Comment by egonschiele | Hacker News Reader

Comment by egonschiele | Hacker News Reader

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Hey there, I'm working on an algorithms book myself: http://www.manning.com/bhargava/

It is meant to be an easier read than CLRS, so I'm excited to see that Khan Academy is thinking along the same lines! I have been thinking about how to make algorithms easier to understand for the last year, so I have some feedback. Some of it is critical, so first I want to say how much I LOVE that Khan Academy is doing this. I really like the interactive nature of this, and I really like that you have comments. I think that's one advantage of e-books vs traditional books: you can't comment on a paper book. I like the sequencing too (it is very similar to my table of contents, which is cool to see).

What I don't like:

I don't understand why you have four sorting algorithms here. What does insertion sort add over selection sort? I chose to only include selection sort and quicksort in my book. I think once you know those two, you can figure out insertion sort and merge sort if needed. It doesn't add a lot for the reader...I would rather they spend mental effort learning something new.

Similarly, why include big-omega notation? I use a writing principle called "just-in-time" vs "just-in-case". It feels like Big-Omega notation was included "just in case" the reader needs to know it for a later section. I would rather it be taught "just-in-time", i.e. right when the reader needs to know big-omega notation to proceed.

I struggled with the recursion section. My challenge was:

- come up with a real-world example that uses recursion.

- come up with an example where the recursive solution is more elegant than a while loop. Otherwise, why use recursion?

It looks like you had the same challenges. I wish you guys would swap out the factorial example for something that solves a real problem: looking through a directory for a file, for example.

It would be great to see more interactivity in the harder sections too. For example, in "overview of quicksort", I would like to see an animation of the sorting (I am a visual learner).

Overall this is still amazing. Algorithms are such a core topic, and there are no good resources for beginners out there. Very happy to see Khan Academy take this step.

Great feedback!

I think it helps to have both the sorts there, because it gives the students another opportunity to solidify their understanding of algorithms and because they are indeed expected in things like AP CS. Personally, I find them different enough that I need to spend time on each of them to grasp them- I always have to draw algorithms out when I'm learning them, so it helped me that we had the different diagrams and visualizations for each one.

When making KA content, we have to think both about the student that's going through the content from top to bottom and the student that's "snacking" on the content, like finding it via Google search. So if you knew that a student was going to do the whole thing, you could do more just-in-time teaching - but if you didn't know, then it'd be doing a disservice to the snacker to leave out something like Big O notation, because it'd sure be strange if someone learned Theta and Omega and came away not knowing that last one existed. We did spend a while restructuring asymptotic notation in particular, that was one of the topics we debated different approaches to.

We also debated the use cases for recursion, and if we should include the classic factorial challenge. We went for it in the end, as you saw. I think recursive art is my favorite, and works well in our ProcessingJS environment, but one could argue if that's real world :-) I believe that Devin is working on another tutorial with recursion and specifically on how students can come up with their own recursive algorithm. I'll suggest the looking through directory example to him.

Yep, we are working on a quick sort visualization. I am also quite a visual learner.

The neat thing about online curriculum is that we can get feedback from all the students that use it and improve it over time. We'll probably look at all the feedback in a few months, once it's been out there for a bit, see where the dropoff points are, see what the common questions are, and use that to decide what needs changing.

Just to address the recursion point that the GP brought up. Here is one of the best explanations I saw where the problem not only lends itself to a recursive solution but where the recursive solution is actually the more intuitive one rather than a loop. Also it explains with 'real-world' problems, albeit in the context of the material (game programming):

http://inventwithpython.com/blog/2011/08/11/recursion-explai...

Hi Pamela, Thanks for the detailed response! It made me realize that Khan Academy does work a little differently than a book. You have a lot more readers "snacking" or looking for a reference. So it makes sense to group the Big-O discussion together, cover more algorithms, etc. I <3 KA, keep up the good work!

Towers of Hanoi problem (simple version with 3 towers) is a good practical recursion problem that is stimulating and good for visualization.

I learned about those four sorting algorithms before ap comp sci in high school. And I know I covered them again in college at some point. Also, I remember talking about big o in the second level cs class in college. So I see them as appropriate curriculum. I am not a genius programmer that wants to figure out two algorithms cause I understand the other two so well. Show them all to me, I'll take in what I can. That being said, I am intrigued that you have a different perspective and I will check out your book to see what you have to say.

It is the typical curriculum. I'm curious about why it is appropriate. This should be about practical knowledge, not about "throw every algorithm at them and see what sticks"! That's why I only cover two sorting algorithms in my book. I cover selection sort to teach arrays, and I cover quicksort to teach recursion.

Mergesort can be a good introduction to the divide-and-conquer pattern, which seems equally important in an algorithms course.

I think that a big part of algorithms knowledge is knowing what exists. So even a though typical curriculum forces the learning of each of these algorithms, I think the value is in knowing the trade offs between each in terms of complexity (space, time) and ordering.

I think a lot of tree code is good for practical recursive examples.

Of course, it really helps to have algebraic types and pattern matching because they more clearly expose the recursive structure of both trees and tree-based algorithms. I've also found that writing things out in a patter-matching style, case by case, really helps convey how to think recursively. Instead of trying to run a recursive algorithm in my head, having the separate cases separate makes it easier to consider them one by one.

Agreed! I snuck a small Haskell example into my book to show the advantages of pattern matching:)

These are all excellent points. As for practical example of recursion, I'd have to say anything implemented with a tree would be a good example.

Try the development of a recursive algorithm for permutations in lexicographical order.

EDIT: added recursive to make the purpose of the suggestion clearer.

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