15.1.4. Partitioning the Array

So, we are now ready to look at another algorithm called Quick sort. So, quick sort was invented by a computer scientist called Tony Hoare in the early 1960’s; that is about 50 years ago. And Tony Hoare is a very well-known computer scientist and he has impact one Turing about which is one of the highest achievements awarded for academic computer scientist.

Quick sort is a sorting algorithm developed by Tony Hoare in the 1960s. It is popular due to its efficiency in sorting large arrays. Hoare is an influential figure in the field of computer science, known for his contributions to algorithms and programming.

Think of Quick sort as a method of organizing a messy room. Tony Hoare came up with this approach similar to how we might decide to separate items into different boxes based on their size or category.

So, what is the purpose of quick sort? Well, the purpose of quick sort is to overcome some of the shortcomings that we saw in the merge sort. One of the things that we saw in the merge sort is that because of the merge operation, we need extra storage and so, this makes merge sort a little expensive.

Quick sort addresses the limitations of merge sort by eliminating the need for additional storage. While merge sort requires extra space to merge sorted subarrays, quick sort can perform the sort in place, requiring less memory.

Imagine trying to organize a library's books but needing a separate table (extra storage) for merges. Quick sort skips this by utilizing the space already on the library shelves.

The reason that we need this extra storage is because we have in the merge operation that we might be pulling out elements from both sides... So, can we divide everything so that this does not happen, everything on the left is smaller and everything on the right is larger, is it possible to do a divide and conquer in this fashion?

To optimize the sorting process, quick sort attempts to rearrange elements such that all values less than a certain point (the pivot) end up on one side and those greater on the other. This division simplifies the sorting process into smaller tasks, a method known as 'divide and conquer.'

This is akin to organizing a school locker where you want to split items into those that are small (paper) and large (books) for easier access and cleaning.

So, what quick sort Tony Hoare algorithm says, do not necessarily pick the medium, just picks some value in A and do what we said... We just pick some value in the array and we take all those values as smaller than that, move it to the left, all those which are bigger than that move it to the right.

In the quick sort algorithm, a pivot element is chosen. Elements smaller than the pivot are moved to its left, and those larger to the right. This simplifies the sorting by ensuring that the pivot's final position will be correctly sorted after partitions are performed.

Think of it as deciding on a VIP seat in a theater. People who are closer to the stage (smaller values) sit to one side, while those far back (larger values) sit on the other.

So, the crucial step is this partitioning, we will see how to do this partitioning... So, if we see something which is lower, then I extend the lower part and I am move to the next element.

The partitioning process involves iterating through the array with two pointers that track the positions of lower and upper partitions. When an element meets the criteria of being lower or higher than the pivot, pointers adjust their positions accordingly, slowly organizing the array.

This can be visualized like sorting groceries at a store. As items come in (elements), we place fruits on one side (lower part) and vegetables on the other (upper part).

Now, I want this pivot element to be in between these two... then I get my final array partition does I want to that pivot in the middle, the lower part on the left and upper part on the right.

Once the lower and upper parts are established, the pivot element is swapped into its correct position, effectively completing the partitioning. This final arrangement ensures that all elements on the left of the pivot are smaller, and those on the right are larger.

It's similar to placing a centerpiece on a dinner table—ensuring that all the plates and cups around it fit into their categories and don’t mix.

In general quick sort will take the array and it will take two pointers, it will say sort from l to r minus 1... if either are then you want value or if I had no values sort, then I do nothing.

Quick sort is recursive. After partitioning, it calls itself to sort the left and right portions of the array independently. The base case for the recursion is reached when the subarray has zero or one element, indicating that it is already sorted.

This is like planning a vacation where you split your itinerary into smaller trips (subarrays). If a destination is small, no need to plan further (base case).

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