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Would a multiply-rooted tree still be a tree? I thought a single root was part of the definition of a tree. Would it instead be a graph?

Sorry for the elementary questions. I'm bad at algorithms and just trying to get a grasp here.


At my university it's common to call acyclic, connected graph a tree. We distinguish between rooted and unrooted trees. For example, minimal spanning tree doesn't really have to be rooted, it just has no cycles.


> acyclic, connected graph a tree

This is the graph theoretic definition of a tree.


Tree is a graph without any cycles, hence the definition still holds. And yes, you can have multiple roots in a tree, ex:

a --> c <---b ^ d-----|


Yes, it's not a tree any more. Which is why I believe this was not the question.


Could you illustrate? I can find plenty of examples of mirroring/reversing a tree (below the root node) but none that really invert it. I haven't even found a definition of what inverting a tree means (aside from some academic papers I haven't been able to read yet), despite quite a bit of googling.


i'm not exactly sure either, too bad he didnt define "invert".

i based my comment on the only thing I could find: https://wwwx.cs.unc.edu/~duozhao/entry/2014/12/binary-tree-u...

this is only slightly harder than the trivial (if u know recursion) "mirroring" a tree problem


Nobody in this thread has even been able to define what inverting a tree means. (Reversing or mirroring? Sure.) My search for how to invert a tree led to a bunch of fairly hairy academic papers.

If you have a definition, please elucidate.


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I met you and James at my first Ruby conference. I didn't ever get to know James well but that was the start of a sea change in my career.

I never heard that interview but I'm smiling imagining the interaction.


It was a typical podcast talk between typical Rubyists. There's a copy of it up on archive.org:


I think the only people who would really have been offended by it are those who hadn't listen to it :) It's the same sort of banter you hear at clubs, conferences, and other podcasts, except that I'm not very smart and James is (or was... ugh, still having a hard time believing he's gone).


I just listened to it and it is full of good quotes, my favourite: "Discussions without good definitions are doomed to fail." (about the upcoming NoSQL dabate). I feel that's still ringing true in that sector.


Angry Birds was that way at some point, IIRC. Haven't looked in a long time though.


I dabbled with the Red Book aeons ago, but never got very far with 3D programming. What would you suggest for learning OpenGL? Or is there some other tool you'd recommend learning?


This is the list I typically see given to newbies (on freenode ##OpenGL, and /r/opengl) wanting to learn modern OpenGL.

1. Arcsynthesis's gltut (http://www.arcsynthesis.org/gltut/) is good and reasonably thorough. He explains things well but not always in the order you'd like him to. At the end you will probably know enough to be able to figure out the rest on your own as you need.

2. http://open.gl/ is good but somewhat short. It also goes in depth into creating/initializing a context with various APIS (SDL, SFML, GLFW, ...). More of a good starting point than a complete guide.

3. http://ogldev.atspace.co.uk/ has a lot of good tutorials on how to do more advanced techniques, as well as many beginner level tutorials. I've never gone through them so I can't speak to their quality, but I've heard good things.

4. http://www.lighthouse3d.com/tutorials/glsl-core-tutorial/ is also good, but focused on the shading language.

See /r/opengl and freenode's ##OpenGL channel for more. Both those places are fairly newbie friendly (/r/opengl moreso than ##OpenGL, but as long as you actually know your language of choice they're nice), so feel free to ask questions.


For OpenGL 1.2 there was nothing better than http://nehe.gamedev.net/ (e.g. http://nehe.gamedev.net/tutorial/lessons_01__05/22004/), but I don't know if something similar exists for modern OpenGL.


I remember this link being posted recently and since I have some interest in looking into this area as well, it stuck with me (and a browser tab ;) While it's not a tutorial or anything, the article addresses the question "where do I start?" and mentions (not only in the title) "modern OpenGL" specifically.



I'd recommend starting with WebGL. It's the same API minus the cruft. You can use it nearly anywhere.

Here's some tutorials I wrote to hopefully make it clear how things work


Everything you learn there will be directly applicable to C OpenGL


I worked at a place where 50% of our time was supposed to be refactoring/boy scouting/cleanup work. The codebase was so bad and delivery so painful that management endorsed it. But the pressure to deliver never let up and so that policy is now a running joke.


I don't get much out of simply reading code. I have to get my hands in there and see how it works.

I load it into a repl and play around. See how changing little things effects tests. I add print statements to give a narrative. I draw diagrams of the code flow, especially startup, shutdown and sometimes error/exception handling.


People found it an interesting topic and started discussing it.



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