using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Incapsulation.RationalNumbers
{
    public class Rational
    {
        public int Numerator { get; set; }
        public int Denominator { get; set; }

        #region private_methods

        private void Reduce1()
        {
            Numerator = Numerator > 0 ? Numerator : -Numerator;
            Denominator = Denominator > 0 ? Denominator : -Denominator;

            int maxval = Numerator > Denominator ? Numerator : Denominator;
            for (int i = maxval; i >= 2; maxval--)
                if (Numerator % maxval == 0 && Denominator % maxval == 0)
                {
                    Numerator /= maxval;
                    Denominator /= maxval;
                    break;
                }
        }

        private static int LowestCommonDenominator(int[] maxmin)
        {
            Array.Sort(maxmin);
            if (maxmin[1] % maxmin[0] == 0)
                return maxmin[1];

            int temp = 0;
            for (int i = 2; ; i++)
            {
                temp = maxmin[1] * i;
                if (temp % maxmin[0] == 0)
                    break;
            }
            return temp;
        }
        #endregion

        public bool IsNan
        {
            get { return Denominator != 0 ? false : true; }
        }

        public Rational(int numerator, int denominator = 1)
        {
            if (numerator == 0)
            {
                Numerator = 0;
                Denominator = 1;
            }
            else if (numerator == denominator)
            {
                Numerator = 1;
                Denominator = 1;
            }
            else if (numerator > 0 && denominator > 0 || numerator < 0 && denominator < 0)
            {
                Numerator = numerator;
                Denominator = denominator;
                Reduce1();

            }
            else if (numerator < 0 || denominator < 0)
            {
                Numerator = numerator;
                Denominator = denominator;
                Reduce1();
                Numerator *= -1;
            }
        }

        public static Rational operator +(Rational a, Rational b)
        {
            if (a.Denominator == 0 || b.Denominator == 0)
                return new Rational(1, 0);

            Rational result1 = new Rational(1), result2 = new Rational(1);
            int minDecominator = LowestCommonDenominator(new int[2] { a.Denominator, b.Denominator });
            result1.Numerator = minDecominator / a.Denominator * a.Numerator;
            result2.Numerator = minDecominator / b.Denominator * b.Numerator;
            return new Rational(result1.Numerator + result2.Numerator, minDecominator);
        }

        public static Rational operator *(Rational a, Rational b)
        {
            if (a.Denominator == 0 || b.Denominator == 0)
                return new Rational(1, 0);

            return new Rational(a.Numerator * b.Numerator, a.Denominator * b.Denominator);
        }

        public static Rational operator -(Rational a, Rational b)
        {
            if (a.Denominator == 0 || b.Denominator == 0)
                return new Rational(1, 0);

            Rational result1 = new Rational(1), result2 = new Rational(1);
            int minDecominator = LowestCommonDenominator(new int[2] { a.Denominator, b.Denominator });
            result1.Numerator = minDecominator / a.Denominator * a.Numerator;
            result2.Numerator = minDecominator / b.Denominator * b.Numerator;
            return new Rational(result1.Numerator - result2.Numerator, minDecominator);
        }

        public static Rational operator /(Rational a, Rational b)
        {
            if (a.Denominator == 0 || b.Numerator == 0 || b.Denominator == 0)
                return new Rational(1, 0);

            return new Rational(a.Numerator / b.Numerator, a.Denominator / b.Denominator);
        }

        public static explicit operator int(Rational a)
        {
            if (a.Numerator == 0 & a.Denominator == 1) return 0;

            if (a.Denominator == 0 ||
                (a.Numerator != 0 && Math.Max(a.Numerator, a.Denominator) % Math.Min(a.Numerator, a.Denominator) != 0
                || (a.Numerator < a.Denominator)))
                throw new ArgumentException();

            return (a.Numerator / a.Denominator);
        }

        public static implicit operator double(Rational a)
        {
            if (a.Denominator == 0 || a.Numerator == 0) return double.NaN;
            return (double)a.Numerator / (double)a.Denominator;
        }


        public static implicit operator Rational(int a) => new Rational(a, 1);
    }
}