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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.stream.IntStream;

public final class Main {
    void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int[][] ab = in.nextVerticalIntArrays(2, m);
        int[] a = decrement(ab[0]);
        int[] b = decrement(ab[1]);
        var uft = new UnionFindTree(n);
        for (int i = 0; i < m; i++) {
            uft.unite(a[i], b[i]);
        }
        out.println(uft.unionCount() - 1);
    }
    static final class UnionFindTree {
        private final int[] parents;
        private final long[] weights;
        private final int[] size;

        UnionFindTree(int elementCount) {
            if (elementCount < 1)
                throw new IllegalArgumentException();
            parents = new int[elementCount];
            Arrays.setAll(parents, i -> i);

            weights = new long[elementCount];

            size = new int[elementCount];
            Arrays.fill(size, 1);
        }
        int rootOf(int x) {
            if (parents[x] == x)
                return x;
            int root = rootOf(parents[x]);
            weights[x] += weights[parents[x]];
            return parents[x] = root;
        }
        boolean same(int x, int y) {
            return rootOf(x) == rootOf(y);
        }
        boolean unite(int x, int y) {
            return unite(x, y, 0);
        }
        boolean unite(int x, int y, long weight) {
            int xRoot = rootOf(x);
            int yRoot = rootOf(y);
            if (xRoot == yRoot)
                return false;
            long w = weight + weightOf(x) - weightOf(y);
            if (size[xRoot] < size[yRoot]) {
                weights[xRoot] = -w;
                parents[xRoot] = yRoot;
                size[yRoot] += size[xRoot];
            } else {
                weights[yRoot] = w;
                parents[yRoot] = xRoot;
                size[xRoot] += size[yRoot];
            }
            return true;
        }
        long weightOf(int x) {
            rootOf(x);
            return weights[x];
        }
        long diff(int x, int y) {
            if (same(x, y))
                return weightOf(y) - weightOf(x);
            throw new IllegalArgumentException();
        }
        int elementCount() {
            return parents.length;
        }
        int unionCount() {
            return (int)IntStream.range(0, elementCount())
                                 .map(this::rootOf)
                                 .distinct()
                                 .count();
        }
        int sizeOf(int x) {
            return size[rootOf(x)];
        }
    }
    private static int[] decrement(int[] a) {
        for (int i = 0; i < a.length; i++)
            a[i]--;
        return a;
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        new Main().solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        private static final int DEFAULT_BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer;
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this(in, DEFAULT_BUFFER_SIZE);
        }
        MyScanner(InputStream in, int bufferSize) {
            this.in = Objects.requireNonNull(in);
            buffer = new byte[bufferSize];
        }
        private int readByte() {
            if (point < readLength) {
                int result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1)
                return -1;
            point = 1;
            return buffer[0];
        }
        private static boolean isVisibleChar(int c) {
            return 33 <= c && c <= 126;
        }
        char nextChar() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c)))
                c = readByte();
            if (c == -1)
                throw new NoSuchElementException();
            return (char)c;
        }
        String next() {
            return next(16);
        }
        String next(int n) {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c)))
                c = readByte();
            if (c == -1)
                throw new NoSuchElementException();
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return b.toString();
        }
        long nextLong() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c)))
                c = readByte();
            if (c == -1)
                throw new NoSuchElementException();
            boolean minus = false;
            long limit = -Long.MAX_VALUE;
            if (c == '-') {
                minus = true;
                limit = Long.MIN_VALUE;
                c = readByte();
            }
            long n = 0L;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                if (n < limit / 10L)
                    throw new InputMismatchException();
                n *= 10L;
                int digit = c - '0';
                if (n < limit + digit)
                    throw new InputMismatchException();
                n -= digit;
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return minus ? n : -n;
        }
        int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE)
                throw new InputMismatchException();
            return (int)n;
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++)
                result[i] = nextInt();
            return result;
        }
        long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++)
                result[i] = nextLong();
            return result;
        }
        char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++)
                result[i] = nextChar();
            return result;
        }
        int[][] next2dIntArray(int h, int w) {
            var result = new int[h][w];
            for (int i = 0; i < h; i++)
                for (int j = 0; j < w; j++)
                    result[i][j] = nextInt();
            return result;
        }
        long[][] next2dLongArray(int h, int w) {
            var result = new long[h][w];
            for (int i = 0; i < h; i++)
                for (int j = 0; j < w; j++)
                    result[i][j] = nextLong();
            return result;
        }
        char[][] next2dCharArray(int h, int w) {
            char[][] result = new char[h][w];
            for (int i = 0; i < h; i++)
                for (int j = 0; j < w; j++)
                    result[i][j] = nextChar();
            return result;
        }
        int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++)
                for (int j = 0; j < arrayCount; j++)
                    result[j][i] = nextInt();
            return result;
        }
        long[][] nextVerticalLongArrays(int arrayCount, int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++)
                for (int j = 0; j < arrayCount; j++)
                    result[j][i] = nextLong();
            return result;
        }
        char[][] nextVerticalCharArrays(int arrayCount, int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++)
                for (int j = 0; j < arrayCount; j++)
                    result[j][i] = nextChar();
            return result;
        }
        List<String> nextStringList(int n) {
            var result = new ArrayList<String>(n);
            for (int i = 0; i < n; i++)
                result.add(next());
            return result;
        }
        List<Integer> nextIntList(int n) {
            var result = new ArrayList<Integer>(n);
            for (int i = 0; i < n; i++)
                result.add(nextInt());
            return result;
        }
        List<Long> nextLongList(int n) {
            var result = new ArrayList<Long>(n);
            for (int i = 0; i < n; i++)
                result.add(nextLong());
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        void println(int[] x) {
            println(x, " ");
        }
        void println(int[] x, String delimiter) {
            Objects.requireNonNull(delimiter);
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(long[] x) {
            println(x, " ");
        }
        void println(long[] x, String delimiter) {
            Objects.requireNonNull(delimiter);
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(Iterable<?> iterable) {
            println(iterable, " ");
        }
        void println(Iterable<?> iterable, String delimiter) {
            Objects.requireNonNull(delimiter);
            Iterator<?> i = iterable.iterator();
            if (i.hasNext()) {
                print(i.next());
                while (i.hasNext()) {
                    print(delimiter);
                    print(i.next());
                }
            }
            println();
        }
        void printLines(int[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(long[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(Iterable<?> iterable) {
            println(iterable, System.lineSeparator());
        }
    }
}