結果

問題 No.3044 よくあるカエルさん
ユーザー tobisatis
提出日時 2025-02-28 22:51:23
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 184 ms / 2,000 ms
コード長 4,426 bytes
コンパイル時間 8,322 ms
コンパイル使用メモリ 171,164 KB
実行使用メモリ 189,868 KB
最終ジャッジ日時 2025-02-28 22:51:35
合計ジャッジ時間 11,264 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 20
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 (108 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 t = Int();
    var k = Int() - 1;
    var l = Int() - 1;

    long i6;
    {
        var m6 = new Matrix(new int[1, 1]);
        m6[0, 0] = 6;
        m6 = m6.Power(Matrix.p - 2);
        i6 = m6[0, 0];
    }
    var v = new Matrix(new int[t, 1]);
    var a = new Matrix(new int[t, t]);
    v[0, 0] = 1;
    for (var i = 1; i < t; i++) a[i - 1, i] = 1;
    a[0, 0] = i6 * k;
    a[1, 0] = i6 * (l - k);
    a[t - 1, 0] = i6 * (6 - l);
    var mns = a.Power(n - 1) * v;
    var ans = mns[0, 0];
    Out(ans);
}

#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().Trim().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();
}

readonly struct Matrix : IAdditionOperators<Matrix, Matrix, Matrix>, IMultiplyOperators<Matrix, Matrix, Matrix>
{
    long[,] V { get; init; }
    public long this[int i, int j] { get => V[i, j]; set { V[i, j] = Mod(value); } }
    public int X => V.GetLength(0);
    public int Y => V.GetLength(1);

    public const int p = 998244353;
    static long Mod(long v)
    {
        var res = v % p;
        if (res < 0) res += p;
        return res;
    }

    public Matrix(int[,] matrix)
    {
        var (x, y) = (matrix.GetLength(0), matrix.GetLength(1));
        var v = new long[x, y];
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++) v[i, j] = Mod(matrix[i, j]);
        V = v;
    }
    public static implicit operator Matrix(int[,] matrix) => new(matrix);
    static Matrix With(long[,] matrix) => new(){ V = matrix };

    public static Matrix IdentityMatrix(int size)
    {
        var v = new long[size, size];
        for (var i = 0; i < size; i++) v[i, i] = 1;
        return With(v);
    }

    public static Matrix operator +(Matrix a, Matrix b)
    {
        var (v, va, vb, x, y) = (new long[a.X, a.Y], a.V, b.V, a.X, a.Y);
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++)
        {
            var sum = va[i, j] + vb[i, j];
            if (sum > p) sum -= p;
            v[i, j] = sum;
        }
        return With(v);
    }

    public static Matrix operator *(Matrix a, Matrix b)
    {
        var (v, va, vb, x, y, z) = (new long[a.X, b.Y], a.V, b.V, a.X, b.Y, a.Y);
        for (var i = 0; i < x; i++) for (var k = 0; k < z; k++)
        {
            var c = va[i, k];
            if (c != 0) for (var j = 0; j < y; j++) v[i, j] += vb[k, j] * c % p;
        }
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++) v[i, j] = Mod(v[i, j]);
        return With(v);
    }

    public static Matrix operator *(Matrix a, long k)
    {
        var (v, va, x, y) = (new long[a.X, a.Y], a.V, a.X, a.Y);
        for (var i = 0; i < x; i++) for (var j = 0; j < y; j++) v[i, j] = va[i, j] * k % p;
        return With(v);
    }

    public Matrix Power(long k)
    {
        var c = IdentityMatrix(X);
        var c2 = this;
        while (k > 0)
        {
            if ((k & 1) > 0) c *= c2;
            c2 *= c2;
            k >>= 1;
        }
        return c;
    }
}
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