結果

問題 No.195 フィボナッチ数列の理解(2)
ユーザー EmKjpEmKjp
提出日時 2015-04-29 01:50:04
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 29 ms / 5,000 ms
コード長 6,656 bytes
コンパイル時間 2,288 ms
コンパイル使用メモリ 114,052 KB
実行使用メモリ 26,104 KB
最終ジャッジ日時 2024-07-05 16:31:19
合計ジャッジ時間 2,920 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 29 ms
24,028 KB
testcase_01 AC 27 ms
21,808 KB
testcase_02 AC 27 ms
26,104 KB
testcase_03 AC 26 ms
23,724 KB
testcase_04 AC 26 ms
25,840 KB
testcase_05 AC 27 ms
21,944 KB
testcase_06 AC 26 ms
24,060 KB
testcase_07 AC 27 ms
24,188 KB
testcase_08 AC 27 ms
23,932 KB
testcase_09 AC 26 ms
21,940 KB
testcase_10 AC 27 ms
24,156 KB
testcase_11 AC 25 ms
24,028 KB
testcase_12 AC 26 ms
23,984 KB
testcase_13 AC 26 ms
24,028 KB
testcase_14 AC 27 ms
24,112 KB
testcase_15 AC 27 ms
25,852 KB
testcase_16 AC 26 ms
25,976 KB
testcase_17 AC 26 ms
24,028 KB
testcase_18 AC 26 ms
23,988 KB
testcase_19 AC 26 ms
24,024 KB
testcase_20 AC 27 ms
23,936 KB
testcase_21 AC 27 ms
21,940 KB
testcase_22 AC 27 ms
23,896 KB
testcase_23 AC 26 ms
21,808 KB
testcase_24 AC 24 ms
21,688 KB
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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.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text;

partial class Solver {
    /// <summary>
    /// ax + by = p
    /// cx + dy = q
    /// </summary>
    static bool CramersRule(long a, long b, long p, long c, long d, long q, out long x, out long y) {
        x = 0; y = 0;
        long det = a * d - b * c;
        if (det == 0) return false;
        long pdbq = p * d - b * q;
        long aqpc = a * q - p * c;

        if (pdbq % det != 0) return false;
        if (aqpc % det != 0) return false;

        x = pdbq / det;
        y = aqpc / det;
        return true;
    }

    public static void Swap<T>(ref T lhs, ref T rhs) { T temp; temp = lhs; lhs = rhs; rhs = temp; }

    static public long ExtendedGcd(long a, long b, ref long x, ref long y) {
        if (b == 0) {
            x = 1; y = 0;
            return a;
        } else {
            long d = ExtendedGcd(b, a % b, ref y, ref x);
            y -= a / b * x;
            return d;
        }
    }

    static public bool ChineseRemainderTheorem(long a1, long m1, long a2, long m2,
             ref long val, ref long mod) {
        a1 %= m1; a2 %= m2;
        if (a1 > a2) return ChineseRemainderTheorem(a2, m2, a1, m1, ref val, ref mod);
        long A = 0, B = 0, g = ExtendedGcd(m1, m2, ref A, ref B);
        if (a1 % g != a2 % g) return false;
        long M = a1 % g;
        a1 /= g; m1 /= g; a2 /= g; m2 /= g;
        long k = (A + m2) * (a2 - a1) % m2;
        mod = m1 * m2 * g;
        val = ((a1 + k * m1) * g + M) % mod;
        return true;
    }

    static public long Inverse(long a, long mod) {
        long x = 0, y = 0;
        if (ExtendedGcd(a, mod, ref x, ref y) == 1)
            return (x + mod) % mod;
        else
            return -1;
    }


    public void Run() {
        long X = nl();
        long Y = nl();
        long Z = nl();
        if (X > Y) Swap(ref X, ref Y);
        if (X > Z) Swap(ref X, ref Z);
        if (Y > Z) Swap(ref Y, ref Z);
        if (X == Y) Swap(ref Y, ref Z);
        var fib = new List<long>();
        fib.Add(1);
        fib.Add(0);
        fib.Add(1);
        while (true) {
            var x = fib[fib.Count - 2] + fib[fib.Count - 1];
            if (x > 2000000000) break;
            fib.Add(x);
        }

        long ansA = -1, ansB = -1;

        if (X == Y && Y == Z) {
            for (int i = 0; i < fib.Count - 1; i++) {
                if (fib[i + 1] == 0) continue;
                long A = 0, B = 0;
                // fib[i] * A + fib[i+1] * B = X
                // B = (X - fib[i] * A) / fib[i+1]

                // X - fib[i] * A = 0 (mod fib[i+1]
                // fib[i] * A = X
                // A = X * inv(fib[i]) mod fib[i+1]
                if (fib[i + 1] == 1) {
                    A = 1;
                } else {
                    A = X * Inverse(fib[i], fib[i + 1]) % fib[i + 1];
                }
                B = (X - fib[i] * A) / (fib[i + 1]);
                if (A > 0 && B > 0) {
                    if (ansA == -1 || (ansA > A || (ansA == A && ansB > B))) {
                        ansA = A;
                        ansB = B;
                    }
                }
            }

        } else {
            for (int i = 0; i < fib.Count - 1; i++) {
                for (int j = 0; j < fib.Count - 1; j++) {
                    // fib[i] * A + fib[i+1] * B = X
                    // fib[j] * A + fib[j+1] * B = Y
                    long A, B;
                    if (CramersRule(fib[i], fib[i + 1], X, fib[j], fib[j + 1], Y, out A, out B)) {
                        if (A > 0 && B > 0) {
                            for (int k = 0; k < fib.Count - 1; k++) {
                                if (fib[k] * A + fib[k + 1] * B == Z) {
                                    if (ansA == -1 || (ansA > A || (ansA == A && ansB > B))) {
                                        ansA = A;
                                        ansB = B;
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }

        if (ansA == -1) cout.WriteLine(-1);
        else cout.WriteLine("{0} {1}", ansA, ansB);
    }
}

// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner {
    public static void Main(string[] args) {


        new Solver(Console.In, Console.Out).Run();
    }

    TextReader cin;
    TextWriter cout;

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

    public int ni() {
        return NextInt();
    }
    public long nl() {
        return NextLong();
    }
    public string ns() {
        return Next();
    }
}

public class Scanner {
    private TextReader Reader;
    private Queue<String> TokenQueue = new Queue<string>();
    private CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        this.Reader = reader;
    }

    public int NextInt() { return Int32.Parse(Next(), ci); }
    public long NextLong() { return Int64.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size) {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size) {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public String Next() {
        if (TokenQueue.Count == 0) {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext() {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }

    private bool StockTokens() {
        while (true) {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Trim().Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}
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