static long distinctCount(IEnumerable <long> source, long length, long remaining, long skippable)
{
if (skippable < 0L)
{
return(0L);
}
if (skippable == 0L)
{
return(Combinatoric.Multinomial(source));
}
var count = source.First();
if (count >= length)
{
return(remaining.Power((int)length));
}
var others = source.Skip(1);
var result = distinctCount(others, length, remaining - 1L, skippable - count);
for (var x = 1L; x <= count; x++)
{
var temp = distinctCount(others, length - x, remaining - 1L, skippable + x - count);
result = checked (result + Combinatoric.Choose(length, x) * temp);
}
return(result);
}
public static void Multinomial()
{
//this example shows how to get multinomial
//use Combinatoric.Multinomial(collection_of_x) to get multinomial
Console.WriteLine(Combinatoric.Multinomial(new[] { 1, 4, 4, 2 }));
}
public static void Choose()
{
//this example shows how to get binomial
//use Combinatoric.Choose(n, k) for n!/(k!*(n-k)!)
Console.WriteLine(Combinatoric.Choose(10, 5));
}
public static void FallingFactorial()
{
//this example shows how to get falling factorial
//use Combinatoric.FallingFactorial(n, r) for n!/r!
Console.WriteLine(Combinatoric.FallingFactorial(10, 5));
}
public static void Factorial()
{
//this example shows how to get factorial
//use Combinatoric.Factorial(n) for n!
Console.WriteLine(Combinatoric.Factorial(10));
}
//constructors
//static methods
static long count(IEnumerable <T> source, int length, CombinatoricModel model)
{
switch (model)
{
case CombinatoricModel.Normal:
return(Combinatoric.FallingFactorial((long)source.Count(), length));
case CombinatoricModel.Repetition:
return(((long)source.Count()).Power(length));
case CombinatoricModel.Distinct:
var lookup = source.ToLookup(x => x);
return(distinctCount(lookup.Select(x => x.LongCount()).OrderBy(x => x).ToList(), length, lookup.Count, source.Count() - length));
case CombinatoricModel.RepetitionDistinct:
return(source.Distinct().LongCount().Power(length));
default:
return(0L);
}
}
static long count(IEnumerable <T> source)
{
var length = source.Count() - 1L;
return(Combinatoric.Choose(2L * length, length) / (length + 1L));
}