diff --git a/ib002/03-time-complexity/2021-03-31-extend.mdx b/ib002/03-time-complexity/2021-03-31-extend.md
similarity index 96%
rename from ib002/03-time-complexity/2021-03-31-extend.mdx
rename to ib002/03-time-complexity/2021-03-31-extend.md
index b1a7110..49568d4 100644
--- a/ib002/03-time-complexity/2021-03-31-extend.mdx
+++ b/ib002/03-time-complexity/2021-03-31-extend.md
@@ -13,8 +13,6 @@ last_update:
date: 2021-03-31
---
-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.
@@ -88,10 +86,8 @@ As we could observe in the example above, `extend` iterates over all of the elem
Consider constructing of this list:
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+
+
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/2023-06-10-rules.mdx b/ib002/08-rb-trees/2023-06-10-rules.md
similarity index 72%
rename from ib002/08-rb-trees/2023-06-10-rules.mdx
rename to ib002/08-rb-trees/2023-06-10-rules.md
index e7d296d..51a85e5 100644
--- a/ib002/08-rb-trees/2023-06-10-rules.mdx
+++ b/ib002/08-rb-trees/2023-06-10-rules.md
@@ -10,8 +10,6 @@ last_update:
date: 2023-06-10
---
-import ThemedSVG from "@site/src/components/ThemedSVG";
-
## Introduction
Have you ever thought about the red-black tree rules in more depth? Why are they
@@ -57,10 +55,8 @@ my child would be colored red.
Example of a red-black tree that keeps count of black nodes on paths to the
leaves follows:
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+
+
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:
@@ -144,15 +140,15 @@ accordingly.
| Usual algorithm with black root | Allowing red root |
| :-----------------------------: | :---------------: |
-| | |
-| | |
-| | |
-| | |
-| | |
-| | |
-| | |
-| | |
-| | |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
+|  |  |
## 3ª Every leaf (`nil`) is black.
@@ -161,7 +157,8 @@ 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:
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+
+
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
@@ -234,11 +231,17 @@ import TabItem from '@theme/TabItem';
-
+
+
+
+
-
+
+
+
+
diff --git a/ib002/10-graphs/2022-04-30-bfs-tree.mdx b/ib002/10-graphs/2022-04-30-bfs-tree.md
similarity index 76%
rename from ib002/10-graphs/2022-04-30-bfs-tree.mdx
rename to ib002/10-graphs/2022-04-30-bfs-tree.md
index 32bb1aa..a0e292c 100644
--- a/ib002/10-graphs/2022-04-30-bfs-tree.mdx
+++ b/ib002/10-graphs/2022-04-30-bfs-tree.md
@@ -10,8 +10,6 @@ last_update:
date: 2022-04-30
---
-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:
@@ -23,11 +21,13 @@ As we have talked on the seminar, if we construct from some vertex $u$ BFS tree
Consider the following graph:
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We run BFS from the vertex $a$ and obtain the following 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:
@@ -42,7 +42,9 @@ 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!
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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.
@@ -54,7 +56,8 @@ Do we need to run BFS after **every** change?
:::
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+
+
Oops, we have gotten a new BFS tree, that has a height difference of 1.