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M content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md

content/Computer Science/Algorithms & Data Structures Analysis/Exercises/3.2.1.md

@@ -70,58 +70,4 @@
 
 To better visualise this example, checkout this [video](https://www.youtube.com/watch?v=7zuGmKfUt7s)
 
-> [!exercise] Exercise 1 - Sort a list whose numbers span from 1 to 9.
-> 
-> Step 1 - Create an array of size $k$, and increment each position by 1 for every occurrence of that position in the array. 
-> 
-> $\text{Unsorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
-> \hline
-> 1 & 4 & 1 & 2 & 7 & 5 & 2 \\
-> \hline
-> \end{array}$
-> 
-> Step 2 - Starting from the second position, we add the value of the previous position to the current position.
-> 
-> $\text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
-> \hline
-> 0 & 2 & 4 & 4 & 5 & 6 & 6 & 7 & 7 & 7 \\
-> \hline
-> \end{array}$
-> 
-> Step 3 - Create a sorted array of length max of previous array (7)
-> 
-> $\text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
-> \hline
->  &  &  &  &  &  &  \\
-> \hline
-> \end{array}$
-> 
-> Step 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.
-> 
-> $\text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
-> \hline
-> 0 & 1 & 4 & 4 & 5 & 6 & 6 & 7 & 7 & 7 \\
-> \hline
-> \end{array}$
-> 
-> $\text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
-> \hline
->  & 1 &  &  &  &  &  \\
-> \hline
-> \end{array}$
-> 
-> Step 5 Repeat this for every element in the unsorted array
-> 
-> $\text{Element Counts:} \quad \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
-> \hline
-> 0 & 0 & 2 & 4 & 4 & 5 & 6 & 6 & 7 & 7 \\
-> \hline
-> \end{array}$
-> 
-> $\text{Sorted Array:} \quad \begin{array}{|c|c|c|c|c|c|c|}
-> \hline
-> 1 & 1 & 2 & 2 & 4 & 5 & 7 \\
-> \hline
-> \end{array}$
+