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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.InputStream;
import java.io.IOException;
import java.io.PrintStream;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int n = sc.nextInt();
    int m = sc.nextInt();
    int k = sc.nextInt();

    Map<Integer, Set<Integer>> fs = new HashMap<>();

    Map<Integer, Set<Integer>> bs = new HashMap<>();

    for (int i = 0; i < m; i++) {
      int a = sc.nextInt() - 1;
      int b = sc.nextInt() - 1;
      Set<Integer> fOa = fs.getOrDefault(a, new HashSet<>());
      fOa.add(b);
      Set<Integer> fOb = fs.getOrDefault(b, new HashSet<>());
      fOb.add(a);
      fs.put(a, fOa);
      fs.put(b, fOb);
    }

    for (int i = 0; i < k; i++) {
      int c = sc.nextInt() - 1;
      int d = sc.nextInt() - 1;
      Set<Integer> bOc = bs.getOrDefault(c, new HashSet<>());
      bOc.add(d);
      Set<Integer> bOd = bs.getOrDefault(d, new HashSet<>());
      bOd.add(c);
      bs.put(c, bOc);
      bs.put(d, bOd);
    }

    UnionFindTree unionFindTree = new UnionFindTree(n);
    for (int i = 0; i < n; i++) {
      unionFindTree.makeSet(i);
    }

    for (Integer a : fs.keySet()) {
      for (Integer f : fs.get(a)) {
        unionFindTree.union(a, f);
      }
    }

//    Map<Integer, Set<Integer>> idxToLink = new HashMap<>();
//    Map<Integer, Set<Integer>> manToLink = new HashMap<>();
//    for (int i = 0; i < n; i++) {
//      Set<Integer> set = idxToLink.getOrDefault(unionFindTree.find(i), new HashSet<>());
//      set.add(i);
//      idxToLink.put(unionFindTree.find(i), set);
//      manToLink.put(i, set);
//    }

    Map<Integer, Set<Integer>> links = new HashMap<>();

    List<String> ans = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      Set<Integer> link;
      if (links.containsKey(i)) {
        link = links.get(i);
      } else {
        link = new HashSet<>();
        dfs(i, fs, link);
        for (Integer friend : link) {
          links.put(friend, link);
        }
      }

//      Set<Integer> link = manToLink.get(i);
      Set<Integer> intersection = new HashSet<>();
      if (link.contains(i)) intersection.add(i);
      if (fs.containsKey(i)) {
        for (Integer f : fs.get(i)) {
          if (link.contains(f)) intersection.add(f);
        }
      }
      if (bs.containsKey(i)) {
        for (Integer b : bs.get(i)) {
          if (link.contains(b)) intersection.add(b);
        }
      }
      ans.add(String.valueOf(link.size() - intersection.size()));
    }
    os.println(String.join(" ", ans));
  }

  private static void dfs(int start, Map<Integer, Set<Integer>> fs, Set<Integer> visited) {
    visited.add(start);
    if (fs.containsKey(start)) {
      for (Integer friend : fs.get(start)) {
        if (visited.contains(friend)) continue;
        dfs(friend, fs, visited);
      }
    }
  }

  private static class UnionFindTree {

    int[] parent;
    int[] rank;

    public UnionFindTree(int size) {
      this.parent = new int[size];
      this.rank = new int[size];

      for (int i = 0; i < size; i++) {
        makeSet(i);
      }
    }

    public void makeSet(int i) {
      parent[i] = i;
      rank[i] = 0;
    }

    public void union(int x, int y) {
      int xRoot = find(x);
      int yRoot = find(y);

      if (rank[xRoot] > rank[yRoot]) {
        parent[yRoot] = xRoot;

      } else if(rank[xRoot] < rank[yRoot]) {
        parent[xRoot] = yRoot;

      } else if (xRoot != yRoot){
        parent[yRoot] = xRoot;
        rank[xRoot]++;
      }
    }

    public int find(int i) {
      if (i != parent[i]) {
        parent[i] = find(parent[i]);
      }
      return parent[i];
    }

    public boolean same(int x, int y) {
      return find(x) == find(y);
    }
  }

  private static long gcd(long m, long n) {
    if (m < n) {
      return gcd(n, m);
    }
    if (n == 0) {
      return m;
    }
    return gcd(n, m % n);
  }

  private static long lcm(long m, long n) {
    return m / gcd(m, n) * n;
  }

  private static class Modular {

    private final long mod;

    private Modular(long mod) {
      this.mod = mod;
    }

    private long inverse(long n) {
      return pow(n, mod - 2) % mod;
    }

    private long pow(long x, long n) {
      /*
      long ans = 1;
      while (n > 0) {
        if ((n & 1) == 1) {
          ans = ans * x % mod;
        }
        x = x * x % mod;
        n >>= 1;
      }
      return ans;
      */
      if (n == 0) {
        return 1;
      }
      return n % 2 == 0 ?
          pow(x * x % mod, n / 2) % mod :
          x % mod * pow(x, n - 1) % mod;
    }
  }

  private static class ModularNFixedCombination {

    private final Modular modular;
    private final long[] comb;
    private final long N;

    public ModularNFixedCombination(long N, int size, long mod) {
      this.modular = new Modular(mod);
      this.comb = new long[size + 1];
      this.N = N;

      comb[0] = 1;

      for (int i = 1; i <= size; i++) {
        comb[i] = ((comb[i - 1] * (N - (i - 1))) % mod * modular.inverse(i)) % mod;
      }
    }

    long combination(int n, int k) {
      if (n != N) {
        throw new IllegalStateException();
      }
      return comb[k];
    }

    long repeatedCombination(int n, int k) {
      return combination(n + k - 1, k);
    }
  }

  private static class ModularCombination {

    private final long fact[];
    private final long mod;
    private final Modular modular;

    public ModularCombination(int size, long mod) {
      this.fact = new long[size + 1];
      this.mod = mod;
      this.modular = new Modular(mod);

      this.fact[0] = 1;
      for (int i = 1; i <= size; i++) {
        fact[i] = (fact[i - 1] * i) % mod;
      }
    }

    private long factorial(int n) {
      return fact[n];
    }

    long combination(int n, int k) {
      return
          (
              (
                  (
                      factorial(n) * modular.inverse(factorial(n - k))
                  ) % mod
              ) * modular.inverse(factorial(k))
          ) % mod;
    }

    long repeatedCombination(int n, int k) {
      return combination(n + k - 1, k);
    }
  }

  private static class Scanner {

    private final InputStream is;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    Scanner(InputStream is) {
      this.is = is;
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = is.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) {
        return buffer[ptr++];
      } else {
        return -1;
      }
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
        ptr++;
      }
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      long nl = nextLong();
      if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
        throw new NumberFormatException();
      }
      return (int) nl;
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }
  }
}