Quicksort in Java

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.

Program

Quicksort.java:--

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;
  }
}

Test.java:-

public class Test
{
public static void main(String args[]){
    Quicksort sorter = new Quicksort();
    int[] test = { 5, 5, 6, 6, 4, 4, 5, 5, 4, 4, 6, 6, 5, 5 };
    sorter.sort(test);
   printResult(test);
  }
 private void printResult(int[] numbers) {
    for (int i = 0; i < numbers.length; i++) {
      System.out.print(numbers[i]);
    }
    System.out.println();
  }
}

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).