Finding the index of a given permutation

Question

I\'m reading the numbers 0, 1, ..., (N - 1) one by one in some order. My goal is to find the lexicography index of this given permutation, using only O(1)

Answer 1

Here is a way to do it if you want to assume that arithmetic operations are constant time:

def permutationIndex(numbers):
  n=len(numbers)
  result=0
  j=0
  while j

I've purposefully written out certain calculations that could be done more simply using some Python built-in operations, but I wanted to make it more obvious that no extra non-constant amount of space was being used.

As maxim1000 noted, the number of bits required to represent the result will grow quickly as n increases, so eventually big integers will be required, which no longer have constant-time arithmetic, but I think this code addresses the spirit of your question.