結果
問題 | No.3182 recurrence relation’s intersection sum |
ユーザー |
|
提出日時 | 2025-06-13 22:21:06 |
言語 | C# (.NET 8.0.404) |
結果 |
AC
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実行時間 | 537 ms / 2,000 ms |
コード長 | 8,138 bytes |
コンパイル時間 | 7,777 ms |
コンパイル使用メモリ | 169,944 KB |
実行使用メモリ | 194,600 KB |
最終ジャッジ日時 | 2025-06-13 22:21:26 |
合計ジャッジ時間 | 18,816 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 40 |
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 (91 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; void Run() { var k = Int(); var l = long.Parse(String()); var r = long.Parse(String()); var a = new Matrix(new int[k + 4, k + 4]); for (var i = 0; i <= k; i++) for (var j = 0; j <= i; j++) a[i, j] = i.C(j); a[k + 1, k + 1] = k; a[k + 2, k] = 1; a[k + 2, k + 1] = 1; a[k + 2, k + 2] = k; a[k + 3, k + 2] = 1; a[k + 3, k + 3] = 1; var v0 = new Matrix(new int[k + 4, 1]); v0[0, 0] = 1; v0[k + 1, 0] = 1; v0[k + 2, 0] = 1; var vr = a.Power(r + 1) * v0; var vl = a.Power(l) * v0; ModInt ans = vr[k + 3, 0] - vl[k + 3, 0]; Out(ans); } #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(); } readonly record struct ModInt // : // IEqualityOperators<ModInt, ModInt, bool>, // IAdditiveGroup<ModInt>, // IMultiplicativeGroup<ModInt> { public const int Mod = 998244353; int V { get; init; } public ModInt(long value) { var v = value % Mod; if (v < 0) v += Mod; V = (int)v; } static ModInt New(int value) => new(){ V = value }; public static implicit operator ModInt(long v) => new(v); public static implicit operator int(ModInt modInt) => modInt.V; public static ModInt AdditiveIdentity => New(0); public static ModInt operator +(ModInt a, ModInt b) { var v = a.V + b.V; if (v >= Mod) v -= Mod; return New(v); } public ModInt AdditiveInverse() { if (V == 0) return AdditiveIdentity; return New(Mod - 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 MultiplicativeIdentity => New(1); public static ModInt operator *(ModInt a, ModInt b) => New((int)((long)a.V * b.V % Mod)); public ModInt MultiplicativeInverse() => V == 0 ? throw new DivideByZeroException() : Power(V, Mod - 2, Mod); public static ModInt operator /(ModInt a, ModInt b) => a * b.MultiplicativeInverse(); 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; } public ModInt Power(long p) => p < 0 ? MultiplicativeInverse().Power(-p) : Power(V, (ulong)p, Mod); public override string ToString() => V.ToString(); } static class FactorialExtensions { public static ModInt Factorial(this int value) { Extend(value); return value < 0 ? _inv.Span[-value] : _fac.Span[value]; } public static ModInt P(this int n, int r) { if (r < 0 || r > n) return 0; if (n <= MaxN) return Factorial(n) * Factorial(r - n); ModInt res = 1; for (var i = 0; i < r; i++) res *= n - i; return res; } public static ModInt C(this int n, int r) { if (r < 0 || r > n) return 0; r = Math.Min(r, n - r); return P(n, r) * Factorial(-r); } public static ModInt H(this int n, int r) => C(r + n - 1, r); public static ModInt ModIntInverse(this int n) { if (n == 0) throw new DivideByZeroException(); if (n < 0) return ModIntInverse(-n).AdditiveInverse(); if (n > MaxN) return ((ModInt)n).MultiplicativeInverse(); return Factorial(n - 1) * Factorial(-n); } // [x^k](1-x)^-n = nHk public static ModInt[] NegativeBinomialSeries(long n, int m) { var res = new ModInt[m + 1]; res[0] = 1; for (var i = 1; i <= m; i++) res[i] = res[i - 1] * (n - 1 + i) * ModIntInverse(i); return res; } const int MaxN = (1 << 24) - 1; static ReadOnlyMemory<ModInt> _fac = new ModInt[]{ 1 }; static ReadOnlyMemory<ModInt> _inv = new ModInt[]{ 1 }; static void Extend(int q) { var l = _fac.Length; if (q < 0) q = -q; if (q < l || MaxN < q) return; while (l <= q) l <<= 1; var fac = new ModInt[l]; var inv = new ModInt[l]; var sf = fac.AsSpan(); sf[0] = 1; for (var i = 1; i < sf.Length; i++) sf[i] = sf[i - 1] * i; var si = inv.AsSpan(); si[l - 1] = sf[l - 1].Power(-1); for (var i = si.Length - 1; i > 0; i--) si[i - 1] = si[i] * i; (_fac, _inv) = (fac, inv); } } 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; } }