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C'est la Z

Arbitrary Trees

It's been 10 days from my last post. Not really a big break for me historically but certainly a big one given how much I've been posting this year.

Been under the weather for the past couple of weeks dealing with COVID-19. Haven't had super bad symptoms and as symptoms have been getting fewer and less severe I'm hoping I'm close to a full recovery.

In any event, I'm feeling good enough for a quick post.

In my data structures class we've been working on binary trees. Most of the unit is focused on Binary Search Trees. They used to be a big part of the B part of the old APCS-AB and are still a mainstay of college CS2 classes.

As usual, we covered all the basics. Creation, insertion, search, traversal, and deletion. We discovered the run times and how a tree structure can yield lgn behavior but can also degenerate to linear. We also give a preview of more advanced data structures like red/back and 2-3 trees that address these issues (not to mention things like BTrees and Splay trees).

One side topic I always like talking about during this unit though are arbitrary trees. That is, trees where each node can have an arbitrary number of children. Students usually start by creating nodes with an array of children and then sometimes a linked list of children but I like discussing something simpler. A tree where in each node you hold two pointers - a pointer to the first child and a pointer to the next sibling. I like this because internally it's the same as a binary search tree where you also have two pointers in each node a left and a right. Same "physical" representation but two very different variations.

<figure class="z_image_center"> <img src="/img/arbtree.png"/> </figure>

The image on the left is the actual arbitrary tree and the one on the right shows the internal representation.

In terms of applications, the file system is a great example of an arbitrary tree. Another one that I like even more is the DOM representation of a web page. That's nice because there are Javascript functions to get the next sibling.

I put a short video together for my class. Here it is in case anyone is interested. It's code agnostic so would be suitable for an APCS-A class that also covers data structures.

<iframe width="560" height="315" src="https://www.youtube.com/embed/K1lR3ssgxLc" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

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