Arrays and Permutations::Looking for Function

OctoberAsh

Greetings:

I'm helping code a php site that takes six arrays each having up to seven elements, and finds every possible combination of those arrays.

For background, this is going to be used for a basketball tourney (5 players and an alt makes 1 team) with each player having seven attributes (player age, height, experience, etc.)

What's needed is a way to get all possible combinations with one player from each team, and then to take those combinations and rank them according to a set of rules (like "team with the most years experience", "team with the shortest players", "team with highest average age", et al.)

There are two 'catches': 1) not all teams have six members, and 2) not all attributes of the players will be known ahead of time.

Does anyone know of a function (or may have had to write something similar) that can take multiple, differently-sized arrays, calculate all possible permutations, and place the resulting combinations in a third array without using nested loops?

If not, any insight into the easiest way to accomplish this would be helpful. I'm looking for ideas here, not finished code...any assistance would be greatly appreciated!

drawmack

discrete mathematics will help with this, dig around on some of those sites for an algorithm.

OctoberAsh

I've done some searching on discrete mathematics, but all seem to point to a single array and computing all possible permutations of its elements. I had hoped to find someone who had to do this sort of thing with multiple non-equal arrays. I guess it could be that no one's ever bothered to 'functionize' this because it rarely has to be invoked outside of the hard sciences.

I started trying to code this with nested cursors in SQL, but they're even more horridly ugly in SQL than 6-deep nested loops in php. Add to that the huge numbers of permutations in even small array sets, and I'm starting to think that I may have to resort to finding a used Cray to build this site!

I'll keep looking, though - thanks for the suggestion!

drawmack

There are well over a billion combinations here, discrete math will give you the formulas for exactly how many permutations there are, but it involves factorials.

OctoberAsh

12 million plus combinations... n!/[(n-k)!k!]. The formula for figuring out how many permutations there are I have, I was looking for programming approaches that keep the code simple and straightforward without resorting to just a series of nested loops.

Still no luck, but I'll keep looking.