B[i]-1)
        fc[A[i]-1]+=1
        fc[B[i]-1]+=1
    for i in range(K):
        friends.add(tup(C[i]-1,D[i]-1))
        if group.find(C[i]-1) == group.find(D[i]-1):
            fc[C[i]-1]+=1
            fc[D[i]-1]+=1
    result = ""
    isFirst = True
    roots = group.roots()
    rootSets = {r: [] for r in roots }
    for i in range(N):
        r = group.find(i)
        rootSets[r].append(i)
    for i in range(N):
        r = group.find(i)
        c = len(rootSets[r]) - fc[i] - 1
        if not isFirst:
            result+=" "
        else:
            isFirst = False
        result+=str(c)
    print(result)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    A = [int()] * (M)  # type: "List[int]"
    B = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    C = [int()] * (K)  # type: "List[int]"
    D = [int()] * (K)  # type: "List[int]"
    for i in range(K):
        C[i] = int(next(tokens))
        D[i] = int(next(tokens))
    solve(N, M, K, A, B, C, D)

if __name__ == '__main__':
    main()


Verdicts: Wrong Answer

Wrong Answer

Accepted