How can I pair socks from a pile efficiently?

Question

Yesterday I was pairing the socks from the clean laundry and figured out the way I was doing it is not very efficient. I was doing a naive search — picking one sock and

Answer 1

My solution does not exactly correspond to your requirements, as it formally requires O(n) "extra" space. However, considering my conditions it is very efficient in my practical application. Thus I think it should be interesting.

Combine with Other Task

The special condition in my case is that I don't use drying machine, just hang my cloths on an ordinary cloth dryer. Hanging cloths requires O(n) operations (by the way, I always consider bin packing problem here) and the problem by its nature requires the linear "extra" space. When I take a new sock from the bucket I to try hang it next to its pair if the pair is already hung. If its a sock from a new pair I leave some space next to it.

Oracle Machine is Better ;-)

It obviously requires some extra work to check if there is the matching sock already hanging somewhere and it would render solution O(n^2) with coefficient about 1/2 for a computer. But in this case the "human factor" is actually an advantage -- I usually can very quickly (almost O(1)) identify the matching sock if it was already hung (probably some imperceptible in-brain caching is involved) -- consider it a kind of limited "oracle" as in Oracle Machine ;-) We, the humans have these advantages over digital machines in some cases ;-)

Have it Almost O(n)!

Thus connecting the problem of pairing socks with the problem of hanging cloths I get O(n) "extra space" for free, and have a solution that is about O(n) in time, requires just a little more work than simple hanging cloths and allows to immediately access complete pair of socks even in a very bad Monday morning... ;-)