Quicksort-Know More

British computer scientist Tony Hoare developed Quicksort, which is a sorting algorithm. The method of systematically arranging data is known as sorting.  If used in a correct way, then it can be faster than merge sort and two or three-timer faster than heapsort.A pivot is chosen as an element and the given array gets segmented around the chosen pivot, depending on whether they are less than or greater than the pivot. It is commonly called partition-exchange sort because of this process. For convenience, in the divided array, the left side is occupied with fewer elements and vice versa for the right-hand side. It has been observed by the outcomes of mathematical analysis that the algorithm takes O (n log n) comparisons to sort and  O(n2) in worst-case scenarios. let us know more about that the Quicksort-Know More.

Quicksort-Know More

History

Tony Hoare is known for the development of Quicksort in 1959. He was a guest student at Moscow State University. As he was working on a machine translation project, he had to sort out Russian sentences, before accessing the Russian-English dictionary, which was on magnetic tape in alphabetical order. He came up with an idea that helped him perform faster algorithms and enabled him to learn about ALGOL and its ability to perform recursion. Quicksort was adopted quickly and it became popular. It became the default library sort subroutine of Unix.

Divide and Conquer Strategy

It is the Divide and Conquer algorithm. It is an easy-to-understand technique of breaking down the algorithms into sub-problems, solving the subproblems, and then combining the results to solve the principle order.  

  • Divide- Pick a pivot element as the first step. The next step is to rearrange the sub-arrays into two parts.
  • Conquer- Sort two sub-arrays recursively using the quicksort algorithm
  • Combine- Combine the sorted array. 

Different Versions

Quicksort is present in different versions based on the method of picking pivot. 

  • The first element is picked as a pivot.
  • The last element is picked as the pivot.
  • Random elements are chosen as the pivot.
  • The median becomes the pivot.

Partition

Partition is a crucial step in sorting. It is performed by a given array and an element n of an array as a pivot is chosen, then n is put at its correct position in a sorted array and all smaller elements are put before n, and all greater elements are kept after n. A linear style of time has to be followed.

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Sorting Algorithms

It means putting elements of a list into order. Numerical and lexicographical order are commonly used. Sorting is crucial for the maximum efficiency of other algorithms. These other algorithms need the input data to be in sorted lists.

Quicksort Applications

It is applied wherever a stable sort is not required. It is tail-recursive, which means that call optimizations can be performed. It proves useful in operational research and event-driven simulation. It is applied when the programming language is apt for recursion.

  • Time complexity 
  • Space complexity 
  • Quicksort complexities

Types of Time Complexities

  • Best-case scenarios- O(n*log n)
  • Worst-case scenarios O (n2)
  • Average O (n*log n)
  • Space complexity O (log n) 

Time Complexity

Worst-case complexity (Big-O)

This situation can be avoided by not picking the pivot element as either the greatest or the smallest element. The pivot element ends up on the far end of the sorted array. The main aspect of this complexity is that one subarray is without elements, and another sub-array contains n-1 elements. 

Best case complexity (Big-omega)

This scenario takes place when the pivot element is close to the middle element or is always the middle element.

Average case complexity (Big-theta)

This kind of scenario tends to take place when the above-mentioned conditions don’t materialize. 

Space Complexity

The space complexity for Quicksort is 0 (log n)

Implementation Issues

Choice of pivot 

In the early versions of Quicksort, the left-most element was chosen as the pivot. To users’ dismay, this results in worst-case scenarios on already sorted arrays. This problem can be solved by taking a random index as the pivot.

Repeated Elements

For the lomuto partition scheme, quicksort exhibits poor performance for inputs that contain repeated elements. To solve this problem, an alternative linear-time partition is used that segregates the values into three distinct groups-

  • Less than the pivot
  • Values equal to the pivot 
  • Values more than than the pivot.

Parallelization

Quicksort poses some problems which hinder efficient parallelization.  The algorithm’s scalability is directly affected by the divide and conquer strategy, and it depends on the kind of pivot. It is hard to parallelize the partitioning step in place. Scratch space can be used to simplify the partitioning step but it ends up harming the algorithm’s memory footprint and incessant overheads.

Preserving randomness

The random shuffle puts the array in a random order. Quicksort treats all elements uniformly so its two sub-arrays are also in a random order. 

Conclusion

As mentioned earlier, Quicksort was developed by Mr. Hoare and it has since evolved to its present refined versions. It is one of the most popular sorting algorithms that take advantage of (nlogn) comparisons to sort an array of n elements in a typical situation. It has a couple of negative aspects, it is still one of the fastest sorting algorithms.

Frequently Asked Questions

Que. What are similar sorting algorithms?

Ans. Merge sort, heap sort, and insertion sort are similar types of algorithms.

Que. What are the benefits of Quicksort?

Ans. 

  • It works rapidly and effectively
  • It shows the best time complexity.
  • It is an excellent choice to make when one has limited space as it has a space complexity of o (logn)

Que. Why is Quicksort popular?

Ans. It is not difficult to implement, is faster than other sorting methods, and works well with different kinds of input data. 

Que. What is the main idea behind Quicksort?

Ans. It divides a large array of data into smaller sub-arrays. The input is split into two components, these components are sorted separately and then recombined at the end to get a final result. 

Que. In what programs can Quicksort be implemented?

Ans. Quicksort can be utilized in programs like Javascript, C++, Python, etc.

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