# density for the _number_ of rolled exploding dices (starting with count), with rerolls
# and up to maxexplode explosions
class ExplodingDieNumberDensity < Density
  def initialize(max,rerolls=[],count=1,maxexplode=10)
    super(0)
    @d.delete(0)
    @uniform=false

    if (rerolls.include?max)
      n=max - rerolls.size + 1
      @d[1]=Rational(n-1,n)
      for k in (2..maxexplode) do
        for r in (1..(k-1)) do
          @d[k]+=Rational(@d[r]*@d[k-r],n)
        end
      end
      @d[maxexplode+1]=1-@d.inject(:+)
    else
      n=max - rerolls.size
      for k in (1..maxexplode) do
        @d[k]=Rational(n-1,n**k)
      end
      @d[maxexplode+1]=Rational(1,n**(e-1))
    end

    self=([z]*count).inject(:+)
    # if we only limit the explosions of individual dices don't do the following command:
    delete_if { |k,v| k > maxexplode + 1}
  end
end