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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using AtCoder;
using AtCoder.GraphAcl;
using AtCoder.IO;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
public partial class Program
{
    [DebuggerBrowsable(DebuggerBrowsableState.Never)] public ConsoleReader cr;
    [DebuggerBrowsable(DebuggerBrowsableState.Never)] public ConsoleWriter cw;
    public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; }
    static void Main() => new Program(new ConsoleReader(), new ConsoleWriter()).Run();
    public void Run()
    {
        var res = Calc();
        if (res is double) cw.WriteLine(((double)res).ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture));
        else if (res is bool) cw.WriteLine(((bool)res) ? "Yes" : "No");
        else if (res != null) cw.WriteLine(res.ToString());
        cw.Flush();
    }
}
public partial class Program
{
    private object Calc()
    {
        N = cr;
        M = cr;
        var dsu = new DSU(N);
        for (int i = 0; i < M; i++)
        {
            int a = cr.Int0;
            int b = cr.Int0;
            dsu.Merge(a, b);
        }
        return dsu.Groups().Length - 1;
    }
    int N;
    int M;
    (int A, int B)[] AB;
}
#region AtCoderLibrary
namespace AtCoder.GraphAcl { public class DSU { public int Count { get; } private readonly int[] ParentOrSize; public DSU(int n) { Count = n; ParentOrSize = new int[n]; for (int i = 0; i < ParentOrSize.Length; i++) ParentOrSize[i] = -1; } public bool Merge(int a, int b) { Debug.Assert(0 <= a && a < Count); Debug.Assert(0 <= b && b < Count); int x = Leader(a), y = Leader(b); if (x == y) return false; if (-ParentOrSize[x] < -ParentOrSize[y]) (x, y) = (y, x); ParentOrSize[x] += ParentOrSize[y]; ParentOrSize[y] = x; return true; } public bool Same(int a, int b) { Debug.Assert(0 <= a && a < Count); Debug.Assert(0 <= b && b < Count); return Leader(a) == Leader(b); } public int Leader(int a) { if (ParentOrSize[a] < 0) return a; while (0 <= ParentOrSize[ParentOrSize[a]]) { (a, ParentOrSize[a]) = (ParentOrSize[a], ParentOrSize[ParentOrSize[a]]); } return ParentOrSize[a]; } public int Size(int a) { Debug.Assert(0 <= a && a < Count); return -ParentOrSize[Leader(a)]; } public int[][] Groups() { int[] leaderBuf = new int[Count]; int[] id = new int[Count]; var result = new List<int[]>(Count); int groupCount = 0; for (int i = 0; i < leaderBuf.Length; i++) { leaderBuf[i] = Leader(i); if (i == leaderBuf[i]) { id[i] = groupCount++; result.Add(new int[-ParentOrSize[i]]); } } int[] ind = new int[groupCount]; for (int i = 0; i < leaderBuf.Length; i++) { var leaderID = id[leaderBuf[i]]; result[leaderID][ind[leaderID]++] = i; } return result.ToArray(); } } } 
namespace AtCoder.IO { [DebuggerStepThrough] public class ConsoleReader { const int BufSize = 1 << 12; private readonly byte[] buffer = new byte[BufSize]; private readonly Stream input; private readonly Encoding encoding; private int pos = 0; private int len = 0; public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; } public ConsoleReader() : this(Console.OpenStandardInput(), Console.InputEncoding) { } [MethodImpl(MethodImplOptions.AggressiveInlining)] private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } } public int Int { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { int res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public int Int0 => Int - 1; public long Long { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { long res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public long Long0 => Long - 1; public string String { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return encoding.GetString(sb.ToArray()); } } public string Ascii { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new StringBuilder(); while (buffer[pos] <= 32) MoveNext(); do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return sb.ToString(); } } public string Line { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13); return encoding.GetString(sb.ToArray()); } } public char Char { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { while (buffer[pos] <= 32) MoveNext(); char res = (char)buffer[pos]; MoveNext(); return res; } } public double Double => double.Parse(Ascii); [DebuggerStepThrough] public ref struct RepeatReader { readonly ConsoleReader cr; readonly int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; } public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } } public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } } public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } } public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } } public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } } public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } } public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } } public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } } public static implicit operator int[](RepeatReader rr) => rr.Int; public static implicit operator long[](RepeatReader rr) => rr.Long; public static implicit operator double[](RepeatReader rr) => rr.Double; public static implicit operator string[](RepeatReader rr) => rr.Ascii; } public RepeatReader Repeat(int count) => new RepeatReader(this, count); [DebuggerStepThrough] public ref struct SplitReader { readonly ConsoleReader cr; public SplitReader(ConsoleReader cr) { this.cr = cr; } public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public static implicit operator int[](SplitReader sr) => sr.Int; public static implicit operator long[](SplitReader sr) => sr.Long; public static implicit operator double[](SplitReader sr) => sr.Double; public static implicit operator string[](SplitReader sr) => sr.Ascii; } public SplitReader Split => new SplitReader(this); public static implicit operator int(ConsoleReader cr) => cr.Int; public static implicit operator long(ConsoleReader cr) => cr.Long; public static implicit operator double(ConsoleReader cr) => cr.Double; public static implicit operator string(ConsoleReader cr) => cr.Ascii; } } 
namespace AtCoder.IO { [DebuggerStepThrough] public class ConsoleWriter { [DebuggerBrowsable(DebuggerBrowsableState.Never)] public readonly StreamWriter sw; public ConsoleWriter() : this(Console.OpenStandardOutput(), Console.OutputEncoding) { } public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); } public void Flush() => sw.Flush(); public ConsoleWriter WriteLine(ReadOnlySpan<char> obj) { sw.WriteLine(obj); return this; } public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; } public ConsoleWriter WriteLineJoin<T>(Span<T> col) => WriteMany(' ', (ReadOnlySpan<T>)col); public ConsoleWriter WriteLineJoin<T>(ReadOnlySpan<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T>(params T[] col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin(params object[] col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T1, T2>(T1 v1, T2 v2) { sw.Write(v1.ToString()); sw.Write(' '); sw.WriteLine(v2.ToString()); return this; } public ConsoleWriter WriteLineJoin<T1, T2, T3>(T1 v1, T2 v2, T3 v3) { sw.Write(v1.ToString()); sw.Write(' '); sw.Write(v2.ToString()); sw.Write(' '); sw.WriteLine(v3.ToString()); return this; } public ConsoleWriter WriteLineJoin<T1, T2, T3, T4>(T1 v1, T2 v2, T3 v3, T4 v4) { sw.Write(v1.ToString()); sw.Write(' '); sw.Write(v2.ToString()); sw.Write(' '); sw.Write(v3.ToString()); sw.Write(' '); sw.WriteLine(v4.ToString()); return this; } public ConsoleWriter WriteLines<T>(Span<T> col) => WriteMany('\n', (ReadOnlySpan<T>)col); public ConsoleWriter WriteLines<T>(ReadOnlySpan<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols) { foreach (var col in cols) WriteLineJoin(col); return this; } private ConsoleWriter WriteMany<T>(char sep, ReadOnlySpan<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } } } 
namespace AtCoder.Algebra{}
namespace AtCoder{}
namespace AtCoder.Internal{}
namespace AtCoder.Collection{}
namespace AtCoder.DataStructure{}
namespace AtCoder.DataStructure.String{}
namespace AtCoder.DataStructure.Bit{}
namespace AtCoder.Graph{}
namespace AtCoder.GraphAcl{}
namespace AtCoder.GraphAcl.Internal{}
namespace AtCoder.IO{}
namespace AtCoder.Util.Internal{}
namespace AtCoder.Util{}
namespace AtCoder.Util.Memo{}
#endregion AtCoderLibrary