結果

問題 No.3243 Multiplication 8 1
ユーザー tobisatis
提出日時 2025-08-22 21:43:40
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 1,872 ms / 2,000 ms
コード長 3,469 bytes
コンパイル時間 9,696 ms
コンパイル使用メモリ 171,464 KB
実行使用メモリ 214,488 KB
最終ジャッジ日時 2025-08-22 21:43:56
合計ジャッジ時間 14,350 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 4
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 (109 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;

#region
var _input = Array.Empty<string>();
var _iter = 0;
string String()
{
    while (_iter >= _input.Length) (_input, _iter) = (Console.ReadLine()!.Split(' '), 0);
    return _input[_iter++];
}
T I<T>() where T : IParsable<T> => T.Parse(String(), null);
#endregion

T[] Range<T>(int n, Func<T> F) => Enumerable.Range(0, n).Select(_ => F()).ToArray();

long Solve(long n)
{
    var v = new Matrix(new int[10, 1]);
    v[0, 0] = 1;
    var a = new Matrix(new int[10, 10]);
    a[0, 0] = a[0, 3] = 1;
    a[1, 0] = a[1, 1] = a[1, 3] = a[1, 4] = 1;
    a[2, 1] = a[2, 2] = a[2, 4] = a[2, 5] = 1;
    a[3, 0] = a[3, 3] = 1;
    a[4, 0] = a[4, 1] = a[4, 3] = a[4, 4] = 1;
    a[5, 1] = a[5, 2] = a[5, 4] = a[5, 5] = 1;
    a[6, 2] = a[6, 5] = a[6, 6] = 1;
    a[7, 2] = a[7, 5] = a[7, 6] = 1;
    a[8, 8] = a[8, 9] = 1;
    a[9, 8] = a[9, 9] = 1;
    var b = Matrix.IdentityMatrix(10);
    b[7, 7] = 0;
    b[0, 7] = 1;
    b[9, 7] = 1;
    v = (b * a).Power(n) * v;
    return v[9, 0];
}

var t = I<int>();
var ans = Range(t, () => Solve(I<long>()));
Console.WriteLine(string.Join(Environment.NewLine, ans));

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);

    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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