結果

問題 No.2679 MODice
コンテスト
ユーザー tobisatis
提出日時 2024-03-20 23:14:46
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 58 ms / 2,000 ms
コード長 5,884 bytes
コンパイル時間 9,708 ms
コンパイル使用メモリ 165,676 KB
実行使用メモリ 189,308 KB
最終ジャッジ日時 2024-09-30 09:22:39
合計ジャッジ時間 10,236 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 15
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 (102 ms)。
MSBuild のバージョン 17.9.6+a4ecab324 (.NET)
  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 # 

namespace AtCoder;

#nullable enable

using System.Numerics;

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

readonly record struct ModInt :
    IEqualityOperators<ModInt, ModInt, bool>,
    IAdditiveIdentity<ModInt, ModInt>,
    IAdditionOperators<ModInt, ModInt, ModInt>,
    IUnaryNegationOperators<ModInt, ModInt>,
    ISubtractionOperators<ModInt, ModInt, ModInt>,
    IMultiplicativeIdentity<ModInt, ModInt>,
    IMultiplyOperators<ModInt, ModInt, ModInt>,
    IDivisionOperators<ModInt, ModInt, ModInt>
{
    int V { get; init; }
    public const int Mod = 998244353;
    public ModInt(long value)
    {
        var v = value % Mod;
        if (v < 0) v += Mod;
        V = (int)v;
    }
    ModInt(int value) { V = value; }

    public static implicit operator ModInt(long v) => new(v);
    public static implicit operator int(ModInt modInt) => modInt.V;
    public static ModInt operator +(ModInt a, ModInt b)
    {
        var v = a.V + b.V;
        if (v >= Mod) v -= Mod;
        return new(v);
    }
    public static ModInt operator -(ModInt a) => new(a.V == 0 ? 0 : Mod - a.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 operator *(ModInt a, ModInt b) => new((int)((long)a.V * b.V % Mod));
    public static ModInt operator /(ModInt a, ModInt b)
    {
        if (b == 0) throw new DivideByZeroException();
        var (d, x, _) = ExtendedGcd(b.V, Mod);
        if (d > 1) throw new DivideByZeroException();
        return x * a.V;
    }

    public ModInt Power(long p)
    {
        if (p < 0) return (MultiplicativeIdentity / V).Power(-p);
        long res = 1;
        long k = V;
        while (p > 0)
        {
            if ((p & 1) > 0) res = res * k % Mod;
            k = k * k % Mod;
            p >>= 1;
        }
        return res;
    }

    static (long d, long x, long y) ExtendedGcd(long a, long b)
    {
        if (b == 0) return (a, 1, 0);
        var (d, x, y) = ExtendedGcd(b, a % b);
        return (d, y, x - a / b * y);
    }

    public static ModInt AdditiveIdentity => new(0);
    public static ModInt MultiplicativeIdentity => new(1);

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

readonly struct Matrix<T> where T :
    IAdditiveIdentity<T, T>,
    IAdditionOperators<T, T, T>,
    IMultiplicativeIdentity<T, T>,
    IMultiplyOperators<T, T, T>
{
    T[,] V { get; init; }

    public T this[int i, int j] { get => V[i, j]; set { V[i, j] = value; } }
    public int X { get => V.GetLength(0); }
    public int Y { get => V.GetLength(1); }

    public Matrix(T[,] matrix)
    {
        V = new T[matrix.GetLength(0), matrix.GetLength(1)];
        Array.Copy(matrix, V, matrix.Length);
    }

    public static Matrix<T> IdentityMatrix(int size)
    {
        var v = new T[size, size];
        for (var i = 0; i < size; i++) for (var j = 0; j < size; j++) v[i, j] = T.AdditiveIdentity;
        for (var i = 0; i < size; i++) v[i, i] = T.MultiplicativeIdentity;
        return new(v);
    }

    public static Matrix<T> operator +(Matrix<T> a, Matrix<T> b)
    {
        if (a.X != b.X || a.Y != b.Y) throw new InvalidOperationException();
        var (v, x, y) = (new T[a.X, a.Y], a.X, a.Y);
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++) v[i, j] = a[i, j] + b[i, j];
        return new(v);
    }

    public static Matrix<T> operator *(Matrix<T> a, Matrix<T> b)
    {
        if (a.Y != b.X) throw new InvalidOperationException();
        var (v, x, y, z) = (new T[a.X, b.Y], a.X, b.Y, a.Y);
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++)
        {
            var e = T.AdditiveIdentity;
            for (var k = 0; k < z; k++) e += a[i, k] * b[k, j];
            v[i, j] = e;
        }
        return new(v);
    }

    public Matrix<T> Power(long k)
    {
        if (X != Y) throw new InvalidOperationException();
        var c = IdentityMatrix(X);
        var c2 = this;
        while (k > 0)
        {
            if ((k & 1) > 0) c *= c2;
            c2 *= c2;
            k >>= 1;
        }
        return c;
    }
}

class AtCoder
{
    object? Solve()
    {
        var n = Int();
        var k = Int();
        var vi = new ModInt[6, 1];
        vi[0, 0] = 1;
        var v = new Matrix<ModInt>(vi);
        var mi = new ModInt[6, 6];
        var o = (ModInt)1 / 6;
        for (var i = 0; i < 6; i++) for (var j = 0; j < 6; j++) mi[i, j] = o;
        var a = new Matrix<ModInt>(mi);
        v = a.Power(n) * v;
        return v[k, 0];
    }

    public static void Main() => new AtCoder().Run();
    public void Run()
    {
        var res = Solve();
        if (res != null)
        {
            if (res is bool yes) res = yes ? "Yes" : "No";
            sw.WriteLine(res);
        }
        sw.Flush();
    }

    string[] input = Array.Empty<string>();
    int iter = 0;
    readonly StreamWriter sw = new(Console.OpenStandardOutput()) { AutoFlush = false };

    #pragma warning disable IDE0051
    string String()
    {
        while (iter >= input.Length) (input, iter) = (Console.ReadLine()!.Split(' '), 0);
        return input[iter++];
    }
    T Input<T>() where T : IParsable<T> => T.Parse(String(), null);
    int Int() => Input<int>();
    void Out(object? x, string? separator = null)
    {
        separator ??= Environment.NewLine;
        if (x is System.Collections.IEnumerable obj and not string)
        {
            var firstLine = true;
            foreach (var item in obj)
            {
                if (!firstLine) sw.Write(separator);
                firstLine = false;
                sw.Write(item);
            }
        }
        else sw.Write(x);
        sw.WriteLine();
    }
    #pragma warning restore IDE0051
}
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