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    <title>DEV Community: Fredrik Meyer</title>
    <description>The latest articles on DEV Community by Fredrik Meyer (@fredrikmeyer).</description>
    <link>https://dev.to/fredrikmeyer</link>
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      <title>DEV Community: Fredrik Meyer</title>
      <link>https://dev.to/fredrikmeyer</link>
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    <item>
      <title>What I self host</title>
      <dc:creator>Fredrik Meyer</dc:creator>
      <pubDate>Sat, 18 Oct 2025 15:02:12 +0000</pubDate>
      <link>https://dev.to/fredrikmeyer/what-i-self-host-ani</link>
      <guid>https://dev.to/fredrikmeyer/what-i-self-host-ani</guid>
      <description>&lt;p&gt;I've always liked reading blogs, and have used several feed readers in the past (Feedly, for example). For a long time I was thinking it would be fun to write my own RSS reader, but instead of diving into the challenge, I did the next best thing, which was finding a decent one, and learning how to self host it.&lt;/p&gt;

&lt;p&gt;In this post I will tell about the self hosting I do, and end by sketching the setup.&lt;/p&gt;

&lt;h2&gt;
  
  
  RSS reader - Miniflux
&lt;/h2&gt;

&lt;p&gt;&lt;a href="https://github.com/miniflux/v2" rel="noopener noreferrer"&gt;Miniflux&lt;/a&gt; is a "minimalist and opinionated feed reader". I host my own instance at &lt;a href="https://rss.fredrikmeyer.net/" rel="noopener noreferrer"&gt;https://rss.fredrikmeyer.net/&lt;/a&gt; It is very easy to set up using Docker, see &lt;a href="https://miniflux.app/docs/docker.html#docker-compose" rel="noopener noreferrer"&gt;the documentation&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fr3aybc25df5j69sl6heo.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fr3aybc25df5j69sl6heo.png" alt="Miniflux" width="800" height="454"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;I do have lots of unread blog posts 🤨.&lt;/p&gt;

&lt;h2&gt;
  
  
  Grafana, Strava Integration
&lt;/h2&gt;

&lt;p&gt;I host a Grafana instance, also using Docker. What first triggered me to make this instance was an old project (that I want to revive one day): I had a Raspberry Pi with some sensors measuring gas and dust at my previous apartment, and a Grafana dashboard showing the data. It was interesting seeing how making food at home had a measurable impact on volatile gas levels.&lt;/p&gt;

&lt;p&gt;Later I discovered the &lt;a href="https://grafana.com/grafana/plugins/grafana-strava-datasource/" rel="noopener noreferrer"&gt;Strava datasource plugin&lt;/a&gt; for Grafana. It is a plugin that lets Grafana connect to the Strava API, and gives you summaries of your Strava activities. Below is an example of how it looks for me:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fnu74qtu339e85sdthk79.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fnu74qtu339e85sdthk79.png" alt="Image of Grafana dashboard" width="800" height="272"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;One gets several other dashboards included in the plugin.&lt;/p&gt;

&lt;h2&gt;
  
  
  Spotify
&lt;/h2&gt;

&lt;p&gt;One day &lt;a href="https://github.com/Yooooomi/your_spotify/" rel="noopener noreferrer"&gt;YourSpotify&lt;/a&gt; was mentioned on HackerNews. It is an application that connects to the Spotify API, and gives you aggregated statistics of artists and albums you've listened to over time (why they chose to store the data in MongoDB I have no idea of!).&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fou439u7uec2xe340pv21.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fou439u7uec2xe340pv21.png" alt="YourSpotify front page" width="800" height="520"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;It is interesting to note that I have listened to less and less music over the years (I have noticed that the more experience I have at work, the less actual programming I do).&lt;/p&gt;

&lt;p&gt;Because I didn't bother setting up DNS, this one is only exposed locally, so I use &lt;a href="https://tailscale.com/" rel="noopener noreferrer"&gt;Tailscale&lt;/a&gt; to be able to access YourSpotify. This works by having Tailscale installed on the host, and connecting to the Tailnet. It lets me access the application by writing &lt;code&gt;http://forgottensuperhero:3001/&lt;/code&gt; in the browser.&lt;/p&gt;

&lt;h2&gt;
  
  
  Bookmark manager
&lt;/h2&gt;

&lt;p&gt;I have a problem with closing tabs, and a tendency to hoard information (don't get me started on the number of unread PDF books on my Remarkable!). So I found Linkding, a bookmark manager, which I access at &lt;a href="https://links.fredrikmeyer.net/bookmarks/shared" rel="noopener noreferrer"&gt;https://links.fredrikmeyer.net/bookmarks/shared&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fvy3juaiyif8cjozf8rc2.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fvy3juaiyif8cjozf8rc2.png" alt="Linkding bookmark manager" width="800" height="600"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;In practice it is a grave yard for interesting things I never have the time to read, but it gives me peace some kind of peace of mind.&lt;/p&gt;

&lt;h2&gt;
  
  
  How
&lt;/h2&gt;

&lt;p&gt;I have an ambition of making the hosting "production grade", but at the moment this setup is a mix of practices of varying levels of quality.&lt;/p&gt;

&lt;p&gt;I pay for a cheap droplet at &lt;a href="https://www.digitalocean.com/" rel="noopener noreferrer"&gt;DigitalOcean&lt;/a&gt;, about $5 per month, and an additional dollar for backup. The domain name and DNS is from &lt;a href="https://domene.shop/" rel="noopener noreferrer"&gt;Domeneshop&lt;/a&gt;. SSL certificates from &lt;a href="https://letsencrypt.org/" rel="noopener noreferrer"&gt;Let's Encrypt&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;All the apps run in different Docker containers, with ports exposed. These ports are then listened to by Nginx, which redirects to HTTPS.&lt;/p&gt;

&lt;p&gt;I manage &lt;em&gt;most of&lt;/em&gt; the configuration using Ansible. Here I must give thanks to &lt;a href="https://www.jeffgeerling.com/" rel="noopener noreferrer"&gt;Jeff Geerling&lt;/a&gt;'s book &lt;a href="https://leanpub.com/ansible-for-devops" rel="noopener noreferrer"&gt;Ansible for DevOps&lt;/a&gt;, which was really good. So if I change my Nginx configuration, I edit it on my laptop, and run&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;ansible-playbook &lt;span class="nt"&gt;-i&lt;/span&gt; inventory.ini docker.yml  &lt;span class="nt"&gt;--ask-become-pass&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;to let Ansible do its magic. In this case, "most" means the Nginx configuration and Grafana.&lt;/p&gt;

&lt;p&gt;Miniflux and YourSpotify are managed by simply doing &lt;code&gt;scp spotify_stats.yml droplet:~&lt;/code&gt; and running &lt;code&gt;sudo docker-compose -f ./spotify_stats.yml up -d&lt;/code&gt; on the host.&lt;/p&gt;

&lt;p&gt;Ideally, I would like to have a 100% "infrastructure as code" approach, but hey, who has time for that!&lt;/p&gt;

&lt;h2&gt;
  
  
  Ideas for the future
&lt;/h2&gt;

&lt;p&gt;It would be nice to combine AI and user manuals of house appliances to make an application that lets you ask questions like "what does the red light on my oven mean?". Or write my own Jira, or... Lots of rabbit holes &lt;a href="https://github.com/awesome-selfhosted/awesome-selfhosted" rel="noopener noreferrer"&gt;in this list&lt;/a&gt; on Github.&lt;/p&gt;

&lt;p&gt;Until next time!&lt;/p&gt;

</description>
      <category>homelab</category>
      <category>programming</category>
      <category>selfhosting</category>
    </item>
    <item>
      <title>Implementing a 2d-tree in Clojure</title>
      <dc:creator>Fredrik Meyer</dc:creator>
      <pubDate>Mon, 08 Apr 2024 07:18:09 +0000</pubDate>
      <link>https://dev.to/fredrikmeyer/implementing-a-2d-tree-in-clojure-2jjj</link>
      <guid>https://dev.to/fredrikmeyer/implementing-a-2d-tree-in-clojure-2jjj</guid>
      <description>&lt;p&gt;Recently I followed the very good Coursera course "&lt;a href="https://www.coursera.org/learn/algorithms-part1/"&gt;Algorithms, Part I&lt;/a&gt;" from Coursera. The exercises were in Java, and the most fun one was implementing a two-dimensional version of a &lt;a href="https://en.wikipedia.org/wiki/K-d_tree"&gt;k-d tree&lt;/a&gt;. Since I sometimes do &lt;a href="https://www.generert.art/"&gt;generative art in Clojure&lt;/a&gt;, I thought this would be a fun algorithm to implement myself.&lt;/p&gt;

&lt;p&gt;There already exists other implementations, for example &lt;a href="https://github.com/abscondment/clj-kdtree"&gt;this one&lt;/a&gt;, but this time I wanted to learn, not use.&lt;/p&gt;

&lt;h2&gt;
  
  
  What is a 2-d tree?
&lt;/h2&gt;

&lt;p&gt;A 2-d tree is a spatial data structure that is efficient for &lt;a href="https://en.wikipedia.org/wiki/Nearest_neighbor_search"&gt;nearest neighbour&lt;/a&gt; and &lt;a href="https://en.wikipedia.org/wiki/Range_searching"&gt;range searches&lt;/a&gt; in a two-dimensional coordinate system.&lt;/p&gt;

&lt;p&gt;It is a generalization of a &lt;a href="https://en.wikipedia.org/wiki/Binary_search_tree"&gt;binary search tree&lt;/a&gt; to two dimensions. Recall that in a binary search tree, one builds a tree structure by inserting elements such that the left nodes always are lower, and the right nodes always are higher. In that way, one only needs $O(\log(n))$ lookups to find a given element. See &lt;a href="https://en.wikipedia.org/wiki/Binary_search_tree"&gt;Wikipedia&lt;/a&gt; for more details.&lt;/p&gt;

&lt;p&gt;In a 2-d tree one manages to do the same with points $(x,y)$ by alternating the comparison on the $x$ or $y$ coordinate. For each insertion, one splits the coordinate system in two.&lt;/p&gt;

&lt;p&gt;Look at the following illustration:&lt;br&gt;
&lt;a href="https://gist.&amp;lt;br&amp;gt;%0Agithub.com/FredrikMeyer/2b2a4fffe77b0997282f40a601b443fd"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F8xwdt83fevt5s999b4o9.png" alt="2-d tree tree structure" width="685" height="209"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;This is the resulting tree structure after having inserted the points $(0.5, 0.5)$, $(0.6, 0.3)$, $(0.7, 0.8)$, $(0.4, 0.8)$, and $(0.4, 0.6)$. For each level of the tree, the coordinate to compare with is alternating.&lt;/p&gt;

&lt;p&gt;The following illustration shows how the tree divides the coordinate system into sub-regions:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://gist.github.com/FredrikMeyer/2b2a4fffe77b0997282f40a601b443fd"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F338qwtp8sz08okkmorb1.png" alt="Subregions of a 2-d tree structure" width="640" height="480"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;To illustrate searching, let's look up $(0.4, 0.6)$. Then we first compare it with $(0.5, 0.5)$. The $x$ coordinate is lower, so we look at the left subtree. Now the $y$ coordinate is lower, so we look at the left subtree again, and we found our point. This is 2 compares instead of the maximum 5.&lt;/p&gt;

&lt;p&gt;There's a lot more explanation &lt;a href="https://en.wikipedia.org/wiki/K-d_tree"&gt;on Wikipedia&lt;/a&gt;.&lt;/p&gt;
&lt;h2&gt;
  
  
  Implementing it in Clojure
&lt;/h2&gt;

&lt;p&gt;Let's jump straight to the implementation in Clojure. We first define a node to contain tree values: the point to insert, a boolean indicating if we are comparing vertically or horizontally (vertical means comparing the $x$-coordinate), and a rectangle, indicating which subregion the node corresponds to.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;defrecord&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;rect&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;(note: we don't really need to carry around the rectangle information - it can be computed from the &lt;code&gt;vertical&lt;/code&gt; boolean and the previous point. I might optimize this later.)&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-cons&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt;&lt;span class="w"&gt;
         &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;true&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="c1"&gt;;; If the current path exists&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;if-let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[{&lt;/span&gt;&lt;span class="no"&gt;:keys&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;]}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;get-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;second&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;&amp;lt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;))]&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;cond&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="c1"&gt;;; If pt already in tree, just return the tree&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="c1"&gt;;; If pt is lower than current value, recur with :lower appended to path&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;not&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="no"&gt;:else&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:higher&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;not&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="p"&gt;))))&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="c1"&gt;;; We are in the case of a non-existing node&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="c1"&gt;;; If path is empty, it means the tree was nil. Return a root node.&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;empty?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;assoc&lt;/span&gt;&lt;span class="w"&gt;
         &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;-&amp;gt;TreeNode&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;-&amp;gt;Rectangle&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:size&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="c1"&gt;;; Otherwise, insert a new node at the current path&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[{&lt;/span&gt;&lt;span class="n"&gt;prev-pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:rect&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;get-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="n"&gt;curr-key&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;peek&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;update&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:size&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;inc&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;assoc-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt;
                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;-&amp;gt;TreeNode&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt;
                                    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt;
                                      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;curr-key&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;below-of&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;top-of&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-pt&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                                      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;curr-key&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;left-of&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;right-of&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prev-pt&lt;/span&gt;&lt;span class="p"&gt;)))))))))))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Insertion is almost identical to insertion into a binary search tree. Where the structure shines, is when looking for nearest neighbour. The strategy is as follows: keep track of the "best so far" point, and only explore subtrees that are worth exploring.&lt;/p&gt;

&lt;p&gt;When is a subtree wort exploring? Only when its region is closer to the search point than the current best point:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;worth-exploring?&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="s"&gt;"Is the `rect` worth exploring when looking for pt?"&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;&amp;lt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;distance-squared&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;In addition, we do one optimization when there are two subtrees. We explore the closest subtree first. Here's the full code:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-nearest&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="s"&gt;"Find the nearest pt in the tree represented by root."&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;nil?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;best-so-far&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
             &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[[]]]&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;peek&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="no"&gt;:keys&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-node&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;get-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;min-key&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;#&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;%&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;cond&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="c1"&gt;;; The stack of paths to be explored is empty, return best-so-far&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;nil?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="n"&gt;best-so-far&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="c1"&gt;;; If pt = value, then no need to do anything more&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="c1"&gt;;; Both children exist&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;and&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;second&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                  &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;&amp;lt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                  &lt;/span&gt;&lt;span class="c1"&gt;;; Explore closest node first&lt;/span&gt;&lt;span class="w"&gt;
                  &lt;/span&gt;&lt;span class="n"&gt;child-nodes&lt;/span&gt;&lt;span class="w"&gt;  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;'&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:higher&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;'&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:higher&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                  &lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;-&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;child-nodes&lt;/span&gt;&lt;span class="w"&gt;
                         &lt;/span&gt;&lt;span class="c1"&gt;;; Filter nodes worth exploring&lt;/span&gt;&lt;span class="w"&gt;
                         &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;transduce&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;comp&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;filter&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;#&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;worth-exploring?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;%&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-node&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                                          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;map&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;#&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;%&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)))]&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;some?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;worth-exploring?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;some?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;worth-exploring?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;current-path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:higher&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="no"&gt;:else&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;best-so-far*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;pop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;paths&lt;/span&gt;&lt;span class="p"&gt;)))))))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;In the recursion, we keep a stack of paths (it looks like &lt;code&gt;[[:higher :lower] [:higher :higher] ...]&lt;/code&gt;{:.language-clojure}). When exploring a new node, we add it to the top of the stack, and when recurring, we pop the current stack.&lt;/p&gt;

&lt;p&gt;Here's how the data structure looks after inserting the same points as in the illustration above:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight ruby"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:value&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
 &lt;span class="ss"&gt;:vertical&lt;/span&gt; &lt;span class="kp"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
 &lt;span class="ss"&gt;:rect&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:xmin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:xmax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
 &lt;span class="ss"&gt;:size&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
 &lt;span class="ss"&gt;:higher&lt;/span&gt;
 &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:value&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.6&lt;/span&gt; &lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="ss"&gt;:vertical&lt;/span&gt; &lt;span class="kp"&gt;false&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="ss"&gt;:rect&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:xmin&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:xmax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
  &lt;span class="ss"&gt;:higher&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:value&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.7&lt;/span&gt; &lt;span class="mf"&gt;0.8&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="ss"&gt;:vertical&lt;/span&gt; &lt;span class="kp"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:rect&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:xmin&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymin&lt;/span&gt; &lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:xmax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;}}},&lt;/span&gt;
 &lt;span class="ss"&gt;:lower&lt;/span&gt;
 &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:value&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.4&lt;/span&gt; &lt;span class="mf"&gt;0.8&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="ss"&gt;:vertical&lt;/span&gt; &lt;span class="kp"&gt;false&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="ss"&gt;:rect&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:xmin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:xmax&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymax&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
  &lt;span class="ss"&gt;:lower&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:value&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.4&lt;/span&gt; &lt;span class="mf"&gt;0.6&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="ss"&gt;:vertical&lt;/span&gt; &lt;span class="kp"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:rect&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="ss"&gt;:xmin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymin&lt;/span&gt; &lt;span class="mf"&gt;0.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:xmax&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="ss"&gt;:ymax&lt;/span&gt; &lt;span class="mf"&gt;0.8&lt;/span&gt;&lt;span class="p"&gt;}}}}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;

&lt;h3&gt;
  
  
  Integrating with core Clojure functions
&lt;/h3&gt;

&lt;p&gt;I wanted the tree structure to behave like a normal Clojure collection. The way to do this, is to implement the required interfaces. For example, to be able to use &lt;code&gt;cons&lt;/code&gt;, &lt;code&gt;conj&lt;/code&gt;, &lt;code&gt;map&lt;/code&gt;, &lt;code&gt;filter&lt;/code&gt;, etc, we have to implement the &lt;code&gt;clojure.lang.ISeq&lt;/code&gt; interface. To find out which methods we need to implement, I found &lt;a href="https://gist.github.com/semperos/3835392"&gt;this Gist&lt;/a&gt; very helpful.&lt;/p&gt;

&lt;p&gt;I create a new type that I call &lt;code&gt;TwoTree&lt;/code&gt; using &lt;code&gt;deftype&lt;/code&gt;:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;deftype&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;TwoTree&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="n"&gt;I2DTree&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;intersect-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;other-rect&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;tree-insersect-rect&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;other-rect&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;nearest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;tree-nearest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="n"&gt;clojure.lang.ISeq&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;letfn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="nf"&gt;first*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[{&lt;/span&gt;&lt;span class="no"&gt;:keys&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;]}]&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;))]&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;first*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;cons&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;TwoTree.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;tree-cons&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;seq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;.more&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;more&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;letfn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="nf"&gt;more*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[{&lt;/span&gt;&lt;span class="no"&gt;:keys&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;node&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;cond&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lower&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;seq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;TwoTree.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;assoc-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="no"&gt;:else&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;TwoTree.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;higher&lt;/span&gt;&lt;span class="p"&gt;)))]&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;more*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[])))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="n"&gt;clojure.lang.Seqable&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;seq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;when&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;contains?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="n"&gt;clojure.lang.IPersistentCollection&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;equiv&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;seq-equals&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;empty&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;TwoTree.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="n"&gt;clojure.lang.Counted&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;count&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;get&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:size&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="n"&gt;clojure.lang.IPersistentSet&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;disjoin&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;throw&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;Exception.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;"Not supported"&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;contains&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;boolean&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;get&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;this&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;get&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;nil?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[]]&lt;/span&gt;&lt;span class="w"&gt;
          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;if-let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[{&lt;/span&gt;&lt;span class="no"&gt;:keys&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;^&lt;/span&gt;&lt;span class="nb"&gt;boolean&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="p"&gt;]}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;get-in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;vertical&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;second&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                  &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;&amp;lt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;comparator-fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;))]&lt;/span&gt;&lt;span class="w"&gt;
              &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;cond&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="n"&gt;current-compare-res&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:lower&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:else&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;recur&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;path&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:higher&lt;/span&gt;&lt;span class="p"&gt;))))&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="p"&gt;)))))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;When implementing &lt;code&gt;TwoTree&lt;/code&gt;, I took a lot of inspiration (and implementation) from &lt;a href="https://wallace.fm/blog/2016/byod-party/"&gt;this blog post&lt;/a&gt; by Nathan Wallace. Also, thanks to the Reddit user &lt;code&gt;joinr&lt;/code&gt; for pointing out a bad &lt;code&gt;equiv&lt;/code&gt; implementation. Here is &lt;a href="https://github.com/FredrikMeyer/generert/commit/22fc333820edf3434ad2796b65c15ed283793234"&gt;the diff&lt;/a&gt; after his comments.&lt;/p&gt;

&lt;p&gt;We can create a helper method to create new trees:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;two-tree&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;xs&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;reduce&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;TwoTree.&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;xs&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Now we can create a new tree like this:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;two-tree&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.4&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="p"&gt;]])&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Also, the following code works:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;filter&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;#&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;second&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;%&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;two-tree&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.3&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.8&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;(get all points whose seconds coordinate is greater than 0.5)&lt;/p&gt;

&lt;p&gt;The full code can be seen &lt;a href="https://github.com/FredrikMeyer/generert/blob/17a70f42bf7ea6eb24abcdbec9571615c806f000/src/clj/tools/2dtree.clj"&gt;here on Github&lt;/a&gt;.&lt;/p&gt;
&lt;h2&gt;
  
  
  Lessons learned
&lt;/h2&gt;

&lt;p&gt;I did this partly to learn a simple geometric data structure, but also to make another tool in my &lt;a href="https://www.youtube.com/watch?v=kZNTozzsNqk"&gt;generative art toolbox&lt;/a&gt;. Implementing an algorithm helps immensely when trying to understand it: I got better and better visualizing how these trees looked like.&lt;/p&gt;

&lt;p&gt;There are two main things about Clojure I want to mention in this section: the &lt;code&gt;clojure.test.check&lt;/code&gt; library, and the Clojure interfaces.&lt;/p&gt;
&lt;h3&gt;
  
  
  The &lt;code&gt;clojure.test.check&lt;/code&gt; library
&lt;/h3&gt;

&lt;p&gt;The &lt;code&gt;test.check&lt;/code&gt; library is a property based testing library. In a few words, given constraints on inputs, in can generate test data for your function. In one particular case, it helped me verify that my code had a bug and produce a minimal example of this (the bug was that I forgot to recur in the &lt;code&gt;:else&lt;/code&gt; clause in the &lt;code&gt;tree-nearest&lt;/code&gt; function). By writing some "simple-ish" code, I got an example of an input that made the &lt;code&gt;tree-nearest&lt;/code&gt; return a wrong answer. Here is the code:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight clojure"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nearest-by-sort&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pts&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;sorted-set-by&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;compare&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pt&lt;/span&gt;&lt;span class="p"&gt;))))&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;into&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pts&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;defn&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;^&lt;/span&gt;&lt;span class="no"&gt;:private&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;points-gen&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;min-length&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;max-length&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="no"&gt;:infinite?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;false&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:max&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:NaN?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;false&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;:min&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="n"&gt;gen/double*&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;gen/vector&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
      &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;gen/vector&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;min-length&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;max-length&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;

&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;prop/for-all&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pts&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;points-gen&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
                        &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;reduce&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;s/two-tree&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pts&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                              &lt;/span&gt;&lt;span class="n"&gt;correct-answer&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;nearest-by-sort&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;pts&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                              &lt;/span&gt;&lt;span class="n"&gt;correct-dist&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;correct-answer&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                              &lt;/span&gt;&lt;span class="n"&gt;tree-answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;s/nearest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                              &lt;/span&gt;&lt;span class="n"&gt;tree-dist&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;

                          &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;correct-dist&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-dist&lt;/span&gt;&lt;span class="p"&gt;))))&lt;/span&gt;&lt;span class="w"&gt;

&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;deftest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nearest-generative&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;is&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nil&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;tc/quick-check&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;prop&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;
               &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;when&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;not&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:pass?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;
                 &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;failed&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;first&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:smallest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="no"&gt;:shrunk&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;&lt;span class="w"&gt;
                       &lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;reduce&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;conj&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;s/two-tree&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;failed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                       &lt;/span&gt;&lt;span class="n"&gt;answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;nearest-by-sort&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;failed&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&lt;span class="w"&gt;
                       &lt;/span&gt;&lt;span class="n"&gt;tree-answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;s/nearest&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;])]&lt;/span&gt;&lt;span class="w"&gt;
                   &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="no"&gt;:tree&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:failed&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;failed&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;.root&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:tree-answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-answ&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:tree-dist&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;tree-answ&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:correct-dist&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;p/distance-sq&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;answ&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;
                    &lt;/span&gt;&lt;span class="no"&gt;:answ&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;answ&lt;/span&gt;&lt;span class="p"&gt;}))))))&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;It is probably more verbose than needed, but the summary is this: the &lt;code&gt;points-gen&lt;/code&gt; function return a &lt;em&gt;generator&lt;/em&gt;, which, given some restraints, can return sample inputs (in this case: vectors of points). Then I compare the result from the tree-search with the brute force result given by first sorting the points, then picking the first point.&lt;/p&gt;

&lt;p&gt;The way I've set it up, whenever I run my tests, &lt;code&gt;clojure.test.check&lt;/code&gt; generates 10000 test cases and fails the test if my implementation doesn't return the correct result. This was very handy, and quite easy to set up.&lt;/p&gt;
&lt;h3&gt;
  
  
  The Clojure core interfaces
&lt;/h3&gt;

&lt;p&gt;It was rewarding to implement the Clojure core interfaces for my &lt;code&gt;TwoTree&lt;/code&gt; type (&lt;code&gt;clojure.lang.ISeq&lt;/code&gt;, &lt;code&gt;clojure.lang.IPersistentSet&lt;/code&gt;, etc.). What was a bit frustrating though, was the lack of documentation. I ended up reading a lot of Clojure source code to understand the control flows. Basically, the only thing I now about &lt;code&gt;IPersistentSet&lt;/code&gt;, is that it is a Java interface like this:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="kn"&gt;package&lt;/span&gt; &lt;span class="nn"&gt;clojure.lang&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;interface&lt;/span&gt; &lt;span class="nc"&gt;IPersistentSet&lt;/span&gt; &lt;span class="kd"&gt;extends&lt;/span&gt; &lt;span class="nc"&gt;IPersistentCollection&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="nc"&gt;Counted&lt;/span&gt;&lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="nc"&gt;IPersistentSet&lt;/span&gt; &lt;span class="nf"&gt;disjoin&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Object&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;;&lt;/span&gt;
    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kt"&gt;boolean&lt;/span&gt; &lt;span class="nf"&gt;contains&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Object&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="nc"&gt;Object&lt;/span&gt; &lt;span class="nf"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Object&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Then I had to search the Clojure source code to understand how it was supposed to be used. It would be nice with a docstring or two. I found many blog posts that implemented custom types (&lt;a href="https://hpincket.com/implementing-an-iseq-conforming-linked-list-in-clojure.html"&gt;this one&lt;/a&gt;, &lt;a href="https://wallace.fm/blog/2016/byod-party/"&gt;this one&lt;/a&gt;, or &lt;a href="https://www.juxt.pro/blog/clojure-ds/"&gt;this one&lt;/a&gt;), but very little in Clojure own documentation.&lt;/p&gt;

&lt;p&gt;On the flip side, I got to read some of the Clojure source code, which was very educational. I also got to understand a bit more the usefulness of protocols (using &lt;code&gt;defprotocol&lt;/code&gt; and &lt;code&gt;defrecord&lt;/code&gt; to provide several implementations). Here it was very useful to read the source code of &lt;a href="https://github.com/thi-ng/geom/tree/feature/no-org/src/thi/ng/geom"&gt;thi-ng/geom&lt;/a&gt;.&lt;/p&gt;
&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;I learned a lot, and I got one more tool to make generative art. Perhaps later I could publish the code as a library, but I should really battle test it a bit more first (anyone can copy the code, it is open source on my Github)&lt;/p&gt;

&lt;p&gt;I used the data structure to create the following pictures (maybe soon I'll link to my own page instead of Instagram). The &lt;code&gt;nearest&lt;/code&gt; function was very useful in making the code fast enough.&lt;/p&gt;


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&lt;p&gt;Until then, thanks for reading this far!&lt;/p&gt;

</description>
      <category>clojure</category>
      <category>graphics</category>
      <category>datastructures</category>
      <category>generativeart</category>
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