## Quicksort in Java

Version 0.6

06.08.2010

Revision History
Revision 0.1 17.05.2009 Lars
Vogel
Created
Revision 0.2 - 0.6 06.08.2010 Lars
Vogel
bug fixes and enhancements

Quicksort with Java

1. Quicksort
1.1. Overview
1.2. Description of the algorithm
2. Quicksort in Java
2.1. Implementation
2.2. Test
3. Complexity Analysis
4. Thank you
5. Questions and Discussion
6.1. Source Code
6.2. General

## 1. Quicksort

### 1.1. Overview

Sort algorithms are ordering the elements of an array according to a predefined order. Quicksort is a divide and conquer algorithm. In a divide and conquer sorting algorithm their the original data is separated into two parts (divide) which are individually sorted (conquered) and then combined.

### 1.2. Description of the algorithm

If the array contains only one element or zero elements then the array is sorted.

If the array contains more then one element then:

• Select an element from the array. This element is called the "pivot element". For example select the element in the middle of the array.

• All elements which are smaller then the pivot element are placed in one array and all elements which are larger are placed in another array.

• Sort both arrays by recursively applying Quicksort to them.

• Combine the arrays

Quicksort can be implemented to sort "in-place". This means that the sorting takes place in the array and that no additional array need to be created.

## 2. Quicksort in Java

### 2.1. Implementation

Create a Java project "de.vogella.algorithms.sort.quicksort" and create the following class.

```package de.vogella.algorithms.sort.quicksort;

public class Quicksort  {
private int[] numbers;
private int number;

public void sort(int[] values) {
// check for empty or null array
if (values ==null || values.length==0){
return;
}
this.numbers = values;
number = values.length;
quicksort(0, number - 1);
}

private void quicksort(int low, int high) {
int i = low, j = high;
// Get the pivot element from the middle of the list
int pivot = numbers[low + (high-low)/2];

// Divide into two lists
while (i <= j) {
// If the current value from the left list is smaller then the pivot
// element then get the next element from the left list
while (numbers[i] < pivot) {
i++;
}
// If the current value from the right list is larger then the pivot
// element then get the next element from the right list
while (numbers[j] > pivot) {
j--;
}

// If we have found a values in the left list which is larger then
// the pivot element and if we have found a value in the right list
// which is smaller then the pivot element then we exchange the
// values.
// As we are done we can increase i and j
if (i <= j) {
exchange(i, j);
i++;
j--;
}
}
// Recursion
if (low < j)
quicksort(low, j);
if (i < high)
quicksort(i, high);
}

private void exchange(int i, int j) {
int temp = numbers[i];
numbers[i] = numbers[j];
numbers[j] = temp;
}
} ```

### 2.2. Test

You can use the following JUnit tests to validate the sort method. To learn about JUnit please see JUnit Tutorial .

```package de.vogella.algorithms.sort.quicksort;

import java.util.Arrays;
import java.util.Random;

import org.junit.Before;
import org.junit.Test;

import static org.junit.Assert.assertTrue;
import static org.junit.Assert.fail;

public class QuicksortTest {

private int[] numbers;
private final static int SIZE = 7;
private final static int MAX = 20;

@Before
public void setUp() throws Exception {
numbers = new int[SIZE];
Random generator = new Random();
for (int i = 0; i < numbers.length; i++) {
numbers[i] = generator.nextInt(MAX);
}
}

@Test
public void testNull() {
Quicksort sorter = new Quicksort();
sorter.sort(null);
}

@Test
public void testEmpty() {
Quicksort sorter = new Quicksort();
sorter.sort(new int[0]);
}

@Test
public void testSimpleElement() {
Quicksort sorter = new Quicksort();
int[] test = new int[1];
test[0] = 5;
sorter.sort(test);
}

@Test
public void testSpecial() {
Quicksort sorter = new Quicksort();
int[] test = { 5, 5, 6, 6, 4, 4, 5, 5, 4, 4, 6, 6, 5, 5 };
sorter.sort(test);
if (!validate(test)) {
fail("Should not happen");
}
printResult(test);
}

@Test
public void testQuickSort() {
for (Integer i : numbers) {
System.out.println(i + " ");
}
long startTime = System.currentTimeMillis();

Quicksort sorter = new Quicksort();
sorter.sort(numbers);

long stopTime = System.currentTimeMillis();
long elapsedTime = stopTime - startTime;
System.out.println("Quicksort " + elapsedTime);

if (!validate(numbers)) {
fail("Should not happen");
}
assertTrue(true);
}

@Test
public void testStandardSort() {
long startTime = System.currentTimeMillis();
Arrays.sort(numbers);
long stopTime = System.currentTimeMillis();
long elapsedTime = stopTime - startTime;
System.out.println("Standard Java sort " + elapsedTime);
if (!validate(numbers)) {
fail("Should not happen");
}
assertTrue(true);
}

private boolean validate(int[] numbers) {
for (int i = 0; i < numbers.length - 1; i++) {
if (numbers[i] > numbers[i + 1]) {
return false;
}
}
return true;
}

private void printResult(int[] numbers) {
for (int i = 0; i < numbers.length; i++) {
System.out.print(numbers[i]);
}
System.out.println();
}
} ```

## 3. Complexity Analysis

The following describes the runtime complexity of quicksort.

Fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. Quicksort will in the best case divide the array into almost two identical parts. It the array contains n elements then the first run will need O(n). Sorting the remaining two sub-arrays takes 2* O(n/2). This ends up in a performance of O(n log n).

In the worst case quicksort selects only one element in each iteration. So it is O(n) + O(n-1) + (On-2).. O(1) which is equal to O(n^2).

The average case of quicksort is O(n log n).