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 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
  private static int solve(int n, int m, int[][] abs) {
    UnionFind unionFind =  new UnionFind(n + 1);
    for (int[] ab : abs) {
      int a = ab[0];
      int b = ab[1];
      unionFind.merge(a, b);
    }
    Set<Integer> set = new HashSet<>();
    for (int i = 1; i <= n; i++) {
      set.add(unionFind.getRoot(i));
    }
    return set.size() - 1;
  }

  private static void execute(ContestReader reader, ContestWriter out) {
    int n = reader.nextInt();
    int m = reader.nextInt();
    int[][] abs = reader.nextInt(m, 2);
    out.println(solve(n, m, abs));
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    ContestWriter out = new ContestWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class UnionFind {
  int[] parents;
  int[] ranks;

  UnionFind(int n) {
    parents = new int[n];
    ranks = new int[n];

    for (int i = 0; i < n; i++) {
      parents[i] = i;
    }
  }

  public int getRoot(int index) {
    if (parents[index] == index) {
      return index;
    } else {
      parents[index] = getRoot(parents[index]);
      return parents[index];
    }
  }

  public boolean sameGroup(int a, int b) {
    return getRoot(a) == getRoot(b);
  }

  public void merge(int a, int b) {
    int rootA = getRoot(a);
    int rootB = getRoot(b);
    if (rootA == rootB) {
      return;
    }
    if (ranks[rootA] < ranks[rootB]) {
      parents[rootA] = rootB;
    } else if (ranks[rootB] < ranks[rootA]) {
      parents[rootB] = rootA;
    } else {
      parents[rootA] = rootB;
      ranks[rootB]++;
    }
  }
  
  public void dump() {
    Map<Integer, Set<Integer>> rootToSetMap = new HashMap<>();
    for (int i = 0; i < parents.length; i++) {
      int root = getRoot(i);
      if (rootToSetMap.get(root) == null) {
        rootToSetMap.put(root, new HashSet<>());
      }
      rootToSetMap.get(root).add(i);
    }
    for (Map.Entry<Integer, Set<Integer>> entry : rootToSetMap.entrySet()) {
      System.err.printf("%d: %s\n", entry.getKey(), entry.getValue());
    }
  }
}

class ContestWriter extends PrintWriter {
  ContestWriter(PrintStream printStream) {
    super(printStream);
  }

  public void printList(List<? extends Object> list) {
    for (Object object : list) {
      println(object);
    }
  }

  public void printListOneLine(List<? extends Object> list) {
    List<String> stringList = new ArrayList<>();
    for (Object object : list) {
      stringList.add(object.toString());
    }
    println(String.join(" ", stringList));
  }
}

class ContestReader {
  private static final int BUFFER_SIZE = 1024;
  
  private final InputStream stream;
  private final byte[] buffer;
  private int pointer;
  private int bufferLength;
  
  ContestReader(InputStream stream) {
    this.stream = stream;
    this.buffer = new byte[BUFFER_SIZE];
    this.pointer = 0;
    this.bufferLength = 0;
  }
  
  private boolean hasNextByte() {
    if (pointer < bufferLength) {
      return true;
    }
    
    pointer = 0;
    try {
      bufferLength = stream.read(buffer);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
    return bufferLength > 0;
  }
  
  private int readByte() {
    if (hasNextByte()) {
      return buffer[pointer++];
    } else {
      return -1;
    }
  }
  
  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }
  
  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[pointer])) {
      pointer++;
    }
    return hasNextByte();
  }
  
  public String next() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b)) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public String nextLine() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b) && b != 0x20) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public char nextChar() {
    return next().charAt(0);
  }
  
  public int nextInt() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    int n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public long nextLong() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    long n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public String[] nextLine(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLine();
    }
    return array;
  }
  
  public char[] nextChar(int n) {
    char[] array = new char[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextChar();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public String[][] next(int n, int m) {
    String[][] matrix = new String[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = next();
      }
    }
    return matrix;
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public char[][] nextChar(int n, int m) {
    char[][] matrix = new char[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextChar();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}

class MyAssert {
  public static void myAssert(boolean flag, String message) {
    if (!flag) {
      throw new RuntimeException(message);
    }
  }
 
  public static void myAssert(boolean flag) {
    myAssert(flag, "");
  }
}