Invert Method

[zsiegel92]

Hey there,

I added an "Invert" method that takes a subset of {1,...,n} as a list, and returns the index of that subset amongst the k-subsets of {1,...,n} in lexicographic order. That is the order in which your generateSubset method generates subsets, so this function is indeed an inverse.

I also changed print statements to be compatible with Python 3.

[zsiegel92]

Hey, I've added an algebraically-generated inversion function. You can include the following as a method of the EnumeratedSubset class.

	def algebraicInvert(self,n,l):
		k=len(l)
		l.sort()
		return  self.choose(n,k) - self.choose(n-l[0],k) + sum([self.choose(n-l[i-1]-1,k-i) - self.choose(n-l[i],k-i) for i in range(1,k)]

This takes an integer n and a subset of {1,...,n}, given as Python list l. It returns the lexicographic index of the subset l.

That is,

a= EnumeratedSubsets()
l = a.generateSubsets(n,k,i)
print(a.algebraicInvert(n,l)) #prints i

prints i.