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fix: revert the ‹ThemedSVG› shite
Signed-off-by: Matej Focko <me@mfocko.xyz>
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3 changed files with 32 additions and 30 deletions
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@ -13,8 +13,6 @@ last_update:
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date: 2021-03-31
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---
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import ThemedSVG from "@site/src/components/ThemedSVG";
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## Introduction
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Each year there is a lot of confusion regarding time complexity of the `extend` operation on the lists in Python. I will introduce two specific examples from previous year and also will try to explain it on one of the possible implementations of `extend` operation.
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@ -88,10 +86,8 @@ As we could observe in the example above, `extend` iterates over all of the elem
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Consider constructing of this list:
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<ThemedSVG
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source="/files/ib002/time-complexity/extend/construction"
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alt="Rendered construction of the list"
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/>
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Let us assume that you extend the result with the list that you get from the recursive call.
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@ -10,8 +10,6 @@ last_update:
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date: 2023-06-10
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---
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import ThemedSVG from "@site/src/components/ThemedSVG";
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## Introduction
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Have you ever thought about the red-black tree rules in more depth? Why are they
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@ -57,10 +55,8 @@ my child would be colored red.
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Example of a red-black tree that keeps count of black nodes on paths to the
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leaves follows:
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<ThemedSVG
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source="/files/ib002/rb-trees/rules/rb_height"
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alt="Red-black tree with black height"
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/>
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We mark the _black heights_ in superscript. You can see that all leaves have the
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black height equal to $1$. Let's take a look at some of the interesting cases:
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@ -144,15 +140,15 @@ accordingly.
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| Usual algorithm with black root | Allowing red root |
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| :-----------------------------: | :---------------: |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_0" alt="1ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_0" alt="1ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_1" alt="2ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_1" alt="2ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_2" alt="3ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_2" alt="3ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_3" alt="4ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_3" alt="4ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_4" alt="5ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_4" alt="5ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_5" alt="6ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_5" alt="6ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_6" alt="7ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_6" alt="7ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_7" alt="8ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_7" alt="8ª insertion" /> |
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| <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/br_8" alt="9ª insertion" /> | <ThemedSVG source="/files/ib002/rb-trees/rules/red-root/rr_8" alt="9ª insertion" /> |
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## 3ª Every leaf (`nil`) is black.
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@ -161,7 +157,8 @@ some other way? Let's go through some of the possible ways I can look at this an
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how would they affect the other rules and balancing.
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We will experiment with the following tree:
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<ThemedSVG source="/files/ib002/rb-trees/rules/rb" />
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We should start by counting the black nodes from root to the `nil` leaves based
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on the rules. We have multiple similar paths, so we will pick only the interesting
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@ -234,11 +231,17 @@ import TabItem from '@theme/TabItem';
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<Tabs>
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<TabItem value="enforcing" label="Enforcing this rule">
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<ThemedSVG source="/files/ib002/rb-trees/rules/red-node-black-children/correct" />
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</TabItem>
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<TabItem value="omitting" label="Omitting this rule">
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<ThemedSVG source="/files/ib002/rb-trees/rules/red-node-black-children/incorrect" />
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</TabItem>
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</Tabs>
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@ -10,8 +10,6 @@ last_update:
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date: 2022-04-30
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---
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import ThemedSVG from "@site/src/components/ThemedSVG";
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## Introduction
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As we have talked on the seminar, if we construct from some vertex $u$ BFS tree on an undirected graph, we can obtain:
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@ -23,11 +21,13 @@ As we have talked on the seminar, if we construct from some vertex $u$ BFS tree
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Consider the following graph:
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<ThemedSVG source="/files/ib002/graphs/bfs-tree/bfs_graph" />
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We run BFS from the vertex $a$ and obtain the following BFS tree:
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<ThemedSVG source="/files/ib002/graphs/bfs-tree/bfs_tree" />
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Let's consider pair of vertices $e$ and $h$. For them we can safely lay, from the BFS tree, following properties:
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@ -42,7 +42,9 @@ Let's keep the same graph, but break the lower bound, i.e. I have gotten a lower
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Now the more important question, is there a shorter path in that graph? The answer is no, there's no shorter path than the one with length $2$. So what can we do about it? We'll add an edge to have a shorter path. Now we have gotten a lower bound of $2$, which means the only shorter path we can construct has $1$ edge and that is ‹$e, h$› (no intermediary vertices). Let's do this!
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<ThemedSVG source="/files/ib002/bfs-tree/bfs_graph_with_additional_edge" />
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Okay, so we have a graph that breaks the rule we have laid. However, we need to run BFS to obtain the new BFS tree, since we have changed the graph.
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@ -54,7 +56,8 @@ Do we need to run BFS after **every** change?
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:::
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<ThemedSVG source="/files/ib002/bfs-tree/bfs_tree_with_additional_edge" />
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Oops, we have gotten a new BFS tree, that has a height difference of 1.
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