namespace SimpleRational
{
    public class Rational
    {
        private int _numerator = 0;
        private int _denominator = 1;

        // コンストラクタ
        public Rational(int int_value)
        {
            set(int_value, 1);
        }

        public Rational(int new_numerator, int new_denominator)
        {
            set(new_numerator, new_denominator);
        }

        // アクセサ
        public void set(int new_numerator, int new_denominator)
        {
            if (new_denominator == 0)
            {
                throw new ArithmeticException("Denominator must not be 0");
            }

            _numerator = new_numerator;
            _denominator = new_denominator;
        }

        public int numerator()
        {
            return _numerator;
        }

        public void numerator(int new_numerator)
        {
            _numerator = new_numerator;
        }

        public int denominator()
        {
            return _denominator;
        }

        public void denominator(int new_denominator)
        {
            if (new_denominator == 0)
            {
                throw new ArithmeticException("Denominator must not be 0");
            }
            _denominator = new_denominator;
        }

        // ---------- 補助関数 ----------

        // 最大公約数
        public static int gcd(int v1, int v2)
        {
            int tmp;

            // どちらかが0だったら即座に終了
            if (v1 == 0 || v2 == 0) return 0;

            // 正の値にしておく
            if (v1 < 0) v1 = -v1;
            if (v2 < 0) v2 = -v2;

            // v1の方を大きくしておく
            if (v2 > v1)
            {
                tmp = v1; v1 = v2; v2 = tmp;
            }

            for (; ; )
            {
                tmp = v1 % v2;
                if (tmp == 0) return v2;

                v1 = v2; v2 = tmp;
            }
        }

        // 通分する
        private void _fix_denominator(Rational other)
        {
            int tmp = _denominator;
            _numerator *= other._denominator;
            _denominator *= other._denominator;

            other._numerator *= tmp;
            other._denominator *= tmp;
        }

        // 正規化
        // ●分子・分母を約分する
        // ●負の符号が分母についている場合、分子にのみつけるようにする
        // ●値が0である場合は「0/1」にする
        private void _regularize()
        {
            int divisor = Math.Sign(_denominator) * gcd(_numerator, _denominator);
            if (divisor == 0)
            {
                // 分子が0の場合
                _numerator = 0;
                _denominator = 1;
            }
            else
            {
                _numerator /= divisor;
                _denominator /= divisor;
            }
        }

        // ---------- 比較 ----------

        public static bool operator ==(Rational r1, Rational r2)
        {
            r1._regularize();
            r2._regularize();
            return (r1._numerator == r2._numerator && r1._denominator == r2._denominator);
        }

        public static bool operator !=(Rational r1, Rational r2)
        {
            return (r1 != r2);
        }

        public static bool operator <(Rational r1, Rational r2)
        {
            r1._fix_denominator(r2);
            return (r1.numerator() < r2.numerator());
        }

        public static bool operator >(Rational r1, Rational r2)
        {
            return (r2 < r1);
        }

        // 以下、他の関数やクラスに使ってもらう際の補助関数
        public override bool Equals(object obj)
        {
            if (obj.GetType() == this.GetType())
            {
                return (this == (Rational)obj);
            }

            return false;
        }

        public override int GetHashCode()
        {
            return (_numerator | (_denominator << 16));
        }

        // ---------- 型変換 ----------

        public static explicit operator double(Rational r)
        {
            return (double)r._numerator / (double)r._denominator;
        }

        public static explicit operator float(Rational r)
        {
            return (float)r._numerator / (float)r._denominator;
        }

        // ---------- 加減乗除 ----------

        public static Rational operator +(Rational r) // 単項演算子
        {
            // 単に自分のコピーを作ればよい
            return new Rational(r._numerator, r._denominator);
        }

        public static Rational operator -(Rational r) // 単項演算子
        {
            return new Rational(-r._numerator, r._denominator);
        }

        public static Rational operator +(Rational r1, Rational r2) // 二項演算子
        {
            r1._fix_denominator(r2);
            return new Rational(r1._numerator + r2._numerator, r1._denominator);
        }

        public static Rational operator -(Rational r1, Rational r2) // 二項演算子
        {
            r1._fix_denominator(r2);
            return new Rational(r1._numerator - r2._numerator, r1._denominator);
        }

        public static Rational operator *(Rational r1, Rational r2)
        {
            return new Rational(r1._numerator * r2._numerator, r1._denominator * r2._denominator);
        }

        public static Rational operator /(Rational r1, Rational r2)
        {
            if (r2._numerator == 0)
            {
                throw new DivideByZeroException();
            }
            return new Rational(r1._numerator * r2._denominator, r1._denominator * r2._numerator);
        }

        // ユーティリティ
        public override string ToString()
        {
            _regularize();
            if (_denominator == 1) return _numerator.ToString();

            return string.Format("({0}/{1})", _numerator, _denominator);
        }
    }
}