Section 2.1: The Bubble Sort

The bubble sort is often the first algorithm that newcomers encounter due to its simplicity. We will not delve deeply into its mechanics, but it's essential to understand its basic operation.

Section 2.2: Optimizing the Bubble Sort

The bubble sort consistently performs a total of (N-1)+(N-2)+(N-3)+...+2+1 comparisons. However, if the array is already sorted during one of these passes, subsequent comparisons become unnecessary. To mitigate this, we can implement a flag that checks if any exchanges occurred during the pass, indicating whether the sorting is complete.

Section 2.3: Handwritten Quick Sort

The quick sort algorithm follows these fundamental steps:

1. Select a pivot element.
2. Position elements smaller than the pivot to its left and those larger to its right.
3. Recursively apply the same process to the left and right subarrays until only single elements remain.
4. Finally, merge the arrays level by level.

Section 2.4: Enhancing Quick Sort Efficiency

Writing quicksort in a way that opens new arrays each time can lead to significant memory consumption, especially with large datasets, risking memory overflow. We can optimize this by executing the sorting in place. Instead of creating new arrays, we swap elements directly within the original array during partitioning.

We introduce a pointer to track the position for swapping elements. As we traverse the array, we exchange elements smaller than the pivot with the current position, incrementing the pointer accordingly.

Section 2.5: Handwritten Merge Sort

The merge sort algorithm, like quick sort, utilizes a divide-and-conquer strategy. However, while quick sort sorts during partitioning, merge sort completes partitioning first before sorting.

Section 2.6: Handwritten Heap Sort

A heap is a unique type of tree, specifically a complete binary tree where each node's value is either greater than or less than its child nodes. Heaps can be classified into max heaps and min heaps based on their node values.

The heap sort process involves:

1. Initializing a max (or min) heap, where the root node contains the largest (or smallest) value.
2. Swapping the root node with the last node of the array.
3. Resizing the heap (excluding the last node) to maintain the heap property, ensuring the root is the largest (or smallest) value.
4. Repeating this process until only one element remains in the heap, completing the sort.

Section 2.7: Comparing Merge Sort, Quick Sort, and Heap Sort

In this section, we will explore the distinctions among merge sort, quick sort, and heap sort, highlighting their unique attributes and use cases.