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Revert "Revert "build(book): optimize for different formats""
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‎.circleci/config.yml

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- run:
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name: generate PDF
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command: cd book/config && make VERSION="$(npx -c 'echo "$npm_package_version"')" pdf
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command: cd book/config && make VERSION="$(npx -c 'echo "$npm_package_version"')"
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- store_artifacts:
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path: book/dist

‎.gitignore

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# Ruby
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######################
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/.bundle/
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/Gemfile.lock
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######################
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# Package Files
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# ln -s ~/OneDrive/Authoring/dsaJS/asciidoc/book/fonts .
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# ln -s ~/OneDrive/Authoring/dsaJS/asciidoc/book/images .
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######################
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Gemfile
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Gemfile.lock
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Makefile
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_conf
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_resources
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extensions
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fonts
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#Gemfile
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#Gemfile.lock
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#Makefile
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#_conf
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#_resources
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#extensions
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#fonts
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######################

‎README.md

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‎book/A-time-complexity-cheatsheet.asc

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[appendix]
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[[a-time-complexity-cheatsheet]]
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== Cheatsheet
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This section summerize what we are going to cover in the rest of this book.
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=== Runtimes
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include::content/part01/big-o-examples.asc[tag=table]
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include::content/part01/algorithms-analysis.asc[tag=table]
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=== Linear Data Structures
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include::content/part02/array-vs-list-vs-queue-vs-stack.asc[tag=table]
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=== Trees and Maps Data Structures
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This section covers Binary Search Tree (BST) time complexity (Big O).
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include::content/part03/time-complexity-graph-data-structures.asc[tag=table]
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include::content/part03/graph.asc[tag=table]
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=== Sorting Algorithms
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include::content/part04/sorting-algorithms.asc[tag=table]
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// // https://algs4.cs.princeton.edu/cheatsheet/
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// // http://bigocheatsheet.com/
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// // https://en.wikipedia.org/wiki/Timsort (Tim Peters)
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// // https://bugs.python.org/file4451/timsort.txt
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// // https://www.youtube.com/watch?v=emeME__917E&list=PLMCXHnjXnTntLcLmA5SqhMspm7burHi3m
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// // https://en.wikipedia.org/wiki/Sorting_algorithm
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// // http://sorting.at/
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// // https://www.toptal.com/developers/sorting-algorithms
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// // https://www.infopulse.com/blog/timsort-sorting-algorithm/

‎book/chapters/tree-self-balancing-rotations.adoc renamed to ‎book/B-self-balancing-binary-search-trees.asc

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ifndef::imagesdir[]
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:imagesdir: ../images
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:codedir: ../../src
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endif::[]
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= Self-balancing Binary Search Trees
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[appendix]
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[[b-self-balancing-binary-search-trees]]
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== Self-balancing Binary Search Trees
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Binary Search Trees (BST) are an excellent data structure to find elements very fast _O(log n)_.
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However, when the BST branches have different branch sizes, then the performance suffers.
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To be more specific we rotated node `1` to the left to balance the tree.
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Let's examine all the possible rotation we can do to balance a tree.
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== Tree Rotations
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[[tree-rotations]]
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=== Tree Rotations
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(((Tree Rotations)))
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We can do single rotations left and right and also we can do double rotations.
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Let's go one by one.
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=== Single Right Rotation
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==== Single Right Rotation
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Right rotation moves a node on the right as a child of another node.
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.Single right rotation implementation
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[source, javascript]
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----
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include::{codedir}/data-structures/trees/tree-rotations.js[tag=rightRotation]
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include::../src/data-structures/trees/tree-rotations.js[tag=rightRotation]
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.In the `rightRotation` we identify 3 nodes:
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.Swap Parent and Child Implementation
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[source, javascript]
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include::{codedir}/data-structures/trees/tree-rotations.js[tag=swapParentChild]
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include::../src/data-structures/trees/tree-rotations.js[tag=swapParentChild]
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After `swapParentChild`, we have the following:
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This rotation is also known as `RR rotation`.
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=== Single Left Rotation
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==== Single Left Rotation
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Left rotation is similar to the `rightRotation` we explained above.
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.Single left rotation implementation
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[source, javascript]
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include::{codedir}/data-structures/trees/tree-rotations.js[tag=leftRotation]
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include::../src/data-structures/trees/tree-rotations.js[tag=leftRotation]
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As you can see, this function is just the opposite of `rightRotation`. Where ever we used the right now we use the left here and vice versa.
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.Set and update parent implementation
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[source, javascript]
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include::{codedir}/data-structures/trees/binary-tree-node.js[tag=setAndUpdateParent]
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include::../src/data-structures/trees/binary-tree-node.js[tag=setAndUpdateParent]
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----
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You can also check out the full
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https://github.com/amejiarosario/dsa.js/blob/adfd8a660bbe0a7068fd7881aff9f51bdb9f92ae/src/data-structures/trees/binary-tree-node.js#L9[binary tree node implementation].
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=== Left Right Rotation
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==== Left Right Rotation
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This time are we going to do a double rotation.
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.Left-Right rotation implementation
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include::{codedir}/data-structures/trees/tree-rotations.js[tag=leftRightRotation]
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include::../src/data-structures/trees/tree-rotations.js[tag=leftRightRotation]
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As you can see we do a left and then a right rotation. This rotation is also known as `LR rotation`
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=== Right Left Rotation
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==== Right Left Rotation
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.Right-Left rotation implementation
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include::{codedir}/data-structures/trees/tree-rotations.js[tag=rightLeftRotation]
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include::../src/data-structures/trees/tree-rotations.js[tag=rightLeftRotation]
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This rotation is also referred to as `RL rotation`.
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== Self-balancing trees implementations
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=== Self-balancing trees implementations
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So far, we have study how to make tree rotations which are the basis for self-balancing trees. There are different implementations of self-balancing trees such a Red-Black Tree and AVL Tree.
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ifndef::imagesdir[]
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:imagesdir: ../images
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:codedir: ../../src
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endif::[]
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= AVL Tree
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[appendix]
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[[c-avl-tree]]
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== AVL Tree
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(((AVL Tree)))
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(((Tree, AVL)))
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AVL Tree is named after their inventors (**A**delson-**V**elsky and **L**andis).
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This self-balancing tree keeps track of subtree sizes to know if a rebalance is needed or not.
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We can compare the size of the left and right subtrees using a balance factor.
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[NOTE]
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====
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=====
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The *balanced factor* on each node is calculated recursively as follows:
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Balance Factor = (left subtree height) - (right subtree height)
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====
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=====
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The implementation will go in the BST node class.
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include::{codedir}/data-structures/trees/binary-tree-node.js[tag=avl, indent=0]
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include::../src/data-structures/trees/binary-tree-node.js[tag=avl, indent=0]
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== Implementing AVL Tree
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=== Implementing AVL Tree
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.AVL Tree class
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include::{codedir}/data-structures/trees/avl-tree.js[tag=AvlTree]
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include::../src/data-structures/trees/avl-tree.js[tag=AvlTree]
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.Balance Upstream for AVL tree
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include::{codedir}/data-structures/trees/avl-tree.js[tag=balanceUpstream]
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include::../src/data-structures/trees/avl-tree.js[tag=balanceUpstream]
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include::../src/data-structures/trees/avl-tree.js[tag=balance]
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The first thing we do is to see if one subtree is longer than the other.
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You can review <<Tree Rotations>> in case you want a refresher.
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You can review <<b-self-balancing-binary-search-trees#tree-rotations>> in case you want a refresher.

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