Tree traversal by Ciro Santilli 40 Updated 2025-07-16
In principle one could talk about tree traversal of unordered trees as a number of possible traversals without a fixed order. But we won't consider that under this section, only deterministic ordered tree traversals.
This is the order in which you would want to transverse to read the chapters of a book.
Like breadth-first search, this also has the property of visiting parents before any children.
Iterative pre-order by Ciro Santilli 40 Updated 2025-07-16
This is the easiest one to do iteratively:
  • pop and visit
  • push right to stack
  • push left to stack
This is the order in which a binary search tree should be traversed for ordered output, i.e.:
This ordering makes sense for binary trees and not k-ary trees in general because if there are more than two nodes it is not clear what the top node should go in the middle of.
This is unlike pre-order depth-first search and post-order depth-first search which generalize obviously to general trees.
Iterative in-order by Ciro Santilli 40 Updated 2025-07-16
This is a bit harder than iterative pre-order: now we have to check if there is a left or right element or not:
  • (START) push current
  • if there is left:
    • move left
  • else:
    • (ELSE) pop
    • visit
    • if there is right
      • move right
      • GOTO START
    • else:
      • GOTO ELSE
The control flow can be slightly simplified if we allow NULLs: www.geeksforgeeks.org/inorder-tree-traversal-without-recursion/
Has the property of visiting all descendants before the parent.
This is the mantra of the semiconductor industry:
  • power and area are the main limiting factors of chips, i.e., your budget:
    • chip area is ultra expensive because there are sporadic errors in the fabrication process, and each error in any part of the chip can potentially break the entire chip. Although there are
      The percentage of working chips is called the yield.
      In some cases however, e.g. if the error only affects single CPU of a multi-core CPU, then they actually deactivate the broken CPU after testing, and sell the worse CPU cheaper with a clear branding of that: this is called binning www.tomshardware.com/uk/reviews/glossary-binning-definition,5892.html
    • power is a major semiconductor limit as of 2010's and onwards. If everything turns on at once, the chip would burn. Designs have to account for that.
  • performance is the goal.
    Conceptually, this is basically a set of algorithms that you want your hardware to solve, each one with a respective weight of importance.
    Serial performance is fundamentally limited by the longest path that electrons have to travel in a given clock cycle.
    The way to work around it is to create pipelines, splitting up single operations into multiple smaller operations, and storing intermediate results in memories.
One of the simplest known seems to be: en.wikipedia.org/wiki/Trichoplax
www.u-tokyo.ac.jp/focus/en/articles/a_00220.html "The simplest multicellular organism unveiled" from 2013 mentions Tetrabaena socialis.
Then of course: Caenorhabditis elegans is a relatively simple and widely studied model organism.
Video 1.
Nicole King (UC Berkeley, HHMI) 1: The origin of animal multicellularity by iBiology (2015)
Source.
Game theory by Ciro Santilli 40 Updated 2025-07-16
As mentioned at Human Compatible by Stuart J. Russell (2019), game theory can be seen as the part of artificial intelligence that deas with scenarios where multiple intelligent agents are involved.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact