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Subject: [boost] More on augmented trees
From: Phil Endecott (spam_from_boost_dev_at_[hidden])
Date: 2012-11-27 12:52:49

Dear All,

A while ago I posted a question about augmented trees:

There has also been other discussion recently in this thread:

Unfortunately I have been manically bug-hunting for the last few weeks
[*] and wasn't able to follow-up properly until now. Here are my thoughts:

I'm aware of 3 applications for augmented trees:
- O(log N) indexing, insertion and deletion; "best of list and vector"
(i.e. Countertree).
- Similar where the "value" of each node is variable, so one can
accumulate over any range in O(log N) time (i.e. stl_ext_adv).
- Interval trees.

In the first two cases, the augmented value is the sum of the augmented
values in the sub-nodes. In the last case, it's the maximum of them.

Is anyone aware of any other applications that are not not very similar
to those, e.g. where the augmentation is some other function of the sub-nodes?

Question: with only three (or two, if the first is considered a special
case of the second) different kinds of augmentation, is it worthwhile
to try to distil out a generic augmented tree?

Here is an interesting augmented tree implementation that attempts to
be generic:

This seems to work by exposing the tree structure in the iterator (i.e.
the iterator has parent(), left() and right() methods that return other
iterators), and by requiring a Customization class that is called to
updated augmented data in a node when its children change.

This looks to me to be a sensible approach, but I'm still not sure that
it's better than just copy-and-paste when there are only two (or three)
useful ways to apply it.

Thoughts anyone?

Regards, Phil.

[*] My recent bug-hunting has really made me value the ease of working
with open-source code like Boost. What might take 5 minutes with grep
instead takes weeks of back-and-forth with "technical support" (or
reverse-engineering with a disassembler) - literally 3 orders of
magnitude less efficient.

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