Problem:
 Score : 400 points    Problem Statement 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?      Constraints  All values in input are integers.  2 ≤ N ≤ 10^5  0 \leq M \leq 10^5  0 \leq K \leq 10^5  1 \leq A_i, B_i \leq N  A_i \neq B_i  1 \leq C_i, D_i \leq N  C_i \neq D_i  (A_i, B_i) \neq (A_j, B_j) (i \neq j)  (A_i, B_i) \neq (B_j, A_j)  (C_i, D_i) \neq (C_j, D_j) (i \neq j)  (C_i, D_i) \neq (D_j, C_j)  (A_i, B_i) \neq (C_j, D_j)  (A_i, B_i) \neq (D_j, C_j)         Input Input is given from Standard Input in the following format:  N  M  K  A_1  B_1  \vdots  A_M  B_M  C_1  D_1  \vdots  C_K  D_K       Output Print the answers in order, with space in between.        Sample Input 1 4 4 1
2 1
1 3
3 2
3 4
4 1      Sample Output 1 0 1 0 1  There is a friendship between User 2 and 3 , and between 3 and 4 . Also, there is no friendship or blockship between User 2 and 4 . Thus, User 4 is a friend candidate for User 2 .  However, neither User 1 or 3 is a friend candidate for User 2 , so User 2 has one friend candidate.       Sample Input 2 5 10 0
1 2
1 3
1 4
1 5
3 2
2 4
2 5
4 3
5 3
4 5      Sample Output 2 0 0 0 0 0  Everyone is a friend of everyone else and has no friend candidate.       Sample Input 3 10 9 3
10 1
6 7
8 2
2 5
8 4
7 3
10 9
6 4
5 8
2 6
7 5
3 1      Sample Output 3 1 3 5 4 3 3 3 3 1 0

Solution (Python):



def solve(*args: str) -> str:
    n, m, k = map(int, args[0].split())

    friends = [set() for _ in range(n+1)]
    blocked = [set() for _ in range(n+1)]

    for a, b in map(str.split, args[1:1+m]):
        friends[int(a)].add(int(b))
        friends[int(b)].add(int(a))

    for c, d in map(str.split, args[1+m:1+m+k]):
        blocked[int(c)].add(int(d))
        blocked[int(d)].add(int(c))

    checked = set()

    ret = [0]*(n+1)
    for a in range(1, n+1):
        if a in checked:
            continue

        chain = set()

        stack = list(friends[a])
        while stack:
            b = stack.pop()
            if b in checked:
                continue

            checked.add(b)
            chain.add(b)
            stack.extend(friends[b])

        count = len(chain) - 1
        for i in chain:
            ret[i] += count - len(chain & (friends[i] | blocked[i]))

    return ' '.join(map(str, ret[1:]))


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))

Solution (Python):
import sys



class UnionFind():
    
    
    def __init__(self, n):
        self.n = n
        
        
        self.root = [-1]*(n+1)
        
        self.rnk = [0]*(n+1)

    
    def Find_Root(self, x):
        if(self.root[x] < 0):
            return x
        else:
            
            self.root[x] = self.Find_Root(self.root[x])
            return self.root[x]
    
    def Unite(self, x, y):
        
        x = self.Find_Root(x)
        y = self.Find_Root(y)
        
        if(x == y):
            return 
        
        elif(self.rnk[x] > self.rnk[y]):
            self.root[x] += self.root[y]
            self.root[y] = x

        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            
            if(self.rnk[x] == self.rnk[y]):
                self.rnk[y] += 1
    
    def isSameGroup(self, x, y):
        return self.Find_Root(x) == self.Find_Root(y)

    
    def Count(self, x):
        return -self.root[self.Find_Root(x)]

def resolve():
    int1 = lambda x: int(x) - 1
    readline=sys.stdin.readline

    n,m,k=map(int, readline().strip().split())

    uf = UnionFind(n)

    exc=[0]*n

    for i in range(m):
        a,b=map(int1, readline().strip().split())
        uf.Unite(a,b)
        exc[a]+=1
        exc[b]+=1
    
    for i in range(k):
        a,b=map(int1, readline().strip().split())
        if uf.isSameGroup(a,b):
            exc[a]+=1
            exc[b]+=1
    
    rescnt=[]

    for i in range(n):
        
        
        if i==(n-1):
            print(uf.Count(i)-1-exc[i])
        else:
            print(uf.Count(i)-1-exc[i],end=" ")
    
        

resolve()

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)
        self.__rank = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x == y:
            return

        if self.__rank[x] < self.__rank[y]:
            self.__table[x] = y
            self.__size[y] += self.__size[x]
        else:
            self.__table[y] = x
            self.__size[x] += self.__size[y]
            if self.__rank[x] == self.__rank[y]:
                self.__rank[x] += 1

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    f = UnionFind()
    for a, b in AB:
        f.union(a, b)

    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)
        self.__rank = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x == y:
            return

        if self.__rank[x] < self.__rank[y]:
            self.__table[x] = y
            self.__size[y] += self.__size[x]
        else:
            self.__table[y] = x
            self.__size[x] += self.__size[y]
            if self.__rank[x] == self.__rank[y]:
                self.__rank[x] += 1

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    f = UnionFind()
    for a, b in AB:
        f.union(a, b)

    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):

from sys import setrecursionlimit


def dfs(node: int):
    if checked[node]:
        return

    checked[node] = True
    chain.add(node)
    for n in friends[node]:
        dfs(n)


def solve(*args: str) -> str:
    setrecursionlimit(2 * 10 ** 9)
    n, m, k = map(int, args[0].split())

    global friends
    friends = {i: set() for i in range(n+1)}
    blocked = {i: set() for i in range(n+1)}

    for a, b in map(str.split, args[1:1+m]):
        friends[int(a)].add(int(b))
        friends[int(b)].add(int(a))

    for c, d in map(str.split, args[1+m:1+m+k]):
        blocked[int(c)].add(int(d))
        blocked[int(d)].add(int(c))

    global checked
    checked = [False]*(n+1)

    ret = [0]*(n+1)
    for a in range(1, n+1):
        if checked[a]:
            continue

        global chain
        chain = set()
        dfs(a)
        count = len(chain) - 1
        for i in chain:
            ret[i] += count - len(chain & (friends[i] | blocked[i]))

    return ' '.join(map(str, ret[1:]))


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if self.size(x) > self.size(y):
            x, y = y, x
        if x != y:
            self.__size[y] += self.__size[x]
            self.__table[x] = y

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    f = UnionFind()
    for a, b in AB:
        f.union(a, b)

    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if self.size(x) < self.size(y):
            x, y = y, x
        if x != y:
            self.__size[y] += self.__size[x]
            self.__table[x] = y

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    f = UnionFind()
    for a, b in AB:
        f.union(a, b)

    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):
from sys import stdin
nii=lambda: map(int, stdin.readline().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())


n,m,k=map(int,input().split())

tree_f=[[] for i in range(n+1)]
tree_g=[[] for i in range(n+1)]

uf=UnionFind(n+1)

for i in range(m):
  a,b=nii()
  tree_f[a].append(b)
  tree_f[b].append(a)
  uf.union(a,b)

for i in range(k):
  a,b=nii()
  if uf.find(a)==uf.find(b):
    tree_g[a].append(b)
    tree_g[b].append(a)

ans=[]
for i in range(n):
  i+=1


  cnt=len(tree_f[i])+len(tree_g[i])
  ans.append(uf.size(i)-cnt-1)

print(*ans)

Solution (Python):
import sys
from io import StringIO
import unittest

class UnionFind():
    
    
    def __init__(self, n):
        self.n = n
        
        
        self.root = [-1]*(n+1)
        
        self.rnk = [0]*(n+1)

    
    def Find_Root(self, x):
        if(self.root[x] < 0):
            return x
        else:
            
            self.root[x] = self.Find_Root(self.root[x])
            return self.root[x]
    
    def Unite(self, x, y):
        
        x = self.Find_Root(x)
        y = self.Find_Root(y)
        
        if(x == y):
            return 
        
        elif(self.rnk[x] > self.rnk[y]):
            self.root[x] += self.root[y]
            self.root[y] = x

        else:
            self.root[y] += self.root[x]
            self.root[x] = y
            
            if(self.rnk[x] == self.rnk[y]):
                self.rnk[y] += 1
    
    def isSameGroup(self, x, y):
        return self.Find_Root(x) == self.Find_Root(y)

    
    def Count(self, x):
        return -self.root[self.Find_Root(x)]

def resolve():
    n,m,k=map(int, sys.stdin.readline().strip().split())
    

    uf = UnionFind(n)

    res=[[] for i in range(n)]
    frd=[0 for i in range(n)]
    blk=[0 for i in range(n)]

    for i in range(m):
        
        a,b=map(int, sys.stdin.readline().strip().split())
        a-=1
        b-=1
        uf.Unite(a,b)
        frd[a]+=1
        frd[b]+=1
    
    for i in range(k):
        
        a,b=map(int, sys.stdin.readline().strip().split())
        a-=1
        b-=1
        if uf.isSameGroup(a,b):
            blk[a]+=1
            blk[b]+=1
    
    rescnt=[]

    for i in range(n):
        ri=uf.Count(i)-1-blk[i]-frd[i]
        rescnt.append(str(ri))
        
    
    print(" ".join(rescnt))

resolve()

Solution (Python):
class UnionFind:
    def __init__(self, n):
        self.par = list(range(n + 1))
        self.size = [1] * (n + 1)

    def root(self, x: int) -> int:
        if self.par[x] == x: return x
        self.par[x] = self.root(self.par[x])
        return self.par[x]

    def unite(self, x: int, y: int):
        root_x, root_y = self.root(x), self.root(y)
        if root_x != root_y:
            if self.size[root_x] < self.size[root_y]:
                root_x, root_y = root_y, root_x
            self.size[root_x] += self.size[root_y]
            self.par[root_y] = root_x

    def check(self, x: int, y: int) -> bool:
        root_x, root_y = self.root(x), self.root(y)
        return root_x == root_y


from collections import defaultdict
N, M, K = map(int, input().split())

u = UnionFind(N)

ABm = defaultdict(list)
for _ in range(M):
    a, b = map(int, input().split())
    ABm[a].append(b)
    ABm[b].append(a)
    u.unite(a, b)

CDk = defaultdict(list)
for _ in range(K):
    c, d = map(int, input().split())
    CDk[c].append(d)
    CDk[d].append(c)

ans = []
for i in range(1, N + 1):
    size = u.size[u.root(i)]
    block = 0
    for x in CDk[i]:
        if u.check(x, i): block += 1

    friends = len(ABm[i])
    res = size - block - friends - 1
    ans.append(str(res))

print(" ".join(ans))

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x != y:
            self.__size[y] += self.__size[x]
            self.__table[x] = y

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    f = UnionFind()
    for a, b in AB:
        f.union(a, b)


    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x != y:
            self.__size[y] += self.__size[x]
            self.__table[x] = y

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    g = defaultdict(set)
    for a, b in AB:
        g[a].add(b)
        g[b].add(a)

    def dfs(u):
        s = [u]
        done = set(s)
        while s:
            u = s.pop()
            for v in g[u]:
                if v not in done:
                    s.append(v)
                    done.add(v)
        return done

    group = dict()
    done = set()
    parent = [-1] * (N+1)
    for i in range(1, N+1):
        if i not in done:
            j = dfs(i)
            done |= j
            for k in j:
                parent[k] = i
            group[i] = j

    error_print('1')

    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)

    error_print('2')

    ans = []
    for i in range(1, N+1):
        e = group[parent[i]]
        cand = len(group[parent[i]])
        for b in block[i]:
            if b in e:
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    error_print('3')
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

    
    
    
    
    
    


if __name__ == '__main__':
    main()

Solution (Python):

import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class UnionFind():
    def __init__(self):
        self.__table = {}
        self.__size = defaultdict(lambda: 1)

    def __root(self, x):
        if x not in self.__table:
            self.__table[x] = x
        elif x != self.__table[x]:
            self.__table[x] = self.__root(self.__table[x])
        return self.__table[x]

    def root(self, x):
        return self.__table[x]

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

    def union(self, x, y):
        x = self.__root(x)
        y = self.__root(y)
        if x != y:
            self.__size[y] += self.__size[x]
            self.__table[x] = y

    def size(self, x):
        return self.__size[self.__root(x)]

    def num_of_group(self):
        g = 0
        for k, v in self.__table.items():
            if k == v:
                g += 1
        return g

@mt
def slv(N, M, K, AB, CD):
    g = defaultdict(set)
    f = UnionFind()
    for a, b in AB:
        g[a].add(b)
        g[b].add(a)
        f.union(a, b)


    direct = defaultdict(int)
    for a, b in AB:
        direct[a] += 1
        direct[b] += 1
    block = defaultdict(set)
    for c, d in CD:
        block[c].add(d)
        block[d].add(c)


    ans = []
    for i in range(1, N+1):
        cand = f.size(i)
        for u in block[i]:
            if f.same(i, u):
                cand -= 1
        cand -= direct[i]
        cand -= 1
        ans.append(cand)
    return ans



def main():
    N, M, K = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    CD = [read_int_n() for _ in range(K)]
    print(*slv(N, M, K, AB, CD))

if __name__ == '__main__':
    main()

Solution (Python):
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines


def main():
    N,M,K = map(int, readline().split())

    F = [[] for _ in range(N+1)]
    for _ in range(M):
        a,b = map(int, readline().split())
        F[a].append(b)
        F[b].append(a)
    
    B = [[] for _ in range(N+1)]
    for _ in range(K):
        c,d = map(int, readline().split())
        B[c].append(d)
        B[d].append(c)


    seen = [-1]*(N+1)
    group = 0
    def dfs(G, s):
        stack = [s]
        seen[s] = group
        n_connection = 1 
        
        while stack:
            u = stack.pop()
            for v in G[u]:
                if seen[v] == -1:
                    n_connection += 1
                    seen[v] = group
                    stack.append(v)
    
        return n_connection


    union = {}
    for i in range(1,N+1):
        if seen[i] == -1:
            n = dfs(F, i)
            union[group] = n
            group += 1
            
    ans = []
    for i in range(1,N+1):
        tmp = 0
        tmp += union[seen[i]] - 1
        tmp -= len(F[i])
        for j in B[i]:
            if seen[j] == seen[i]:
                tmp -= 1
        ans.append(tmp)
    
    print(" ".join(map(str, ans)))


if __name__ == "__main__":
    main()