Quick sort is comparison sort based on divide and conquer approach. It is in-place sorting algorithm so it require small additional amount of memory to perform sorting.

Quick sort was developed by Tony Hoare in 1959.

#### Complexity(Big O notation)

- Best-case – O(n log n)
- Average-case – O(n log n)
- Worst-case – O(n²)

Quicksort or partition-exchange sort, is a fast sorting algorithm, which is using divide and conquer algorithm. Quicksort first divides a large list into two smaller sub-lists: the low elements and the high elements. Quicksort can then recursively sort the sub-lists.

There are many different versions of quickSort that pick pivot in different ways.

- Always pick first element as pivot.
- Always pick last element as pivot (implemented below)
- Pick a random element as pivot.
- Pick median as pivot.

**Steps to implement Quick sort:**

1) Choose an element, called pivot, from the list. Generally pivot can be the middle index element.

2) Reorder the list so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way). After this partitioning, the pivot is in its final position. This is called the partition operation.

3) Recursively apply the above steps to the sub-list of elements with smaller values and separately the sub-list of elements with greater values.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | public class QuickSortTest { private int array[]; private int length; public void sort(int[] inputArr) { if (inputArr == null || inputArr.length == 0) { return; } this.array = inputArr; length = inputArr.length; quickSort(0, length - 1); } private void quickSort(int lowerIndex, int higherIndex) { int i = lowerIndex; int j = higherIndex; // calculate pivot number, I am taking pivot as middle index number int pivot = array[lowerIndex+(higherIndex-lowerIndex)/2]; // Divide into two arrays while (i <= j) { /** * In each iteration, we will identify a number from left side which * is greater then the pivot value, and also we will identify a number * from right side which is less then the pivot value. Once the search * is done, then we exchange both numbers. */ while (array[i] < pivot) { i++; } while (array[j] > pivot) { j--; } if (i <= j) { exchangeNumbers(i, j); //move index to next position on both sides i++; j--; } } // call quickSort() method recursively if (lowerIndex < j) quickSort(lowerIndex, j); if (i < higherIndex) quickSort(i, higherIndex); } private void exchangeNumbers(int i, int j) { int temp = array[i]; array[i] = array[j]; array[j] = temp; } public static void main(String a[]){ QuickSortTest sorter = new QuickSortTest(); int[] input = {4,21,5,20,51,71,12,56,94, 83,12}; sorter.sort(input); for(int i:input){ System.out.print(i); System.out.print(" "); } } } |