結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー 紙ぺーぱー紙ぺーぱー
提出日時 2015-05-23 15:00:07
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 117 ms / 5,000 ms
コード長 10,094 bytes
コンパイル時間 2,698 ms
コンパイル使用メモリ 110,652 KB
実行使用メモリ 35,716 KB
最終ジャッジ日時 2023-09-20 10:52:16
合計ジャッジ時間 6,958 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge13
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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 55 ms
20,708 KB
testcase_01 AC 54 ms
20,724 KB
testcase_02 AC 67 ms
25,096 KB
testcase_03 AC 57 ms
22,772 KB
testcase_04 AC 65 ms
27,092 KB
testcase_05 AC 64 ms
24,968 KB
testcase_06 AC 64 ms
22,956 KB
testcase_07 AC 64 ms
23,032 KB
testcase_08 AC 55 ms
20,820 KB
testcase_09 AC 65 ms
23,088 KB
testcase_10 AC 56 ms
20,708 KB
testcase_11 AC 55 ms
18,724 KB
testcase_12 AC 65 ms
23,036 KB
testcase_13 AC 56 ms
20,740 KB
testcase_14 AC 56 ms
20,756 KB
testcase_15 AC 63 ms
20,944 KB
testcase_16 AC 64 ms
24,984 KB
testcase_17 AC 55 ms
20,812 KB
testcase_18 AC 65 ms
23,148 KB
testcase_19 AC 65 ms
25,072 KB
testcase_20 AC 55 ms
20,772 KB
testcase_21 AC 117 ms
35,716 KB
testcase_22 AC 55 ms
20,648 KB
testcase_23 AC 57 ms
22,812 KB
testcase_24 AC 87 ms
27,456 KB
testcase_25 AC 83 ms
28,924 KB
testcase_26 AC 80 ms
26,572 KB
testcase_27 AC 89 ms
28,512 KB
testcase_28 AC 62 ms
23,992 KB
testcase_29 AC 113 ms
34,440 KB
testcase_30 AC 67 ms
25,196 KB
testcase_31 AC 55 ms
22,676 KB
testcase_32 AC 65 ms
23,056 KB
testcase_33 AC 65 ms
25,016 KB
testcase_34 AC 65 ms
25,000 KB
testcase_35 AC 67 ms
25,088 KB
testcase_36 AC 65 ms
23,016 KB
testcase_37 AC 56 ms
18,596 KB
testcase_38 AC 65 ms
22,932 KB
testcase_39 AC 65 ms
23,100 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
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.Collections.Generic;
using System.Linq;
using Debug = System.Diagnostics.Debug;
using Watch = System.Diagnostics.Stopwatch;
using StringBuilder = System.Text.StringBuilder;
using System.Numerics;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var n = sc.Integer();
            var k = sc.Long();
            var a = sc.Integer(n);
            var dp = new ModInteger[Math.Min(1000050, k + 50)];
            var cum = new ModInteger[Math.Min(1000050, k + 50)];
            for (int i = 0; i < n; i++)
                dp[i + 1] = a[i];
            for (int i = 1; i <= n; i++)
                cum[i] = dp[i] + cum[i - 1];
            if (n > 30)
            {
                for (int i = n + 1; i <= k; i++)
                {
                    dp[i] = cum[i - 1] - cum[Math.Max(0, i - 1 - n)];
                    cum[i] = dp[i] + cum[i - 1];
                }
                IO.Printer.Out.WriteLine("{0} {1}", dp[k], cum[k]);
            }
            else
            {
                var mat = new FastModMatrix(n + 1, n + 1);
                for (int i = 0; i < n; i++)
                    mat[0, i] = 1;
                for (int i = 1; i < n; i++)
                    mat[i, i - 1] = 1;
                mat[n, n - 1] = mat[n, n] = 1;
                var res = FastModMatrix.Pow(mat, k - 1);
                ModInteger ans = 0;
                ModInteger sum = 0;
                for (int i = 0; i < n; i++)
                {
                    ans += res[n - 1, i] * dp[n - i];
                    sum += res[n, i] * dp[n - i];
                }


                IO.Printer.Out.WriteLine("{0} {1}", ans, sum+ans);
            }


        }

        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }

    }
}

#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer : StreamWriter
    {
        static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
        public static Printer Out { get; set; }
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
        public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
        public void Write<T>(string format, IEnumerable<T> source) { base.Write(format, source.OfType<object>().ToArray()); }
        public void WriteLine<T>(string format, IEnumerable<T> source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            if (isEof) return long.MinValue;
            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';
            }
        }
        public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n) { return enumerate(n, Char); }
        public string[] Scan(int n) { return enumerate(n, Scan); }
        public double[] Double(int n) { return enumerate(n, Double); }
        public int[] Integer(int n) { return enumerate(n, Integer); }
        public long[] Long(int n) { return enumerate(n, Long); }
    }
}
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
    static public void Main()
    {
        var solver = new Program.Solver();
        solver.Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion

#region ModNumber
public struct ModInteger
{
    public const long Mod = (long)1e9 + 7;
    public long num;
    public ModInteger(long n) : this() { num = n % Mod; }
    public override string ToString() { return num.ToString(); }
    public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod)n -= Mod; return new ModInteger(n); }
    public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num - r.num; if (n < 0)n += Mod; return new ModInteger(n); }
    public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger((l.num * r.num) % Mod); }
    public static implicit operator ModInteger(long n) { return new ModInteger(n); }
}
#endregion

#region ModMatrix
public class FastModMatrix
{
    int row, col;
    public ulong[] mat;
    const int sz = 18;
    public ModInteger this[int r, int c]
    {
        get { return new ModInteger((long)mat[r * col + c]); }
        set { mat[r * col + c] = (ulong)value.num; }
    }
    public FastModMatrix(int r, int c)
    {
        if (r % sz > 0) r += sz - r % sz;
        if (c % sz > 0) c += sz - c % sz;
        row = r; col = c;
        mat = new ulong[row * col];
    }
    public static FastModMatrix operator +(FastModMatrix l, FastModMatrix r)
    {
        check(l, r);
        var ret = new FastModMatrix(l.row, l.col);
        for (int i = 0; i < l.row; i++)
            for (int j = 0; j < l.col; j++)
            {
                ret.mat[i * ret.col + j] = l.mat[i * l.col + j] + r.mat[i * r.col + j];
                if (ret.mat[i * ret.col + j] >= ModInteger.Mod) ret.mat[i * ret.col + j] -= ModInteger.Mod;
            }
        return ret;

    }
    //ループアンローリングパワーで高速化(剰余演算回数を減らしている)
    public static FastModMatrix operator *(FastModMatrix l, FastModMatrix r)
    {
        checkMul(l, r);
        var ret = new FastModMatrix(l.row, l.col);
        for (int i = 0; i < l.row; i++)
            for (int k = 0; k < l.row; k += sz)
                for (int j = 0; j < l.col; j++)
                    ret.mat[i * l.col + j] = (ret.mat[i * l.col + j] +
                        l.mat[i * l.col + k] * r.mat[k * l.col + j] +
                        l.mat[i * l.col + k + 1] * r.mat[(k + 1) * l.col + j] +
                        l.mat[i * l.col + k + 2] * r.mat[(k + 2) * l.col + j] +
                        l.mat[i * l.col + k + 3] * r.mat[(k + 3) * l.col + j] +
                        l.mat[i * l.col + k + 4] * r.mat[(k + 4) * l.col + j] +
                        l.mat[i * l.col + k + 5] * r.mat[(k + 5) * l.col + j] +
                        l.mat[i * l.col + k + 6] * r.mat[(k + 6) * l.col + j] +
                        l.mat[i * l.col + k + 7] * r.mat[(k + 7) * l.col + j] +
                        l.mat[i * l.col + k + 8] * r.mat[(k + 8) * l.col + j] +
                        l.mat[i * l.col + k + 9] * r.mat[(k + 9) * l.col + j] +
                        l.mat[i * l.col + k + 10] * r.mat[(k + 10) * l.col + j] +
                        l.mat[i * l.col + k + 11] * r.mat[(k + 11) * l.col + j] +
                        l.mat[i * l.col + k + 12] * r.mat[(k + 12) * l.col + j] +
                        l.mat[i * l.col + k + 13] * r.mat[(k + 13) * l.col + j] +
                        l.mat[i * l.col + k + 14] * r.mat[(k + 14) * l.col + j] +
                        l.mat[i * l.col + k + 15] * r.mat[(k + 15) * l.col + j] +
                        l.mat[i * l.col + k + 16] * r.mat[(k + 16) * l.col + j] +
                        l.mat[i * l.col + k + 17] * r.mat[(k + 17) * l.col + j]) % ModInteger.Mod;
        return ret;
    }
    public static FastModMatrix Pow(FastModMatrix m, long n)
    {
        var ret = new FastModMatrix(m.row, m.col);
        for (int i = 0; i < m.row; i++)
            ret.mat[i * m.col + i] = 1;
        for (; n > 0; m *= m, n >>= 1)
            if ((n & 1) == 1)
                ret = ret * m;
        return ret;

    }
    public static FastModMatrix Trans(FastModMatrix m)
    {
        var ret = new FastModMatrix(m.col, m.row);
        for (int i = 0; i < m.row; i++)
            for (int j = 0; j < m.col; j++)
                ret.mat[j * m.col + i] = m.mat[i * m.col + j];
        return ret;
    }
    [System.Diagnostics.Conditional("DEBUG")]
    static private void check(FastModMatrix a, FastModMatrix b)
    {
        if (a.row != b.row || a.col != b.col)
            throw new Exception("row and col have to be same.");

    }
    [System.Diagnostics.Conditional("DEBUG")]
    static private void checkMul(FastModMatrix a, FastModMatrix b)
    {
        if (a.col != b.row)
            throw new Exception("row and col have to be same.");

    }
}
#endregion
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