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Computer Algorithms: Quicksort

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Introduction

When it comes to sorting items by comparing them merge sort is one very natural approach. It is natural, because simply divides the list into two equal sub-lists then sort these two partitions applying the same rule. That is a typical divide and conquer algorithm and it just follows the intuitive approach of speeding up the sorting process by reducing the number of comparisons. However there are other “divide and conquer” sorting algorithms that do not follow the merge sort scheme, while they have practically the same success. Such an algorithm is quicksort.

Overview

Back in 1960 C. A. R. Hoare comes with a brilliant sorting algorithm. In general quicksort consists of some very simple steps. First we’ve to choose an element from the list (called a pivot) then we must put all the elements with value less than the pivot on the left side of the pivot and all the items with value greater than the pivot on its right side. After that we must repeat these steps for the left and the right sub-lists. That is quicksort! Simple and elegant!

Quicksort
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Computer Algorithms: Merge Sort

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Introduction

Basically sorting algorithms can be divided into two main groups. Such based on comparisons and such that are not. I already posted about some of the algorithms of the first group. Insertion sort, bubble sort and Shell sort are based on the comparison model. The problem with these three algorithms is that their complexity is O(n2) so they are very slow.

So is it possible to sort a list of items by comparing their items faster than O(n2)? The answer is yes and here’s how we can do it.

The nature of those three algorithms mentioned above is that we almost compared each two items from initial list.

Insertion sort and bubble sort make too many comparisons, exactly what merge sort tries to overcome!
Insertion sort and bubble sort make too many comparisons, exactly what merge sort tries to overcome!

This, of course, is not the best approach and we don’t need to do that. Instead we can try to divide the list into smaller lists and then sort them. After sorting the smaller lists, which is supposed to be easier than sorting the entire initial list, we can try to merge the result into one sorted list. This technique is typically known as “divide and conquer”.

Normally if a problem is too difficult to solve, we can try to break it apart into smaller sub-sets of this problem and try to solve them. Then somehow we can merge the results of the solved problems.

If it's too difficult to sort a large list of items, we can break it apart into smaller sub-lists and try to sort them!
If it's too difficult to sort a large list of items, we can break it apart into smaller sub-lists and try to sort them!

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