結果

問題 No.280 歯車の問題(1)
コンテスト
ユーザー くれちー
提出日時 2017-08-11 03:19:37
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 41 ms / 1,000 ms
コード長 4,953 bytes
コンパイル時間 1,239 ms
コンパイル使用メモリ 119,316 KB
実行使用メモリ 20,224 KB
最終ジャッジ日時 2024-10-12 19:21:58
合計ジャッジ時間 4,747 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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
other AC * 31
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.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Extentions;

class IO
{
    int idx;
    string[] input = In.ReadToEnd().Split(new[] { " ", "\n", "\r" },
        StringSplitOptions.RemoveEmptyEntries);

    T Get<T>(Func<string, T> parser) => parser(input[idx++]);

    public string S => Get(s => s);
    public char C => Get(char.Parse);
    public int I => Get(int.Parse);
    public long L => Get(long.Parse);
    public double F => Get(double.Parse);
    public decimal D => Get(decimal.Parse);
    public BigInteger B => Get(BigInteger.Parse);

    T[] Gets<T>(int n, Func<string, T> parser)
        => input.Skip((idx += n) - n).Take(n).Select(parser).ToArray();

    public string[] Ss(int n) => Gets(n, s => s);
    public char[] Cs(int n) => Gets(n, char.Parse);
    public int[] Is(int n) => Gets(n, int.Parse);
    public long[] Ls(int n) => Gets(n, long.Parse);
    public double[] Fs(int n) => Gets(n, double.Parse);
    public decimal[] Ds(int n) => Gets(n, decimal.Parse);
    public BigInteger[] Bs(int n) => Gets(n, BigInteger.Parse);

    public void Write<T>(params T[] xs) => WriteLine(string.Join(" ", xs));
    public void Write(params object[] xs) => WriteLine(string.Join(" ", xs));
}

struct Rational : IComparable<Rational>, IEquatable<Rational>
{
    BigInteger numer;
    BigInteger denom;
    public BigInteger Numer { get { this.Reduce(); return numer; } }
    public BigInteger Denom { get { this.Reduce(); return denom; } }

    public int Sign => numer.CompareTo(0) * denom.CompareTo(0);

    public Rational(BigInteger numer, BigInteger denom)
    {
        this.numer = numer;
        this.denom = denom;
    }

    void Reduce()
    {
        if (numer == 0) { denom = 1; return; }
        var d = Gcd(numer, denom);
        numer /= d; denom /= d;
        if (denom < 0) { numer *= -1; denom *= -1; }
    }

    public Rational Invert() => new Rational(denom, numer);

    public static Rational operator -(Rational r)
        => new Rational(-r.numer, r.denom);

    public static Rational operator +(Rational left, Rational right)
    {
        left.Reduce(); right.Reduce();
        var d = Lcm(left.denom, right.denom);
        var n = left.numer * d / left.denom + right.numer * d / right.denom;
        return new Rational(n, d);
    }

    public static Rational operator *(Rational left, Rational right)
    {
        left.Reduce(); right.Reduce();
        var n = left.numer * right.numer;
        var d = left.denom * right.denom;
        return new Rational(n, d);
    }

    public static Rational operator -(Rational left, Rational right)
        => left + -right;

    public static Rational operator /(Rational left, Rational right)
        => left * right.Invert();

    public static bool operator ==(Rational left, Rational right)
        => left.Equals(right);

    public static bool operator !=(Rational left, Rational right)
        => !left.Equals(right);

    public static bool operator <(Rational left, Rational right)
        => left.CompareTo(right) < 0;

    public static bool operator >(Rational left, Rational right)
        => left.CompareTo(right) > 0;

    public static bool operator <=(Rational left, Rational right)
        => left < right || left == right;

    public static bool operator >=(Rational left, Rational right)
        => left > right || left == right;

    public static implicit operator Rational(BigInteger x)
        => new Rational(x, 1);

    public int CompareTo(Rational other) => (this - other).Sign;

    public bool Equals(Rational other)
    {
        var r = this / other;
        return r.numer == r.denom;
    }

    public override bool Equals(object obj)
    {
        if (!(obj is Rational)) return false;
        var r = (Rational)obj / this;
        return r.numer == r.denom;
    }

    public override int GetHashCode()
        => this.Numer.GetHashCode() ^ this.Denom.GetHashCode();

    public override string ToString() => $"{this.Numer} / {this.Denom}";
}

static class Extentions
{
    public static BigInteger Gcd(BigInteger x, BigInteger y)
        => BigInteger.GreatestCommonDivisor(x, y);

    public static BigInteger Lcm(BigInteger x, BigInteger y)
        => x * y / Gcd(x, y);
}

static class Program
{
    public static void Main()
    {
        var sw = new StreamWriter(OpenStandardOutput()) { NewLine = "\n" };
#if DEBUG
        sw.AutoFlush = true;
#else
        sw.AutoFlush = false;
#endif
        SetOut(sw);
        Solve(new IO());
        Out.Flush();
    }
    
    static void Solve(IO io)
    {
        var n = io.I;
        var z = io.Bs(n);

        var t = new Rational(1, 1);
        for (var i = 0; i < n - 1; i++) t = t * z[i] / z[i + 1];

        var gr = new BigInteger(1) / t;
        io.Write(gr.Numer + "/" + gr.Denom);
    }
}
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