Skip to main content

Rose Forests

Carl Masak blogged about tree data structures, which caught my interest because of a pet-project of mine (tailor; a structure description and measurement tool) where I found myself using trees a lot. An awful lot. Perhaps ... too much.

Anyway, a related tweet by AudreyT mentioned an article called "Origami Programming" by Jeremy Gibbons. Which is in haskell (perhaps not surprisingly), a language I don't speak very well. However, while reading - and not understanding it - I did get one thing which was the idea of having a tree datatype where the node (called a 'rose') references a forest (a list of roses). I think that's right.

In any case, it solves a object-modelling problem for me that I had. The difficulty was that protein structures are hierarchical, yes, but have a strange mixed hierarchy of types. Perhaps this is obvious to haskell programmers and compiler-code writers, but this makes it very difficult to use the 'simple' tree datatype, where a Node class has a List of Node children.

Specifically, I mean situations like: a Chain composed of Atoms or a Chain of SSEs of Residues of Atoms. The 'rose tree' way of doing things makes this possible, at the price of a more complex model. Now here is a picture of a sketch of it:

So, for example, you can have a Protein:ChainList(Chain:AtomList(Atom),Chain:ResidueList(Residue...)) or several other possibilities. Also a visitor to the hierarchy can do separate things to a Tree than to a LeafList. Neat! Oh, and the code for the implementation (just the bare bones, not usable) is here.


Popular posts from this blog

How many isomers of C4H11N are there?

One of the most popular queries that lands people at this blog is about the isomers of C4H11N - which I suspect may be some kind of organic chemistry question on student homework. In any case, this post will describe how to find all members of a small space like this by hand rather than using software.

Firstly, lets connect all the hydrogens to the heavy atoms (C and N, in this case). For example:

Now eleven hydrogens can be distributed among these five heavy atoms in various ways. In fact this is the problem of partitioning a number into a list of other numbers which I've talked about before. These partitions and (possible) fragment lists are shown here:

One thing to notice is that all partitions have to have 5 parts - even if one of those parts is 0. That's not strictly a partition anymore, but never mind. The other important point is that some of the partitions lead to multiple fragment lists - [3, 3, 2, 2, 1] could have a CH+NH2 or an NH+CH2.

The final step is to connect u…

Havel-Hakimi Algorithm for Generating Graphs from Degree Sequences

A degree sequence is an ordered list of degrees for the vertices of a graph. For example, here are some graphs and their degree sequences:

Clearly, each graph has only one degree sequence, but the reverse is not true - one degree sequence can correspond to many graphs. Finally, an ordered sequence of numbers (d1 >= d2 >= ... >= dn > 0) may not be the degree sequence of a graph - in other words, it is not graphical.

The Havel-Hakimi (HH) theorem gives us a way to test a degree sequence to see if it is graphical or not. As a side-effect, a graph is produced that realises the sequence. Note that it only produces one graph, not all of them. It proceeds by attaching the first vertex of highest degree to the next set of high-degree vertices. If there are none left to attach to, it has either used up all the sequence to produce a graph, or the sequence was not graphical.

The image above shows the HH algorithm at work on the sequence [3, 3, 2, 2, 1, 1]. Unfortunately, this produce…

Generating Dungeons With BSP Trees or Sliceable Rectangles

So, I admit that the original reason for looking at sliceable rectangles was because of this gaming stackoverflow question about generating dungeon maps. The approach described there uses something called a binary split partition tree (BSP Tree) that's usually used in the context of 3D - notably in the rendering engine of the game Doom. Here is a BSP tree, as an example:

In the image, we have a sliced rectangle on the left, with the final rectangles labelled with letters (A-E) and the slices with numbers (1-4). The corresponding tree is on the right, with the slices as internal nodes labelled with 'h' for horizontal and 'v' for vertical. Naturally, only the leaves correspond to rectangles, and each internal node has two children - it's a binary tree.

So what is the connection between such trees and the sliceable dual graphs? Well, the rectangles are related in exactly the expected way:

Here, the same BSP tree is on the left (without some labels), and the slicea…