Keeping track of the N largest values

[Dan Stromberg]

On Sat, Dec 25, 2010 at 7:42 AM, Roy Smith <roy at panix.com> wrote:
> I'm processing a stream of N numbers and want to keep track of the K
> largest.  There's too many numbers in the stream (i.e. N is too large)
> to keep in memory at once.  K is small (100 would be typical).
>
> >From a theoretical point of view, I should be able to do this in N log K
> time.  What I'm doing now is essentially:
>
> top = [-1]    # Assume all x are >= 0
> for x in input():
>    if x <= top[0]:
>        continue
>    top.append(x)
>    if len(top) > K:
>        top.sort()
>        top.pop(0)
>
> I can see pathological cases (say, all input values the same) where
> running time would be N K log K, but on average (N >> K and random
> distribution of values), this should be pretty close to N.
>
> Is there a better way to do this, either from a theoretical running time
> point of view, or just a nicer way to code this in Python?
> --
> http://mail.python.org/mailman/listinfo/python-list
>

heapq is probably fine, but I've empirically found a treap faster than
a heap under some conditions:

http://stromberg.dnsalias.org/~strombrg/treap/
http://stromberg.dnsalias.org/~strombrg/highest/