using System; using System.Buffers; using System.Collections.Generic; using System.Diagnostics; using System.IO; using System.Linq; using System.Numerics; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Runtime.Intrinsics.X86; using System.Text; using YukicoderContest350.Problems; namespace YukicoderContest350.Problems { public class ProblemD : ProblemBase { public ProblemD() : base(false) { } [MethodImpl(MethodImplOptions.AggressiveOptimization)] protected override void SolveEach(IOManager io) { var n = io.ReadLong(); var m = io.ReadInt(); var edges = new long[2 * (m + 1)]; for (int i = 0; i < m; i++) { edges[2 * i] = io.ReadInt(); edges[2 * i + 1] = io.ReadInt(); } edges[^2] = 1; edges[^1] = n; var compressed = new CompressedCoordinate(edges); var graph = new WeightedGraph(compressed.UniqueCount); for (int i = 0; i < m; i++) { var cost = 2 * edges[2 * i + 1] - 2 * edges[2 * i] - 1; graph.AddEdge(compressed.Compressed[2 * i], compressed.Compressed[2 * i + 1], cost); } var values = edges.Distinct().OrderBy(i => i).ToArray(); for (int i = 0; i + 1 < values.Length; i++) { graph.AddEdge(i, i + 1, 2 * (values[i + 1] - values[i])); } var dijkstra = new Dijkstra(graph); var distances = dijkstra.GetDistancesFrom(0); var d = long.MaxValue; for (int i = 0; i < m + 1; i++) { var v = compressed.Compressed[2 * i + 1]; d.ChangeMin(distances[v] + 2 * (n - edges[2 * i + 1])); } io.WriteLine(d); } public interface IEdge { int To { get; } } public interface IWeightedEdge : IEdge { long Weight { get; } } public interface IGraph where TEdge : IEdge { ReadOnlySpan this[int node] { get; } int NodeCount { get; } } public interface IWeightedGraph : IGraph where TEdge : IWeightedEdge { } public readonly struct BasicEdge : IEdge { public int To { get; } public BasicEdge(int to) { To = to; } public override string ToString() => To.ToString(); public static implicit operator BasicEdge(int edge) => new BasicEdge(edge); public static implicit operator int(BasicEdge edge) => edge.To; } [StructLayout(LayoutKind.Auto)] public readonly struct WeightedEdge : IWeightedEdge { public int To { get; } public long Weight { get; } public WeightedEdge(int to) : this(to, 1) { } public WeightedEdge(int to, long weight) { To = to; Weight = weight; } public override string ToString() => $"[{Weight}]-->{To}"; public void Deconstruct(out int to, out long weight) => (to, weight) = (To, Weight); } public class BasicGraph : IGraph { private readonly List> _edges; public ReadOnlySpan this[int node] => _edges[node].AsSpan(); public int NodeCount => _edges.Count; public BasicGraph(int nodeCount) { _edges = new List>(nodeCount); for (int i = 0; i < nodeCount; i++) { _edges.Add(new List()); } } public void AddEdge(int from, int to) => _edges[from].Add(to); public void AddNode() => _edges.Add(new List()); } public class WeightedGraph : IGraph { private readonly List> _edges; public ReadOnlySpan this[int node] => _edges[node].AsSpan(); public int NodeCount => _edges.Count; public WeightedGraph(int nodeCount) { _edges = new List>(nodeCount); for (int i = 0; i < nodeCount; i++) { _edges.Add(new List()); } } public void AddEdge(int from, int to, long weight) => _edges[from].Add(new WeightedEdge(to, weight)); public void AddNode() => _edges.Add(new List()); } public class Dijkstra { private readonly WeightedGraph _graph; public Dijkstra(WeightedGraph graph) { _graph = graph; } public long[] GetDistancesFrom(int startNode) { const long Inf = 1L << 60; var distances = Enumerable.Repeat(Inf, _graph.NodeCount).ToArray(); distances[startNode] = 0; var todo = new PriorityQueue(PriorityQueue.Order.Ascending); todo.Enqueue(new State(startNode, 0)); while (todo.Count > 0) { var current = todo.Dequeue(); if (current.Distance > distances[current.Node]) { continue; } foreach (var edge in _graph[current.Node]) { var nextDistance = current.Distance + edge.Weight; if (distances[edge.To] > nextDistance) { distances[edge.To] = nextDistance; todo.Enqueue(new State(edge.To, nextDistance)); } } } return distances; } private readonly struct State : IComparable { public int Node { get; } public long Distance { get; } public State(int node, long distance) { Node = node; Distance = distance; } public int CompareTo(State other) => Distance.CompareTo(other.Distance); public void Deconstruct(out int node, out long distance) => (node, distance) = (Node, Distance); } } public class PriorityQueue : IEnumerable where T : IComparable { const int InitialSize = 4; private readonly int _reverseFactor; private T[] _heap; public int Count { get; private set; } public bool IsDescending => _reverseFactor == 1; public PriorityQueue(Order order) { _reverseFactor = order == Order.Ascending ? -1 : 1; _heap = new T[InitialSize]; Count = 0; } public PriorityQueue(Order order, IEnumerable collection) : this(order) { foreach (var item in collection) { Enqueue(item); } } public void Enqueue(T item) { if (Count >= _heap.Length) { var temp = new T[_heap.Length << 1]; _heap.AsSpan().CopyTo(temp); _heap = temp; } var index = Count++; ref var child = ref _heap[index]; child = item; while (index > 0) { index = (index - 1) >> 1; ref var parent = ref _heap[index]; if (Compare(child, parent) <= 0) { break; } Swap(ref child, ref parent); child = ref parent; } } public T Dequeue() { var index = 0; ref var parent = ref _heap[index]; var item = parent; parent = _heap[--Count]; var span = _heap.AsSpan(0, Count); while (true) { index = (index << 1) + 1; if (unchecked((uint)index < (uint)span.Length)) { ref var child = ref span[index]; var r = index + 1; if (unchecked((uint)r < (uint)span.Length)) { ref var brother = ref span[r]; if (Compare(child, brother) < 0) { child = ref brother; index = r; } } if (Compare(parent, child) < 0) { Swap(ref parent, ref child); parent = ref child; } else { break; } } else { break; } } return item; } public T Peek() => _heap[0]; public void Clear() => Count = 0; private int Compare(T a, T b) => _reverseFactor * a.CompareTo(b); private void Swap(ref T a, ref T b) { var temp = a; a = b; b = temp; } public IEnumerator GetEnumerator() { var copy = new T[_heap.Length]; var cnt = Count; _heap.AsSpan().CopyTo(copy); try { while (Count > 0) { yield return Dequeue(); } } finally { _heap = copy; Count = cnt; } } System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public enum Order { Ascending, Descending } } public class CompressedCoordinate where T : IComparable, IEquatable { readonly int[] _compressed; readonly T[] _raw; readonly Dictionary _converter; readonly T[] _inverter; public int UniqueCount => _inverter.Length; /// /// 座圧前のデータ列を返します。 /// public ReadOnlySpan Raw => _raw; /// /// 座圧後のデータ列を返します。 /// public ReadOnlySpan Compressed => _compressed; /// /// 座圧前のデータを座圧後のインデックスに変換します。 /// public int Convert(T value) => _converter[value]; /// /// 座圧後のインデックスを座圧前のデータに変換します。 /// public T Invert(Index index) => _inverter[index]; public CompressedCoordinate(IEnumerable data) { _raw = data.ToArray(); _converter = new Dictionary(); _inverter = _raw.Distinct().ToArray(); Array.Sort(_inverter); _compressed = new int[_raw.Length]; var span = _inverter.AsSpan(); for (int i = 0; i < _compressed.Length; i++) { _compressed[i] = span.BinarySearch(_raw[i]); } for (var i = 0; i < _inverter.Length; i++) { _converter[_inverter[i]] = i; } } } } } namespace YukicoderContest350 { internal class Program { static void Main(string[] args) { IProblem question = new ProblemD(); using var io = new IOManager(Console.OpenStandardInput(), Console.OpenStandardOutput()); question.Solve(io); } } } #region Base Class namespace YukicoderContest350.Problems { public interface IProblem { string Solve(string input); void Solve(IOManager io); } public abstract class ProblemBase : IProblem { protected bool HasMultiTestCases { get; } protected ProblemBase(bool hasMultiTestCases) => HasMultiTestCases = hasMultiTestCases; public string Solve(string input) { var inputStream = new MemoryStream(Encoding.UTF8.GetBytes(input)); var outputStream = new MemoryStream(); using var manager = new IOManager(inputStream, outputStream); Solve(manager); manager.Flush(); outputStream.Seek(0, SeekOrigin.Begin); var reader = new StreamReader(outputStream); return reader.ReadToEnd(); } public void Solve(IOManager io) { var tests = HasMultiTestCases ? io.ReadInt() : 1; for (var t = 0; t < tests; t++) { SolveEach(io); } } protected abstract void SolveEach(IOManager io); } } #endregion #region Utils namespace YukicoderContest350 { public class IOManager : IDisposable { private readonly BinaryReader _reader; private readonly StreamWriter _writer; private bool _disposedValue; private byte[] _buffer = new byte[1024]; private int _length; private int _cursor; private bool _eof; const char ValidFirstChar = '!'; const char ValidLastChar = '~'; public IOManager(Stream input, Stream output) { _reader = new BinaryReader(input); _writer = new StreamWriter(output) { AutoFlush = false }; } [MethodImpl(MethodImplOptions.AggressiveInlining)] private char ReadAscii() { if (_cursor == _length) { _cursor = 0; _length = _reader.Read(_buffer); if (_length == 0) { if (!_eof) { _eof = true; return char.MinValue; } else { ThrowEndOfStreamException(); } } } return (char)_buffer[_cursor++]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public char ReadChar() { char c; while (!IsValidChar(c = ReadAscii())) { } return c; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public string ReadString() { var builder = new StringBuilder(); char c; while (!IsValidChar(c = ReadAscii())) { } do { builder.Append(c); } while (IsValidChar(c = ReadAscii())); return builder.ToString(); } public int ReadInt() => (int)ReadLong(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public long ReadLong() { long result = 0; bool isPositive = true; char c; while (!IsNumericChar(c = ReadAscii())) { } if (c == '-') { isPositive = false; c = ReadAscii(); } do { result *= 10; result += c - '0'; } while (IsNumericChar(c = ReadAscii())); return isPositive ? result : -result; } [MethodImpl(MethodImplOptions.AggressiveInlining)] private Span ReadChunk(Span span) { var i = 0; char c; while (!IsValidChar(c = ReadAscii())) { } do { span[i++] = c; } while (IsValidChar(c = ReadAscii())); return span.Slice(0, i); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public double ReadDouble() => double.Parse(ReadChunk(stackalloc char[32])); [MethodImpl(MethodImplOptions.AggressiveInlining)] public decimal ReadDecimal() => decimal.Parse(ReadChunk(stackalloc char[32])); public int[] ReadIntArray(int n) { var a = new int[n]; for (int i = 0; i < a.Length; i++) { a[i] = ReadInt(); } return a; } public long[] ReadLongArray(int n) { var a = new long[n]; for (int i = 0; i < a.Length; i++) { a[i] = ReadLong(); } return a; } public double[] ReadDoubleArray(int n) { var a = new double[n]; for (int i = 0; i < a.Length; i++) { a[i] = ReadDouble(); } return a; } public decimal[] ReadDecimalArray(int n) { var a = new decimal[n]; for (int i = 0; i < a.Length; i++) { a[i] = ReadDecimal(); } return a; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Write(T value) => _writer.Write(value.ToString()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public void WriteLine(T value) => _writer.WriteLine(value.ToString()); public void WriteLine(IEnumerable values, char separator) { var e = values.GetEnumerator(); if (e.MoveNext()) { _writer.Write(e.Current.ToString()); while (e.MoveNext()) { _writer.Write(separator); _writer.Write(e.Current.ToString()); } } _writer.WriteLine(); } public void WriteLine(T[] values, char separator) => WriteLine((ReadOnlySpan)values, separator); public void WriteLine(Span values, char separator) => WriteLine((ReadOnlySpan)values, separator); public void WriteLine(ReadOnlySpan values, char separator) { for (int i = 0; i < values.Length - 1; i++) { _writer.Write(values[i]); _writer.Write(separator); } if (values.Length > 0) { _writer.Write(values[^1]); } _writer.WriteLine(); } public void Flush() => _writer.Flush(); [MethodImpl(MethodImplOptions.AggressiveInlining)] private static bool IsValidChar(char c) => ValidFirstChar <= c && c <= ValidLastChar; [MethodImpl(MethodImplOptions.AggressiveInlining)] private static bool IsNumericChar(char c) => ('0' <= c && c <= '9') || c == '-'; private void ThrowEndOfStreamException() => throw new EndOfStreamException(); protected virtual void Dispose(bool disposing) { if (!_disposedValue) { if (disposing) { _reader.Dispose(); _writer.Flush(); _writer.Dispose(); } _disposedValue = true; } } public void Dispose() { Dispose(disposing: true); GC.SuppressFinalize(this); } } public static class UtilExtensions { public static bool ChangeMax(ref this T value, T other) where T : struct, IComparable { if (value.CompareTo(other) < 0) { value = other; return true; } return false; } public static bool ChangeMin(ref this T value, T other) where T : struct, IComparable { if (value.CompareTo(other) > 0) { value = other; return true; } return false; } public static void SwapIfLargerThan(ref this T a, ref T b) where T : struct, IComparable { if (a.CompareTo(b) > 0) { (a, b) = (b, a); } } public static void SwapIfSmallerThan(ref this T a, ref T b) where T : struct, IComparable { if (a.CompareTo(b) < 0) { (a, b) = (b, a); } } public static void Sort(this T[] array) where T : IComparable => Array.Sort(array); public static void Sort(this T[] array, Comparison comparison) => Array.Sort(array, comparison); } public static class CollectionExtensions { private class ArrayWrapper { #pragma warning disable CS0649 public T[] Array; #pragma warning restore CS0649 } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span AsSpan(this List list) { return Unsafe.As>(list).Array.AsSpan(0, list.Count); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span GetRowSpan(this T[,] array, int i) { var width = array.GetLength(1); return MemoryMarshal.CreateSpan(ref array[i, 0], width); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span GetRowSpan(this T[,,] array, int i, int j) { var width = array.GetLength(2); return MemoryMarshal.CreateSpan(ref array[i, j, 0], width); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span GetRowSpan(this T[,,,] array, int i, int j, int k) { var width = array.GetLength(3); return MemoryMarshal.CreateSpan(ref array[i, j, k, 0], width); } public static void Fill(this T[] array, T value) => array.AsSpan().Fill(value); public static void Fill(this T[,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(value); public static void Fill(this T[,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(value); public static void Fill(this T[,,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(value); } public static class SearchExtensions { private struct LowerBoundComparer : IComparer where T : IComparable { public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1; } private struct UpperBoundComparer : IComparer where T : IComparable { public int Compare(T x, T y) => 0 < x.CompareTo(y) ? 1 : -1; } // https://trsing.hatenablog.com/entry/2019/08/27/211038 public static int GetGreaterEqualIndex(this ReadOnlySpan span, T inclusiveMin) where T : IComparable => ~span.BinarySearch(inclusiveMin, new UpperBoundComparer()); public static int GetGreaterThanIndex(this ReadOnlySpan span, T exclusiveMin) where T : IComparable => ~span.BinarySearch(exclusiveMin, new LowerBoundComparer()); public static int GetLessEqualIndex(this ReadOnlySpan span, T inclusiveMax) where T : IComparable => ~span.BinarySearch(inclusiveMax, new LowerBoundComparer()) - 1; public static int GetLessThanIndex(this ReadOnlySpan span, T exclusiveMax) where T : IComparable => ~span.BinarySearch(exclusiveMax, new UpperBoundComparer()) - 1; public static int GetGreaterEqualIndex(this Span span, T inclusiveMin) where T : IComparable => ((ReadOnlySpan)span).GetGreaterEqualIndex(inclusiveMin); public static int GetGreaterThanIndex(this Span span, T exclusiveMin) where T : IComparable => ((ReadOnlySpan)span).GetGreaterThanIndex(exclusiveMin); public static int GetLessEqualIndex(this Span span, T inclusiveMax) where T : IComparable => ((ReadOnlySpan)span).GetLessEqualIndex(inclusiveMax); public static int GetLessThanIndex(this Span span, T exclusiveMax) where T : IComparable => ((ReadOnlySpan)span).GetLessThanIndex(exclusiveMax); public static int BoundaryBinarySearch(Predicate predicate, int ok, int ng) { while (Math.Abs(ok - ng) > 1) { var mid = (ok + ng) / 2; if (predicate(mid)) { ok = mid; } else { ng = mid; } } return ok; } public static long BoundaryBinarySearch(Predicate predicate, long ok, long ng) { while (Math.Abs(ok - ng) > 1) { var mid = (ok + ng) / 2; if (predicate(mid)) { ok = mid; } else { ng = mid; } } return ok; } public static BigInteger BoundaryBinarySearch(Predicate predicate, BigInteger ok, BigInteger ng) { while (BigInteger.Abs(ok - ng) > 1) { var mid = (ok + ng) / 2; if (predicate(mid)) { ok = mid; } else { ng = mid; } } return ok; } public static double BoundaryBinarySearch(Predicate predicate, double ok, double ng, double eps = 1e-9, int loopLimit = 1000) { var count = 0; while (Math.Abs(ok - ng) > eps && count++ < loopLimit) { var mid = (ok + ng) * 0.5; if (predicate(mid)) { ok = mid; } else { ng = mid; } } return (ok + ng) * 0.5; } public static double Bisection(Func f, double a, double b, double eps = 1e-9, int loopLimit = 100) { double mid = (a + b) / 2; var fa = f(a); if (fa * f(b) >= 0) { throw new ArgumentException("f(a)とf(b)は異符号である必要があります。"); } for (int i = 0; i < loopLimit; i++) { var fmid = f(mid); var sign = fa * fmid; if (sign < 0) { b = mid; } else if (sign > 0) { a = mid; fa = fmid; } else { return mid; } mid = (a + b) / 2; if (Math.Abs(b - a) < eps) { break; } } return mid; } } } #endregion