15.1.5. Recursive Sorting

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. It was created in the early 1960s and has significantly influenced computer science. It highlights quick and efficient sorting techniques that are still relevant today.

Imagine organizing a series of books. Instead of checking each one sequentially, you could quickly categorize them into larger sections by selecting a representative book (the pivot) and then sorting the remaining titles around it, saving time.

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. So, 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 aims to address the limitations of merge sort, especially regarding the need for additional storage during the merging process, which can be costly. Quick sort is designed to sort in-place, minimizing the need for extra memory.

Think of quick sort like tidying up a room without needing to take everything out into the hallway (extra storage), whereas merge sort is like taking everything out and then organizing it, which requires more space.

Well, this is the case, then what we need to do is, we need to put the middle value in the center. So, supposing we can find the median. So, remember what the median is, the median is the value such that exactly half the values in the array are bigger and half a smaller.

The process begins by identifying a middle value known as the median, where half the values are smaller and half are larger. This helps structure the sorting by dividing the array into two logical segments without the need for merging later.

Imagine splitting a group of people based on their heights. If you find someone in the middle (the median), everyone on one side is shorter, and everyone on the other side is taller, simplifying the organization.

Now, I do this recursive thing, I sort this and I sort this and now remember this no need to merge, because everything on the left is already smaller than everything on the right.

Quick sort uses a recursive approach. After dividing the array based on a pivot, it sorts the left side and the right side without needing to merge them back together, as the organization is guaranteed by the pivot.

Think of this as setting up a tournament bracket. After each round, the winners from one side compete exclusively with the winners from the other side until only one remains, without needing to reintroduce the whole group.

So, of course, there must be a catch and the catch is how do we find the median? Right at the beginning of our discussion, we said that one of the reasons that we want to sort is to do statistical things like find the median.

A challenge arises because we aim to sort the array in order to find the median, creating a paradox: we can't use the median to sort if we haven't sorted yet. This is where picking a different reference point, called a pivot, becomes vital.

It's like trying to determine the average score of students before you've collected all their scores. Instead, you can pick a random score to begin organizing, leading to a proper distribution sooner.

So, we just pick some value in the array and we take all those value as smaller than that, move it to the left, all those which have bigger than that move it to the right. And then, we sort them recursively.

Instead of the median, a pivot element is chosen to divide the array into two sections - those smaller than the pivot go left, and those larger go right. This partitioning forms the basis for recursive sorting.

This is similar to setting up a line in a school where all students shorter than a specific height stand on one side and all taller stand on the other. Then, you focus on organizing each side further without needing to mix.

So, the first thing that we need to understand is how to do this partition. So, there are two ways to partition.

There are different strategies for partitioning the array. The goal is always to clearly separate elements based on the chosen pivot, ensuring efficient and accurate sorting.

Think of partitioning as preparing food by separating ingredients into smaller bowls based on whether they are sweet or savory before mixing them into new dishes.

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