結果

問題 No.194 フィボナッチ数列の理解(1)
コンテスト
ユーザー eitaho
提出日時 2015-04-27 20:45:20
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 1,400 ms / 5,000 ms
コード長 5,607 bytes
コンパイル時間 1,056 ms
コンパイル使用メモリ 110,976 KB
実行使用メモリ 27,392 KB
最終ジャッジ日時 2024-07-05 04:55:02
合計ジャッジ時間 17,822 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 37
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
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

diff # 

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using Enu = System.Linq.Enumerable;

class Program
{
    static readonly int SmallN = (int)1e6;
    static readonly int Mod = (int)1e9 + 7;

    public void Solve()
    {
        int L = Reader.Int();
        long N = Reader.Long();
        var F = new[] { 0 }.Concat(Reader.IntArray(L)).Concat(new int[SmallN]).ToArray();
        var S = new int[SmallN + 1];
        for (int i = 1; i <= L; i++) S[i] = (F[i] + S[i - 1]) % Mod;

        if (N <= SmallN)
        {
            for (int i = L + 1; i <= N; i++)
            {
                F[i] = (S[i - 1] - S[i - L - 1] + Mod) % Mod;
                S[i] = (F[i] + S[i - 1]) % Mod;
            }
            Console.WriteLine(F[N] + " " + S[N]);
        }
        else
        {
            var M = new Matrix(L, L, Mod);
            for (int c = 0; c < L; c++) M[0, c] = 1;
            for (int r = 1; r < L; r++) M[r, r - 1] = 1;
            var Fmat = new Matrix(F.Skip(1).Take(L).Reverse().ToArray(), Mod);
            long f = (M.Power(N - L) * Fmat)[0, 0];
            long s = (S[L] + (Rec(M, N - L) * Fmat)[0, 0]) % Mod;
            Console.WriteLine(f + " " + s);
        }
    }

    Matrix Rec(Matrix A, long pow)
    {
        if (pow == 1) return A;
        var halfSum = Rec(A, pow / 2);
        var res = A.Power(pow / 2) * halfSum;
        res = res + halfSum;
        if (pow % 2 == 1) res += A.Power(pow);
        return res;
    }

    class Matrix
    {
        public readonly int H, W;
        public readonly long Mod;
        private readonly long[] M;

        public long this[int r, int c]
        {
            get { return M[r * W + c]; }
            set { M[r * W + c] = (value % Mod + Mod) % Mod; }
        }
        public Matrix(int h, int w, long mod)
        {
            H = h; W = w; Mod = mod; M = new long[h * w];
        }
        public Matrix(long[] vec, long mod)
        {
            H = vec.Length; W = 1; Mod = mod; M = new long[H];
            for (int i = 0; i < H; i++) this[i, 0] = vec[i];
        }
        public Matrix(int[] vec, long mod)
        {
            H = vec.Length; W = 1; Mod = mod; M = new long[vec.Length];
            for (int i = 0; i < H; i++) this[i, 0] = vec[i];
        }
        public static Matrix operator +(Matrix A, Matrix B)
        {
            Debug.Assert(A.H == B.H && A.W == B.W && A.Mod == B.Mod);
            var res = A.Clone();
            for (int i = 0; i < A.M.Length; i++)
                Add(ref res.M[i], B.M[i], A.Mod);
            return res;
        }
        public static Matrix operator *(Matrix A, Matrix B)
        {
            Debug.Assert(A.W == B.H && A.Mod == B.Mod);
            long mod = A.Mod;
            var res = new Matrix(A.H, B.W, mod);
            for (int r = 0; r < res.H; r++)
                for (int i = 0; i < A.W; i++)
                    for (int c = 0; c < res.W; c++)
                        Add(ref res.M[r * res.W + c], A.M[r * A.W + i] * B.M[i * B.W + c] % mod, mod);
            return res;
        }
        public Matrix Power(long pow)
        {
            Debug.Assert(H == W);
            var A = Clone();
            var res = new Matrix(H, W, Mod);
            for (int i = 0; i < H; i++) res[i, i] = 1;
            while (pow > 0)
            {
                if ((pow & 1) == 1) res = res * A;
                A = A * A;
                pow >>= 1;
            }
            return res;
        }
        private static void Add(ref long a, long b, long mod)
        {
            if ((a += b) >= mod) a -= mod;
            if (a < 0) a += mod;
        }
        public Matrix Clone()
        {
            var res = new Matrix(H, W, Mod);
            Array.Copy(M, res.M, M.Length);
            return res;
        }
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    private static TextReader reader = Console.In;
    private static readonly char[] separator = { ' ' };
    private static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    private static string[] A = new string[0];
    private static int i;
    private static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); }
    public static int[][] IntTable(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); }
    public static string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Line()).ToArray(); }
    public static string Line() { return reader.ReadLine().Trim(); }
    private static string[] Split(string s) { return s.Split(separator, op); }
    private static string Next() { CheckNext(); return A[i++]; }
    private static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}
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