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chore: switch to ‹ThemedSVG› where possible

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Signed-off-by: Matej Focko <mfocko@redhat.com>
This commit is contained in:
Matej Focko 2023-07-20 20:30:38 +02:00
parent 568b9194d2
commit b841daccf7
Signed by: mfocko
GPG key ID: 7C47D46246790496
3 changed files with 32 additions and 10 deletions
ib002/08-rb-trees
rules.mdx

25
ib002/08-rb-trees/rules.md → ib002/08-rb-trees/rules.mdx
View file

@ -7,6 +7,8 @@ tags:
- balanced trees
---
import ThemedSVG from "@site/src/components/ThemedSVG";
## Introduction
Have you ever thought about the red-black tree rules in more depth? Why are they
@ -52,7 +54,10 @@ my child would be colored red.
Example of a red-black tree that keeps count of black nodes on paths to the
leaves follows:
![Red-black tree with black height](/files/ib002/rb-trees/rules/rb_height_light.svg#gh-light-mode-only)![Red-black tree with black height](/files/ib002/rb-trees/rules/rb_height_dark.svg#gh-dark-mode-only)
<ThemedSVG
source="/files/ib002/rb-trees/rules/rb_height"
alt="Red-black tree with black height"
/>
We mark the _black heights_ in superscript. You can see that all leaves have the
black height equal to $1$. Let's take a look at some of the interesting cases:
@ -134,6 +139,7 @@ black root property.
If we decide to omit this condition, we need to address it in the pseudocodes
accordingly.
{/* TODO: Switch to the themed SVG */}
| Usual algorithm with black root | Allowing red root |
| :-----------------------------: | :---------------: |
| ![1ª insertion](/files/ib002/rb-trees/rules/red-root/br_0_light.svg#gh-light-mode-only)![1ª insertion](/files/ib002/rb-trees/rules/red-root/br_0_dark.svg#gh-dark-mode-only) | ![1ª insertion](/files/ib002/rb-trees/rules/red-root/rr_0_light.svg#gh-light-mode-only)![1ª insertion](/files/ib002/rb-trees/rules/red-root/rr_0_dark.svg#gh-dark-mode-only) |
@ -153,7 +159,7 @@ some other way? Let's go through some of the possible ways I can look at this an
how would they affect the other rules and balancing.
We will experiment with the following tree:
![Red-black tree](/files/ib002/rb-trees/rules/rb_light.svg#gh-light-mode-only)![Red-black tree](/files/ib002/rb-trees/rules/rb_dark.svg#gh-dark-mode-only)
<ThemedSVG source="/files/ib002/rb-trees/rules/rb" />
We should start by counting the black nodes from root to the `nil` leaves based
on the rules. We have multiple similar paths, so we will pick only the interesting
@ -221,9 +227,18 @@ further.
Let's assume that we do not enforce this rule, you can see how it breaks the
balancing of the tree below.
| Enforcing this rule | Omitting this rule |
| :-----------------: | :----------------: |
| ![correct](/files/ib002/rb-trees/rules/red-node-black-children/correct_light.svg#gh-light-mode-only)![correct](/files/ib002/rb-trees/rules/red-node-black-children/correct_dark.svg#gh-dark-mode-only) | ![incorrect](/files/ib002/rb-trees/rules/red-node-black-children/incorrect_light.svg#gh-light-mode-only)![incorrect](/files/ib002/rb-trees/rules/red-node-black-children/incorrect_dark.svg#gh-dark-mode-only) |
import Tabs from '@theme/Tabs';
import TabItem from '@theme/TabItem';
<Tabs>
<TabItem value="enforcing" label="Enforcing this rule">
<ThemedSVG source="/files/ib002/rb-trees/rules/red-node-black-children/correct" />
</TabItem>
<TabItem value="omitting" label="Omitting this rule">
<ThemedSVG source="/files/ib002/rb-trees/rules/red-node-black-children/incorrect" />
</TabItem>
</Tabs>
We can create a **big** subtree with only red nodes and **even** when keeping
the rest of the rules maintained, it will break the time complexity. It stops us