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Show HN: Illustrated Quicksort algorithm

illustrated-algorithms.now.sh

187 pointsskidding48 comments

This is neat. If you enjoyed this you might also like the Hungarian folk dancers demonstrating sorting algorithms on youube:

https://www.youtube.com/watch?v=ywWBy6J5gz8

That was simply amazing.

I agree. It never gets old :)

Damn it, you beat me to it. ;-)

Hi. This is my 2nd algoritm visualization. Creating them is fun.

Besides designing the illustrations, I've spent a lot of time crafting the framework so expect more of these in the future. Ongoing effort, but also tried to make the codebase approachable for others to learn from and be able to contribute: https://github.com/skidding/illustrated-algorithms

How would you make algorithms fun? Looking forward to ideas and feedback. Thanks!

Looks great. Have an option to slow it down though. I couldn't follow the animation and the code on the right it was going so quickly.

Makes sense. I'm curious, is the fact that you can drag the progress bar back&forth to create a slow motion obvious?

Without ever testing it (bad me, bad!) I assumed it was (at least) for jumping back to a frame.

It would be more obvious that it could be used as a slider if it had a graphical slider. [1]

Either way, great work!

[1] http://www.infotuts.com/wp-content/uploads/2015/12/rangeslid...

Sure but it would be nice to step through at your own pace rather than by intricately dragging a mouse and having to hold the click.

You mean via back/fwd buttons? Those are definitely useful. Fun trivia, this is how the 1st prototype worked: https://github.com/skidding/illustrated-algorithms/releases (scroll to bottom)

That would be nice but auto play is good. Just allow 2-3 options for the speed of a tick.

yup, I naturally grabbed it to go back and forth.

some constructive feedback: one of the greatest features of quicksort is that it is an in-place algorithm, it doesn't use any additional storage. qsort cleverest trick is to switch an element greater than the pivot with one smaller in a single step, and all of that is lost in the animation when the first thing it does is to group the fruits into the "less" and "greater" piles. as it is, your animation is great, but it doesn't really illustrate qsort, especially the most fundamental aspects that set it apart from other sorting algorithms.

Good points. I'll think about this and read more on Quicksort.

Do you think these aspects can be incorporated without adding extra baggage for beginners (the primary target for this visualizations)?

To me, I think that the space savings is exactly what should be emphasized to beginners. I love functional programming as much as the next person...well maybe almost as much...but quicksort without mutation is not quicksort.

Showing beginners quicksort with mutation pulls back the curtain on functional programming and reveals the wizard. Functional programming, so long as we have Von Neumann machines, is a layer of abstraction and who am I to argue with Abelson and the Sussmans that beginning programmers should be introduced to abstraction layers as quickly as possible?

Absolutely: https://www.cs.usfca.edu/~galles/visualization/ComparisonSor...

With so few elements, I think you can perform the in-place swap as one animation. Take the pivot out, put an arrow on the first and last elements in the list, then

- if the left arrow points to an element greater than the pivot, swap the elements under the arrows and move the right arrow one cell left

- else if the right arrow points to an element less than the pivot, swap the elements under the arrows and move the left arrow one cell right

- else if one of the arrows points at the pivot, move the other arrow towards it

until the two arrows point at the same cell, which now contains the pivot. You could show the full selection animation the first time and then just move all elements to their final places at once every subsequent time. I would also replace the random pivot selection with selecting the middle-valued element among the first, middle and last element of the array.

Nice work! One other note, in addition to the comments here: the algorithm as it's currently written will drop repeated elements. You can easily fix that by changing `greater` to filter elements greater than or equal to the pivot.

I was watching this: https://www.youtube.com/watch?v=ywWBy6J5gz8 and wondering why it was different from this post's animation.

It depends on whether pedagogy is the primary goal. For teaching, the in-place implementation can come after the conceptual "pick a pivot, partition accordingly, then recurse" is made concrete.

I agree. I find https://visualgo.net/sorting to provide easier to understand animations. Also, the fruits are less understandable to me than simple numbers.

Update: I realize the featured example is not the most optimal Quicksort implementation. I doesn't even handle duplicates. Indeed this variant was chosen primarely because of its aesthetics.

While I'd like to keep the mission of this project to "illustrating the basic mechanics of algorithms as elegantly as possible", I realize this can be a) annoying for people who understand the specifics in depth, and b) not enough (or confusing) for people just picking this up. Which is why I'm thinking of creating an info page for each algorithm to:

  - Outline the limitations of the featured version
  - List a number of possible improvements (e.g. pivot strategies)
  - Link to external resources for complete examples & docs

Open discussion. What do you think?

Reminds me of some of my own side projects: great vision, massive effort, but then it just might not be 100% on point / what "the market" needs. You've accomplished a lot - as you know finishing any project is not easy at all and this one has quite a few clever and unique ideas in it!

Best thing imo is the idea to go forward and backward through code and see the results live. I'd love to have this to study or debug code, and to really see and understand the magic of some operations in a visualization like this.

The thing is, algorithms like Quicksort are quite involved. In order to understand I'd need at least 2 intermediate steps between the animation and the code:

- The core concepts, like "recursion, in place sorting, complexity/performance average/worst case, trouble when list already sorted" etc.

- The programming ideas, like "we pick a pivot, we use a random element from the list but you could use any", "our recursion stops when there is only 1 item in the sub-list" etc.

If these things were linked to a) the animation and b) the code and I could experience it all at once, that would be amazing (but a lot of work for you of course :-))

Also: - I kept sorting the fruits by size somehow, and due to the language barrier a "P"ineapple would be an "A"nanas for me - If I commit to learning something I like to go to a place that has comprehensive information, even if various places to one thing well. - Preventing zoom and the scrolling code is not ideal imo. - Code could be simpler and clearer. - Maybe the task to explain Quicksort like this is just too huge

Thanks for this. It's often hard to miss the effort put into something by only pointing out flaws.

> Best thing imo is the idea to go forward and backward through code and see the results live

Yeah, this is the main idea and driver for me. The reason why I chose algorithms is because I could get reasonably small bits of code that accomplish a job on their own, and build something up top of that. Code is already open source and reusable, but turning this into a general purpose tool requires much more dedication. But you're right, introducing algorithms along with this concept also opens Pandora's box in terms of confusion & opinions.

Personally I find https://visualgo.net/ to be more helpful. I don't think the fruits are too intuitive.

visualgo.net is a great resource for understanding algorithms indeed, I wouldn't dare try to compete.

I intended to compare objects of different heights at first, but ended up reusing the emoji tiles from Binary Search to reduce implementation time. I'll try to get more creative with the next (e.g. a maze for BFS).

Good work, looks great!

I have the following comments, hope you find them useful: * I find counter intuitive that the animation goes up, i think it should go down, but that probably just me. * Would recommend using something different than fruit which is probably one of the last things that comes to mind when thinking of ordered sets, also the picture keeps getting in the way of me sorting lexicographically in my mind. * A per step mode would also come in handy.

Appreciate the feedback!

If you enjoy visual or interactive explanations, we're currently building a community for that on Reddit: https://www.reddit.com/r/explorables/

Update 2: I've taken action to try to alleviate some of the confusion and integrate the helpful feedback you've sent me.

  - Added Disclaimer to clarify the project mission and limitations
  - Created Footnotes section for insights collected from the community

Both can be found here: https://github.com/skidding/illustrated-algorithms/blob/mast...

Thanks!

Hey, love it! I know that you know it can handle duplicates, but a simple fix can work here.

Make an array called `equal` before making the `less` and `greater` arrays.

  const equal = arr.filter(i => i === pivot);

Then, instead of adding the pivot, add the equal array.

  return [
    ...quicksort(less),
    ...equal,
    ...quicksort(greater)
  ]

This was cool, the highlighted code tour is a great touch.

For anyone else who enjoyed this, you might also enjoy this blog post full of animated algorithms by Mike Bostock: https://bost.ocks.org/mike/algorithms/

That's amazing. Just two questions

1) on quicksort:

    const less = list.filter(i => i < pivot);
    const greater = list.filter(i => i > pivot);

Wouldn't this be faster:

    less    = what's < pivot
    greater = the rest

2) What is the algorithm people use?

1) It's written in a functional way where you don't mutate the initial list. Edit: I guess you could iterate once and populate both left and right sides at the same time, but that would make the code more verbose (personal bias).

2) What do you mean?

2) Isn't one of these sorting algorithm faster than the other? The complexity of this one is n*log(n) right?

In the average case, yes, but it depends on the pivot strategy.

I may not have parsed your question correctly, so I apologize in advance. Assuming you are asking about what happens to the "equal" elements-

Yes, there is a bug in this code. It doesn't handle repeated elements.

If you fix the code by including an equality in one of the two groups, then it works, but it degrades when there are many repeated elements. In the worst case, you can only shrink your groups by one each time, which means the complexity changes to O(n^2) :(

You can fix THIS issue using a 3-way partition. That is the algorithm I've used. With a good pivot choice (random or median of three), this gives you an in-place sort which is guaranteed to be O(nlgn). Nice!

Thank you for this. The work to both understand the algorithm and then animate it, much appreciated

That's snazzy, good work!

I found myself wanting to set my own initial order of the list to see what some specific edge cases (already sorted, one element off from being sorted, in reverse order, etc) look like.

There was another interesting animated sorting page I found on here many months ago. I haven't seen it in the comments yet and I can't find it anywhere, but this stuff is cool.

This one? https://www.toptal.com/developers/sorting-algorithms

that's it, thanks!

Why do people keep using Quicksort as an example?

I find Mergesort to be much more intuitive. And better yet, it has a much better worst-case performance.

Illustrating both seems most advantageous then :)

A lot of things get called 'quicksort' that are not as quick as Hoare's original algorithm. Pragmatically, it was quick compared to Von Neumann's merge sort.

Sure both are time O{n log n}. Sure both are space O{n}. But merge sort is ~2n + c space and quicksort is n + c space. In the days when computers had kilobytes of memory and rooms full of tape drives, the memory efficiency of quicksort made it much quicker.

Which brings up the difference between mathematical worst case performance and engineering worst case performance. Statistically, the use of a random pivot (which was part of Hoare's paper) gives quicksort similar worst case performance to merge sort. In production with 'big data', hitting slow secondary memory such as persistent storage will dominate throughput.

> Sure both are time O{n log n}.

Nope. Quicksort is much worse: time O(n^2). See [1].

[1] https://en.wikipedia.org/wiki/Quicksort#Worst-case_analysis

Because it uses a randomized pivot, the worst case for Hoare's implementation has a probability on the order 1/n!. With twenty inputs, that's 1/(2.4 * 10^18).

Probabalistic analysis [1] is the difference between theory and practice. Hoare knew what he was doing and it's no accident was recognized with a Turing Award.

[1] https://www.cs.cmu.edu/afs/cs/academic/class/15451-s07/www/l...

I like merge sort, but quick sort is also very elegant.

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