Merge c40a8a9d58 into b1f1a9fc1c

algorithms/99-rank-balanced-trees/01-avl.md

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+---
+id: avl
+slug: /rank-balanced-trees/avl
+title: AVL tree
+description: |
+  Explaining the idea behind the AVL tree.
+tags:
+  - balanced trees
+  - avl tree
+last_update:
+  date: 2024-06-30
+---
+
+Let's start by checking out the AVL tree. We will cover the historic context
+first, then go through the idea behind it and finally we will be able to discuss
+the insertion and deletion corrections that are used to maintain the property of
+a balanced tree.
+
+## Historic context
+
+_TODO_
+
+## Idea
+
+_TODO_
+
+## Insertion
+
+_TODO_
+
+## Deletion
+
+_TODO_

algorithms/99-rank-balanced-trees/02-rank-balanced-tree.md

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+---
+id: core
+slug: /rank-balanced-trees/core
+title: Rank-balanced trees
+description: |
+  Explaining the idea behind the rank-balanced tree.
+tags:
+  - balanced trees
+  - rank-balanced trees
+last_update:
+  date: 2024-06-30
+---

algorithms/99-rank-balanced-trees/03-avl-with-rank.md

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+---
+id: avl-with-rank
+slug: /rank-balanced-trees/avl-with-rank
+title: AVL with rank
+description: |
+  Implementing the AVL tree via rank-balanced tree.
+tags:
+  - balanced trees
+  - rank-balanced trees
+  - avl tree
+last_update:
+  date: 2024-06-30
+---

algorithms/99-rank-balanced-trees/04-rb-with-rank.md

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+---
+id: rb-with-rank
+slug: /rank-balanced-trees/rb-with-rank
+title: Red-black tree with rank
+description: |
+  Implementing the red-black tree via rank-balanced tree.
+tags:
+  - balanced trees
+  - rank-balanced trees
+  - red-black trees
+last_update:
+  date: 2024-06-30
+---

algorithms/99-rank-balanced-trees/05-avl-relaxations.md

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+---
+id: avl-relaxations
+slug: /rank-balanced-trees/avl-relaxations
+title: Relaxations of the AVL tree
+description: |
+  Implementing the WAVL and rAVL trees.
+tags:
+  - balanced trees
+  - rank-balanced trees
+  - avl tree
+  - wavl tree
+  - ravl tree
+last_update:
+  date: 2024-06-30
+---

algorithms/99-rank-balanced-trees/index.md

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+---
+id: index
+slug: /rank-balanced-trees/
+title: Rank-Balanced Trees
+description: |
+  Explaining the rank-balanced trees. The web version of my bachelor thesis.
+tags:
+  - balanced trees
+  - red-black trees
+  - avl tree
+  - wavl tree
+last_update:
+  date: 2024-06-08
+---
+
+Data structures have become a regular part of the essential toolbox for
+problem-solving. In many cases, they also help to improve the existing
+algorithms’ performance, e.g., using a priority queue in _Dijkstra’s algorithm_
+_for the shortest path_. This thesis will mainly discuss the implementation of
+a set.
+
+Currently, the most commonly used implementations of sets use hash tables, but
+we will talk about another common alternative, implementation via self-balancing
+search trees. Compared to a hash table, they provide consistent time complexity,
+but at the cost of a requirement for ordering on the elements. The most
+implemented self-balancing binary tree is a _red-black tree_, as described by
+_Guibas and Sedgewick_[^1]. Among other alternatives, we can find (non-binary)
+_B-tree_[^2] and _AVL tree_[^3].
+
+We will focus on the _Weak AVL_ (_WAVL_) _tree_[^4] that is a relaxed variant of
+the AVL tree, but still provides better balancing than a red-black tree.
+
+We will start by describing the AVL tree, then we will introduce the idea
+of a _rank-balanced tree_. Given this insight we will be able to explore various
+implementations of aforementioned trees using the rank-balanced tree. At the end
+we will focus on the _Weak AVL tree_
+
+[^1]: [A dichromatic framework for balanced trees.](https://doi.org/10.1109/SFCS.1978.3)
+[^2]: [Organization and Maintenance of Large Ordered Indices.](https://doi.org/10.1145/1734663.1734671)
+[^3]:
+    ADELSON-VELSKIJ, Georgij; LANDIS, Evgenij. An algorithm for the
+    organization of information. _Doklady Akad. Nauk SSSR._ 1962, vol. 146,
+    pp. 263–266.
+
+[^4]: [Rank-Balanced Trees](https://doi.org/10.1145/2689412)