Quick Sort

Quicksort is a divide and conquer algorithm. Quicksort first divides a large array into two smaller sub-arrays: the low elements and the high elements. Quicksort can then recursively sort the sub-arrays. Quicksort is an O(nlogn) runtime sorting algorithm, and can be faster than Mergesort and Heapsort when implemented correctly.

Algorithm:

1. Pick an element (called a pivot).
2. Reorder the array 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-array of elements with smaller values and separately to the sub-array of elements with greater values.

The base case of the recursion is arrays of size < 2, which are in order by definition, so they never need to be sorted.

The pivot selection and partitioning steps can be done in several different ways; the choice of specific implementation schemes greatly affects the algorithm's performance. We will always pick the pivot to be the middle element (not always most efficient way).

Solution (in java):

import java.util.Arrays;

public class QuickSort {
    private static int partition(int[] arr, int left, int right) {
        int i = left, j = right;
        int tmp;

        // pivot will be middle element
        int pivot = arr[(left + right) / 2];

        while (i <= j) {
            while (arr[i] < pivot)
                i++;
            while (arr[j] > pivot)
                j--;
            if (i <= j) {
                tmp = arr[i];
                arr[i] = arr[j];
                arr[j] = tmp;
                i++;
                j--;
            }
        }
        return i;
    }

    private static int[] quickSort(int[] arr, int left, int right) {
        int index = partition(arr, left, right);
        if (left < index - 1)
            quickSort(arr, left, index - 1);
        if (index < right)
            quickSort(arr, index, right);

        return arr;
    }

    private static int[] quickSort(int[] arr) {
        if (arr.length < 2)
            return arr;
        return quickSort(arr, 0, arr.length - 1);
    }

    public static void main(String[] args) {
        int arr[] = {1, 2, 4, 90, 0, -1, 30};
        System.out.println(Arrays.toString(quickSort(arr)));
    }
}

output:

[-1, 0, 1, 2, 4, 30, 90]