結果

問題 No.1907 DETERMINATION
ユーザー KumaTachiRenKumaTachiRen
提出日時 2023-10-09 12:52:17
言語 C#
(.NET 8.0.203)
結果
AC  
実行時間 2,852 ms / 4,000 ms
コード長 20,072 bytes
コンパイル時間 19,483 ms
コンパイル使用メモリ 171,020 KB
実行使用メモリ 187,272 KB
最終ジャッジ日時 2024-07-26 18:29:33
合計ジャッジ時間 104,871 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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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 47 ms
24,192 KB
testcase_01 AC 48 ms
24,064 KB
testcase_02 AC 48 ms
24,308 KB
testcase_03 AC 47 ms
24,192 KB
testcase_04 AC 47 ms
24,192 KB
testcase_05 AC 48 ms
24,064 KB
testcase_06 AC 47 ms
24,192 KB
testcase_07 AC 874 ms
28,160 KB
testcase_08 AC 384 ms
27,136 KB
testcase_09 AC 621 ms
29,536 KB
testcase_10 AC 1,588 ms
29,428 KB
testcase_11 AC 497 ms
28,288 KB
testcase_12 AC 1,937 ms
29,184 KB
testcase_13 AC 1,682 ms
29,184 KB
testcase_14 AC 1,537 ms
29,184 KB
testcase_15 AC 334 ms
27,520 KB
testcase_16 AC 166 ms
26,752 KB
testcase_17 AC 1,440 ms
29,440 KB
testcase_18 AC 1,119 ms
28,660 KB
testcase_19 AC 84 ms
26,496 KB
testcase_20 AC 1,681 ms
29,312 KB
testcase_21 AC 209 ms
26,880 KB
testcase_22 AC 1,475 ms
28,160 KB
testcase_23 AC 1,890 ms
29,428 KB
testcase_24 AC 598 ms
27,764 KB
testcase_25 AC 52 ms
24,192 KB
testcase_26 AC 2,046 ms
29,568 KB
testcase_27 AC 2,246 ms
29,440 KB
testcase_28 AC 2,249 ms
29,440 KB
testcase_29 AC 2,237 ms
29,440 KB
testcase_30 AC 47 ms
24,440 KB
testcase_31 AC 1,996 ms
29,408 KB
testcase_32 AC 1,933 ms
29,440 KB
testcase_33 AC 1,937 ms
29,312 KB
testcase_34 AC 1,952 ms
29,312 KB
testcase_35 AC 48 ms
24,320 KB
testcase_36 AC 49 ms
24,320 KB
testcase_37 AC 48 ms
24,320 KB
testcase_38 AC 1,938 ms
29,440 KB
testcase_39 AC 2,050 ms
29,568 KB
testcase_40 AC 2,810 ms
29,688 KB
testcase_41 AC 1,951 ms
29,696 KB
testcase_42 AC 2,852 ms
29,412 KB
testcase_43 AC 2,802 ms
29,440 KB
testcase_44 AC 2,253 ms
29,312 KB
testcase_45 AC 2,403 ms
29,408 KB
testcase_46 AC 2,012 ms
29,312 KB
testcase_47 AC 1,901 ms
29,568 KB
testcase_48 AC 1,916 ms
29,312 KB
testcase_49 AC 1,922 ms
29,312 KB
testcase_50 AC 1,914 ms
29,568 KB
testcase_51 AC 1,902 ms
29,568 KB
testcase_52 AC 44 ms
24,064 KB
testcase_53 AC 2,076 ms
28,160 KB
testcase_54 AC 2,098 ms
28,160 KB
testcase_55 AC 46 ms
24,320 KB
testcase_56 AC 1,544 ms
28,416 KB
testcase_57 AC 1,532 ms
28,416 KB
testcase_58 AC 930 ms
29,308 KB
testcase_59 AC 1,267 ms
29,184 KB
testcase_60 AC 1,287 ms
29,568 KB
testcase_61 AC 1,478 ms
29,568 KB
testcase_62 AC 1,298 ms
29,568 KB
testcase_63 AC 1,967 ms
29,440 KB
testcase_64 AC 46 ms
24,192 KB
testcase_65 AC 45 ms
24,064 KB
testcase_66 AC 48 ms
187,272 KB
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 (88 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

diff # 

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;
        Matrix<Mod998244353> m0, m1;
        {
            var a = new ModInt[n, n];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    a[i, j] = ri;
            m0 = new Matrix<Mod998244353>(a);
        }
        {
            var a = new ModInt[n, n];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    a[i, j] = ri;
            m1 = new Matrix<Mod998244353>(a);
        }
        WriteJoin("\n", MatrixLib.DetLinearPoly(m0, m1));
    }

    const long INF = 1L << 60;
    int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
    (int, int) ri2 { [MethodImpl(256)] get => (ri, ri); }
    (int, int, int) ri3 { [MethodImpl(256)] get => (ri, ri, ri); }
    (int, int, int, int) ri4 { [MethodImpl(256)] get => (ri, ri, ri, ri); }
    (int, int, int, int, int) ri5 { [MethodImpl(256)] get => (ri, ri, ri, ri, ri); }
    long rl { [MethodImpl(256)] get => sc.Integer(); }
    (long, long) rl2 { [MethodImpl(256)] get => (rl, rl); }
    (long, long, long) rl3 { [MethodImpl(256)] get => (rl, rl, rl); }
    (long, long, long, long) rl4 { [MethodImpl(256)] get => (rl, rl, rl, rl); }
    (long, long, long, long, long) rl5 { [MethodImpl(256)] get => (rl, rl, rl, rl, rl); }
    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 (long x, long y, long g) ExtGcd(long a, long b) { if (b == 0) return (Sign(a), 0, Math.Abs(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)] 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; } [MethodImpl(256)] public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => Sign(t - val), l, r); [MethodImpl(256)] public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r); [MethodImpl(256)] public static int LowerBound<T>(T[] arr, T val, int l = -1, int r = -1) where T : IComparable<T> => LowerBound(arr.AsSpan(), t => t.CompareTo(val), l, r); [MethodImpl(256)] public static int LowerBound<T>(T[] arr, Func<T, int> comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r); [MethodImpl(256)] 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(256)] 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(256)] 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(); } 
public static partial class MatrixLib { public static StaticModInt<Mod>[] DetLinearPoly<Mod>(Matrix<Mod> a, Matrix<Mod> b) where Mod : struct, IStaticMod { Contract.Requires(a.Height == a.Width); Contract.Requires(b.Height == b.Width); Contract.Requires(a.Height == b.Height); int n = a.Height; if (n == 0) return new StaticModInt<Mod>[] { 1 }; int multiply_by_x = 0; StaticModInt<Mod> detAdetBinv = 1; for (int p = 0; p < n; p++) { int pivot = -1; for (int row = p; row < n; row++) if (b[row, p] != 0) { pivot = row; break; } if (pivot < 0) { multiply_by_x++; if (multiply_by_x > n) return new StaticModInt<Mod>[n + 1]; for (int row = 0; row < p; row++) { var u = b[row, p]; b[row, p] = 0; for (int i = 0; i < n; i++) a[i, p] -= u * a[i, row]; } for (int i = 0; i < n; i++) { var tmp = a[i, p]; a[i, p] = b[i, p]; b[i, p] = tmp; } p--; continue; } if (pivot != p) { a.SwapRows(pivot, p); b.SwapRows(pivot, p); detAdetBinv = -detAdetBinv; } var v = b[p, p]; var vinv = v.Inv(); detAdetBinv *= v; for (int col = 0; col < n; col++) { a[p, col] *= vinv; b[p, col] *= vinv; } for (int row = 0; row < n; row++) { if (row == p) continue; v = b[row, p]; for (int col = 0; col < n; col++) { a[row, col] -= a[p, col] * v; b[row, col] -= b[p, col] * v; } } } for (int row = 0; row < n; row++) for (int col = 0; col < n; col++) a[row, col] = -a[row, col]; var poly = CharacteristicPolynomial(a); for (int i = 0; i < poly.Length; i++) poly[i] *= detAdetBinv; var ret = new StaticModInt<Mod>[n + 1]; for (int i = multiply_by_x; i < poly.Length; i++) ret[i - multiply_by_x] = poly[i]; return ret; } }
public struct Matrix<Mod> where Mod : struct, IStaticMod { public int Height { get; private set; } public int Width { get; private set; } int size; StaticModInt<Mod>[] mat; [MethodImpl(256)] int GetIndex(int i, int j) => Width * i + j; [MethodImpl(256)] public StaticModInt<Mod> Get(int i, int j) => mat[GetIndex(i, j)]; [MethodImpl(256)] public StaticModInt<Mod> Set(int i, int j, StaticModInt<Mod> v) => mat[GetIndex(i, j)] = v; public StaticModInt<Mod> this[int i, int j] { [MethodImpl(256)] get => mat[GetIndex(i, j)]; [MethodImpl(256)] set => mat[GetIndex(i, j)] = value; } public Matrix(int n, int m) { Height = n; Width = m; size = n * m; mat = new StaticModInt<Mod>[size]; } public Matrix(StaticModInt<Mod>[,] _mat) { Height = _mat.GetLength(0); Width = _mat.GetLength(1); size = Height * Width; mat = new StaticModInt<Mod>[size]; for (int i = 0; i < Height; i++) for (int j = 0; j < Width; j++) mat[GetIndex(i, j)] = _mat[i, j]; } public Matrix(Matrix<Mod> _mat) { Height = _mat.Height; Width = _mat.Width; size = _mat.size; mat = (StaticModInt<Mod>[])_mat.mat.Clone(); } public static Matrix<Mod> operator +(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Height == b.Height && a.Width == b.Width); var c = new Matrix<Mod>(a); for (int i = 0; i < b.size; i++) c.mat[i] += b.mat[i]; return c; } public static Matrix<Mod> operator -(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Height == b.Height && a.Width == b.Width); var c = new Matrix<Mod>(a); for (int i = 0; i < b.size; i++) c.mat[i] -= b.mat[i]; return c; } public static Matrix<Mod> operator *(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Width == b.Height); var c = new Matrix<Mod>(a.Height, b.Width); for (int i = 0; i < a.Height; i++) for (int k = 0; k < a.Width; k++) for (int j = 0; j < b.Width; j++) c.mat[c.GetIndex(i, j)] += a.mat[a.GetIndex(i, k)] * b.mat[b.GetIndex(k, j)]; return c; } [MethodImpl(256)] public void SwapRows(int u, int v) { StaticModInt<Mod> tmp; for (int i = 0; i < Width; i++) { tmp = this[u, i]; this[u, i] = this[v, i]; this[v, i] = tmp; } } [MethodImpl(256)] public void SwapColumns(int u, int v) { StaticModInt<Mod> tmp; for (int i = 0; i < Height; i++) { tmp = this[i, u]; this[i, u] = this[i, v]; this[i, v] = tmp; } } [MethodImpl(256)] public StaticModInt<Mod> Determinant() { Contract.Requires(Height == Width); int n = Height; var a = new Matrix<Mod>(this); StaticModInt<Mod> det = 1, inv, coeff; for (int y = 0; y < n - 1; y++) { if (a[y, y] == 0) { int z = y + 1; for (; z < n; z++) if (a[z, y] != 0) break; if (z == n) return 0; a.SwapRows(y, z); det = -det; } inv = a[y, y].Inv(); for (int x = y + 1; x < n; x++) { coeff = a[x, y] * inv; for (int z = y; z < n; z++) a[x, z] -= coeff * a[y, z]; } det *= a[y, y]; } det *= a[n - 1, n - 1]; return det; } }
public static partial class MatrixLib { public static StaticModInt<Mod>[] CharacteristicPolynomial<Mod>(Matrix<Mod> mat) where Mod : struct, IStaticMod { Contract.Requires(mat.Height == mat.Width); int n = mat.Height; if (n == 0) return new StaticModInt<Mod>[] { 1 }; var T = new StaticModInt<Mod>[n]; for (int y = 1; y < n; y++) { int y1 = y; while (y1 < n && mat.Get(y1, y - 1) == 0) y1++; if (y1 == n) continue; if (y != y1) { mat.SwapRows(y, y1); mat.SwapColumns(y, y1); } T[y] = mat.Get(y, y - 1).Inv(); for (int y2 = y + 1; y2 < n; y2++) T[y2] = T[y] * mat[y2, y - 1]; for (int y2 = y + 1; y2 < n; y2++) for (int x = y - 1; x < n; x++) mat[y2, x] -= mat[y, x] * T[y2]; for (int y2 = 0; y2 < n; y2++) for (int x = y + 1; x < n; x++) mat[y2, y] += mat[y2, x] * T[x]; } for (int y = 0; y < n; y++) { StaticModInt<Mod> tmp = 1; for (int x = y + 1; x < n; x++) mat[y, x] *= (tmp *= -mat[x, x - 1]); } int n1 = n + 1; var dp = new StaticModInt<Mod>[n1 * n1]; dp[0] = 1; for (int y = 0; y < n; y++) { for (int x = 0; x <= y; x++) dp[n1 * (y + 1) + x + 1] -= dp[n1 * y + x]; for (int x = 0; x <= y; x++) dp[n1 * (y + 1) + x] += dp[n1 * y + x] * mat[y, y]; for (int y2 = 0; y2 < y; y2++) for (int x = 0; x <= y2; x++) dp[n1 * (y + 1) + x] += dp[n1 * y2 + x] * mat[y2, y]; } var ret = new StaticModInt<Mod>[n + 1]; for (int i = 0; i <= n; i++) ret[i] = (n % 2 == 1) ? -dp[n1 * n + i] : dp[n1 * n + i]; return ret; } }
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