Java Sorting Algorithms: Quick Sort


Welcome back to this overview about the Java world! Today, we are going to talk about a renowned sorting algorithm: the Quick Sort.

The Quick Sort is not very suitable for educational purposes because its implementation may not be trivial, but at the performance level it offers some advantages that are not indifferent, unlike the previously trated Bubble Sort.

Let's try to understand better what is Quick Sort.

First of all, let's see an image that gives us an idea of how the algorithm works.

QuickSortScheme

Foundamental features and description

The Quick Sort is one of the most used algorithms, expecially when huge amounts of data have to be treated. Just like some other algorithms, it is part of the Divide and Conquer family.

It means that the processing is not done on the entire data collection, but it is recursively done on finite subsets of the collection. This feature makes the sorting operations lighter from the moment that the values that have to be compared are two at most.

Let's remember that the Quick Sort is a stable and in-place algorithm. Generally no algorithm is stable, but it can be made stable using indexes as meter of comparison.

These are the main steps of the algorithm.

If the collection is composed of zero or one element, then it is sorted. Otherwise the following steps are performed:

  1. A pivot is chosen;
  2. The elements of the array are divided into two parts: the one of the elements before the pivot and the one of the elements after the pivot;
  3. The elements are sorted recursively repeating the 1 and 2 steps;

Implementation

import java.util.*;
public class QuickSort 
{ 
/* 
This function takes the last element as pivot,
place the pivot element in its right position
in the sorted array. It also puts every element smaller than the pivot 
on the left and every element bigger than the pivot on the right.
*/
private static int partition(int arr[], int low, int high) 
{ 
int pivot = arr[high]; 
int index = (low-1); // index of the smaller element. -1 at the beginning
for (int j=low; j<high; j++) 
{ 
// if the current element is smaller than pivot
if (arr[j] < pivot) 
{ 
index++; 
// swap arr[index] and arr[j] 
int temp = arr[index]; 
arr[index] = arr[j]; 
arr[j] = temp; 
} 
} 
// swap arr[index+1] and arr[high] (or pivot) 
int temp = arr[index+1]; 
arr[index+1] = arr[high]; 
arr[high] = temp; 
return index+1; 
} 
/* The main function that implements QuickSort() 
arr[] --> array to be sorted, 
low --> starting index, 
high --> ending index */
public static void sort(int arr[], int low, int high) 
{ 
if (low < high) 
{ 
/* pi is the partitioning index, arr[pi] is now in the right place */
int pi = partition(arr, low, high); 
// Recursively order the elements before
// partition and after partition 
sort(arr, low, pi-1); 
sort(arr, pi+1, high); 
} 
} 
// Driver program.
public static void main(String args[]) 
{ 
int arr[] = {10, 7, 8, 9, 1, 5}; 
int n = arr.length; 
QuickSort.sort(arr, 0, n-1); 
System.out.println("sorted array"); 
System.out.println(Arrays.toString(arr)); 
} 
} 

Let's understand the code

The most important element is the choice of the pivot. The ideal pivot should be the medium element of the collection but it is too difficult to find in an unsorted collection. The choices can be different. The first element, the last element, the middle element or a random element can be chosen as pivot.

The main method is partition that takes as parameters the collection to sort, that is an array of integer numbers, and the two extremes of the array, low and high.

In this method every swapping operation is done. This is the method that implements the majority of the algorithm.

The method's body contains simply some swapping operations done only under certain conditions. The very easy principle is the one that exchanging two sorted elements is useless, so the current element j is compared to the pivot.

The indexes have the following meanings:

  • index stands for the minimum element that has been examined;
  • j is the current element;

The sort method is the wrapper for partition. The control on low and high is performed in order to verify that they "make sense" and that situations where low=2 and high=1 don't occurr since inconsistent situations can happen.

The partition index is calculated.

At the end we have the main method, where the array to sort is created. Then the sort method is called on the array with 0 and n-1 as indexes (where n is the array's length).

Must be precised that I chose to make the sort method static. I decided to implement it as a static method because I imagined the code presented above as a part of a bigger class that implements more than one algorithm. Since sort is static, partition must be static.

A non-static method could have been implemented and the effect would have been the same.

Clearly, just like the majority of the situations that happen in Computer Science, there are many different variations of the implementation of the Quick Sort. Every variant has the same final result. The implementation details change.

Hints about complexity

The time taken from the Quick Sort can be expressed as:

T(n) = T(k) + T(n-k-1) + theta(n)

The first two terms represent the two recursive calls and k stands for the element "smaller" than the pivot. The effective time depends on the pivot choice. Let's look at some particular cases:

Worst case: 

T(n) = T(n-1) + theta(n)

It happens when the smallest or the biggest element is chosen as pivot.

The complexity can be written as theta(n2). Notice the exponential growth.

Best case:

T(n) = 2T(n/2) + theta(n)

The complexity can be written as  theta(nLogn).

Average case:

T(n) = T(n/9) + T(9n/10) + theta(n)

In order to make an accurate analysis of the complexity in the average case we should calculate every possible permutation of the elements of the collection and it is not easy. We can have an idea of the complexity considering the case where partition puts O(n/9) elements in a subset and O(9n/10) in the other subset.

The complexity can be written as   theta(nLogn) also in this case.

Curiosity: what is three-way-quick-sort?

Il three-way-quick-sort è una versione del Quick Sort dove la collezione da ordinare viene divisa così come segue:

The three-way-quick-sort is a version of the Quick Sort where the array to sort is divided as shown below: 

  • array[low...i] is the subset of the elements smaller than the pivot;
  • array[i...j-1] is the subset of the element equals to the pivot;
  • array[j...high] is the subset of the element bigger than the pivot;

E' evidente che questa versione sia conveniente solo quando ci sono diversi elementi ridondanti nella collezione. In caso contrario sarebbe priva di senso.

Clearly this version has to be used only if there are many redundant element in the collection. In the other case it would not make any sense.

 
by Alessio Mungelli Date: 14-12-2019 java jdk source code explanation tutorial educational quick sort sortingmethod developing developers hits : 10978  
 
Alessio Mungelli

Alessio Mungelli

Computer Science student at UniTo (University of Turin), Network specializtion, blogger and writer. I am a kind of expert in Java desktop developement with interests in AI and web developement. Unix lover (but not Windows hater). I am interested in Linux scripting. I am very inquisitive and I love learning new stuffs.

 
 
 

Related Posts

How to upload files to the server using JavaScript

In this tutorial we are going to see how you can upload files to a server using Node.js using JavaScript, which is very common. For example, you might want to…

How to combine multiple objects in JavaScript

In JavaScript you can merge multiple objects in a variety of ways. The most commonly used methods are the spread operator ... and the Object.assign() function.   How to copy objects with…

The Payment Request API: Revolutionizing Online Payments (Part 2)

In the first part of this series, we explored the fundamentals of the Payment Request API and how it simplifies the payment experience. Now, let's delve deeper into advanced features…

The Payment Request API: Revolutionizing Online Payments (Part 1)

The Payment Request API has emerged as the new standard for online payments, transforming the way transactions are conducted on the internet. In this two-part series, we will delve into…

Android Hidden Codes: unveiling custom dialer codes and their functionality

In the world of Android smartphones, there exist numerous hidden codes that can unlock a treasure trove of functionalities and features. These codes, known as custom dialer codes, provide access…

Let's create a Color Picker from scratch with HTML5 Canvas, Javascript and CSS3

HTML5 Canvas is a technology that allows developers to generate real-time graphics and animations using JavaScript. It provides a blank canvas on which graphical elements, such as lines, shapes, images…

How do you stop JavaScript execution for a while: sleep()

A sleep()function is a function that allows you to stop the execution of code for a certain amount of time. Using a function similar to this can be interesting for…

Mastering array sorting in JavaScript: a guide to the sort() function

In this article, I will explain the usage and potential of the sort() function in JavaScript.   What does the sort() function do?   The sort() function allows you to sort the elements of…

Hidden Gmail codes to find a lost e-mail

If you have a lot of emails in Gmail, there are a few codes that will help you find what you need faster and more accurately than if you do…

How to download an email in PDF format in Gmail for Android

You will see how easy it is to save an email you have received or sent yourself from Gmail in PDF format, all with your Android smartphone. Here's how it's…

Infinite scrolling with native JavaScript using the Fetch API

I have long wanted to talk about how infinite scroll functionality can be implemented in a list of items that might be on any Web page. Infinite scroll is a technique…

Sorting elements with SortableJS and storing them in localStorage

SortableJS is a JavaScript extension that you will be able to use in your developments to offer your users the possibility to drag and drop elements in order to change…

Clicky