What's the quickest way to find all possible pairs in list?

Question

Basically I have list of players, and I want to pair them up so that each player will play everyone once. What\'s the quickest way to find this data?

Answer 1

A simple divide and conquer algorithm:

1. If there are only two people: Pair them and return them.

2. Otherwise:

   1. Split the group in two groups of equal size.
   2. Find all pairings in each group using this algorithm recursively.

   3. Join the two lists.

      E.g. [[(a,b)]] and [[(c,d)]] becomes [[(a,b),(c,d)]].

   4. Find pairs across of the two groups, by rotating group two.

      E.g. [[(a,c),(b,d)],[(a,d),(b,c)]]

   5. Return (3) + (4)

This algorithm runs in O(n^2) time, which is optimal, as it generates (n-1) rounds of n/2 pairings.

For eight players you would get 7 rounds:

[(a,b), (c,d), (e,f), (g,h)]
[(a,c), (b,d), (e,g), (f,h)]
[(a,d), (b,c), (e,h), (f,g)]
[(a,e), (b,f), (c,g), (e,h)]
[(a,f), (b,g), (c,h), (e,e)]
[(a,g), (b,h), (c,e), (e,f)]
[(a,h), (b,e), (c,f), (e,g)]