Recursion can be difficult to understand even in c or a functional programming language. Sticking a [print] in various stages should help visualization. Here's how I'd describe it:
Input list. Split it in half – [>> 1]-[list split] – and send the left side for processing first and the right side last. Depth-first ensures that all of the left-side processing will happen before any of the right side. Keep splitting and sending left sides until a list arrives whose length is less than 2 – [list split 2] at the top. If it is, it's either an empty list or a singleton, so it doesn't need to be processed further – [spigot] – and we can send it out (filtering out any empty lists). Then the right side of the most recent list to be sent in for processing (let's name that list Greg) is sent for processing, and when Greg's right side has all been split and output, then the right side of Greg's parent list can be sent.
As with most binary procedures you could graph the process as a simple binary tree where the root node represents the initial list and daughter nodes are the left and right halves of lists that have been split. Traversing the tree means that when you get to a node you haven't visited yet, always take the left side of the fork first to get to the next level down. When you return to that node you can then take the right side of the fork. Once you've taken both paths all the way to the branches you can go back up a level. Continue this until you've taken both branches of the root node.
The [>> 1] isn't just to avoid a stack overflow – splitting the lists as close as possible to half also happens to be the fastest way of going about the recursion. It's one of the reasons quick sort is still one of the fastest available sorts.
On Oct 5, 2015 3:16 AM, "Jonathan Wilkes" jancsika@yahoo.com wrote:
Yes that's true about iterative approaches and dataflow in general.
What gets me about [list-drip] is the necessity of the [>> 1] to prevent stack overflow. So even if you can follow the order of operations with recursion through that object chain, you have to also keep track of the order in which those two branches interact during the recursion.
I can visualize that using a small set of data to the inlet, and taking my time. But at that point the diagram itself isn't elucidating anything useful about the flow of data. For that you'd need some way to animate the flow through the wires in greater than zero logical time. And even then you'd want to show the actual data associated with each cycle of animation.
-Jonathan
On Monday, October 5, 2015 1:59 AM, Matt Barber brbrofsvl@gmail.com wrote:
Not supporting recursion in a dataflow environment is not a huge problem IMO, especially since so many classically recursive problems (binary search, quick sort, etc.) can be solved iteratively. The iterative solution is almost always going to be clearer in an environment like Pd.
[list-drip] is a decent model for how recursion would have to work -- [list-rdrip] even more, since it can take advantage of the native right-to-left output to reduce the number of objects. Anything solved using a divide-and-conquer strategy could even be a bit faster using the stack vs. an until loop. A while back I made a kind of clunky iterative quick sort; I wonder if it would be possible to throw ranges to partition onto Pd's stack without it overflowing ... probably not since there's nothing to guarantee that quick sort doesn't run at O(n^2) in the worst case. Binary search almost certainly could; I'll do that in the next few days and post benchmarks comparing an [until] loop solution with recursion.
On Sun, Oct 4, 2015 at 4:12 PM, Jonathan Wilkes jancsika@yahoo.com wrote:
I think matju wrote the [list-drip] algorithm partly to show the difficulty of using recursion in Pd. That the actual author of Pd's messaging system refrains from using recursion to solve the same problem adds weight to that point.
-Jonathan
On Sunday, October 4, 2015 3:45 PM, Matt Barber brbrofsvl@gmail.com wrote:
It takes almost a full second to output a list of n=1,000,000 with a 100-cycle until on my computer.
On Sun, Oct 4, 2015 at 3:38 PM, Matt Barber brbrofsvl@gmail.com wrote:
This is still much slower than [list-drip], and it freezes Pd for me when I get up to lists of n=100,000 or so. I think it's because Pd has to copy the list to an output every cycle of [until], so when n=10, you're only outputting something of size 10 10 times, but that grows by n^2 so when it's n=10,000 times 10,000 outputs, it's a lot. 1,000,000 seems impossible unless the list decreases in size each cycle, which it does in [list-drip], recursively.
On Sun, Oct 4, 2015 at 2:48 PM, Miller Puckette msp@ucsd.edu wrote:
Here's a way to serialize a list in (I believe) linear time:
#N canvas 881 291 450 300 10; #X msg 136 14 list 3 . 1 4 1 5 9; #X obj 83 97 list length; #X obj 77 211 list split; #X obj 101 186 list; #X obj 139 55 t l b l; #X obj 83 119 until; #X obj 83 141 f; #X obj 114 142 + 1; #X msg 166 117 0; #X obj 83 163 t b f; #X obj 117 278 print; #X obj 116 250 list split 1; #X connect 0 0 4 0; #X connect 1 0 5 0; #X connect 2 1 11 0; #X connect 3 0 2 0; #X connect 4 0 1 0; #X connect 4 1 8 0; #X connect 4 2 3 1; #X connect 5 0 6 0; #X connect 6 0 7 0; #X connect 6 0 9 0; #X connect 7 0 6 1; #X connect 8 0 6 1; #X connect 9 0 3 0; #X connect 9 1 2 1; #X connect 11 0 10 0;
cheers Miller
On Sun, Oct 04, 2015 at 02:27:37PM -0400, Matt Barber wrote:
Your [pd drip] does a lot of extra work. It's go basically linear stack performance, and you're recopying the list every loop (an until loop
would
solve this for a little extra cpu time). The secret of [list-drip] is
that
it doesn't recopy the list using the [list] object, and it avoids stack overflows by doing the recursion split at the midpoint of the list and
only
outputting when it's done the binary split down to lists of size 1, which are the elements, or size zero, which are bangs (and which are filtered out).
Since it's binary recursion on the list, the stack only grows proportionally to log_2(n), which is about 20 for n=1,000,000. It's still going to be slower than an object written in C that can just iterate over the contents in a single loop, and lists in Pd are slower in general than arrays, so an until loop and tabread over an array is going to be
quicker.
It is much slower for copying though -- an until loop with tabread and tabwrite has way more overhead than an [array get]-[array set] pair.
On Sun, Oct 4, 2015 at 1:06 PM, Christof Ressi christof.ressi@gmx.at wrote:
Please don't use the previous version of the multi-dimensional
arrays!!!
First, I forget to get rid of one [drip] object. Second, I discovered
that
[pd drip] will create a stack overflow if there are more than ca. 300 elements! (Why???) So I replaced it with [list-drip] which works fine.
So here's the corrected pure vanilla version + a zexy version using [drip]. I prefer to use the latter one because it's waaaaay faster
than all
the drip abstractions based on [list split].
Vanilla:
https://www.dropbox.com/s/wd0avxtaneqgdic/carray_vanilla.zip?dl=0
Zexy: https://www.dropbox.com/s/ea8kihwbdqhcajr/carray_zexy.zip?dl=0
Christof
PS: I did a benchmark test of iterating through an array of 1 million elements, using [realtime], and here's what I found on my system:
[array get] + [drip] --> ca. 6.5-9ms [until] + [tabread] --> ca. 120-200ms [array get] + [list-drip] --> ca. 340-400ms
To me this result was a bit surprising...
You can test yourself with the attached patch. *Gesendet:* Sonntag, 04. Oktober 2015 um 17:32 Uhr *Von:* "Christof Ressi" christof.ressi@gmx.at *An:* "Matt Barber" brbrofsvl@gmail.com
*Cc:* Pd-List pd-list@lists.iem.at *Betreff:* Re: [PD] array-abs Wow, looks cool!
Just a few days ago I reworked some of my personal table abstractions, which also make use of the [array] object. However, some of them
depend on
zexy externals (I hope I didn't miss any other dependencies). I haven't shared them yet so the documentation is quite poor (no help files, docs inside the abstraction) and they look a bit messy. But maybe you can
get
some inspiration for your library... https://www.dropbox.com/s/xvj031korqw8guf/ctab-abs.zip?dl=0
Additionally I've been working on three basic abstractions for
creating,
setting and reading multi-dimensional arrays of any number of
dimensions.
They are pure vanilla style and even come with a help file :-D. (a
object
for array resizing is yet to be done...) https://www.dropbox.com/s/6xfgdyt697138e6/carray.zip?dl=0
Would be cool to hear your opinion on the multi-dimensional array
stuff!
Christof
*Gesendet:* Samstag, 03. Oktober 2015 um 22:32 Uhr *Von:* "Matt Barber" brbrofsvl@gmail.com *An:* "IOhannes m zmölnig" zmoelnig@iem.at *Cc:* Pd-List pd-list@lists.iem.at *Betreff:* Re: [PD] array-abs Thanks.
Yes. Right now I'm just looking to see if these would be useful, if there's anything awful about the syntax, if they try to do too much or
are
too fussy, if anyone would want to contribute, etc. When I get them polished a bit I'll do a regular release on the normal channels (I
can't
remember if I have access to anything officially Pd related).
Matt
On Sat, Oct 3, 2015 at 4:22 PM, IOhannes m zmölnig zmoelnig@iem.at wrote:
hi,
great!
On 10/03/2015 07:36 PM, Matt Barber wrote:
https://www.dropbox.com/s/45tk62dpz0z2mqo/array-abs.zip?dl=0
db?
would you like to put those on a version control system of sorts, e.g. the puredata svn or some publicly available git repository (e.g.
github)?
(read as: please let us not go back to the dark ages, where code was shared by sending files around by on floppy disks and you never new which version was the current one)
fgmards IOhannes
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