Fast Sequences

[Ross Paterson]

On Thu, Mar 30, 2006 at 04:08:23PM -0500, Jim Apple wrote:
> On 3/27/06, Ross Paterson <ross at soi.city.ac.uk> wrote:
> > On Sun, Mar 26, 2006 at 10:54:59PM -0500, Jim Apple wrote:
> > > How about
> > >
> > > (flip index i) . reverse
> > >
> > > Is that O(i)?
> >
> > index i is O(log(min(i,n-i))), because the index operation skips many
> > subtrees on the way.  This skipping will also mean that putting a
> > reverse first won't change the big-O complexity.
> 
> Ok, so, let my try once more:
> 
> Are there any operations f such that f . reverse has a worse big-O
> time bound than f does alone?

The big-O will be the same in all cases, but the constant factor will
be a little larger, because reverse does a constant amount of work on
each node, if that node is demanded.