Introduction:

Sorting algorithms are essential in computer science, enabling efficient organization and retrieval of data. Among the numerous sorting algorithms, Quicksort stands out for its simplicity and impressive performance. In this blog, we will explore how to implement the Quicksort algorithm using Hoare's partition scheme in C#. We will provide a comprehensive explanation of the algorithm's inner workings, step by step, along with code snippets, outputs, and performance considerations. By the end, you will have a thorough understanding of Quicksort's power and be able to apply it to your own programming projects.

Understanding the Quicksort Algorithm

Quicksort is a divide-and-conquer algorithm that recursively partitions an array into two sub-arrays. It selects a pivot element, rearranges the array, and ensures that all elements less than the pivot come before it, while all elements greater than the pivot come after it. This process continues until the entire array is sorted.

Hoare's Partition Scheme

Hoare's partition scheme, named after British computer scientist C.A.R. Hoare, is an efficient and widely used partitioning method for Quicksort. Unlike the Lomuto partition scheme, which always selects the rightmost element as the pivot, Hoare's scheme selects two pointers from both ends of the array and moves them towards each other, swapping elements if they are in the wrong order. This partitioning method reduces the number of comparisons and performs better in practice.

Implementing Quicksort with Hoare's Partition Scheme in C#

Let's dive into the implementation of Quicksort using Hoare's partition scheme in C#. Here's the code:

class Quicksort
{
    public static void Sort(int[] array, int low, int high)
    {
        if (low < high)
        {
            int pivotIndex = Partition(array, low, high);
            Sort(array, low, pivotIndex);
            Sort(array, pivotIndex + 1, high);
        }
    }

    private static int Partition(int[] array, int low, int high)
    {
        int pivot = array[low];
        int i = low - 1;
        int j = high + 1;

        while (true)
        {
            do
            {
                i++;
            } while (array[i] < pivot);

            do
            {
                j--;
            } while (array[j] > pivot);

            if (i >= j)
                return j;

            int temp = array[i];
            array[i] = array[j];
            array[j] = temp;
        }
    }
}

Testing the Quicksort Algorithm

Let's test our Quicksort implementation using a sample array:

int[] array = { 7, 2, 1, 6, 8, 5, 3, 4 };
Quicksort.Sort(array, 0, array.Length - 1);

Console.WriteLine("Sorted Array:");
foreach (int num in array)
{
    Console.Write(num + " ");
}

Output:

Sorted Array:
1 2 3 4 5 6 7 8

Conclusion:

In this blog, we explored the Quicksort algorithm with Hoare's partition scheme and implemented it in C#. We provided a step-by-step explanation, code snippets, and demonstrated the output with a sample array. Quicksort's efficiency and simplicity make it a powerful tool for sorting large datasets.