#898751 (C#) No.2405 Minimal Matrix Decomposition

提出ソース

結果

問題	No.2405 Minimal Matrix Decomposition
ユーザー	KumaTachiRen
提出日時	2023-08-04 22:55:10
言語	C# (.NET 8.0.203)
結果	WA
実行時間	-
コード長	15,550 bytes
コンパイル時間	9,224 ms
コンパイル使用メモリ	170,272 KB
実行使用メモリ	187,020 KB
最終ジャッジ日時	2024-04-22 21:16:35
合計ジャッジ時間	36,132 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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	41 ms 24,444 KB
testcase_01	AC	41 ms 24,576 KB
testcase_02	AC	41 ms 24,576 KB
testcase_03	AC	41 ms 24,448 KB
testcase_04	WA	-
testcase_05	AC	1,853 ms 39,040 KB
testcase_06	AC	42 ms 24,704 KB
testcase_07	AC	41 ms 24,704 KB
testcase_08	AC	40 ms 24,704 KB
testcase_09	AC	40 ms 24,676 KB
testcase_10	AC	1,168 ms 35,584 KB
testcase_11	TLE	-
testcase_12	AC	52 ms 26,108 KB
testcase_13	AC	317 ms 28,516 KB
testcase_14	AC	361 ms 29,568 KB
testcase_15	WA	-
testcase_16	AC	93 ms 26,880 KB
testcase_17	AC	823 ms 30,592 KB
testcase_18	AC	280 ms 29,184 KB
testcase_19	AC	261 ms 29,440 KB
testcase_20	AC	51 ms 26,240 KB
testcase_21	WA	-
testcase_22	AC	1,646 ms 33,792 KB
testcase_23	AC	47 ms 26,112 KB
testcase_24	AC	50 ms 26,112 KB
testcase_25	AC	56 ms 26,752 KB
testcase_26	AC	865 ms 33,276 KB
testcase_27	AC	298 ms 28,288 KB
testcase_28	AC	523 ms 31,360 KB
testcase_29	AC	122 ms 27,904 KB
testcase_30	AC	997 ms 34,560 KB
testcase_31	AC	343 ms 29,824 KB
testcase_32	AC	66 ms 26,240 KB
testcase_33	AC	1,106 ms 31,616 KB
testcase_34	AC	162 ms 27,264 KB
testcase_35	AC	42 ms 25,088 KB
testcase_36	AC	263 ms 28,160 KB
testcase_37	AC	536 ms 29,440 KB
testcase_38	AC	331 ms 30,080 KB
testcase_39	AC	1,267 ms 34,432 KB
testcase_40	AC	354 ms 29,056 KB
testcase_41	AC	71 ms 26,752 KB
testcase_42	AC	1,397 ms 32,896 KB
testcase_43	AC	223 ms 28,160 KB
testcase_44	AC	240 ms 28,288 KB
testcase_45	AC	67 ms 26,852 KB
testcase_46	AC	145 ms 27,620 KB
testcase_47	AC	312 ms 28,772 KB
testcase_48	AC	125 ms 26,748 KB
testcase_49	AC	51 ms 187,020 KB

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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 (101 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

raw source code

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;

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 p = ri;
        int n = ri, m = ri;

        ModInt.Mod = p;
        var a = new ModInt[n][];
        for (int i = 0; i < n; i++)
        {
            a[i] = new ModInt[m];
            for (int j = 0; j < m; j++) a[i][j] = ri;
        }

        const bool debug = true;

        var r = Calc(a, n, m).ms;
        Write(r.Count);
        ModInt[][] prod = null;
        foreach (var b in r)
        {
            Write($"{b.Length} {b[0].Length}");
            WriteMat(b);

            if (debug)
            {
                if (prod == null) prod = b;
                else prod = Mul(prod, b);
            }
        }
        if (debug)
        {
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    Debug.Assert(a[i][j] == prod[i][j], $"{i}, {j}");
        }
    }

    ModInt[][] Mul(ModInt[][] a, ModInt[][] b)
    {
        int l = a.Length;
        int n = b.Length;
        int m = b[0].Length;
        var c = new ModInt[l][];
        for (int i = 0; i < l; i++) c[i] = new ModInt[m];
        for (int i = 0; i < l; i++)
            for (int j = 0; j < m; j++)
                for (int k = 0; k < n; k++)
                    c[i][j] += a[i][k] * b[k][j];
        return c;
    }

    (int score, List<ModInt[][]> ms) Calc(ModInt[][] a, int n, int m)
    {
        if (n == 1 || m == 1) return (n * m, new List<ModInt[][]>() { a });
        var acopy = new ModInt[n][];
        for (int i = 0; i < n; i++)
        {
            acopy[i] = new ModInt[m];
            for (int j = 0; j < m; j++)
                acopy[i][j] = a[i][j];
        }
        {
            var tmp = a;
            a = acopy;
            acopy = tmp;
        }

        var f = new bool[n];
        var coeff = new List<ModInt[]>();
        var basis = new List<ModInt[]>();
        for (int k = 0; k < m; k++)
        {
            int x = 0;
            while (x < n && (f[x] || a[x][k] == 0)) x++;
            if (x == n) break;
            f[x] = true;
            ModInt inv = a[x][k].Inv();
            var cs = new ModInt[n];
            for (int i = 0; i < n; i++)
            {
                if (i == x)
                {
                    cs[i] = 1;
                    continue;
                }
                if (f[i]) continue;
                ModInt c = a[i][k] * inv;
                cs[i] = c;
                for (int j = 0; j < m; j++) a[i][j] -= a[x][j] * c;
            }
            coeff.Add(cs);
            basis.Add(a[x]);
        }
        int dim = basis.Count;
        if (dim == 0)
        {
            basis.Add(new ModInt[m]);
            coeff.Add(new ModInt[n]);
            dim++;
        }

        if (dim == Math.Min(n, m))
        {
            return (n * m, new List<ModInt[][]> { acopy });
        }

        var b = new ModInt[n][];
        for (int i = 0; i < n; i++)
        {
            b[i] = new ModInt[dim];
            for (int j = 0; j < dim; j++) b[i][j] = coeff[j][i];
        }
        var res1 = Calc(b, n, dim);
        var res2 = Calc(basis.ToArray(), dim, m);
        if (res1.score + res2.score < m * n)
        {
            var ret = res1.ms;
            foreach (var mat in res2.ms) ret.Add(mat);
            return (res1.score + res2.score, ret);
        }
        else
        {
            return (n * m, new List<ModInt[][]> { acopy });
        }
    }

    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());
}

struct ModInt
{
    public static long Mod = 998244353;
    public long Val { get; private set; }
    public ModInt(long v) { Val = SafeMod(v, Mod); }
    public override string ToString() { return Val.ToString(); }
    public override bool Equals(object obj) => obj is ModInt other && this.Equals(other);
    public bool Equals(ModInt x) => Val == x.Val;
    public override int GetHashCode() => Val.GetHashCode();
    public static bool operator ==(ModInt a, ModInt b) { return a.Val == b.Val; }
    public static bool operator !=(ModInt a, ModInt b) { return a.Val != b.Val; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long n) => new ModInt(SafeMod(n, Mod));
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, ModInt b)
    {
        long r = a.Val + b.Val;
        return new ModInt(r < Mod ? r : r - Mod);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, ModInt b)
    {
        long r = a.Val - b.Val;
        return new ModInt(r < 0 ? r + Mod : r);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a) => new ModInt(a.Val == 0 ? 0 : Mod - a.Val);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt(a.Val * b.Val % Mod);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt a, ModInt b) => a * b.Inv();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Pow(long n)
    {
        long t = Val, r = 1;
        while (n > 0)
        {
            if ((n & 1) == 1) r = r * t % Mod;
            t = t * t % Mod;
            n >>= 1;
        }
        return new ModInt(r);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Inv() => Gcd(Val, Mod).x;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private static (long x, long y, long g) Gcd(long a, long b)
    {

        if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -a);
        long c = a % b;
        if (c < 0) c += b;
        var r = Gcd(b, c);
        long x = SafeMod(r.y, b);
        long g = r.g;
        long y = (g - a * x) / b;
        return (x, y, g);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private static long SafeMod(long x, long m)
    {
        long r = x % m;
        return r < 0 ? r + m : r;
    }
}

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");
}

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結果

テストケース

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ソースコード