結果
| 問題 | No.1100 Boxes |
| ユーザー |
 yupiteru_kun
|
| 提出日時 | 2020-06-30 02:02:59 |
| 言語 | C#(csc) (csc 3.9.0) |
| 結果 |
AC
|
| 実行時間 | 442 ms / 2,000 ms |
| コード長 | 17,203 bytes |
| コンパイル時間 | 2,893 ms |
| コンパイル使用メモリ | 116,480 KB |
| 実行使用メモリ | 37,516 KB |
| 最終ジャッジ日時 | 2024-07-19 06:12:37 |
| 合計ジャッジ時間 | 11,777 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 36 |
コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc) Copyright (C) Microsoft Corporation. All rights reserved.
ソースコード
using System;using System.Collections.Generic;using System.IO;using System.Linq;using static System.Math;using System.Text;using System.Threading;using System.Globalization;using System.Runtime.CompilerServices;using Library;namespace Program{public static class ProblemA{static bool SAIKI = false;static public int numberOfRandomCases = 0;static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker){}static public void Solve(){var N = NN;var K = NN;LIB_Mod._mod = 998244353;LIB_Mod ans = 0;var stirling = LIB_Mod.LIB_StirlingSecond(N, K);for (var i = 0; i < K; i++){if (i % 2 == 0) continue;var pat = LIB_Mod.Comb(K, i);var hakoCnt = K - i;if (hakoCnt > N) continue;ans += pat * stirling[hakoCnt] * LIB_Mod.Perm(hakoCnt,hakoCnt);}Console.WriteLine(ans);}class Printer : StreamWriter{public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }}static LIB_FastIO fastio = new LIB_FastIODebug();static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }static long NN => fastio.Long();static double ND => fastio.Double();static string NS => fastio.Scan();static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }static IEnumerator<uint> _xsi = _xsc();static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true){ var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }}}namespace Library {class LIB_NTT{uint mod;uint root;[MethodImpl(MethodImplOptions.AggressiveInlining)]LIB_NTT(uint mod, uint root) { this.mod = mod; this.root = root; }[MethodImpl(MethodImplOptions.AggressiveInlining)]uint add(uint x, uint y) => (x + y < mod) ? (x + y) : (x + y - mod);[MethodImpl(MethodImplOptions.AggressiveInlining)]uint sub(uint x, uint y) => (x >= y) ? (x - y) : (mod - y + x);[MethodImpl(MethodImplOptions.AggressiveInlining)]uint mul(uint x, uint y) => (uint)((ulong)x * y % mod);[MethodImpl(MethodImplOptions.AggressiveInlining)]uint pow(uint x, uint n){uint res = 1;while (n > 0){if ((n & 1) != 0) res = mul(res, x);x = mul(x, x);n >>= 1;}return res;}[MethodImpl(MethodImplOptions.AggressiveInlining)]uint inverse(uint x){long b = mod, r = 1, u = 0, t = 0, x2 = x;while (b > 0){var q = x2 / b;t = u;u = r - q * u;r = t;t = b;b = x2 - q * b;x2 = t;}return (uint)(r < 0 ? r + mod : r);}[MethodImpl(MethodImplOptions.AggressiveInlining)]void ntt(ref uint[] a, bool rev = false){var n = (uint)a.Length;if (n == 1) return;var b = new uint[n];var s = pow(root, rev ? (mod - 1 - (mod - 1) / n) : (mod - 1) / n);var kp = Enumerable.Repeat((uint)1, (int)(n / 2 + 1)).ToArray();uint i, j, k, l, r;for (i = 0; i < n / 2; ++i) kp[i + 1] = mul(kp[i], s);for (i = 1, l = n / 2; i < n; i <<= 1, l >>= 1){for (j = 0, r = 0; j < l; ++j, r += i){for (k = 0, s = kp[i * j]; k < i; ++k){var p = a[k + r]; var q = a[k + r + n / 2];b[k + 2 * r] = add(p, q);b[k + 2 * r + i] = mul(sub(p, q), s);}}var t = a; a = b; b = t;}if (rev){s = inverse(n);for (i = 0; i < n; ++i) a[i] = mul(a[i], s);}}[MethodImpl(MethodImplOptions.AggressiveInlining)]static uint[] Multiply(uint[] a, uint[] b, uint mod, uint root){var n = a.Length + b.Length - 1;var t = 1;while (t < n) t <<= 1;var na = new uint[t];var nb = new uint[t];for (var i = 0; i < a.Length; ++i) na[i] = a[i];for (var i = 0; i < b.Length; ++i) nb[i] = b[i];var ntt = new LIB_NTT(mod, root);ntt.ntt(ref na);ntt.ntt(ref nb);for (var i = 0; i < t; ++i) na[i] = ntt.mul(na[i], nb[i]);ntt.ntt(ref na, true);return na.Take(n).ToArray();}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public long[] Multiply(long[] a, long[] b) => Multiply(a.Select(e => (uint)e).ToArray(), b.Select(e => (uint)e).ToArray(), 998244353,3).Select(e => (long)e).ToArray();[MethodImpl(MethodImplOptions.AggressiveInlining)]static public long[] Multiply(long[] a, long[] b, long mod){if (mod == 998244353) return Multiply(a, b);var m1 = new LIB_NTT(1045430273, 3);var m2 = new LIB_NTT(1051721729, 6);var m3 = new LIB_NTT(1053818881, 7);var uinta = a.Select(e => (uint)e).ToArray();var uintb = b.Select(e => (uint)e).ToArray();var x = Multiply(uinta, uintb, m1.mod, m1.root);var y = Multiply(uinta, uintb, m2.mod, m2.root);var z = Multiply(uinta, uintb, m3.mod, m3.root);var m1_inv_m2 = m2.inverse(m1.mod);var m12_inv_m3 = m3.inverse(m3.mul(m1.mod, m2.mod));var m12_mod = (long)m1.mod * m2.mod % mod;var ret = new long[x.Length];for (var i = 0; i < x.Length; ++i){var v1 = m2.mul(m2.sub(m2.add(y[i], m2.mod), x[i]), m1_inv_m2);var v2 = m3.mul(m3.sub(m3.sub(m3.add(z[i], m3.mod), x[i]), m3.mul(m1.mod, v1)), m12_inv_m3);ret[i] = (x[i] + ((long)m1.mod * v1 % mod) + ((long)m12_mod * v2 % mod)) % mod;}return ret;}}partial struct LIB_Mod : IEquatable<LIB_Mod>, IEquatable<long>{static public long _mod = 1000000007; long v;[MethodImpl(MethodImplOptions.AggressiveInlining)]public LIB_Mod(long x){if (x < _mod && x >= 0) v = x;else if ((v = x % _mod) < 0) v += _mod;}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public implicit operator LIB_Mod(long x) => new LIB_Mod(x);[MethodImpl(MethodImplOptions.AggressiveInlining)]static public implicit operator long(LIB_Mod x) => x.v;[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Add(LIB_Mod x) { if ((v += x.v) >= _mod) v -= _mod; }[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Sub(LIB_Mod x) { if ((v -= x.v) < 0) v += _mod; }[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Mul(LIB_Mod x) => v = (v * x.v) % _mod;[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Div(LIB_Mod x) => v = (v * Inverse(x.v)) % _mod;[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod operator +(LIB_Mod x, LIB_Mod y) { var t = x.v + y.v; return t >= _mod ? new LIB_Mod { v = t - _mod } : new LIB_Mod { v= t }; }[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod operator -(LIB_Mod x, LIB_Mod y) { var t = x.v - y.v; return t < 0 ? new LIB_Mod { v = t + _mod } : new LIB_Mod { v = t}; }[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod operator *(LIB_Mod x, LIB_Mod y) => x.v * y.v;[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod operator /(LIB_Mod x, LIB_Mod y) => x.v * Inverse(y.v);[MethodImpl(MethodImplOptions.AggressiveInlining)]static public bool operator ==(LIB_Mod x, LIB_Mod y) => x.v == y.v;[MethodImpl(MethodImplOptions.AggressiveInlining)]static public bool operator !=(LIB_Mod x, LIB_Mod y) => x.v != y.v;[MethodImpl(MethodImplOptions.AggressiveInlining)]static public long Inverse(long x){long b = _mod, r = 1, u = 0, t = 0;while (b > 0){var q = x / b;t = u;u = r - q * u;r = t;t = b;b = x - q * b;x = t;}return r < 0 ? r + _mod : r;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public bool Equals(LIB_Mod x) => v == x.v;[MethodImpl(MethodImplOptions.AggressiveInlining)]public bool Equals(long x) => v == x;[MethodImpl(MethodImplOptions.AggressiveInlining)]public override bool Equals(object x) => x == null ? false : Equals((LIB_Mod)x);[MethodImpl(MethodImplOptions.AggressiveInlining)]public override int GetHashCode() => v.GetHashCode();[MethodImpl(MethodImplOptions.AggressiveInlining)]public override string ToString() => v.ToString();static List<LIB_Mod> _fact = new List<LIB_Mod>() { 1 };static long _factm = _mod;[MethodImpl(MethodImplOptions.AggressiveInlining)]static void B(long n){if (_factm != _mod) _fact = new List<LIB_Mod>() { 1 };if (n >= _fact.Count)for (int i = _fact.Count; i <= n; ++i)_fact.Add(_fact[i - 1] * i);_factm = _mod;}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod Comb(long n, long k){B(n);if (n == 0 && k == 0) return 1;if (n < k || n < 0) return 0;return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k];}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod CombOK(long n, long k){LIB_Mod ret = 1;for (var i = 0; i < k; i++) ret *= n - i;for (var i = 1; i <= k; i++) ret /= i;return ret;}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod Perm(long n, long k){B(n);if (n == 0 && k == 0) return 1;if (n < k || n < 0) return 0;return _fact[(int)n] / _fact[(int)(n - k)];}[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod Pow(LIB_Mod x, long y){LIB_Mod a = 1;while (y != 0){if ((y & 1) == 1) a.Mul(x);x.Mul(x);y >>= 1;}return a;}}class LIB_FastIO{[MethodImpl(MethodImplOptions.AggressiveInlining)]public LIB_FastIO() { str = Console.OpenStandardInput(); }readonly Stream str;readonly byte[] buf = new byte[1024];int len, ptr;public bool isEof = false;public bool IsEndOfStream{[MethodImpl(MethodImplOptions.AggressiveInlining)]get { return isEof; }}[MethodImpl(MethodImplOptions.AggressiveInlining)]byte read(){if (isEof) throw new EndOfStreamException();if (ptr >= len){ptr = 0;if ((len = str.Read(buf, 0, 1024)) <= 0){isEof = true;return 0;}}return buf[ptr++];}[MethodImpl(MethodImplOptions.AggressiveInlining)]char Char(){byte b = 0;do b = read();while (b < 33 || 126 < b);return (char)b;}[MethodImpl(MethodImplOptions.AggressiveInlining)]virtual public string Scan(){var sb = new StringBuilder();for (var b = Char(); b >= 33 && b <= 126; b = (char)read())sb.Append(b);return sb.ToString();}[MethodImpl(MethodImplOptions.AggressiveInlining)]virtual public long Long(){long ret = 0; byte b = 0; var ng = false;do b = read();while (b != '-' && (b < '0' || '9' < b));if (b == '-') { ng = true; b = read(); }for (; true; b = read()){if (b < '0' || '9' < b)return ng ? -ret : ret;else ret = ret * 10 + b - '0';}}[MethodImpl(MethodImplOptions.AggressiveInlining)]virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }}class LIB_FastIODebug : LIB_FastIO{Queue<string> param = new Queue<string>();[MethodImpl(MethodImplOptions.AggressiveInlining)]string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public LIB_FastIODebug() { }[MethodImpl(MethodImplOptions.AggressiveInlining)]public override string Scan() => NextString();[MethodImpl(MethodImplOptions.AggressiveInlining)]public override long Long() => long.Parse(NextString());[MethodImpl(MethodImplOptions.AggressiveInlining)]public override double Double() => double.Parse(NextString());}/// copy key class LIB_StirlingSecondpartial struct /* not copy key */ LIB_Mod{[MethodImpl(MethodImplOptions.AggressiveInlining)]static public LIB_Mod[] LIB_StirlingSecond(long n, long k){var a = new LIB_Mod[k + 1];for (var i = 0; i <= k; i++) a[i] = (i % 2 == 1 ? -1 : 1) / Perm(i, i);var b = new LIB_Mod[k + 1];for (var i = 0; i <= k; i++) b[i] = Pow(i, n) / Perm(i, i);return LIB_NTT.Multiply(a.Select(e => (long)e).ToArray(), b.Select(e => (long)e).ToArray(), _mod).Take((int)k + 1).Select(e => (LIB_Mod)e).ToArray();}}}