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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public final class Main {

    private static final class UnionFind {
        private final int[] parent;
        private final int[] size;
        private int count;

        private UnionFind(int n) {
            parent = new int[n];
            size = new int[n];
            count = n;
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                size[i] = 1;
            }
        }

        public int find(int p) {
            // path compression
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            final int rootP = find(p);
            final int rootQ = find(q);
            if (rootP == rootQ) {
                return;
            }
            // union by size
            if (size[rootP] > size[rootQ]) {
                parent[rootQ] = rootP;
                size[rootP] += size[rootQ];
            } else {
                parent[rootP] = rootQ;
                size[rootQ] += size[rootP];
            }
            count--;
        }

        public int count() { return count; }

        public int[] size() { return size; }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        UnionFind uf = new UnionFind(n);
        final int m = fs.nextInt();
        for (int i = 0; i < m; i++) {
            uf.union(fs.nextInt() - 1, fs.nextInt() - 1);
        }
        System.out.println(uf.count - 1);
    }

    static final class Utils {
        public static void shuffleSort(int[] arr) {
            shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffleSort(long[] arr) {
            shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffle(int[] arr) {
            final Random r = new Random();

            for (int i = 0; i <= arr.length - 2; i++) {
                final int j = i + r.nextInt(arr.length - i);
                swap(arr, i, j);
            }
        }

        public static void shuffle(long[] arr) {
            final Random r = new Random();

            for (int i = 0; i <= arr.length - 2; i++) {
                final int j = i + r.nextInt(arr.length - i);
                swap(arr, i, j);
            }
        }

        public static void swap(int[] arr, int i, int j) {
            final int t = arr[i];
            arr[i] = arr[j];
            arr[j] = t;
        }

        public static void swap(long[] arr, int i, int j) {
            final long t = arr[i];
            arr[i] = arr[j];
            arr[j] = t;
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}