Key differences between Quick Sort and Merge Sort

Quick Sort

Quick Sort is a highly efficient sorting algorithm and is based on the divide-and-conquer principle. It works by selecting a ‘pivot’ element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quick Sort is preferred for large datasets because its average and best-case time complexity is O(nlogn), although its worst-case complexity is O(n^2). The choice of pivot and the splitting mechanism can significantly affect the algorithm’s performance, making its efficient implementation dependent on the scenario.

Functions of Quick Sort:

• Divide and Conquer Approach:

Quick Sort utilizes a divide and conquer strategy, breaking the problem into smaller, easier-to-solve problems and then combining the solutions.

• Efficient for Large Lists:

It is one of the fastest sorting algorithms for large datasets due to its average-case time complexity of (𝑛log⁡𝑛)O(nlogn).

• In-Place Sorting:

It requires minimal extra space as it is an in-place sorting algorithm. This means it rearranges the numbers within the array, using only a small, constant amount of additional storage space.

• Good Cache Performance:

Due to its in-place nature and locality of reference, it generally has good cache performance.

• Easily Parallelizable:

The divide and conquer nature of Quick Sort makes it suitable for parallel execution. Different parts of the array can be sorted in parallel.

• Choice of Pivots:

Flexibility in choosing the pivot (can be median, first, last, or a random element) which can help in optimizing the performance in different scenarios.

• Performance Enhancement:

It can be optimized by tailoring the algorithm, such as using insertion sort for small arrays.

• Recursive Algorithm:

It uses recursion for sorting the elements, which simplifies the code, although it can increase stack space usage.

Example of Quick Sort:

This example illustrates the process of sorting an array of integers using the Quick Sort algorithm with the last element as the pivot.

public class QuickSortExample {

   

    // Method to perform the quicksort

    private static void quickSort(int[] array, int low, int high) {

        if (low < high) {

            // Find the partitioning index

            int pivotIndex = partition(array, low, high);

            // Recursively sort elements before and after partition

            quickSort(array, low, pivotIndex – 1);

            quickSort(array, pivotIndex + 1, high);

        }

    }

    // Method to partition the array on the basis of pivot element

    private static int partition(int[] array, int low, int high) {

        int pivot = array[high];  // Pivot is the last element

        int i = (low – 1);  // Index of smaller element

        for (int j = low; j < high; j++) {

            // If current element is smaller than the pivot

            if (array[j] < pivot) {

                i++;

                // Swap array[i] and array[j]

                int temp = array[i];

                array[i] = array[j];

                array[j] = temp;

            }

        }

        // Swap array[i+1] and array[high] (or pivot)

        int temp = array[i + 1];

        array[i + 1] = array[high];

        array[high] = temp;

        return i + 1;  // Return the partitioning index

    }

    // Utility method to start the quicksort algorithm

    public static void sort(int[] array) {

        quickSort(array, 0, array.length – 1);

    }

    // Main method to run the example

    public static void main(String[] args) {

        int[] numbers = {10, 7, 8, 9, 1, 5};

        System.out.println(“Original array:”);

        for (int number : numbers) {

            System.out.print(number + ” “);

        }

        System.out.println();

        sort(numbers);

        System.out.println(“Sorted array:”);

        for (int number : numbers) {

            System.out.print(number + ” “);

        }

    }

}

This code defines a QuickSortExample class that contains methods to perform Quick Sort on an array. The partition method organizes the array such that all elements less than a chosen pivot are on the left of the pivot and all greater are on the right, then it recursively sorts the sub-arrays on either side of the pivot. The main method provides a demonstration with a sample array.                               

Merge Sort

Merge Sort is a highly efficient, stable sorting algorithm based on the divide-and-conquer strategy. It involves dividing the input array into two halves, recursively sorting each half, and then merging the two sorted halves into a single sorted sequence. The division continues until the segments are reduced to individual elements, which are inherently sorted. The real work happens during the merge step, where the elements from the two halves are compared and combined in sorted order. Merge Sort is particularly useful for large data sets because its worst-case, average, and best-case time complexity is consistently O(nlogn). Additionally, it performs well on linked lists and is stable, meaning the relative order of equal elements is preserved.

Functions of Merge Sort:

• Divide the Array:

Merge Sort splits the array into halves recursively until each subset has only one element or no elements, which naturally makes every individual element a sorted array.

• Merge Subarrays:

After dividing, it merges those subarrays to produce new sorted subarrays. This process continues until the entire array becomes a single sorted array.

• Stable Sorting:

It maintains the relative order of equal elements, meaning it is a stable sort. This is crucial in contexts where the relative order of records with equal keys is important.

• Not In–place Sorting:

Typically, Merge Sort requires additional space proportional to the array size for the merging process, making it not an in-place sorting algorithm.

• Efficient for Large Data:

It is very efficient for sorting large lists, as its time complexity is consistently O(nlogn), which is better than O(n^2) of simple sorting algorithms like Bubble Sort and Insertion Sort.

• Recursive Algorithm:

The process is recursive, with each recursive call handling a smaller part of the array, which simplifies the merging of elements.

• Good for External Sorting:

Due to its ability to handle massive amounts of data and its use of additional arrays efficiently, it’s well-suited for external sorting applications (sorting data that is too large to fit into memory).

• Parallelizable:

The divide-and-conquer nature of Merge Sort allows it to be effectively parallelized, as different processors can sort different segments of the array concurrently before merging them together.

Example of Merge Sort:

This example includes the mergeSort function, which recursively divides the array into halves, and the merge function, which merges two halves while sorting them.

public class MergeSort {

    // Merges two subarrays of arr[].

    // First subarray is arr[l..m]

    // Second subarray is arr[m+1..r]

    void merge(int arr[], int l, int m, int r) {

        // Find sizes of two subarrays to be merged

        int n1 = m – l + 1;

        int n2 = r – m;

        /* Create temp arrays */

        int L[] = new int[n1];

        int R[] = new int[n2];

        /*Copy data to temp arrays*/

        for (int i = 0; i < n1; ++i)

            L[i] = arr[l + i];

        for (int j = 0; j < n2; ++j)

            R[j] = arr[m + 1 + j];

        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays

        int i = 0, j = 0;

        // Initial index of merged subarray array

        int k = l;

        while (i < n1 && j < n2) {

            if (L[i] <= R[j]) {

                arr[k] = L[i];

                i++;

            } else {

                arr[k] = R[j];

                j++;

            }

            k++;

        }

        /* Copy remaining elements of L[] if any */

        while (i < n1) {

            arr[k] = L[i];

            i++;

            k++;

        }

        /* Copy remaining elements of R[] if any */

        while (j < n2) {

            arr[k] = R[j];

            j++;

            k++;

        }

    }

    // Main function that sorts arr[l..r] using

    // merge()

    void mergeSort(int arr[], int l, int r) {

        if (l < r) {

            // Find the middle point

            int m = (l + r) / 2;

            // Sort first and second halves

            mergeSort(arr, l, m);

            mergeSort(arr, m + 1, r);

            // Merge the sorted halves

            merge(arr, l, m, r);

        }

    }

    // Utility method to print array of size n

    static void printArray(int arr[]) {

        int n = arr.length;

        for (int i = 0; i < n; ++i)

            System.out.print(arr[i] + ” “);

        System.out.println();

    }

    // Driver method

    public static void main(String args[]) {

        int arr[] = {12, 11, 13, 5, 6, 7};

        System.out.println(“Given Array”);

        printArray(arr);

        MergeSort ob = new MergeSort();

        ob.mergeSort(arr, 0, arr.length – 1);

        System.out.println(“\nSorted array”);

        printArray(arr);

    }

}

This code illustrates the entire process of Merge Sort from splitting the arrays to merging them back in a sorted manner. It starts by printing the original array, performs the sort, and then prints the sorted array.

Key differences between Quick Sort and Merge Sort

Key Similarities between Quick Sort and Merge Sort

• Divide and Conquer Algorithm:

Both Quick Sort and Merge Sort employ a divide and conquer strategy. This approach involves breaking the problem (i.e., the array to be sorted) into smaller subproblems, solving these independently, and then combining the solutions.

• Time Complexity:

In their best and average cases, both algorithms offer a time complexity of O(n log n), making them efficient for sorting large datasets compared to simpler algorithms like Bubble Sort or Insertion Sort.

• Recursive:

Both algorithms are inherently recursive; they repeatedly break down the array into smaller segments, process those segments, and then, in the case of Merge Sort, merge them back together in a sorted order. Quick Sort recurses after partitioning around a pivot.

• Usage in Real-world Applications:

Due to their efficiency, both sorting methods are widely used in practice. They are suitable for sorting large arrays and are often chosen based on their specific characteristics (like stability or space efficiency) relevant to the application’s needs.

• Optimization of Comparison-based Sorting:

Both algorithms represent ways to optimize sorting beyond the basic comparison-based algorithms by reducing the overhead associated with comparisons and swaps in different scenarios.

• Non-Adaptive:

Neither Quick Sort nor Merge Sort is considered adaptive. That is, their performance does not change depending on the initial order of elements in the input.