結果

問題 No.3100 Parallel Translated
ユーザー tobisatis
提出日時 2025-04-11 23:19:58
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 94 ms / 2,000 ms
コード長 10,222 bytes
コンパイル時間 10,567 ms
コンパイル使用メモリ 169,448 KB
実行使用メモリ 199,628 KB
最終ジャッジ日時 2025-04-11 23:20:18
合計ジャッジ時間 14,541 ms
ジャッジサーバーID
(参考情報)
judge5 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 32
権限があれば一括ダウンロードができます
コンパイルメッセージ
  復元対象のプロジェクトを決定しています...
  /home/judge/data/code/main.csproj を復元しました (101 ミリ秒)。
  main -> /home/judge/data/code/bin/Release/net8.0/main.dll
  main -> /home/judge/data/code/bin/Release/net8.0/publish/

ソースコード

diff #

#nullable enable

using System.Numerics;

void Run()
{
    var n = Int();
    var pz = n.Repeat(() => new Geometry2D.Point(Int(), Int()));
    var h = new Geometry2D.ConvexHull(pz);
    var s = (ModInt)h.Area2().Value / 2;
    Out(s);
}

#region
AtCoderIO _io_;
var _backend_ = new StandardIOBackend();
_io_ = new(){ Backend = _backend_ };
Run();
_backend_.Flush();

string String() => _io_.Next();
int Int() => int.Parse(String());
void Out(object? x, string? sep = null) => _io_.Out(x, sep);

class AtCoderIO
{
    public required StandardIOBackend Backend { get; init; }

    Memory<string> _input = Array.Empty<string>();
    int _iter = 0;
    public string Next()
    {
        while (_iter >= _input.Length) (_input, _iter) = (Backend.ReadLine().Split(' '), 0);
        return _input.Span[_iter++];
    }

    public void Out(object? x, string? separator = null)
    {
        if (x == null) return;
        separator ??= Environment.NewLine;
        if (x is System.Collections.IEnumerable a and not string)
        {
            var objects = a.Cast<object>();
            if (separator == Environment.NewLine && !objects.Any()) return;
            x = string.Join(separator, objects);
        }
        Backend.WriteLine(x);
    }
}

class StandardIOBackend
{
    readonly StreamReader _sr = new(Console.OpenStandardInput());
    readonly StreamWriter _sw = new(Console.OpenStandardOutput()) { AutoFlush = false };
    public string ReadLine() => _sr.ReadLine()!;
    public void WriteLine(object? value) => _sw.WriteLine(value);
    public void Flush() => _sw.Flush();
}
#endregion

static class Extensions
{
    public static T[] Repeat<T>(this int time, Func<T> F) => Enumerable.Range(0, time).Select(_ => F()).ToArray();
}

static partial class Geometry2D
{
    public readonly struct Number
    {
        public readonly long Value = 0;
        public Number(long value) { Value = value; }
        public static implicit operator long(Number s) => s.Value;
        public static implicit operator Number(long s) => new(s);
        public static Number Sqrt(Number s) => throw new Exception();
        public override string ToString() => Value.ToString();
    }

    public readonly struct Point
    {
        public readonly Number X, Y;
        public Point(Number x, Number y) { (X, Y) = (x, y); }
        public Point AdditionalInverse => new(-X, -Y);
        public static Point operator +(Point l, Point r) => new(l.X + r.X, l.Y + r.Y);
        public static Point operator -(Point l, Point r) => new(l.X - r.X, l.Y - r.Y);

        public Point Mul(Number k) => new(X * k, Y * k);
        public Point Div(Number k) => new(X / k, Y / k);
        public Number DotProduct(Point other) => X * other.X + Y * other.Y;
        public Number CrossProduct(Point other) => X * other.Y - Y * other.X;
        public Number Magnitude2() => DotProduct(this);
        public Number Magnitude() => Number.Sqrt(Magnitude2());
        public Point Rotated90() => new(Y, -X);

        public override bool Equals(object? obj) => obj is Point s && s.X == X && s.Y == Y;
        public override int GetHashCode() => (X, Y).GetHashCode();
        public override string ToString() => X + " " + Y;
        public static bool operator ==(Point l, Point r) => l.Equals(r);
        public static bool operator !=(Point l, Point r) => !(l == r);
    }

    public record struct DirectedSegment(Point Ab, Point Ad, bool Ends)
    {
        public readonly Point Vector => Ad - Ab;
        public readonly DirectedSegment Rotated90() => new(Ab, (Ad - Ab).Rotated90() + Ab, Ends);
    }

    public static int CounterClockwise(DirectedSegment ds, Point target)
    {
        var v = target - ds.Ab;
        var crossProduct = ds.Vector.CrossProduct(v);
        if (crossProduct == 0)
        {
            if (!ds.Ends) return 0;
            if (ds.Vector.DotProduct(v) < 0) return -1; // other side
            if (v.Magnitude2() - ds.Vector.Magnitude2() > 0) return 1;
            return 0; // on the segment
        }
        return crossProduct > 0 ? 2 : -2;
    }

    public static Point? Intersection(DirectedSegment ds1, DirectedSegment ds2)
    {
        var (v1, v2, v3) = (ds1.Vector, ds2.Vector, ds2.Ab - ds1.Ab);
        var k = v1.CrossProduct(v2);
        if (k == 0) return null;
        var s = v3.CrossProduct(v2) / k;
        var t = v3.CrossProduct(v1) / k;
        if (
            (ds1.Ends && (s < 0 || 1 < s)) ||
            (ds2.Ends && (t < 0 || 1 < t))
        ) return null;
        return ds1.Ab + v1.Mul(s);
    }

    // atan2
    public static List<Point> SortByArgument(IEnumerable<Point> points, Point origin)
    {
        bool Upper(Point v) => v.Y > origin.Y || v.Y == origin.Y && v.X < origin.X;
        var uppers = points.Where(Upper).ToList();
        var lowers = points.Where(p => p != origin && !Upper(p)).ToList();
        int Comparer(Point l, Point r)
        {
            if (l == r) return 0;
            return CounterClockwise(new DirectedSegment(origin, l, true), r) > 0 ? -1 : 1;
        }
        uppers.Sort(Comparer);
        lowers.Sort(Comparer);
        lowers.AddRange(points.Where(p => p == origin));
        lowers.AddRange(uppers);
        return lowers;
    }
}

// convex hull
static partial class Geometry2D
{
    public class ConvexHull
    {
        public readonly ReadOnlyMemory<Point> Vertices = new();
        public Point this[int i] => Vertices.Span[i];
        public int Count => Vertices.Length;
        public Number Area2()
        {
            Number res = 0;
            for (var i = 0; i < Count; i++) res += this[i].CrossProduct(this[(i + 1) % Count]);
            return res;
        }

        public int Inside(Point point)
        {
            var (li, ri) = (1, Count - 1);
            var (l, r) = (li, ri);
            var vs = Vertices.Span;
            var o = vs[0];
            while (r - l > 1)
            {
                var m = (l + r) >> 1;
                var ccw = CounterClockwise(new DirectedSegment(o, vs[m], true), point);
                if (ccw > 1) l = m; else r = m;
            }
            var ccwl = CounterClockwise(new DirectedSegment(o, vs[l], true), point);
            var ccwr = CounterClockwise(new DirectedSegment(vs[r], o, true), point);
            var ccwm = CounterClockwise(new DirectedSegment(vs[l], vs[r], true), point);
            var ccws = new[]{ ccwl, ccwr, ccwm };
            foreach (var ccw in ccws) if (!(ccw == 0 || ccw > 1)) return -1;
            if (ccwm == 0) return 0;
            if (l == li && ccwl == 0) return 0;
            if (r == ri && ccwr == 0) return 0;
            return 1;
        }

        public ConvexHull(IEnumerable<Point> points)
        {
            if (!points.Any()) return;
            points = points.Distinct();
            var min = points.MinBy(e => (e.Y.Value, e.X.Value));
            var sorted = new List<Point>(new[]{ min });
            sorted.AddRange(SortByArgument(points.Where(e => e != min), min));
            var hull = new Stack<Point>(new[]{ min });
            if (points.Count() > 1)
            {
                var (l1, l2) = (sorted[1], hull.Pop());
                for (var i = 2; i < sorted.Count; i++)
                {
                    var point = sorted[i];
                    var empty = false;
                    while (CounterClockwise(new DirectedSegment(l2, l1, true), point) != 2)
                    {
                        if (hull.Count == 0)
                        {
                            empty = true;
                            break;
                        }
                        (l1, l2) = (l2, hull.Pop());
                    }
                    if (!empty)
                    {
                        hull.Push(l2);
                        l2 = l1;
                    }
                    l1 = point;
                }
                hull.Push(l2);
                hull.Push(l1);
            }
            Vertices = hull.Reverse().ToArray();
        }
    }
}

readonly record struct ModInt // :
    // IEqualityOperators<ModInt, ModInt, bool>,
    // IAdditiveGroup<ModInt>,
    // IMultiplicativeGroup<ModInt>
{
    public const int Mod = 998244353;
    int V { get; init; }
    public ModInt(long value)
    {
        var v = value % Mod;
        if (v < 0) v += Mod;
        V = (int)v;
    }
    static ModInt New(int value) => new(){ V = value };

    public static implicit operator ModInt(long v) => new(v);
    public static implicit operator int(ModInt modInt) => modInt.V;

    public static ModInt AdditiveIdentity => New(0);
    public static ModInt operator +(ModInt a, ModInt b)
    {
        var v = a.V + b.V;
        if (v >= Mod) v -= Mod;
        return New(v);
    }
    public ModInt AdditiveInverse()
    {
        if (V == 0) return AdditiveIdentity;
        return New(Mod - V);
    }
    public static ModInt operator -(ModInt a, ModInt b)
    {
        var v = a.V - b.V;
        if (v < 0) v += Mod;
        return New(v);
    }

    public static ModInt MultiplicativeIdentity => New(1);
    public static ModInt operator *(ModInt a, ModInt b) => New((int)((long)a.V * b.V % Mod));
    public ModInt MultiplicativeInverse()
    {
        if (V == 0) throw new DivideByZeroException();
        var (d, x, _) = ExtendedGCD(V, Mod);
        if (d > 1) throw new DivideByZeroException();
        return x;
    }
    public static ModInt operator /(ModInt a, ModInt b) => a * b.MultiplicativeInverse();

    static long Power(long v, ulong p, long mod)
    {
        var (res, k) = (1L, v);
        while (p > 0)
        {
            if ((p & 1) > 0) res = res * k % mod;
            k = k * k % mod;
            p >>= 1;
        }
        return res;
    }
    public ModInt Power(long p) => p < 0 ? (MultiplicativeIdentity / V).Power(-p) : Power(V, (ulong)p, Mod);

    static (long d, long x, long y) ExtendedGCD(long a, long b)
    {
        var (x0, y0, x1, y1) = (1L, 0L, 0L, 1L);
        while (b != 0)
        {
            var q = a / b;
            (a, b) = (b, a - q * b);
            (x0, y0, x1, y1) = (x1, y1, x0 - q * x1, y0 - q * y1);
        }
        return (a, x0, y0);
    }

    public override string ToString() => V.ToString();
}
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