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)

// ReSharper disable RedundantUsingDirective
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Runtime.CompilerServices;
using System.IO;
using System.Linq;
using System.Numerics;
using static Solve.Methods;
using static Solve.Input;
using static Solve.Output;
using static System.Math;

// Resharper restore RedundantUsingDirective

namespace Solve
{
    public partial class Solver
    {
        public void Main()
        {
            var (N, M) = Int;
            var (A, B) = nextArray<int, int>(M);
            var uf = new UnionFind(N);
            for (int i = 0; i < M; i++)
            {
                uf.Connect(A[i] - 1, B[i] - 1);

            }
            print(uf.AllParents.Count()-1);
        }

        public const int MOD = 1000000007;
    }
    
    [DebuggerDisplay("Count of Parents = {" + nameof(ParentsCount) + "}")]
    public class UnionFind
    {
        readonly int[] _parent;
        public UnionFind(int count) { _parent = Enumerable.Repeat(-1, count).ToArray(); }

        public IEnumerable<int> AllParents =>
            _parent.Select((x, i) => (x, i))
                .Where(x => x.Item1 < 0)
                .Select(x => x.Item2);

        int ParentsCount => _parent.Count(x => x < 0);
        public int Size(int x) => -_parent[Find(x)];
        public int Find(int x) => _parent[x] < 0 ? x : _parent[x] = Find(_parent[x]);
        public bool Connect(int x, int y) {
            int rx = Find(x), ry = Find(y);
            if (rx == ry) return false;
            if (Size(rx) > Size(ry)) (rx, ry) = (ry, rx);
            _parent[rx] += _parent[ry];
            _parent[ry] = rx;

            return true;
        }
        public bool Same(int x, int y) => Find(x) == Find(y);
        public ILookup<int, int> ToLookup() => EnumeratePairs().ToLookup(x => x.par, x => x.val);
        IEnumerable<(int par, int val)> EnumeratePairs() {
            for (int i = 0; i < _parent.Length; i++) yield return (Find(i), i);
        }
    }
    
    public static class Methods
    {
        [MethodImpl(256)] public static bool Assert(in bool b, in string message = null) =>
            b ? true : throw new Exception(message ?? "Assert failed.");
        [MethodImpl(256)] public static string JoinSpace<T>(this IEnumerable<T> source) => source.Join(" ");
        [MethodImpl(256)] public static string JoinEndline<T>(this IEnumerable<T> source) => source.Join("\n");
        [MethodImpl(256)] public static string Join<T>(this IEnumerable<T> source, string s) => string.Join(s, source);
        [MethodImpl(256)] public static string Join<T>(this IEnumerable<T> source, char c) =>
            string.Join(c.ToString(), source);
        public static int Gcd(int a, int b) => (int) Gcd((long) a, b);
        public static long Gcd(long a, long b) {
            while (true) {
                if (a < b) (a, b) = (b, a);
                if (a % b == 0) return b;
                (a, b) = (b, a % b);
            }
        }
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;
        public static bool IsPrime(long value) {
            if (value <= 1) return false;
            for (long i = 2; i * i <= value; ++i) if (value % i == 0) return false;
            return true;
        }
        public static long Pow(long a, int b) {
            long res = 1;
            while (b > 0) { if (b % 2 != 0) res *= a; a *= a; b >>= 1; }
            return res;
        }
        public static int PowMod(long a, long b, int p) => (int) PowMod(a, b, (long) p);
        public static long PowMod(long a, long b, long p) {
            long res = 1;
            while (b > 0) { if (b % 2 != 0) res = res * a % p; a = a * a % p; b >>= 1; }
            return res;
        }
        public static IEnumerable<long> Factors(long n) {
            Assert(n >= 0, "n must be greater than 0.");
            for (long i = 1; i * i <= n; ++i) {
                var div = DivRem(n, i, out var rem);
                if (rem > 0) continue;
                yield return div;
                if (i != div) yield return i;
            }
        }
        public static IEnumerable<int> Factors(int n) => Factors((long) n).Select(Convert.ToInt32);
        [MethodImpl(256)] public static int DivCeil(int a, int b) => (a + b - 1) / b;
        [MethodImpl(256)] public static long DivCeil(long a, long b) => (a + b - 1) / b;
        public static IEnumerable<T[]> Permutations<T>(IEnumerable<T> src) {
            var ret = new List<T[]>();
            Search(ret, new Stack<T>(), src.ToArray());
            return ret;

            static void Search(ICollection<T[]> perms, Stack<T> stack, T[] a) {
                int N = a.Length;
                if (N == 0) perms.Add(stack.Reverse().ToArray());
                else {
                    var b = new T[N - 1];
                    Array.Copy(a, 1, b, 0, N - 1);
                    for (int i = 0; i < a.Length; ++i) {
                        stack.Push(a[i]);
                        Search(perms, stack, b);
                        if (i < b.Length) b[i] = a[i];
                        stack.Pop();
                    }
                }
            }
        }
        public static long BinarySearch(long low, long high, Func<long, bool> expression) {
            while (low < high) {
                long middle = (high - low) / 2 + low;
                if (!expression(middle))
                    high = middle;
                else
                    low = middle + 1;
            }

            return high;
        }
        public static int LowerBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer) {
            int low = start;
            int high = end;
            while (low < high) {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }

            return low;
        }
        public static int LowerBound<T>(T[] arr, T value) where T : IComparable =>
            LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        public static int UpperBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer) {
            var (low, high) = (start, end);
            while (low < high) {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0) low = mid + 1;
                else high = mid;
            }

            return low;
        }
        public static int UpperBound<T>(T[] arr, T value) => 
            UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        [MethodImpl(256)]
        public static IEnumerable<TResult> Repeat<TResult>(TResult value, int count) => Enumerable.Repeat(value, count);
        [MethodImpl(256)] public static string AsString(this IEnumerable<char> source) => new string(source.ToArray());
        public static IEnumerable<long> CumSum(this IEnumerable<long> source) {
            long sum = 0; foreach (var item in source) yield return sum += item;
        }
        public static IEnumerable<int> CumSum(this IEnumerable<int> source) {
            int sum = 0; foreach (var item in source) yield return sum += item;
        }
        [MethodImpl(256)] public static bool IsIn<T>(this T value, T l, T r) where T : IComparable<T> =>
            l.CompareTo(r) > 0 ? throw new ArgumentException() : l.CompareTo(value) <= 0 && value.CompareTo(r) < 0;
        [MethodImpl(256)] public static bool IsIn(this in int value, in Range range) =>
            value.IsIn(range.Start.Value, range.End.Value);
        [MethodImpl(256)] public static bool IsIn(this in Index value, in Range range) =>
            value.IsFromEnd && value.Value.IsIn(range.Start.Value, range.End.Value);
        public static IEnumerable<int> Range(int start, int end, int step = 1) {
            for (var i = start; i < end; i += step) yield return i;
        }
        public static IEnumerable<int> Range(int end) => Range(0, end);
        public static IEnumerable<int> Range(Range range, int step = 1) =>
            Range(range.Start.Value, range.End.Value, step);
        [MethodImpl(256)] public static T[] Sort<T>(this T[] arr) where T : IComparable<T> {
            var array = arr[..]; Array.Sort(array); return array;
        }
        [MethodImpl(256)]
        public static T[] Sort<T, U>(this T[] arr, Func<T, U> selector) where U : IComparable<U> {
            var array = arr[..];
            Array.Sort(array, (a, b) => selector(a).CompareTo(selector(b)));
            return array;
        }
        [MethodImpl(256)] public static T[] SortDescending<T>(this T[] arr) where T : IComparable<T> {
            var array = arr[..];
            Array.Sort(array, (a, b) => b.CompareTo(a));
            return array;
        }
        [MethodImpl(256)]
        public static T[] SortDescending<T, U>(this T[] arr, Func<T, U> selector) where U : IComparable<U> {
            var array = arr[..];
            Array.Sort(array, (a, b) => selector(b).CompareTo(selector(a)));
            return array;
        }
        public static T[] Unique<T>(this IEnumerable<T> arr) {
            var source = arr.ToArray();
            var ret = new List<T>(source.Length);
            var set = new SortedSet<T>();
            ret.AddRange(source.Where(val => set.Add(val)));

            return ret.ToArray();
        }
        [MethodImpl(256)] public static bool chmin<T>(ref T a, T b)
            where T : IComparable<T> {
            if (a.CompareTo(b) > 0) { a = b; return true; }
            return false;
        } 
        [MethodImpl(256)] public static bool chmax<T>(ref T a, T b)
            where T : IComparable<T> {
            if (a.CompareTo(b) < 0) { a = b; return true; }
            return false;
        }
        public static T[] InitArray<T>(int n, Func<int, T> init) {
            var res = new T[n];
            for (int i = 0; i < n; i++) res[i] = init(i);
            return res;
        }
        public static T[][] JaggedArray2D<T>(int a, int b, T defaultValue = default) {
            var ret = new T[a][];
            for (int i = 0; i < a; ++i) ret[i] = Enumerable.Repeat(defaultValue, b).ToArray();
            return ret;
        }
        public static T[,] Array2D<T>(int a, int b, T defaultValue = default) {
            var ret = new T[a, b];
            for (int i = 0; i < a; ++i) for (int j = 0; j < b; ++j) ret[i, j] = defaultValue;
            return ret;
        }
        public static T[,] To2DArray<T>(this T[][] array) {
            if (!array.Any()) return new T[0, 0];

            int len = array[0].Length;
            if (array.Any(x => x.Length != len))
                throw new ArgumentException("Length of each array must be same.", nameof(array));

            var ret = new T[array.Length, len];
            for (int i = 0; i < array.Length; ++i) for (int j = 0; j < len; ++j) ret[i, j] = array[i][j];
            return ret;
        }
        [MethodImpl(256)] public static T Min<T>(params T[] col) => col.Min();
        [MethodImpl(256)] public static T Max<T>(params T[] col) => col.Max();
        [MethodImpl(256)] public static IEnumerable<(T, int)> WithIndex<T>(this IEnumerable<T> source) =>
            source.Select((x, i) => (x, i));
        [MethodImpl(256)] public static (T, U, V)[] Zip<T, U, V>(
            IReadOnlyCollection<T> t,
            IReadOnlyCollection<U> u,
            IReadOnlyCollection<V> v
        ) {
            Assert(t.Count == u.Count && u.Count == v.Count);
            return t.Zip(u, (a, b) => (a, b))
                .Zip(v, (tuple, c) => (tuple.Item1, tuple.Item2, c)).ToArray();
        }
        [MethodImpl(256)] public static void rep(in int start, in int end, Action<int> func) {
            for (int i = start; i < end; ++i) func(i);
        }
        [MethodImpl(256)] public static void rep(in int end, Action<int> func) => rep(0, end, func);
        [MethodImpl(256)] public static void rep1(in int end, Action<int> func) => rep(1, end + 1, func);
        [MethodImpl(256)] public static void repr(in int end, Action<int> func) {
            for (int i = end - 1; i >= 0; --i) func(i);
        }
        [MethodImpl(256)]
        public static void each<T>(this IEnumerable<T> source, Action<T> func) {
            foreach (var item in source) func(item);
        }
        [MethodImpl(256)]
        public static void eachWithIndex<T>(this IEnumerable<T> source, Action<T, int> func) {
            int index = 0; foreach (var item in source) func(item, index++);
        }
        [MethodImpl(256)] public static int bit(in int x) => 1 << x;
        [MethodImpl(256)] public static long bitl(in int x) => 1L << x;
    }
    public class UnorderedMap<T, U> : Dictionary<T, U>
    {
        public new U this[T k] {
            get =>
                TryGetValue(k, out var v) ? v : base[k] = default;
            set =>
                base[k] = value;
        }
    }
    public class Map<T, U> : SortedDictionary<T, U>
    {
        readonly U _default;
        public Map(U defaultValue = default) {
            _default = defaultValue;
        }
        public new U this[T k] {
            get =>
                TryGetValue(k, out var v) ? v : base[k] = _default;
            set =>
                base[k] = value;
        }
    }
    public class Scanner<T>
    {
        public T r => next<T>();
        public T next() => r;

        IEnumerable<T> enumerable(int N) { for (int i = 0; i < N; ++i) yield return r; }

        public T[] array(in int N) => enumerable(N).ToArray();
        public List<T> list(in int N) => enumerable(N).ToList();
        public T[,] array2d(in int N, in int M) => next2DArray<T>(N, M);
        public T[][] listArray(in int n) {
            var ret = new T[n][];
            for (int i = 0; i < n; i++) ret[i] = array(next<int>());
            return ret;
        }

        public void Deconstruct(out T _1, out T _2) => (_1, _2) = (r, r);
        public void Deconstruct(out T _1, out T _2, out T _3) => (_1, _2, _3) = (r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4) =>
            (_1, _2, _3, _4) = (r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4, out T _5) =>
            (_1, _2, _3, _4, _5) = (r, r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4, out T _5, out T _6) =>
            (_1, _2, _3, _4, _5, _6) = (r, r, r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4, out T _5, out T _6, out T _7) =>
            (_1, _2, _3, _4, _5, _6, _7) = (r, r, r, r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4, out T _5, out T _6, out T _7, out T _8) =>
            (_1, _2, _3, _4, _5, _6, _7, _8) = (r, r, r, r, r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4, 
            out T _5, out T _6, out T _7, out T _8, out T _9) =>
            (_1, _2, _3, _4, _5, _6, _7, _8, _9) = (r, r, r, r, r, r, r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4,
            out T _5, out T _6, out T _7, out T _8, out T _9, out T _10) =>
            (_1, _2, _3, _4, _5, _6, _7, _8, _9, _10) = (r, r, r, r, r, r, r, r, r, r);
        
        public static implicit operator T(Scanner<T> sc) => sc.r;
    }
    public static class Input
    {
        const char _separator = ' ';
        static readonly Queue<string> _input = new Queue<string>();
        static readonly StreamReader sr =
#if FILE
            new StreamReader("in.txt");
#else
            new StreamReader(Console.OpenStandardInput());
#endif

        public static string ReadLine => sr.ReadLine();
        static string ReadStr => Read;
        static int ReadInt => int.Parse(Read);
        static long ReadLong => long.Parse(Read);
        static ulong ReadULong => ulong.Parse(Read);
        static double ReadDouble => double.Parse(Read);
        static BigInteger ReadBigInteger => BigInteger.Parse(Read);

        public static string Read {
            get {
                if (_input.Any()) return _input.Dequeue();
                foreach (var val in sr.ReadLine().Split(_separator)) _input.Enqueue(val);
                return _input.Dequeue();
            }
        }

        public static string next() => Read;
        public static T next<T>() =>
            default(T) switch {
                sbyte _ => (T) (object) (sbyte) ReadInt,
                short _ => (T) (object) (short) ReadInt,
                int _ => (T) (object) ReadInt,
                long _ => (T) (object) ReadLong,
                byte _ => (T) (object) (byte) ReadULong,
                ushort _ => (T) (object) (ushort) ReadULong,
                uint _ => (T) (object) (uint) ReadULong,
                ulong _ => (T) (object) ReadULong,
                float _ => (T) (object) (float) ReadDouble,
                double _ => (T) (object) ReadDouble,
                string _ => (T) (object) ReadStr,
                char _ => (T) (object) ReadStr[0],
                BigInteger _ => (T) (object) ReadBigInteger,
                _ => typeof(T) == typeof(string)
                    ? (T) (object) ReadStr
                    : throw new NotSupportedException(),
            };
        public static (T, U) next<T, U>() => (next<T>(), next<U>());
        public static (T, U, V) next<T, U, V>() => (next<T>(), next<U>(), next<V>());
        public static (T, U, V, W) next<T, U, V, W>() => (next<T>(), next<U>(), next<V>(), next<W>());
        public static (T, U, V, W, X) next<T, U, V, W, X>() => (next<T>(), next<U>(), next<V>(), next<W>(), next<X>());
        public static T[] nextArray<T>(in int size) {
            var ret = new T[size]; for (int i = 0; i < size; ++i) ret[i] = next<T>(); return ret;
        }
        public static T[,] next2DArray<T>(int n, in int m) {
            var ret = new T[n, m];
            for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) ret[i, j] = next<T>(); return ret;
        }
        public static (T[], U[]) nextArray<T, U>(in int size) {
            var ret1 = new T[size]; var ret2 = new U[size];
            for (int i = 0; i < size; ++i) (ret1[i], ret2[i]) = next<T, U>();
            return (ret1, ret2);
        }
        public static (T[], U[], V[]) nextArray<T, U, V>(in int size) {
            var ret1 = new T[size]; var ret2 = new U[size]; var ret3 = new V[size];
            for (int i = 0; i < size; ++i) (ret1[i], ret2[i], ret3[i]) = next<T, U, V>();
            return (ret1, ret2, ret3);
        }
    }
    public static class Output
    {
        [MethodImpl(256)] public static void print() => Console.WriteLine();
        [MethodImpl(256)] public static void print(in string s, bool endline = true) {
            if (endline) Console.WriteLine(s); else Console.Write(s);
        }
        [MethodImpl(256)] public static void print(in char s, bool endline = true) {
            if (endline) Console.WriteLine(s); else Console.Write(s);
        }
        [MethodImpl(256)] public static void print(in int v, bool endline = true) {
            if (endline) Console.WriteLine(v); else Console.Write(v);
        }
        [MethodImpl(256)] public static void print(in long v, bool endline = true) {
            if (endline) Console.WriteLine(v); else Console.Write(v);
        }
        [MethodImpl(256)] public static void print(in ulong v, bool endline = true) {
            if (endline) Console.WriteLine(v); else Console.Write(v);
        }
        [MethodImpl(256)] public static void print(in bool b) => PrintBool(b);
        [MethodImpl(256)] public static void print(in object v) => Console.WriteLine(v);
        [MethodImpl(256)] public static void print<T>(in IEnumerable<T> array, string separator = " ") =>
            Console.WriteLine(array.Join(separator));
        [MethodImpl(256)] public static void prints<T>(params T[] t) => print(t);
        
#if LOCAL
        [MethodImpl(256)] public static void debug<T>(in T value, bool endline = true) {
            if (endline) Console.WriteLine(value);else Console.Write(value);
        }
#else
        public static void debug(params object[] obj) { }
#endif

        [MethodImpl(256)] static void PrintBool(in bool val, in string yes = null, in string no = null) =>
            print(val ? yes ?? _yes : no ?? _no);
        static string _yes = "Yes", _no = "No";

        public static void SetYesNoString(in YesNoType t) => (_yes, _no) = YesNoString[t];
        public static void SetYesNoString(in string yes, in string no) => (_yes, _no) = (yes, no);

        static readonly Dictionary<YesNoType, (string yes, string no)>
            YesNoString = new Dictionary<YesNoType, (string, string)> {
                    {YesNoType.Yes_No, ("Yes", "No")},
                    {YesNoType.YES_NO, ("YES", "NO")},
                    {YesNoType.Upper, ("YES", "NO")},
                    {YesNoType.yes_no, ("yes", "no")},
                    {YesNoType.Lower, ("yes", "no")},
                    {YesNoType.Possible_Impossible, ("Possible", "Impossible")},
                    {YesNoType.Yay, ("Yay!", ":(")},
                };

        public static readonly (string yes, string no) YN_Possible = ("Possible", "Impossible"),
            YN_lower = ("yes", "no"), YN_upper = ("YES", "NO"), YN_Yay = ("Yay!", ":(");

        public static void Yes() => print(_yes);
        public static void No() => print(_no);

        public static object cout { set => Console.WriteLine(value); }
#if LOCAL
        public static object dout { set => Console.WriteLine(value); }
#else
        public static object dout { set { } }
#endif
        public static object cerr { set => Console.Error.WriteLine(value); }

        public const string endl = "\n";

        public enum YesNoType { Yes_No, YES_NO, Upper, yes_no, Lower, Possible_Impossible, Yay }
    }
    public class Program
    {
        public static void Main(string[] args) {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
            new Solver().Main();
            Console.Out.Flush();
        }
    }
    partial class Solver
    {
        readonly Scanner<int> Int;
        readonly Scanner<long> Long;
        readonly Scanner<string> String;
        public Solver() => (Int, String, Long) = (new Scanner<int>(), new Scanner<string>(), new Scanner<long>());
        const int INF = 1000000010;
        const long LINF = 1000000000000000100;
        const double EPS = 1e-9;
        public static readonly int[] dx = {-1, 0, 0, 1, -1, -1, 1, 1}, dy = {0, 1, -1, 0, -1, 1, -1, 1};
    }
}