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Comment by torusle | Hacker News Reader

"I could only find a couple tutorials/guides and both were imperative"

Aren't Quadtrees covered by almost all basic data-structure books? It is the most simple form of taking the binary tree into the next (2D) dimension.

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The problem is rather, that most data structure tutorials and books don't even get the idea, to introduce a purely functional version, but merely state the imperative versions. Coming up with the functional versions of data structures can be difficult. Papers about it can be hard to understand and often require one to already know some niche language, that a researcher used for the paper. Even if you can find a functional implementation of a data structure, there is often not a good explanation and you need to, sort of, reverse engineer it and translate it to the language you are using.

In short, it seems relatively few people have the skills to implement them and even fewer have the skills to come up with functional versions of ordinary data structures. They are almost completely absent from university lectures as well, as far as I am aware. For example for AVL trees I could only find a document from ETH from a lecture, that no longer exists or is taught. The language is Isabel and I need to understand its syntax first, before being able to translate it to Scheme.

If anyone has an obscure source for implementations one can learn from and implement oneself in another language, please share.

I've been looking for the same for scheme and clojure. Here are a few I've found:

Functional Data Structures and Algorithms, A Proof Assistant Approach by Tobias Nipkow (Ed.) [https://fdsa-book.net/functional_data_structures_algorithms....]

Purely Functional Data Structures thesis by Chris Okasaki [https://www.cs.cmu.edu/~rwh/students/okasaki.pdf]

https://en.wikipedia.org/wiki/Purely_functional_data_structu...

[1] are the exercises with solutions (!) of a lecture [2] at ETH Zurich, which include AVL trees in Isabel. The whole list of exercise PDFs is at [3]. I started porting the AVL trees to Scheme [4], but lately have not worked more on this. I also try to make it easy to understand the implementation by providing explanatory comments.

[1]: https://archiv.infsec.ethz.ch/education/permanent/csmr/exerc...

[2]: https://archiv.infsec.ethz.ch/education/permanent/csmr.html

[3]: https://archiv.infsec.ethz.ch/education/permanent/csmr/exerc...

[4]: https://codeberg.org/ZelphirKaltstahl/guile-data-structures/...

Okasaki's is basically the Bible for this stuff. Anyone writing data structure libraries in a functional language will have read this or have it on their to-read list.

I have the book, but it also doesn't contain that many data structures. Some of the maybe most used (AVL tree?) are not in there.

Not all exercises have solutions. I get stuck on some exercise and have a hard time finding solutions to them, that I can compare with my implementations in Scheme. Not being a Haskell user (yet), I also have some issues translating Haskell to Scheme. In languages like Haskell one often controls flow by pattern matching on type. In Scheme one needs to make structures or records explicitly and use their predicates to explicitly check the type. It's all possible, but not exactly great for learning. Sort of the road has many sticks and stones to stumble.

You can even build them with basically one line of code by sorting points using Morton / Z-curve order. It's linear time if you use a counting/radix sort.

Edit: lol, downvoted for this post. Never change, HN.

I'd love to see that. Could you link me to an implementation or explain this in more detail please?

Here's a 3D version used in the creation of sparse voxel octrees:

https://forceflow.be/2013/10/07/morton-encodingdecoding-thro...

Here's an example from AWS, where lat/long pairs are put into a Z-index, which is used as a DynamoDB sort key, letting you efficiently query for items near a point.

https://aws.amazon.com/blogs/database/z-order-indexing-for-m...

I would like to know about this more, too. Is there a code anywhere, ideally with comments? But I am fine without comments, too, I would just like to see the code and possibly with an example usage.

Okay, I was intrigued and I did some digging. Morton / Z-order is all about interleaving the individual bits of the x and y coordinates. You end up grouping by quadrants. Python one liner:

    points.sort(key=lambda p: sum(((p[0]>>i&1)<<(2*i))|((p[1]>>i&1)<<(2*i+1)) for i in range(16)))

Yeah good point, they are downsides for sure but it's a simple enough approach and most of all it can be shoved in a database (or b-tree or any 1d-sorted data structure).

And for a z-curve, the order is basically a depth-first traversal of a quadtree.

It’s super easy to click the downvote button by accident on mobile when you meant to upvote. And this UI will never be fixed because this is HN after all.

I just implemented an HN UI. This is good feedback as I'm aiming to have a mobile friendly web version.

https://proc0.github.io/HackerZen (it's also open source)

This is precisely the reason that I do not log in to HN on my phone. My phone is read-only and if I want to upvote or comment then I have to switch to my laptop. Pretty easy with firefox because I can send tabs to other devices.

Zoom in or unvote/revote

That is why I like harmonic app, there is an invite button separating the upvote and downvote. Never going to have this kind of issue

This is true, however you can see if you downvoted by the "undown" link displayed instead of "unvote".

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