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chore: switch to ‹ThemedSVG› where possible
Signed-off-by: Matej Focko <mfocko@redhat.com>
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3 changed files with 32 additions and 10 deletions
ib002
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@ -10,6 +10,8 @@ tags:
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- recursion
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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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@ -83,7 +85,10 @@ 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/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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@ -7,6 +7,8 @@ tags:
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- balanced trees
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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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@ -52,7 +54,10 @@ 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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@ -134,6 +139,7 @@ black root property.
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If we decide to omit this condition, we need to address it in the pseudocodes
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accordingly.
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{/* TODO: Switch to the themed SVG */}
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| Usual algorithm with black root | Allowing red root |
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| :-----------------------------: | :---------------: |
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|  |  |
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@ -153,7 +159,7 @@ 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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@ -221,9 +227,18 @@ further.
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Let's assume that we do not enforce this rule, you can see how it breaks the
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balancing of the tree below.
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| Enforcing this rule | Omitting this rule |
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| :-----------------: | :----------------: |
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|  |  |
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import Tabs from '@theme/Tabs';
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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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We can create a **big** subtree with only red nodes and **even** when keeping
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the rest of the rules maintained, it will break the time complexity. It stops us
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@ -7,6 +7,8 @@ tags:
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- bfs
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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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@ -18,11 +20,11 @@ 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/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/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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@ -37,7 +39,7 @@ 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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@ -49,7 +51,7 @@ 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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