Compute rank of a combination?

Question

I want to pre-compute some values for each combination in a set of combinations. For example, when choosing 3 numbers from 0 to 12, I\'ll compute some value for each one:

Answer 1

I would suggest a specialised hash table. The hash for a combination should be the exclusive-or of the hashes for the values. Hashes for values are basically random bit-patterns.

You could code the table to cope with collisions, but it should be fairly easy to derive a minimal perfect hash scheme - one where no two three-item combinations give the same hash value, and where the hash-size and table-size are kept to a minimum.

This is basically Zobrist hashing - think of a "move" as adding or removing one item of the combination.

EDIT

The reason to use a hash table is that the lookup performance O(n) where n is the number of items in the combination (assuming no collisions). Calculating lexicographical indexes into the combinations is significantly slower, IIRC.

The downside is obviously the up-front work done to generate the table.