From 922b87bc1cd72f883148a1b6d743bfe08e158c23 Mon Sep 17 00:00:00 2001
From: santiagosayshey <sayheysantiago@proton.me>
Date: Mon, 4 Mar 2024 02:11:33 +1030
Subject: [PATCH] Backup of Obsidian Vault on 04-03-24 : 02:11:32 from SamPC |
 1 files changed

Details:
M content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md
---
 .../Exercises/3.2.1.md                        | 75 +++++++++----------
 1 file changed, 37 insertions(+), 38 deletions(-)

diff --git a/content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md b/content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md
index 19bfedd0..32a155fd 100644
--- a/content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md	
+++ b/content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md	
@@ -1,69 +1,68 @@
-
 > [!exercise]+ Exercise 1 - Sort a list whose numbers span from 1 to 9. 
-
-
-> [!exercise]+ 1. Create an array of size $k$, and increment each position by 1 for every occurrence of that position in the array. 
 > 
-> $$
-> \text{Unsorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
+>  1. Create an array of size $k$, and increment each position by 1 for every occurrence of that position in the array. 
+> $$\begin{array}{l}
+> \text{Unsorted Array:} \\
+> \begin{array}{|c|c|c|c|c|c|c|}
 > \hline
 > 1 & 4 & 1 & 2 & 7 & 5 & 2 \\
 > \hline
 > \end{array}
-> $$
+> \end{array}$$
 > 
-> $$
-> \text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
-> \hline
-> 0 & 2 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\
-> \hline
-> \end{array}
-> $$
-> 2. Starting from the second position, we add the value of the previous position to the current position.
->  $$
-> \text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
+>  2. Starting from the second position, we add the value of the previous position to the current position.
+> $$\begin{array}{l}
+> \text{Element Counts:} \\
+> \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
 > \hline
 > 0 & 2 & 4 & 4 & 5 & 6 & 6 & 7 & 7 & 7 \\
 > \hline
 > \end{array}
-> $$
-> 3. Create a sorted array of length max of previous array (7)
-> $$
-> \text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
+> \end{array}$$
+> 
+>  3. Create a sorted array of length max of previous array (7)
+> $$\begin{array}{l}
+> \text{Sorted Array:} \\
+> \begin{array}{|c|c|c|c|c|c|c|}
 > \hline
 >  &  &  &  &  &  &  \\
 > \hline
 > \end{array}
-> $$
-> 4. Iterate through the unsorted array. For each element $i$ in the unsorted array, find the value at position $i$ in the element counts array. This value is the position that $i$ will be in the sorted array. Decrement the value in the counts array by 1.  
-> - For example, the first element in the unsorted array is 1. We go to $counts[1]$ and find that the value is $2$. We place $1$ at position $2$ in the sorted array, and decrement $counts[1]$ by 1. 
->  $$
-> \text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
+> \end{array}$$
+> 
+>  4. Iterate through the unsorted array. For each element $i$ in the unsorted array, find the value at position $i$ in the element counts array. This value is the position that $i$ will be in the sorted array. Decrement the value in the counts array by 1.  
+> - For example, the first element in the unsorted array is 1. We go to $\text{counts}[1]$ and find that the value is $2$. We place $1$ at position $2$ in the sorted array, and decrement $\text{counts}[1]$ by 1. 
+> $$\begin{array}{l}
+> \text{Element Counts:} \\
+> \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
 > \hline
 > 0 & 1 & 4 & 4 & 5 & 6 & 6 & 7 & 7 & 7 \\
 > \hline
 > \end{array}
-> $$
-> $$
-> \text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
+> \end{array}$$
+> $$\begin{array}{l}
+> \text{Sorted Array:} \\
+> \begin{array}{|c|c|c|c|c|c|c|}
 > \hline
 >  & 1 &  &  &  &  &  \\
 > \hline
 > \end{array}
-> $$
-> 5. Repeat this for every element in the unsorted array
-> $$
-> \text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
+> \end{array}$$
+> 
+>  5. Repeat this for every element in the unsorted array
+> $$\begin{array}{l}
+> \text{Element Counts:} \\
+> \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
 > \hline
 > 0 & 0 & 2 & 4 & 4 & 5 & 6 & 6 & 7 & 7 \\
 > \hline
 > \end{array}
-> $$
-> $$
-> \text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
+> \end{array}$$
+> $$\begin{array}{l}
+> \text{Sorted Array:} \\
+> \begin{array}{|c|c|c|c|c|c|c|}
 > \hline
 > 1 & 1 & 2 & 2 & 4 & 5 & 7 \\
 > \hline
 > \end{array}
-> $$
-
+> \end{array}$$