The Beauty of the Heap

In the quiet aftermath of creation, J.W.J. Williams might have gazed upon the Heap Sort algorithm, pondering if his work had indeed added a new dimension of depth and sophistication to the world.

And perhaps staring down at his proofs he may have quietly whispered:
“With this dance, I have added more beauty and understanding to the ethos”.

Perhaps.

Reflections like these resonate deeply with me, and would hope other developers as well, who see our craft not just as a science but as an art form — a pursuit of an elegant ‘dance’ in our digital realm.

My journey into the heart of this algorithm began with me live streaming my coding sessions on Twitch. Having limited access to senior developers to explain the nuances of such a loose language during my study, I started by constructing a custom AI assistant (custom GPT) designed to tutor all levels of proficiency in JavaScript. Algorithms and data structures were not meant to be the focal point of my streams but it quickly became the lions share of my live-streamed coding sessions, transforming what was intended to be a minor focus into a central theme. This unexpected shift has been a valuable development.

Recently during a deep dive into the quick sort algorithm, I asked for clarification around the use of ‘concat’ in the implementation and my trusty JavaScript tutor described it as ‘eloquent’. Its choice of word, ‘eloquent,’ I think perfectly captures the essence of a developer and our desire to make intelligent and clever decisions.

A large language model that sounds like a dev, how wicked.

Starting with sorting algorithms, I began with the basics like bubble sort and selection sort, each stream offering a chance to dissect these algorithms’ underlying logic and wisdom. We drew out representations of the each stage of the algorithm in question and each stream we would review the previous days lesson and attempt to re-create them from memory. This repetitive exploration, shared live with viewers, not only re-enforces my understanding but also makes the intricate world of algorithms more accessible to newcomers. This has immense value to me. I want to curate a space where people of all skill levels, especially those starting out, can find a place.

And should I need help or clarification along the way, my faithful GPT tutor is patiently there for me. I’m very clear when asking for a gentle nudge should I get stuck. I’m not looking for answers, I’m looking for guidance. Answers complete Leetcode questions and finish home work assignments but I’m seeking the real wisdom that comes from understanding these paradigms.

Recently during my stream I was introduced to the heap sort algorithm, courtesy of my custom GPT tutor, and it has signaled a pivotal moment in my coding exploration.

The heap sort algorithm’s elegance and the accompanying data structure’s complexity are breath taking.

I often ask the GPT to explain sophisticated concepts to me as parables or stories, turning complicated ideas into engaging narratives. For example, the heap sort’s implementation was explained to the me and the stream as a gardener’s magical tree, which rearranges its fruit to always present the largest and most succulent piece at the top each morning. Somewhat complicated principles examined as tales transform abstract algorithms into relatable stories, enriching my learning experience and allowing me to hold onto the stories wisdom in more profound ways.

Computer science can be cute and memorable if we want it to be.

A large part of my fascination was the mathematical beauty underlying the heap sort. The principle is as magical as any story:

• The left and right children of any given root are determined by the formulas iLeftChild(i) = 2⋅i + 1 and iRightChild(i) = 2⋅i + 2, respectively.
• Conversely, the parent of any node (root) is found using iParent(i) = floor((i−1) / 2).

It’s beautiful.

This simple yet sophisticated principle, coupled with the conditional checks in our ‘heapify’ function, enables the initial ‘heapification’ of the input array. This ensures that the root and every subsequent tree adhere to these principles, maintaining the heap’s integrity through each iteration and adjustment of the structure.

There’s more to be said about the wonder I felt as I reviewed the recursive nature implemented in both the algorithms and data structure, neither having a ‘base case’ for their recursive calls and neither blowing the call stack as it completed the sort. I could go on and on about how rad all of this is to me.

Before I was a developer, I was a carpenter, but in all my endeavors, I’ve remained an artist first. This perspective has allowed me to appreciate the deep beauty and significance in the work I’ve encountered, including the intricate dance between the heap sort algorithm and its data structure.

‘Who built this!’, I wondered, marveling at the creativity and ingenuity required to conceive such an elegant solution.

And so I learned all about dear Bill Williams.

When I study and reflect on the contributions of J.W.J. Williams and others in the field, it’s clear that we, as developers, truly stand on the shoulders of giants. With the vast array of tools and knowledge available today, it’s humbling to consider the achievements of those who had less at their disposal.

Today we have highly advanced tools to help with our challenges and work flows. We have the sum total of human knowledge available to us 24 hours a day, usually in our pockets or on our desks. Today I have large language models explaining concepts to me like I was ten years old so I can grasp them quickly.

In 1963 Bill Williams had challenges to solve, idea’s to approach them with, and CS degree.

And that’s not to say that Bill didn’t have resources, I’m simply saying that what he did, he did with less.

At the time Bill worked for a company called Elliot Bro’s and through his algorithm and data structure and with the help of C. A. R. (Tony) Hoare they created the event-driven Elliott Simulator Package (ESP).

The thought that in 1963 these gentle men sat with the cognitive overhead until the utility and functionality of this idea came to fruition is beautiful.

The heap sort algorithm and its underlying data structure are more than just tools; they’re expressions of beauty in the realm of computer science, a living testament to the artistry and innovation that drive our field forward.

This is art manifest in the shape of data.

And the shape of data is beautiful.

I’m going to continue to stream these explorations live on Twitch, inviting the community to join in on the discovery and creativity that programming offers.

I’m often reminded of the elegance that lies at the intersection of art and technology and I’m curious if you’ve encountered any beauty in the algorithms and structures you’ve worked with.

Please feel free to join me on this journey where we can celebrate the creativity and eloquence that underpins our digital world.

And of course, please keep making beautiful things.

~Hope