結果

問題 No.3175 転移迷宮 (Easy)
ユーザー tobisatis
提出日時 2025-06-06 23:12:52
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 1,793 ms / 3,000 ms
コード長 6,861 bytes
コンパイル時間 14,734 ms
コンパイル使用メモリ 171,160 KB
実行使用メモリ 200,708 KB
最終ジャッジ日時 2025-06-06 23:13:55
合計ジャッジ時間 59,883 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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 * 44
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 (106 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;

const int Mod = 998244353;

void Run()
{
    var t = Int();
    var ans = new long[t][];
    for (var i = 0; i < t; i++) ans[i] = Solve();
    for (var i = 0; i < t; i++) Out(ans[i], " ");
}

long[] Solve()
{
    var n = Int();
    var k = Int();
    var s = new Matrix(new long[n, n]);
    var a = new Matrix(new long[n, n]);
    for (var i = 0; i < n; i++) s[i, i] = 1;
    var pb = Extensions.Power(k * 2 + 1, Mod - 2, Mod);
    for (var i = 0; i < n; i++)
    {
        for (var d = -k; d <= k; d++)
        {
            var j = i + d;
            if (j < 0 || j >= n) continue;
            a[i, j] += pb;
        }
    }
    var e = new Matrix(new long[n, n]);
    for (var i = 0; i < n; i++) e[i, i] = 1;
    var na = new Matrix(new long[n, n]);
    for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) na[i, j] = -a[i, j];
    var iea = Extensions.Inverse(e + na);
    s = iea * s;
    var res = new long[n];
    for (var i = 0; i < n; i++)
    {
        for (var c = 0; c < n; c++) res[i] += s[i, c];
        res[i] %= Mod;
    }
    return res;
}

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

    ReadOnlyMemory<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();

    public 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;
    }

    const int Mod = 998244353;

    public static Matrix Inverse(this Matrix matrix)
    {
        var n = matrix.X;
        if (n != matrix.Y) throw new Exception("the matrix must be square");
        var a = new long[n][].AsSpan();
        var b = new long[n][].AsSpan();
        for (var i = 0; i < n; i++)
        {
            a[i] = new long[n];
            for (var j = 0; j < n; j++) a[i][j] = matrix[i, j];
            b[i] = new long[n];
            b[i][i] = 1;
        }
        for (var k = 0; k < n; k++)
        {
            var f = true;
            for (var i = k; i < n; i++) if (a[i][k] != 0)
            {
                (a[i], a[k]) = (a[k], a[i]);
                (b[i], b[k]) = (b[k], b[i]);
                f = false;
                break;
            }
            if (f) throw new DivideByZeroException();
            var z = Power(a[k][k], Mod - 2, Mod);
            for (var j = 0; j < n; j++)
            {
                a[k][j] *= z;
                a[k][j] %= Mod;
                b[k][j] *= z;
                b[k][j] %= Mod;
            }
            for (var i = 0; i < n; i++) if (i != k)
            {
                var p = a[i][k];
                for (var j = 0; j < n; j++)
                {
                    a[i][j] -= a[k][j] * p + Mod;
                    a[i][j] %= Mod;
                    if (a[i][j] < 0) a[i][j] += Mod;
                    b[i][j] -= b[k][j] * p;
                    b[i][j] %= Mod;
                    if (b[i][j] < 0) b[i][j] += Mod;
                }
            }
        }
        var res = new Matrix(new long[n, n]);
        for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) res[i, j] = b[i][j];
        return res;
    }
}

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(long[,] 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(long[,] 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;
    }
}
0