結果
| 問題 | No.2384 Permutations of Permutations |
| ユーザー |
 KumaTachiRen
|
| 提出日時 | 2023-07-14 23:00:27 |
| 言語 | C# (.NET 8.0.203) |
| 結果 |
AC
|
| 実行時間 | 52 ms / 2,000 ms |
| コード長 | 20,389 bytes |
| コンパイル時間 | 8,465 ms |
| コンパイル使用メモリ | 168,884 KB |
| 実行使用メモリ | 187,840 KB |
| 最終ジャッジ日時 | 2024-09-16 08:08:08 |
| 合計ジャッジ時間 | 10,432 ms |
|
ジャッジサーバーID （参考情報） |
judge6 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 42 ms
23,040 KB |
| testcase_01 | AC | 42 ms
23,152 KB |
| testcase_02 | AC | 42 ms
23,040 KB |
| testcase_03 | AC | 42 ms
23,016 KB |
| testcase_04 | AC | 42 ms
23,040 KB |
| testcase_05 | AC | 46 ms
24,832 KB |
| testcase_06 | AC | 46 ms
24,960 KB |
| testcase_07 | AC | 46 ms
25,080 KB |
| testcase_08 | AC | 46 ms
24,960 KB |
| testcase_09 | AC | 42 ms
23,040 KB |
| testcase_10 | AC | 51 ms
25,728 KB |
| testcase_11 | AC | 52 ms
25,728 KB |
| testcase_12 | AC | 52 ms
25,728 KB |
| testcase_13 | AC | 51 ms
25,728 KB |
| testcase_14 | AC | 51 ms
25,728 KB |
| testcase_15 | AC | 46 ms
24,320 KB |
| testcase_16 | AC | 46 ms
24,444 KB |
| testcase_17 | AC | 46 ms
24,704 KB |
| testcase_18 | AC | 45 ms
23,936 KB |
| testcase_19 | AC | 43 ms
23,168 KB |
| testcase_20 | AC | 42 ms
23,168 KB |
| testcase_21 | AC | 45 ms
24,448 KB |
| testcase_22 | AC | 42 ms
23,168 KB |
| testcase_23 | AC | 45 ms
187,840 KB |
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 ms)。 MSBuild のバージョン 17.9.6+a4ecab324 (.NET) 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
using System;
using System.ComponentModel;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.Intrinsics.X86;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;
using static Functions;
using static OutputLib;
using ModInt = StaticModInt<Mod998244353>;
static class Program
{
static public void Main(string[] args)
{
Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
new Solver();
Console.Out.Flush();
}
}
public class Solver
{
public Solver()
{
Solve();
}
void Solve()
{
int n = ri;
int k = ri;
var f = new ModFact<Mod998244353>(n);
if (n == 2)
{
Write(1);
}
else if (n == 6)
{
Write(Calc6(k));
}
else
{
Write(k * f.Fact(n - k));
}
}
int Calc6(int k)
{
const int n = 6;
var g = new List<Perm>(720);
var p = new Permutation(6);
var s = new Perm[]{
new Perm(new int[] { 1, 0, 3, 2, 5, 4 }),
new Perm(new int[] { 5, 3, 4, 1, 2, 0 }),
new Perm(new int[] { 3, 2, 1, 0, 5, 4 }),
new Perm(new int[] { 5, 4, 3, 2, 1, 0 }),
new Perm(new int[] { 2, 3, 0, 1, 5, 4 }),
};
do
{
var a = new int[6];
for (int i = 0; i < 6; i++) a[i] = p[i];
var r = new Perm(6);
for (int i = 0; i < 6; i++)
{
for (int j = 6 - 1; j > i; j--)
{
if (a[j] == i)
{
r *= s[j - 1];
Swap(ref a[j], ref a[j - 1]);
}
}
}
g.Add(r);
} while (p.Next());
int ans = 0;
var xarr = new int[6] { 0, 1, 2, 3, 4, 5 };
for (int i = 0; i < k; i++) xarr[i] = (i + 1) % k;
var x = new Perm(xarr);
p = new Permutation(6);
do
{
var a = new int[n];
for (int i = 0; i < n; i++) a[i] = p[i];
var y = new Perm(a);
{
var q = y * x * y.Inv();
bool ok = true;
for (int i = 0; i < k; i++) ok &= q.p[i] == (i + 1) % k;
if (ok) ans++;
}
{
var q = g[(y * x * y.Inv()).Number()];
bool ok = true;
for (int i = 0; i < k; i++) ok &= q.p[i] == (i + 1) % k;
if (ok) ans++;
}
} while (p.Next());
return ans;
}
struct Perm
{
public int[] p;
public Perm(int n)
{
p = new int[n];
for (int i = 0; i < n; i++) p[i] = i;
}
public Perm(int[] a)
{
p = (int[])a.Clone();
}
public static Perm operator *(Perm x, Perm y)
{
var z = new int[x.p.Length];
for (int i = 0; i < x.p.Length; i++) z[i] = y.p[x.p[i]];
return new Perm(z);
}
public Perm Inv()
{
var r = new int[p.Length];
for (int i = 0; i < p.Length; i++) r[p[i]] = i;
return new Perm(r);
}
public int Number()
{
int r = 0, n = p.Length;
var a = (int[])p.Clone();
var f = new int[n + 1];
f[0] = 1;
for (int i = 0; i < n; i++) f[i + 1] = (i + 1) * f[i];
for (int i = 0; i < n; i++)
{
r += f[n - 1 - i] * a[i];
for (int j = i + 1; j < n; j++) if (a[j] > a[i]) a[j]--;
}
return r;
}
}
const long INF = 1L << 60;
int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
long rl { [MethodImpl(256)] get => sc.Integer(); }
uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); }
ulong rul { [MethodImpl(256)] get => sc.UInteger(); }
double rd { [MethodImpl(256)] get => sc.Double(); }
string rs { [MethodImpl(256)] get => sc.Scan(); }
string rline { [MethodImpl(256)] get => sc.Line(); }
public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
}
public static class Functions
{
[MethodImpl(256)]
public static int Popcount(ulong x)
{
x = (x & 0x5555555555555555UL) + ((x >> 1) & 0x5555555555555555UL);
x = (x & 0x3333333333333333UL) + ((x >> 2) & 0x3333333333333333UL);
x = (x & 0x0f0f0f0f0f0f0f0fUL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fUL);
x = (x & 0x00ff00ff00ff00ffUL) + ((x >> 8) & 0x00ff00ff00ff00ffUL);
x = (x & 0x0000ffff0000ffffUL) + ((x >> 16) & 0x0000ffff0000ffffUL);
x = (x & 0x00000000ffffffffUL) + ((x >> 32) & 0x00000000ffffffffUL);
return (int)x;
}
[MethodImpl(256)]
public static int Popcount(int x)
{
x = (x & 0x55555555) + ((x >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
x = (x & 0x0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + ((x >> 8) & 0x00ff00ff);
x = (x & 0x0000ffff) + ((x >> 16) & 0x0000ffff);
return x;
}
[MethodImpl(256)]
public static int Ctz(long x)
{
if (x == 0) return -1;
return Popcount((ulong)((x & -x) - 1));
}
[MethodImpl(256)]
public static int CeilPow2(int n)
{
int x = 0;
while ((1 << x) < n) x++;
return x;
}
[MethodImpl(256)]
public static int SafeMod(int x, int m)
{
int r = x % m;
return r < 0 ? r + Math.Abs(m) : r;
}
[MethodImpl(256)]
public static long SafeMod(long x, long m)
{
long r = x % m;
return r < 0 ? r + Math.Abs(m) : r;
}
[MethodImpl(256)] public static int Sign(long x) => x == 0 ? 0 : (x < 0 ? -1 : 1);
[MethodImpl(256)] public static int Sign(double x) => x == 0 ? 0 : (x < 0 ? -1 : 1);
[MethodImpl(256)] public static int DigitSum(long n, int d = 10) { long s = 0; while (n > 0) { s += n % d; n /= d; } return (int)s; }
[MethodImpl(256)] public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1;
[MethodImpl(256)] public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b;
[MethodImpl(256)] public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b);
[MethodImpl(256)] public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b);
[MethodImpl(256)] public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; }
[MethodImpl(256)] public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; }
[MethodImpl(256)] public static void Swap<T>(ref T x, ref T y) { T t = y; y = x; x = t; }
[MethodImpl(256)] public static T Clamp<T>(T x, T l, T r) where T : IComparable<T> => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r);
[MethodImpl(256)] public static T Clamp<T>(ref T x, T l, T r) where T : IComparable<T> => x = x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r);
[MethodImpl(256)] public static void Chmin<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) > 0) x = y; }
[MethodImpl(256)] public static void Chmax<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) < 0) x = y; }
public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound<long>(arr.AsSpan(), t => Sign(t - val), l, r);
public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound<int>(arr.AsSpan(), t => t - val, l, r);
public static int LowerBound<T>(T[] arr, Func<T, int> comp, int l = -1, int r = -1) => LowerBound<T>(arr.AsSpan<T>(), comp, l, r);
public static int LowerBound<T>(Span<T> data, Func<T, int> comp, int l = -1, int r = -1)
{
if (data.Length == 0) return -1;
if (l == -1) l = 0;
if (r == -1) r = data.Length;
while (l < r)
{
int x = (l + r) / 2;
if (comp(data[x]) < 0) l = x + 1;
else r = x;
}
return l;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static string ToBase2(long v, int digit = -1)
{
if (digit == -1)
{
digit = 0;
while ((v >> digit) > 0) digit++;
}
var c = new string[digit];
for (int i = 0; i < digit; i++) c[digit - 1 - i] = ((v >> i) & 1) == 0 ? "0" : "1";
return string.Join("", c);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static string ToBaseN(long v, int n, int digit = -1)
{
if (digit == -1)
{
digit = 0;
long pow = 1;
while (v >= pow) { digit++; pow *= n; }
}
var c = new int[digit];
for (int i = 0; i < digit; i++, v /= n) c[digit - 1 - i] = (int)(v % n);
return string.Join("", c);
}
}
public class StreamScanner
{
public StreamScanner(Stream stream) { str = stream; }
private readonly Stream str;
private readonly byte[] buf = new byte[1024];
private int len, ptr;
public bool isEof = false;
public bool IsEndOfStream { get { return isEof; } }
[MethodImpl(256)]
private 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(256)]
public char Char()
{
byte b = 0;
do b = read();
while (b < 33 || 126 < b);
return (char)b;
}
[MethodImpl(256)]
public string Line()
{
var sb = new StringBuilder();
for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b);
return sb.ToString();
}
[MethodImpl(256)]
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(256)]
public long Integer()
{
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(256)]
public ulong UInteger()
{
ulong ret = 0; byte b = 0;
do b = read();
while (b < '0' || '9' < b);
for (; true; b = read())
{
if (b < '0' || '9' < b) return ret;
else ret = ret * 10 + b - '0';
}
}
[MethodImpl(256)]
public double Double() => double.Parse(Scan());
}
public static class OutputLib
{
[MethodImpl(256)] public static void WriteJoin<T>(string s, IEnumerable<T> t) => Console.WriteLine(string.Join(s, t));
[MethodImpl(256)]
public static void WriteMat<T>(T[,] a)
{
int sz1 = a.GetLength(0);
int sz2 = a.GetLength(1);
for (int i = 0; i < sz1; i++)
{
var b = new T[sz2];
for (int j = 0; j < sz2; j++) b[j] = a[i, j];
WriteJoin(" ", b);
}
}
[MethodImpl(256)] public static void WriteMat<T>(T[][] a) { for (int i = 0; i < a.Length; i++) WriteJoin(" ", a[i]); }
[MethodImpl(256)] public static void Write(object t) => Console.WriteLine(t.ToString());
[MethodImpl(256)] public static void Write(string str) => Console.WriteLine(str);
[MethodImpl(256)] public static void Write(string str, object arg1) => Console.WriteLine(str, arg1);
[MethodImpl(256)] public static void Write(string str, object arg1, object arg2) => Console.WriteLine(str, arg1, arg2);
[MethodImpl(256)] public static void Write(string str, object arg1, object arg2, object arg3) => Console.WriteLine(str, arg1, arg2, arg3);
[MethodImpl(256)] public static void Write(string str, params object[] arg) => Console.WriteLine(str, arg);
[MethodImpl(256)] public static void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); }
[MethodImpl(256)] public static void WriteError(object t) => Console.Error.WriteLine(t.ToString());
[MethodImpl(256)] public static void Flush() => Console.Out.Flush();
[MethodImpl(256)] public static void YN(bool t) => Console.WriteLine(t ? "YES" : "NO");
[MethodImpl(256)] public static void Yn(bool t) => Console.WriteLine(t ? "Yes" : "No");
[MethodImpl(256)] public static void yn(bool t) => Console.WriteLine(t ? "yes" : "no");
}
public interface IStaticMod
{
uint Mod { get; }
bool IsPrime { get; }
}
public readonly struct Mod1000000007 : IStaticMod
{
public uint Mod => 1000000007;
public bool IsPrime => true;
}
public readonly struct Mod998244353 : IStaticMod
{
public uint Mod => 998244353;
public bool IsPrime => true;
}
public readonly struct StaticModInt<T> : IEquatable<StaticModInt<T>>, IFormattable where T : struct, IStaticMod
{
internal readonly uint _v;
private static readonly T op = default;
public int Value => (int)_v;
public static int Mod => (int)op.Mod;
public static StaticModInt<T> Zero => default;
public static StaticModInt<T> One => new StaticModInt<T>(1u);
[MethodImpl(256)]
public static StaticModInt<T> Raw(int v)
{
var u = unchecked((uint)v);
return new StaticModInt<T>(u);
}
[MethodImpl(256)]
public StaticModInt(long v) : this(Round(v)) { }
[MethodImpl(256)]
public StaticModInt(ulong v) : this((uint)(v % op.Mod)) { }
[MethodImpl(256)]
private StaticModInt(uint v) => _v = v;
[MethodImpl(256)]
private static uint Round(long v)
{
var x = v % op.Mod;
if (x < 0) x += op.Mod;
return (uint)x;
}
[MethodImpl(256)]
public static StaticModInt<T> operator ++(StaticModInt<T> v)
{
var x = v._v + 1;
if (x == op.Mod) x = 0;
return new StaticModInt<T>(x);
}
[MethodImpl(256)]
public static StaticModInt<T> operator --(StaticModInt<T> v)
{
var x = v._v;
if (x == 0) x = op.Mod;
return new StaticModInt<T>(x - 1);
}
[MethodImpl(256)]
public static StaticModInt<T> operator +(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
var v = lhs._v + rhs._v;
if (v >= op.Mod) v -= op.Mod;
return new StaticModInt<T>(v);
}
[MethodImpl(256)]
public static StaticModInt<T> operator -(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
unchecked
{
var v = lhs._v - rhs._v;
if (v >= op.Mod) v += op.Mod;
return new StaticModInt<T>(v);
}
}
[MethodImpl(256)]
public static StaticModInt<T> operator *(StaticModInt<T> lhs, StaticModInt<T> rhs) => new StaticModInt<T>((uint)((ulong)lhs._v * rhs._v % op.Mod));
[MethodImpl(256)]
public static StaticModInt<T> operator /(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs * rhs.Inv();
[MethodImpl(256)]
public static StaticModInt<T> operator +(StaticModInt<T> v) => v;
[MethodImpl(256)]
public static StaticModInt<T> operator -(StaticModInt<T> v) => new StaticModInt<T>(v._v == 0 ? 0 : op.Mod - v._v);
[MethodImpl(256)]
public static bool operator ==(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v == rhs._v;
[MethodImpl(256)]
public static bool operator !=(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v != rhs._v;
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(int v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(uint v) => new StaticModInt<T>((long)v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(long v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(ulong v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator long(StaticModInt<T> v) => v._v;
[MethodImpl(256)]
public static implicit operator ulong(StaticModInt<T> v) => v._v;
[MethodImpl(256)]
public StaticModInt<T> Pow(long n)
{
var x = this;
var r = new StaticModInt<T>(1U);
while (n > 0)
{
if ((n & 1) > 0) r *= x;
x *= x;
n >>= 1;
}
return r;
}
[MethodImpl(256)]
public StaticModInt<T> Inv()
{
var (x, y, g) = ExtGcd(_v, op.Mod);
return new StaticModInt<T>(x);
}
[MethodImpl(256)]
static (long x, long y, long g) ExtGcd(long a, long b)
{
if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -a);
long c = SafeMod(a, b);
var (x2, y2, g) = ExtGcd(b, c);
long x = SafeMod(y2, b);
long y = (g - a * x) / b;
return (x, y, g);
}
[MethodImpl(256)]
static long SafeMod(long x, long m)
{
long r = x % m;
if (r < 0) r += m;
return r;
}
[MethodImpl(256)]
public override string ToString() => _v.ToString();
[MethodImpl(256)]
public string ToString(string format, IFormatProvider formatProvider) => _v.ToString(format, formatProvider);
[MethodImpl(256)]
public override bool Equals(object obj) => obj is StaticModInt<T> m && Equals(m);
[MethodImpl(256)]
public bool Equals(StaticModInt<T> other) => _v == other._v;
[MethodImpl(256)]
public override int GetHashCode() => _v.GetHashCode();
}
class ModFact<TMod> where TMod : struct, IStaticMod
{
StaticModInt<TMod>[] fact;
StaticModInt<TMod>[] factinv;
StaticModInt<TMod>[] inv;
public ModFact(long n)
{
fact = new StaticModInt<TMod>[n + 1];
factinv = new StaticModInt<TMod>[n + 1];
inv = new StaticModInt<TMod>[n + 1];
fact[0] = 1;
for (long i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1);
factinv[n] = fact[n].Inv();
for (long i = n; i > 0; i--) factinv[i - 1] = factinv[i] * i;
for (long i = 1; i <= n; i++) inv[i] = fact[i - 1] * factinv[i];
}
[MethodImpl(256)]
public StaticModInt<TMod> Fact(long n) => fact[n];
[MethodImpl(256)]
public StaticModInt<TMod> FactInv(long n) => factinv[n];
[MethodImpl(256)]
public StaticModInt<TMod> Inv(long n)
{
if (n == 0) throw new DivideByZeroException();
return inv[n];
}
[MethodImpl(256)]
public StaticModInt<TMod> Binom(long n, long k)
{
if (n < 0) return 0;
if (n == 0) return k == 0 ? 1 : 0;
return 0 <= k && k <= n ? fact[n] * factinv[k] * factinv[n - k] : 0;
}
}
public class Permutation
{
int n;
int[] p;
public Permutation(int[] _p)
{
n = _p.Length;
p = (int[])_p.Clone();
}
public Permutation(int _n)
{
n = _n;
p = new int[n];
for (int i = 0; i < n; i++) p[i] = i;
}
public bool Next()
{
for (int i = n - 2; i >= 0; i--)
{
if (p[i] < p[i + 1])
{
int j = n - 1;
while (!(p[i] < p[j])) j--;
Swap(ref p[i], ref p[j]);
for (int k = 1; i + k < n - k; k++) Swap(ref p[i + k], ref p[n - k]);
return true;
}
}
for (int i = 0; i < n - 1 - i; i++) Swap(ref p[i], ref p[n - 1 - i]);
return false;
}
public bool Prev()
{
for (int i = n - 2; i >= 0; i--)
{
if (p[i] > p[i + 1])
{
int j = n - 1;
while (!(p[i] > p[j])) j--;
Swap(ref p[i], ref p[j]);
for (int k = 1; i + k < n - k; k++) Swap(ref p[i + k], ref p[n - k]);
return true;
}
}
for (int i = 0; i < n - 1 - i; i++) Swap(ref p[i], ref p[n - 1 - i]);
return false;
}
public int this[int k]
{
get
{
if (k < 0 || k >= n) throw new IndexOutOfRangeException();
return p[k];
}
}
}