Permutations of subsets and subsequent run-time analysis

Question

I have 2 questions:

1. I would like to generate the permutations of subsets eg There are 20 possible amino acids and 5 positions where they can occur. What are the total permutations that can occur (in text)

2. Once I have this list of permutations certain values will be assinged to each one and I would like to look up any given permutation at run time. The first idea that comes to mind is a look-up table, but I was wondering if there might be a better way of doing this.

Answer 1

1. You want combinations of length 5, not permutations. This is a standard problem, which can be solved with recursion. Use CombinationGenerator if you don't want to write it yourself.

2. Number the combinations using base 20 (not to be confused with the chemical definition of base). Use a hashtable if you'll be storing data for a limited subset of combinations, or a look-up array if you'll be most of them.