algorithms(avl): add WIP

Signed-off-by: Matej Focko <me@mfocko.xyz>

algorithms/08-rb-trees/2024-01-22-avl.md

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+---
+id: avl
+title: AVL tree
+description: |
+  Looking at a tree that's very similar to the red-black tree.
+tags:
+  - AVL tree
+  - balanced trees
+  - zig
+last_update:
+  date: 2024-01-22
+---
+
+## Introduction
+
+AVL tree is the first self-balanced tree to be ever invented. However if we look
+at the commonly used data structures to represent the set or a map, we will find
+out that red-black trees (or even its relaxation LLRB[^1]) or hash tables are
+the most used.
+
+Let's look into the AVL tree and how it is related to its “successor” red-black
+tree, they are closer than you can imagine.
+
+## Properties
+
+AVL tree is height-balanced same as the red-black tree. The key difference lies
+in the invariants that need to be satisfied. In this case we require that
+subtrees of any node differ in their heights at most by 1. If we were to write
+it as a condition for node $n$, we can write it like:
+
+$$
+\vert Height(Right(n)) - Height(Left(n)) \vert \leq 1
+$$
+
+Because the only allowed values here are $\left\{ -1, 0, 1 \right\}$, it is
+possible to simplify the structure of the nodes in memory by using a one byte of
+memory to store the “state” of the subtrees in a node.
+
+:::tip
+
+Some representations use a _sign_ notation of `+`, `0` and `-` which represent
+where is the tree leaning to:
+
+- `-` means the left subtree has bigger height ⇒ tree is leaning to left
+- `0` means both subtrees have the same height ⇒ they're equal
+- `+` means the right subtree has bigger height ⇒ tree is leaning to right
+
+:::
+
+It is also possible to find representations that allow leaning only to one side,
+by enforcing this requirement you can use just boolean to represent the state,
+i.e. the tree _is_ leaning to one side, or _is not_.
+
+## Implementation
+
+Let's have a look at the implementation of the AVL tree in some language.
+
+## Insertion
+
+## Deletion
+
+## Comparison with the red-black tree
+
+## Bonus: Implementation of the BST in Java
+
+[^1]: [Left-leaning Red-Black trees](https://sedgewick.io/wp-content/themes/sedgewick/papers/2008LLRB.pdf)

static/files/algorithms/rb-trees/avl/.editorconfig

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+root = true
+
+# All files
+[*]
+indent_style = space
+
+# Xml files
+[*.xml]
+indent_size = 2
+
+# C# files
+[*.cs]
+
+#### Core EditorConfig Options ####
+
+# Indentation and spacing
+indent_size = 4
+tab_width = 4
+
+# New line preferences
+end_of_line = crlf
+insert_final_newline = false
+
+#### .NET Coding Conventions ####
+[*.{cs,vb}]
+
+# Organize usings
+dotnet_separate_import_directive_groups = true
+dotnet_sort_system_directives_first = true
+file_header_template = unset
+
+# this. and Me. preferences
+dotnet_style_qualification_for_event = false:silent
+dotnet_style_qualification_for_field = false:silent
+dotnet_style_qualification_for_method = false:silent
+dotnet_style_qualification_for_property = false:silent
+
+# Language keywords vs BCL types preferences
+dotnet_style_predefined_type_for_locals_parameters_members = true:silent
+dotnet_style_predefined_type_for_member_access = true:silent
+
+# Parentheses preferences
+dotnet_style_parentheses_in_arithmetic_binary_operators = always_for_clarity:silent
+dotnet_style_parentheses_in_other_binary_operators = always_for_clarity:silent
+dotnet_style_parentheses_in_other_operators = never_if_unnecessary:silent
+dotnet_style_parentheses_in_relational_binary_operators = always_for_clarity:silent
+
+# Modifier preferences
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+# Expression-level preferences
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+dotnet_style_collection_initializer = true:suggestion
+dotnet_style_explicit_tuple_names = true:suggestion
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+dotnet_style_prefer_simplified_boolean_expressions = true:suggestion
+dotnet_style_prefer_simplified_interpolation = true:suggestion
+
+# Field preferences
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+# Parameter preferences
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+[*.cs]
+
+# var preferences
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+csharp_style_var_when_type_is_apparent = false:silent
+
+# Expression-bodied members
+csharp_style_expression_bodied_accessors = true:silent
+csharp_style_expression_bodied_constructors = false:silent
+csharp_style_expression_bodied_indexers = true:silent
+csharp_style_expression_bodied_lambdas = true:suggestion
+csharp_style_expression_bodied_local_functions = false:silent
+csharp_style_expression_bodied_methods = false:silent
+csharp_style_expression_bodied_operators = false:silent
+csharp_style_expression_bodied_properties = true:silent
+
+# Pattern matching preferences
+csharp_style_pattern_matching_over_as_with_null_check = true:suggestion
+csharp_style_pattern_matching_over_is_with_cast_check = true:suggestion
+csharp_style_prefer_not_pattern = true:suggestion
+csharp_style_prefer_pattern_matching = true:silent
+csharp_style_prefer_switch_expression = true:suggestion
+
+# Null-checking preferences
+csharp_style_conditional_delegate_call = true:suggestion
+
+# Modifier preferences
+csharp_prefer_static_local_function = true:warning
+csharp_preferred_modifier_order = public,private,protected,internal,static,extern,new,virtual,abstract,sealed,override,readonly,unsafe,volatile,async:silent
+
+# Code-block preferences
+csharp_prefer_braces = true:silent
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+
+# Expression-level preferences
+csharp_prefer_simple_default_expression = true:suggestion
+csharp_style_deconstructed_variable_declaration = true:suggestion
+csharp_style_inlined_variable_declaration = true:suggestion
+csharp_style_pattern_local_over_anonymous_function = true:suggestion
+csharp_style_prefer_index_operator = true:suggestion
+csharp_style_prefer_range_operator = true:suggestion
+csharp_style_throw_expression = true:suggestion
+csharp_style_unused_value_assignment_preference = discard_variable:suggestion
+csharp_style_unused_value_expression_statement_preference = discard_variable:silent
+
+# 'using' directive preferences
+csharp_using_directive_placement = outside_namespace:silent
+
+#### C# Formatting Rules ####
+
+# New line preferences
+csharp_new_line_before_catch = false
+csharp_new_line_before_else = false
+csharp_new_line_before_finally = false
+csharp_new_line_before_members_in_anonymous_types = false
+csharp_new_line_before_members_in_object_initializers = false
+csharp_new_line_before_open_brace = false
+csharp_new_line_between_query_expression_clauses = true
+
+# Indentation preferences
+csharp_indent_block_contents = true
+csharp_indent_braces = false
+csharp_indent_case_contents = true
+csharp_indent_case_contents_when_block = true
+csharp_indent_labels = one_less_than_current
+csharp_indent_switch_labels = true
+
+# Space preferences
+csharp_space_after_cast = false
+csharp_space_after_colon_in_inheritance_clause = true
+csharp_space_after_comma = true
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+csharp_space_after_semicolon_in_for_statement = true
+csharp_space_around_binary_operators = before_and_after
+csharp_space_around_declaration_statements = false
+csharp_space_before_colon_in_inheritance_clause = true
+csharp_space_before_comma = false
+csharp_space_before_dot = false
+csharp_space_before_open_square_brackets = false
+csharp_space_before_semicolon_in_for_statement = false
+csharp_space_between_empty_square_brackets = false
+csharp_space_between_method_call_empty_parameter_list_parentheses = false
+csharp_space_between_method_call_name_and_opening_parenthesis = false
+csharp_space_between_method_call_parameter_list_parentheses = false
+csharp_space_between_method_declaration_empty_parameter_list_parentheses = false
+csharp_space_between_method_declaration_name_and_open_parenthesis = false
+csharp_space_between_method_declaration_parameter_list_parentheses = false
+csharp_space_between_parentheses = false
+csharp_space_between_square_brackets = false
+
+# Wrapping preferences
+csharp_preserve_single_line_blocks = true
+csharp_preserve_single_line_statements = true
+
+#### Naming styles ####
+[*.{cs,vb}]
+
+# Naming rules
+
+dotnet_naming_rule.types_and_namespaces_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.types_and_namespaces_should_be_pascalcase.symbols = types_and_namespaces
+dotnet_naming_rule.types_and_namespaces_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.interfaces_should_be_ipascalcase.severity = suggestion
+dotnet_naming_rule.interfaces_should_be_ipascalcase.symbols = interfaces
+dotnet_naming_rule.interfaces_should_be_ipascalcase.style = ipascalcase
+
+dotnet_naming_rule.type_parameters_should_be_tpascalcase.severity = suggestion
+dotnet_naming_rule.type_parameters_should_be_tpascalcase.symbols = type_parameters
+dotnet_naming_rule.type_parameters_should_be_tpascalcase.style = tpascalcase
+
+dotnet_naming_rule.methods_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.methods_should_be_pascalcase.symbols = methods
+dotnet_naming_rule.methods_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.properties_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.properties_should_be_pascalcase.symbols = properties
+dotnet_naming_rule.properties_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.events_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.events_should_be_pascalcase.symbols = events
+dotnet_naming_rule.events_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.local_variables_should_be_camelcase.severity = suggestion
+dotnet_naming_rule.local_variables_should_be_camelcase.symbols = local_variables
+dotnet_naming_rule.local_variables_should_be_camelcase.style = camelcase
+
+dotnet_naming_rule.local_constants_should_be_camelcase.severity = suggestion
+dotnet_naming_rule.local_constants_should_be_camelcase.symbols = local_constants
+dotnet_naming_rule.local_constants_should_be_camelcase.style = camelcase
+
+dotnet_naming_rule.parameters_should_be_camelcase.severity = suggestion
+dotnet_naming_rule.parameters_should_be_camelcase.symbols = parameters
+dotnet_naming_rule.parameters_should_be_camelcase.style = camelcase
+
+dotnet_naming_rule.public_fields_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.public_fields_should_be_pascalcase.symbols = public_fields
+dotnet_naming_rule.public_fields_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.private_fields_should_be__camelcase.severity = suggestion
+dotnet_naming_rule.private_fields_should_be__camelcase.symbols = private_fields
+dotnet_naming_rule.private_fields_should_be__camelcase.style = _camelcase
+
+dotnet_naming_rule.private_static_fields_should_be_s_camelcase.severity = suggestion
+dotnet_naming_rule.private_static_fields_should_be_s_camelcase.symbols = private_static_fields
+dotnet_naming_rule.private_static_fields_should_be_s_camelcase.style = s_camelcase
+
+dotnet_naming_rule.public_constant_fields_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.public_constant_fields_should_be_pascalcase.symbols = public_constant_fields
+dotnet_naming_rule.public_constant_fields_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.private_constant_fields_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.private_constant_fields_should_be_pascalcase.symbols = private_constant_fields
+dotnet_naming_rule.private_constant_fields_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.public_static_readonly_fields_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.public_static_readonly_fields_should_be_pascalcase.symbols = public_static_readonly_fields
+dotnet_naming_rule.public_static_readonly_fields_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.private_static_readonly_fields_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.private_static_readonly_fields_should_be_pascalcase.symbols = private_static_readonly_fields
+dotnet_naming_rule.private_static_readonly_fields_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.enums_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.enums_should_be_pascalcase.symbols = enums
+dotnet_naming_rule.enums_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.local_functions_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.local_functions_should_be_pascalcase.symbols = local_functions
+dotnet_naming_rule.local_functions_should_be_pascalcase.style = pascalcase
+
+dotnet_naming_rule.non_field_members_should_be_pascalcase.severity = suggestion
+dotnet_naming_rule.non_field_members_should_be_pascalcase.symbols = non_field_members
+dotnet_naming_rule.non_field_members_should_be_pascalcase.style = pascalcase
+
+# Symbol specifications
+
+dotnet_naming_symbols.interfaces.applicable_kinds = interface
+dotnet_naming_symbols.interfaces.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.interfaces.required_modifiers =
+
+dotnet_naming_symbols.enums.applicable_kinds = enum
+dotnet_naming_symbols.enums.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.enums.required_modifiers =
+
+dotnet_naming_symbols.events.applicable_kinds = event
+dotnet_naming_symbols.events.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.events.required_modifiers =
+
+dotnet_naming_symbols.methods.applicable_kinds = method
+dotnet_naming_symbols.methods.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.methods.required_modifiers =
+
+dotnet_naming_symbols.properties.applicable_kinds = property
+dotnet_naming_symbols.properties.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.properties.required_modifiers =
+
+dotnet_naming_symbols.public_fields.applicable_kinds = field
+dotnet_naming_symbols.public_fields.applicable_accessibilities = public, internal
+dotnet_naming_symbols.public_fields.required_modifiers =
+
+dotnet_naming_symbols.private_fields.applicable_kinds = field
+dotnet_naming_symbols.private_fields.applicable_accessibilities = private, protected, protected_internal, private_protected
+dotnet_naming_symbols.private_fields.required_modifiers =
+
+dotnet_naming_symbols.private_static_fields.applicable_kinds = field
+dotnet_naming_symbols.private_static_fields.applicable_accessibilities = private, protected, protected_internal, private_protected
+dotnet_naming_symbols.private_static_fields.required_modifiers = static
+
+dotnet_naming_symbols.types_and_namespaces.applicable_kinds = namespace, class, struct, interface, enum
+dotnet_naming_symbols.types_and_namespaces.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.types_and_namespaces.required_modifiers =
+
+dotnet_naming_symbols.non_field_members.applicable_kinds = property, event, method
+dotnet_naming_symbols.non_field_members.applicable_accessibilities = public, internal, private, protected, protected_internal, private_protected
+dotnet_naming_symbols.non_field_members.required_modifiers =
+
+dotnet_naming_symbols.type_parameters.applicable_kinds = namespace
+dotnet_naming_symbols.type_parameters.applicable_accessibilities = *
+dotnet_naming_symbols.type_parameters.required_modifiers =
+
+dotnet_naming_symbols.private_constant_fields.applicable_kinds = field
+dotnet_naming_symbols.private_constant_fields.applicable_accessibilities = private, protected, protected_internal, private_protected
+dotnet_naming_symbols.private_constant_fields.required_modifiers = const
+
+dotnet_naming_symbols.local_variables.applicable_kinds = local
+dotnet_naming_symbols.local_variables.applicable_accessibilities = local
+dotnet_naming_symbols.local_variables.required_modifiers =
+
+dotnet_naming_symbols.local_constants.applicable_kinds = local
+dotnet_naming_symbols.local_constants.applicable_accessibilities = local
+dotnet_naming_symbols.local_constants.required_modifiers = const
+
+dotnet_naming_symbols.parameters.applicable_kinds = parameter
+dotnet_naming_symbols.parameters.applicable_accessibilities = *
+dotnet_naming_symbols.parameters.required_modifiers =
+
+dotnet_naming_symbols.public_constant_fields.applicable_kinds = field
+dotnet_naming_symbols.public_constant_fields.applicable_accessibilities = public, internal
+dotnet_naming_symbols.public_constant_fields.required_modifiers = const
+
+dotnet_naming_symbols.public_static_readonly_fields.applicable_kinds = field
+dotnet_naming_symbols.public_static_readonly_fields.applicable_accessibilities = public, internal
+dotnet_naming_symbols.public_static_readonly_fields.required_modifiers = readonly, static
+
+dotnet_naming_symbols.private_static_readonly_fields.applicable_kinds = field
+dotnet_naming_symbols.private_static_readonly_fields.applicable_accessibilities = private, protected, protected_internal, private_protected
+dotnet_naming_symbols.private_static_readonly_fields.required_modifiers = readonly, static
+
+dotnet_naming_symbols.local_functions.applicable_kinds = local_function
+dotnet_naming_symbols.local_functions.applicable_accessibilities = *
+dotnet_naming_symbols.local_functions.required_modifiers =
+
+# Naming styles
+
+dotnet_naming_style.pascalcase.required_prefix =
+dotnet_naming_style.pascalcase.required_suffix =
+dotnet_naming_style.pascalcase.word_separator =
+dotnet_naming_style.pascalcase.capitalization = pascal_case
+
+dotnet_naming_style.ipascalcase.required_prefix = I
+dotnet_naming_style.ipascalcase.required_suffix =
+dotnet_naming_style.ipascalcase.word_separator =
+dotnet_naming_style.ipascalcase.capitalization = pascal_case
+
+dotnet_naming_style.tpascalcase.required_prefix = T
+dotnet_naming_style.tpascalcase.required_suffix =
+dotnet_naming_style.tpascalcase.word_separator =
+dotnet_naming_style.tpascalcase.capitalization = pascal_case
+
+dotnet_naming_style._camelcase.required_prefix = _
+dotnet_naming_style._camelcase.required_suffix =
+dotnet_naming_style._camelcase.word_separator =
+dotnet_naming_style._camelcase.capitalization = camel_case
+
+dotnet_naming_style.camelcase.required_prefix =
+dotnet_naming_style.camelcase.required_suffix =
+dotnet_naming_style.camelcase.word_separator =
+dotnet_naming_style.camelcase.capitalization = camel_case
+
+dotnet_naming_style.s_camelcase.required_prefix = s_
+dotnet_naming_style.s_camelcase.required_suffix =
+dotnet_naming_style.s_camelcase.word_separator =
+dotnet_naming_style.s_camelcase.capitalization = camel_case

static/files/algorithms/rb-trees/avl/.gitignore

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+## Ignore Visual Studio temporary files, build results, and
+## files generated by popular Visual Studio add-ons.
+##
+## Get latest from `dotnet new gitignore`
+
+# dotenv files
+.env
+
+# User-specific files
+*.rsuser
+*.suo
+*.user
+*.userosscache
+*.sln.docstates
+
+# User-specific files (MonoDevelop/Xamarin Studio)
+*.userprefs
+
+# Mono auto generated files
+mono_crash.*
+
+# Build results
+[Dd]ebug/
+[Dd]ebugPublic/
+[Rr]elease/
+[Rr]eleases/
+x64/
+x86/
+[Ww][Ii][Nn]32/
+[Aa][Rr][Mm]/
+[Aa][Rr][Mm]64/
+bld/
+[Bb]in/
+[Oo]bj/
+[Ll]og/
+[Ll]ogs/
+
+# Visual Studio 2015/2017 cache/options directory
+.vs/
+# Uncomment if you have tasks that create the project's static files in wwwroot
+#wwwroot/
+
+# Visual Studio 2017 auto generated files
+Generated\ Files/
+
+# MSTest test Results
+[Tt]est[Rr]esult*/
+[Bb]uild[Ll]og.*
+
+# NUnit
+*.VisualState.xml
+TestResult.xml
+nunit-*.xml
+
+# Build Results of an ATL Project
+[Dd]ebugPS/
+[Rr]eleasePS/
+dlldata.c
+
+# Benchmark Results
+BenchmarkDotNet.Artifacts/
+
+# .NET
+project.lock.json
+project.fragment.lock.json
+artifacts/
+
+# Tye
+.tye/
+
+# ASP.NET Scaffolding
+ScaffoldingReadMe.txt
+
+# StyleCop
+StyleCopReport.xml
+
+# Files built by Visual Studio
+*_i.c
+*_p.c
+*_h.h
+*.ilk
+*.meta
+*.obj
+*.iobj
+*.pch
+*.pdb
+*.ipdb
+*.pgc
+*.pgd
+*.rsp
+*.sbr
+*.tlb
+*.tli
+*.tlh
+*.tmp
+*.tmp_proj
+*_wpftmp.csproj
+*.log
+*.tlog
+*.vspscc
+*.vssscc
+.builds
+*.pidb
+*.svclog
+*.scc
+
+# Chutzpah Test files
+_Chutzpah*
+
+# Visual C++ cache files
+ipch/
+*.aps
+*.ncb
+*.opendb
+*.opensdf
+*.sdf
+*.cachefile
+*.VC.db
+*.VC.VC.opendb
+
+# Visual Studio profiler
+*.psess
+*.vsp
+*.vspx
+*.sap
+
+# Visual Studio Trace Files
+*.e2e
+
+# TFS 2012 Local Workspace
+$tf/
+
+# Guidance Automation Toolkit
+*.gpState
+
+# ReSharper is a .NET coding add-in
+_ReSharper*/
+*.[Rr]e[Ss]harper
+*.DotSettings.user
+
+# TeamCity is a build add-in
+_TeamCity*
+
+# DotCover is a Code Coverage Tool
+*.dotCover
+
+# AxoCover is a Code Coverage Tool
+.axoCover/*
+!.axoCover/settings.json
+
+# Coverlet is a free, cross platform Code Coverage Tool
+coverage*.json
+coverage*.xml
+coverage*.info
+
+# Visual Studio code coverage results
+*.coverage
+*.coveragexml
+
+# NCrunch
+_NCrunch_*
+.*crunch*.local.xml
+nCrunchTemp_*
+
+# MightyMoose
+*.mm.*
+AutoTest.Net/
+
+# Web workbench (sass)
+.sass-cache/
+
+# Installshield output folder
+[Ee]xpress/
+
+# DocProject is a documentation generator add-in
+DocProject/buildhelp/
+DocProject/Help/*.HxT
+DocProject/Help/*.HxC
+DocProject/Help/*.hhc
+DocProject/Help/*.hhk
+DocProject/Help/*.hhp
+DocProject/Help/Html2
+DocProject/Help/html
+
+# Click-Once directory
+publish/
+
+# Publish Web Output
+*.[Pp]ublish.xml
+*.azurePubxml
+# Note: Comment the next line if you want to checkin your web deploy settings,
+# but database connection strings (with potential passwords) will be unencrypted
+*.pubxml
+*.publishproj
+
+# Microsoft Azure Web App publish settings. Comment the next line if you want to
+# checkin your Azure Web App publish settings, but sensitive information contained
+# in these scripts will be unencrypted
+PublishScripts/
+
+# NuGet Packages
+*.nupkg
+# NuGet Symbol Packages
+*.snupkg
+# The packages folder can be ignored because of Package Restore
+**/[Pp]ackages/*
+# except build/, which is used as an MSBuild target.
+!**/[Pp]ackages/build/
+# Uncomment if necessary however generally it will be regenerated when needed
+#!**/[Pp]ackages/repositories.config
+# NuGet v3's project.json files produces more ignorable files
+*.nuget.props
+*.nuget.targets
+
+# Microsoft Azure Build Output
+csx/
+*.build.csdef
+
+# Microsoft Azure Emulator
+ecf/
+rcf/
+
+# Windows Store app package directories and files
+AppPackages/
+BundleArtifacts/
+Package.StoreAssociation.xml
+_pkginfo.txt
+*.appx
+*.appxbundle
+*.appxupload
+
+# Visual Studio cache files
+# files ending in .cache can be ignored
+*.[Cc]ache
+# but keep track of directories ending in .cache
+!?*.[Cc]ache/
+
+# Others
+ClientBin/
+~$*
+*~
+*.dbmdl
+*.dbproj.schemaview
+*.jfm
+*.pfx
+*.publishsettings
+orleans.codegen.cs
+
+# Including strong name files can present a security risk
+# (https://github.com/github/gitignore/pull/2483#issue-259490424)
+#*.snk
+
+# Since there are multiple workflows, uncomment next line to ignore bower_components
+# (https://github.com/github/gitignore/pull/1529#issuecomment-104372622)
+#bower_components/
+
+# RIA/Silverlight projects
+Generated_Code/
+
+# Backup & report files from converting an old project file
+# to a newer Visual Studio version. Backup files are not needed,
+# because we have git ;-)
+_UpgradeReport_Files/
+Backup*/
+UpgradeLog*.XML
+UpgradeLog*.htm
+ServiceFabricBackup/
+*.rptproj.bak
+
+# SQL Server files
+*.mdf
+*.ldf
+*.ndf
+
+# Business Intelligence projects
+*.rdl.data
+*.bim.layout
+*.bim_*.settings
+*.rptproj.rsuser
+*- [Bb]ackup.rdl
+*- [Bb]ackup ([0-9]).rdl
+*- [Bb]ackup ([0-9][0-9]).rdl
+
+# Microsoft Fakes
+FakesAssemblies/
+
+# GhostDoc plugin setting file
+*.GhostDoc.xml
+
+# Node.js Tools for Visual Studio
+.ntvs_analysis.dat
+node_modules/
+
+# Visual Studio 6 build log
+*.plg
+
+# Visual Studio 6 workspace options file
+*.opt
+
+# Visual Studio 6 auto-generated workspace file (contains which files were open etc.)
+*.vbw
+
+# Visual Studio 6 auto-generated project file (contains which files were open etc.)
+*.vbp
+
+# Visual Studio 6 workspace and project file (working project files containing files to include in project)
+*.dsw
+*.dsp
+
+# Visual Studio 6 technical files
+*.ncb
+*.aps
+
+# Visual Studio LightSwitch build output
+**/*.HTMLClient/GeneratedArtifacts
+**/*.DesktopClient/GeneratedArtifacts
+**/*.DesktopClient/ModelManifest.xml
+**/*.Server/GeneratedArtifacts
+**/*.Server/ModelManifest.xml
+_Pvt_Extensions
+
+# Paket dependency manager
+.paket/paket.exe
+paket-files/
+
+# FAKE - F# Make
+.fake/
+
+# CodeRush personal settings
+.cr/personal
+
+# Python Tools for Visual Studio (PTVS)
+__pycache__/
+*.pyc
+
+# Cake - Uncomment if you are using it
+# tools/**
+# !tools/packages.config
+
+# Tabs Studio
+*.tss
+
+# Telerik's JustMock configuration file
+*.jmconfig
+
+# BizTalk build output
+*.btp.cs
+*.btm.cs
+*.odx.cs
+*.xsd.cs
+
+# OpenCover UI analysis results
+OpenCover/
+
+# Azure Stream Analytics local run output
+ASALocalRun/
+
+# MSBuild Binary and Structured Log
+*.binlog
+
+# NVidia Nsight GPU debugger configuration file
+*.nvuser
+
+# MFractors (Xamarin productivity tool) working folder
+.mfractor/
+
+# Local History for Visual Studio
+.localhistory/
+
+# Visual Studio History (VSHistory) files
+.vshistory/
+
+# BeatPulse healthcheck temp database
+healthchecksdb
+
+# Backup folder for Package Reference Convert tool in Visual Studio 2017
+MigrationBackup/
+
+# Ionide (cross platform F# VS Code tools) working folder
+.ionide/
+
+# Fody - auto-generated XML schema
+FodyWeavers.xsd
+
+# VS Code files for those working on multiple tools
+.vscode/*
+!.vscode/settings.json
+!.vscode/tasks.json
+!.vscode/launch.json
+!.vscode/extensions.json
+*.code-workspace
+
+# Local History for Visual Studio Code
+.history/
+
+# Windows Installer files from build outputs
+*.cab
+*.msi
+*.msix
+*.msm
+*.msp
+
+# JetBrains Rider
+*.sln.iml
+.idea
+
+##
+## Visual studio for Mac
+##
+
+
+# globs
+Makefile.in
+*.userprefs
+*.usertasks
+config.make
+config.status
+aclocal.m4
+install-sh
+autom4te.cache/
+*.tar.gz
+tarballs/
+test-results/
+
+# Mac bundle stuff
+*.dmg
+*.app
+
+# content below from: https://github.com/github/gitignore/blob/master/Global/macOS.gitignore
+# General
+.DS_Store
+.AppleDouble
+.LSOverride
+
+# Icon must end with two \r
+Icon
+
+
+# Thumbnails
+._*
+
+# Files that might appear in the root of a volume
+.DocumentRevisions-V100
+.fseventsd
+.Spotlight-V100
+.TemporaryItems
+.Trashes
+.VolumeIcon.icns
+.com.apple.timemachine.donotpresent
+
+# Directories potentially created on remote AFP share
+.AppleDB
+.AppleDesktop
+Network Trash Folder
+Temporary Items
+.apdisk
+
+# content below from: https://github.com/github/gitignore/blob/master/Global/Windows.gitignore
+# Windows thumbnail cache files
+Thumbs.db
+ehthumbs.db
+ehthumbs_vista.db
+
+# Dump file
+*.stackdump
+
+# Folder config file
+[Dd]esktop.ini
+
+# Recycle Bin used on file shares
+$RECYCLE.BIN/
+
+# Windows Installer files
+*.cab
+*.msi
+*.msix
+*.msm
+*.msp
+
+# Windows shortcuts
+*.lnk
+
+# Vim temporary swap files
+*.swp

static/files/algorithms/rb-trees/avl/avl.csproj

@@ -0,0 +1,25 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>net8.0</TargetFramework>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+
+    <IsPackable>false</IsPackable>
+    <IsTestProject>true</IsTestProject>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <PackageReference Include="Microsoft.NET.Test.Sdk" Version="17.6.0" />
+    <PackageReference Include="xunit" Version="2.4.2" />
+    <PackageReference Include="xunit.runner.visualstudio" Version="2.4.5">
+      <IncludeAssets>runtime; build; native; contentfiles; analyzers; buildtransitive</IncludeAssets>
+      <PrivateAssets>all</PrivateAssets>
+    </PackageReference>
+    <PackageReference Include="coverlet.collector" Version="6.0.0">
+      <IncludeAssets>runtime; build; native; contentfiles; analyzers; buildtransitive</IncludeAssets>
+      <PrivateAssets>all</PrivateAssets>
+    </PackageReference>
+  </ItemGroup>
+
+</Project>

static/files/algorithms/rb-trees/avl/avl.sln

@@ -0,0 +1,25 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.5.002.0
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "avl", "avl.csproj", "{82C655B9-83B6-4AB4-8449-1309913DDC8F}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{82C655B9-83B6-4AB4-8449-1309913DDC8F}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{82C655B9-83B6-4AB4-8449-1309913DDC8F}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{82C655B9-83B6-4AB4-8449-1309913DDC8F}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{82C655B9-83B6-4AB4-8449-1309913DDC8F}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {C5C6C0D8-FFA4-4D7A-BE93-6CF1A159F1F2}
+	EndGlobalSection
+EndGlobal

static/files/algorithms/rb-trees/avl/src/AVL.cs

@@ -0,0 +1,49 @@
+using System.Collections;
+
+namespace avl;
+
+class AVL<T>(IComparer<T> comparator) : IEnumerable<T> {
+    private Node<T>? _root = null;
+
+    public AVL() : this(Comparer<T>.Default) { }
+
+    public int Count { get; private set; } = 0;
+    public IComparer<T> Comparator { get; } = comparator;
+
+    public bool Add(T item) {
+        throw new NotImplementedException();
+    }
+
+    public bool Remove(T item) {
+        throw new NotImplementedException();
+    }
+
+    public void Clear() => _root = null;
+
+    public bool Contains(T item) {
+        var node = _root;
+
+        while (node != null) {
+            var cmp = Comparator.Compare(node.Value, item);
+            if (cmp < 0) {
+                node = node.Right;
+            } else if (cmp == 0) {
+                return true;
+            } else {
+                node = node.Left;
+            }
+        }
+
+        return false;
+    }
+
+    public void CopyTo(T[] array, int arrayIndex) {
+        throw new NotImplementedException();
+    }
+
+    public IEnumerator<T> GetEnumerator() {
+        throw new NotImplementedException();
+    }
+
+    IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
+}

static/files/algorithms/rb-trees/avl/src/Node.cs

@@ -0,0 +1,12 @@
+namespace avl;
+
+class Node<T> {
+    public T Value { get; init; }
+
+    public readonly Node<T>? Parent;
+    public readonly Node<T>? Left, Right;
+
+    public Node(T value) {
+        Value = value;
+    }
+}

static/files/algorithms/rb-trees/avl/test/AVL.cs

@@ -0,0 +1,24 @@
+namespace avl.test;
+
+public class AVL {
+    [Fact]
+    public void EmptyTree() {
+        var t = new AVL<int>();
+
+        Assert.Equal(0, t.Count);
+
+        for (int i = 0; i < 10; ++i) {
+            Assert.False(t.Contains(i));
+        }
+    }
+
+    [Fact]
+    public void OneNode() {
+        var t = new AVL<int> {
+            123
+        };
+
+        Assert.Equal(1, t.Count);
+        Assert.True(t.Contains(1));
+    }
+}

static/files/algorithms/rb-trees/avl/test/GlobalUsings.cs

@@ -0,0 +1 @@
+global using Xunit;

static/files/algorithms/rb-trees/avl/test/Node.cs

@@ -0,0 +1,8 @@
+namespace avl.test;
+
+public class Node {
+    [Fact]
+    public void Test1() {
+
+    }
+}