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 in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]pub mod pcl{pub mod polyfil{pub mod num{pub trait Zero{fn zero()->Self;fn is_zero(&self)->bool;}pub trait One{fn one()->Self;}}}pub mod stdin{use std::io::prelude::*;use std::io::stdin;use std::str::FromStr;pub fn read_line()->String{let mut s=String::new();stdin().read_line(&mut s).unwrap();s.trim().to_string()}pub fn read<T:FromStr>()->T{read_from(stdin())}pub fn read_token()->String{read_token_from(stdin())}pub fn read_ascii()->char{read_ascii_from(stdin())}pub fn read_from<R:Read,T:FromStr>(read:R)->T{read_token_from(read).parse().unwrap_or_else(|_|panic!("failed to parse a value"))}pub fn read_token_from<R:Read>(read:R)->String{read.bytes().flat_map(|x|x.map(|x|x as char)).skip_while(|x|x.is_whitespace()).take_while(|x|!x.is_whitespace()).collect()}pub fn read_ascii_from<R:Read>(read:R)->char{read.bytes().flat_map(|x|x.map(|x|x as char)).skip_while(|x|x.is_whitespace()).next().expect("failed to get a next character")}}pub mod math{pub mod disjoint_set{use std::mem::swap;pub struct DisjointSet{par:Vec<i64>,size:usize,}impl DisjointSet{pub fn new(n:usize)->DisjointSet{DisjointSet{par:vec![-1;n],size:n,}}pub fn merge(&mut self,mut x:usize,mut y:usize)->bool{let len=self.par.len();assert!(x<len,"index out of range:x is{}but len is{}",x,len);assert!(y<len,"index out of range:y is{}but len is{}",y,len);x=self.root(x);y=self.root(y);if x==y{return false;}if self.par[x]<self.par[y]{swap(&mut x,&mut y);}debug_assert!(self.par[x]<0&&self.par[y]<0,"critical error:parent has invalid value for rank");self.par[x]+=self.par[y];self.par[y]=x as i64;self.size-=1;true}pub fn in_same(&mut self,x:usize,y:usize)->bool{self.root(x)==self.root(y)}pub fn root(&mut self,x:usize)->usize{let parx=self.par[x];if parx<0{x}else{let root=self.root(parx as usize);self.par[x]=root as i64;root}}pub fn size_of(&mut self,mut x:usize)->usize{x=self.root(x);debug_assert!(self.par[x]<0,"critical error:parent has invalid value for rank");-self.par[x]as usize}pub fn size(&self)->usize{self.size}}}pub mod modint{#[macro_use]pub mod consts{use super::ModintInnerType;pub trait ModintConst{fn get_modulus()->ModintInnerType;}macro_rules!define_modint_const{(pub const $ name:ident=$ value:expr;)=>{pub enum $ name{}impl $ crate::pcl::math::modint::consts::ModintConst for $ name{fn get_modulus()->ModintInnerType{$ value}}};}}use pcl::polyfil::num::{One,Zero};use self::consts::ModintConst;use std::cmp::Ordering;use std::fmt;use std::hash::{Hash,Hasher};use std::iter::{Product,Sum};use std::marker::PhantomData;use std::mem;use std::ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Rem,RemAssign,Sub,SubAssign};pub type ModintInnerType=i64;define_modint_const!{pub const MOD17=1_000_000_007;}pub type Modint17=Modint<MOD17>;pub struct Modint<C>{value:ModintInnerType,marker:PhantomData<C>,}impl<C>Modint<C>{pub unsafe fn new_unchecked(value:ModintInnerType)->Modint<C>{#[allow(unknown_lints,renamed_and_removed_lints,redundant_field_names)]Modint{value:value,marker:PhantomData,}}pub fn inner(self)->ModintInnerType{self.value}}impl<C:ModintConst>Modint<C>{pub fn new(mut value:ModintInnerType)->Modint<C>{let modulus=C::get_modulus();assert_ne!(modulus,0,"MOD is 0");if value<0{let m=(-value)/modulus;value+=(m+1)*modulus;}unsafe{Modint::new_unchecked(value%modulus)}}pub fn inv(self)->Modint<C>{let mut modulus=C::get_modulus();let mut a=self.value;let mut u=1;let mut v=0;while modulus>0{let t=a/modulus;a-=t*modulus;u-=t*v;mem::swap(&mut a,&mut modulus);mem::swap(&mut u,&mut v);}Modint::new(u)}}impl<C:ModintConst>PartialEq for Modint<C>{fn eq(&self,other:&Self)->bool{self.inner()==other.inner()}}impl<C:ModintConst>PartialOrd for Modint<C>{fn partial_cmp(&self,other:&Self)->Option<Ordering>{self.inner().partial_cmp(&other.inner())}}impl<C:ModintConst>Eq for Modint<C>{}impl<C:ModintConst>Ord for Modint<C>{fn cmp(&self,other:&Self)->Ordering{self.inner().cmp(&other.inner())}}impl<C:ModintConst>Hash for Modint<C>{fn hash<H:Hasher>(&self,state:&mut H){self.inner().hash(state);}}impl<C>fmt::Debug for Modint<C>{fn fmt<'a>(&self,f:&mut fmt::Formatter<'a>)->fmt::Result{write!(f,"{}",self.inner())}}impl<C>Clone for Modint<C>{fn clone(&self)->Self{*self}}impl<C>Copy for Modint<C>{}impl<C:ModintConst>AddAssign for Modint<C>{fn add_assign(&mut self,rhs:Modint<C>){let modulus=C::get_modulus();self.value+=rhs.value;if self.value>=modulus{self.value-=modulus;}}}impl<C:ModintConst>SubAssign for Modint<C>{fn sub_assign(&mut self,rhs:Modint<C>){let modulus=C::get_modulus();self.value-=rhs.value;if self.value<0{self.value+=modulus;}}}impl<C:ModintConst>MulAssign for Modint<C>{fn mul_assign(&mut self,rhs:Modint<C>){let modulus=C::get_modulus();self.value*=rhs.value;self.value%=modulus;}}impl<C:ModintConst>DivAssign for Modint<C>{fn div_assign(&mut self,rhs:Modint<C>){if rhs.value==0{panic!("attempted to divide by zero");}*self*=rhs.inv();}}impl<C:ModintConst>RemAssign for Modint<C>{fn rem_assign(&mut self,rhs:Modint<C>){if rhs.value==0{panic!("attempted to divide by zero.")}self.value%=rhs.value;}}macro_rules!impl_arith_by_assign{(impl $ traitname:ident::$ fnname:ident{use $ op:tt;})=>{impl<C:ModintConst>$ traitname for Modint<C>{type Output=Modint<C>;fn $ fnname(mut self,rhs:Modint<C>)->Modint<C>{self $ op rhs;self}}};}impl_arith_by_assign!(impl Add::add{use+=;});impl_arith_by_assign!(impl Sub::sub{use-=;});impl_arith_by_assign!(impl Mul::mul{use*=;});impl_arith_by_assign!(impl Div::div{use/=;});impl_arith_by_assign!(impl Rem::rem{use%=;});impl<C:ModintConst>One for Modint<C>{fn one()->Modint<C>{let modulus=C::get_modulus();assert_ne!(modulus,1,"one()is called for Modint with MOD=1");unsafe{Modint::new_unchecked(1)}}}impl<C:ModintConst>Sum for Modint<C>{fn sum<I:Iterator<Item=Modint<C>>>(iter:I)->Modint<C>{iter.fold(Modint::zero(),Add::add)}}impl<C:ModintConst>Product for Modint<C>{fn product<I:Iterator<Item=Modint<C>>>(iter:I)->Self{iter.fold(Modint::one(),Mul::mul)}}impl<C:ModintConst>Zero for Modint<C>{fn zero()->Modint<C>{unsafe{Modint::new_unchecked(0)}}fn is_zero(&self)->bool{self.inner()==0}}impl<C>fmt::Display for Modint<C>{fn fmt(&self,b:&mut fmt::Formatter)->fmt::Result{write!(b,"{}",self.inner())}}}pub use self::disjoint_set::DisjointSet;pub use self::modint::{Modint,Modint17};}}
use pcl::math::DisjointSet;
use pcl::stdin::*;
fn main() {
    let num_persons: usize = read();
    let num_friend_edges: usize = read();
    let num_blocking_edges: usize = read();
    let mut friends = vec![0; num_persons];
    let mut blocking = vec![Vec::new(); num_persons];
    let mut friend_groups = DisjointSet::new(num_persons);
    for _ in 0..num_friend_edges {
        let a = read::<usize>() - 1;
        let b = read::<usize>() - 1;
        friends[a] += 1;
        friends[b] += 1;
        friend_groups.merge(a, b);
    }
    for _ in 0..num_blocking_edges {
        let a = read::<usize>() - 1;
        let b = read::<usize>() - 1;
        blocking[a].push(b);
        blocking[b].push(a);
    }
    let mut res = vec![];
    for i in 0..num_persons {
        let all = friend_groups.size_of(i);
        let num_friends = friends[i];
        let num_blocking = blocking[i]
            .iter()
            .filter(|&&x| friend_groups.in_same(i, x))
            .count();
        let num = all - num_friends - num_blocking - 1;
        res.push(num.to_string());
    }
    println!("{}", res.join(" "));
}