/// <summary>
/// https://projecteuler.net/problem=73
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result CountingFractionsInRange(Problem arguments)
{
var d = arguments.IntNumber;
var bounds = arguments.ListOfNumbers;
var begin = new UtilityMath.Fraction(bounds[0], bounds[1]);
var end = new UtilityMath.Fraction(bounds[2], bounds[3]);
var list = UtilityMath.GenerateFareySequence(d);
var count = list.Count(fraction => fraction > begin && fraction < end);
var answer = count.ToString();
var message = string.Format("The number of fractions lie between {0} and {1} in the sorted set of reduced proper fractions for d ≤ {2} is {3}.", begin.ToString(), end.ToString(), d, answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=71
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result OrderedFractions(Problem arguments)
{
var integers = arguments.ListOfNumbers;
var key = new UtilityMath.Fraction(integers[0], integers[1]);
var d = arguments.IntNumber;
var sort_list = UtilityMath.GetReducedProperFractions(d, key, true).ToList();
string answer = sort_list[0].Numerator.ToString();
var message = string.Format("The numerator of the fraction immediately to the left of {0} is {1}.", key.ToString(), answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}