結果
| 問題 |
No.3175 転移迷宮 (Easy)
|
| コンテスト | |
| 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 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 44 |
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
#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;
}
}