Problem:
Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).

Solution in Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

class DSU {
  private int n;
  private int[] parentOrSize;

  public DSU(int n) {
    this.n = n;
    this.parentOrSize = new int[n];
    java.util.Arrays.fill(parentOrSize, -1);
  }

  int merge(int a, int b) {
    if (!(0 <= a && a < n))
      throw new IndexOutOfBoundsException("a=" + a);
    if (!(0 <= b && b < n))
      throw new IndexOutOfBoundsException("b=" + b);

    int x = leader(a);
    int y = leader(b);
    if (x == y)
      return x;
    if (-parentOrSize[x] < -parentOrSize[y]) {
      int tmp = x;
      x = y;
      y = tmp;
    }
    parentOrSize[x] += parentOrSize[y];
    parentOrSize[y] = x;
    return x;
  }

  boolean same(int a, int b) {
    if (!(0 <= a && a < n))
      throw new IndexOutOfBoundsException("a=" + a);
    if (!(0 <= b && b < n))
      throw new IndexOutOfBoundsException("b=" + b);
    return leader(a) == leader(b);
  }

  int leader(int a) {
    if (parentOrSize[a] < 0) {
      return a;
    } else {
      parentOrSize[a] = leader(parentOrSize[a]);
      return parentOrSize[a];
    }
  }

  int size(int a) {
    if (!(0 <= a && a < n))
      throw new IndexOutOfBoundsException("" + a);
    return -parentOrSize[leader(a)];
  }

  java.util.ArrayList<java.util.ArrayList<Integer>> groups() {
    int[] leaderBuf = new int[n];
    int[] groupSize = new int[n];
    for (int i = 0; i < n; i++) {
      leaderBuf[i] = leader(i);
      groupSize[leaderBuf[i]]++;
    }
    java.util.ArrayList<java.util.ArrayList<Integer>> result = new java.util.ArrayList<>(n);
    for (int i = 0; i < n; i++) {
      result.add(new java.util.ArrayList<>(groupSize[i]));
    }
    for (int i = 0; i < n; i++) {
      result.get(leaderBuf[i]).add(i);
    }
    result.removeIf(java.util.ArrayList::isEmpty);
    return result;
  }
}

@SuppressWarnings("unused")
public class Main {

  private static void solve() {
    int n = ni();
    int m = ni();

    DSU ds = new DSU(n);
    for (int i = 0; i < m; i++) {
      ds.merge(ni() - 1, ni() - 1);
    }

    int ret = ds.groups().size() - 1;
    System.out.println(ret);
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}