diff --git a/ib002/03-time-complexity/extend.md b/ib002/03-time-complexity/extend.mdx
similarity index 96%
rename from ib002/03-time-complexity/extend.md
rename to ib002/03-time-complexity/extend.mdx
index 2d697ca..a9ce564 100644
--- a/ib002/03-time-complexity/extend.md
+++ b/ib002/03-time-complexity/extend.mdx
@@ -10,6 +10,8 @@ tags:
- recursion
---
+import ThemedSVG from "@site/src/components/ThemedSVG";
+
## Introduction
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.
@@ -83,7 +85,10 @@ As we could observe in the example above, `extend` iterates over all of the elem
Consider constructing of this list:
-![Rendered construction of the list](/files/ib002/extend/construction_light.svg#gh-light-mode-only)![Rendered construction of the list](/files/ib002/extend/construction_dark.svg#gh-dark-mode-only)
+
Let us assume that you extend the result with the list that you get from the recursive call.
diff --git a/ib002/08-rb-trees/rules.md b/ib002/08-rb-trees/rules.mdx
similarity index 93%
rename from ib002/08-rb-trees/rules.md
rename to ib002/08-rb-trees/rules.mdx
index e6387ce..386ca3c 100644
--- a/ib002/08-rb-trees/rules.md
+++ b/ib002/08-rb-trees/rules.mdx
@@ -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)
+
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)
+
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';
+
+
+
+
+
+
+
+
+
+
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
diff --git a/ib002/10-graphs/bfs-tree.md b/ib002/10-graphs/bfs-tree.mdx
similarity index 76%
rename from ib002/10-graphs/bfs-tree.md
rename to ib002/10-graphs/bfs-tree.mdx
index 388d17b..bef5f0d 100644
--- a/ib002/10-graphs/bfs-tree.md
+++ b/ib002/10-graphs/bfs-tree.mdx
@@ -7,6 +7,8 @@ tags:
- bfs
---
+import ThemedSVG from "@site/src/components/ThemedSVG";
+
## Introduction
As we have talked on the seminar, if we construct from some vertex $u$ BFS tree on an undirected graph, we can obtain:
@@ -18,11 +20,11 @@ As we have talked on the seminar, if we construct from some vertex $u$ BFS tree
Consider the following graph:
-![BFS graph](/files/ib002/bfs-tree/bfs_graph_light.svg#gh-light-mode-only)![BFS graph](/files/ib002/bfs-tree/bfs_graph_dark.svg#gh-dark-mode-only)
+
We run BFS from the vertex $a$ and obtain the following BFS tree:
-![BFS tree](/files/ib002/bfs-tree/bfs_tree_light.svg#gh-light-mode-only)![BFS tree](/files/ib002/bfs-tree/bfs_tree_dark.svg#gh-dark-mode-only)
+
Let's consider pair of vertices $e$ and $h$. For them we can safely lay, from the BFS tree, following properties:
@@ -37,7 +39,7 @@ Let's keep the same graph, but break the lower bound, i.e. I have gotten a lower
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!
-![BFS tree](/files/ib002/bfs-tree/bfs_graph_with_additional_edge_light.svg#gh-light-mode-only)![BFS tree](/files/ib002/bfs-tree/bfs_graph_with_additional_edge_dark.svg#gh-dark-mode-only)
+
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.
@@ -49,7 +51,7 @@ Do we need to run BFS after **every** change?
:::
-![BFS tree](/files/ib002/bfs-tree/bfs_tree_with_additional_edge_light.svg#gh-light-mode-only)![BFS tree](/files/ib002/bfs-tree/bfs_tree_with_additional_edge_dark.svg#gh-dark-mode-only)
+
Oops, we have gotten a new BFS tree, that has a height difference of 1.