[Haskell-cafe] Motivation for having indexed access in Data.Map?
sh006d3592 at blueyonder.co.uk
Sat Jan 7 14:25:31 CET 2012
On 07/01/2012 12:17, Christoph Breitkopf wrote:
> I wonder why Data.Map provides the indexed access functions:
> These functions seem rather out-of-place to me in the map api. The
> only use case I could think of so far would be to find the median, or
> in general n-th smallest key, but that does not seem sufficient reason
> (also, I think there are faster methods for that). Anything else?
I don't know the motivation in Data.Map, but here's some thoughts from a
C++ home-rolled data structures perspective...
Somewhere around a decade ago, I started an in-memory C++ multiway tree
library, initially an experiment seeing if I could improve sequential
access performance. This half-worked, but I still use the data structure
primarily because it's a bit safer in some cases than the STL
containers, and also has some extra functionality that makes it more
1. "cursor maintenance" (when I insert/delete, cursors/iterators are
not invalidated except in the special case that the cursor
references an item that is deleted. There are two tricks for this
case - the cursor will at least know that the item is deleted, plus
there are special cursors that can defer deletion (mainly for
delete-the-current-item within loops).
2. Searching based on custom "comparisons" - mainly searching based on
a partial key (certain fields), so you can find the first/last item
equal to a partial key, ignoring less significant fields.
3. Finding the first key that is *not* in the container (for unsigned
integer keys only).
4. Subscripted access - finding a given index, determining the index to
an item referenced by a cursor, stepping forward/backward by a given
number of items.
The subscripted access isn't massively useful - it was implemented
because I was curious how to handle it efficiently. However, cases do
come up from time to time in strange places. For example, sometimes it's
more convenient to store an index (into a container that won't change)
than a cursor or a full key. And using an ordered container does tend to
imply, after all, that you're interested somehow in the order (or else
why not use a hash table?).
One case, I guess, relates to DSL-generated data structures. The point
there is that when the generated code runs, the map instance is long
dead. Within the generated code, ranges etc tend to be identified by
subscript - so the DSL needs to be able to translate from key to
subscript, and (maybe) back again. OTOH, don't forget that laziness
thing - if the code generator was working from a sorted array it would
know the subscripts anyway.
A particularly surprising side-effect - along with the map, multimap,
set and multiset wrappers, I have a vector wrapper. When you have a huge
array and do lots of inserts and deletes within that array, a multiway
tree (with subscripted access) turns out to be a good trade-off. Some
accesses are more awkward (because the items aren't all contiguous in
memory), but the log-time inserts and deletes can be worth it.
The first-key-not-in-the-container stuff was mostly a side-effect of the
data structure augmentation I did for subscripted access. That is very
convenient, but with costs.
The no. 1 killer feature that keeps me using and maintaining this
library is the partial-key search thing. This is so useful, I even added
a feature to a DSL (used mainly for AST nodes and multiple dispatch -
originally based on treecc) to make it more convenient to generate
The cursor maintenance makes it a lot easier to write algorithms that
update the container, but it's perhaps surprising how rare that's necessary.
The issue with all this is of course partly overhead, but also because I
got lazy - keeping these things hanging around throughout whole program
runs like cheap second-rate databases. They are quite convenient to work
with, but for a long time I stopped even considering pulling all the
data out into a flat array, processing it there, then rebuilding a new
indexed data structure only if I really needed it, or keeping data
mostly in an array and sorting it ready for binary searches just at the
key point where that's needed.
Some programs I've written using them are maybe an order of magnitude
slower than they should be, and in quite a few cases there's an
asymptotic difference, not just a constant factor - a lot of algorithms
are O(n log n) where without the convenience containers they could be O(n).
Very little of this would be relevant in a pure functional programming
world, of course, but anyway - yes, subscripting can be (occasionally)
useful. It's just hard to give specific examples, because they're buried
in all the technicalities of quite large programs.
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