What is a comparison-based sorting algorithm?

We have a collection of comparison based sorting algorithms such as bubble sort, insertion sort, selection sort, merge sort, quick sort or heapsort, relay on comparing elements pairwise to determine the relative order. While these algorithms are conceptionally simple and easy to implement, but their time complexity is not optimal. They can result in poor performance, especially for large datasets. They are inherently sequential in nature, which prohibit from exploiting parallelism to improve efficiency on multicore processors or distributed systems. Despite these downsides, comparison based sorting algorithms remain widely used due to their simplicity, versality, and ease of implementation.

Comparison-based sorting algorithms sort elements by comparing pairs and rearranging based on comparison results. Popular ones include: 1. Bubble Sort - O(n^2): Repeatedly compares adjacent elements, swapping them to place the largest element correctly. 2. Insertion Sort - O(n^2): Builds the sorted array incrementally by inserting each unsorted element into its correct position. 3. Selection Sort - O(n^2): Selects the smallest (or largest) element from the unsorted part and swaps it into its position. 4. Merge Sort - O(n log n): Divides the array, sorts each half recursively, then merges them together. 5. Quick Sort - O(n log n): Selects a pivot, partitions the array, and sorts each partition recursively.

Comparison-based sorting algorithms as the name itself suggests sort a list of elements by comparing them against each other. The most common characteristic among all comparison-based sorting algorithms is that they determine the sorted order based on comparing the pair of elements.

There are plenty of excellent references for comparison sorts online, with wiki being one of them, including some nice animations. Of the many comparison sorts available I have a particular fondness for my go-to, the merge sort. I like the symmetrical divide-and-conquer code aesthetic, and with O(n log n) performance it is plenty fast for my needs. Honorable mention to the heap sort, another one I use quite a bit.

Definition: Comparison-based sorting algorithms arrange data by comparing pairs of elements and swapping them if they are out of order. Operation Independence: These algorithms don't rely on the internal structure or representation of data; sorting is determined solely by the outcomes of the comparison operations. Example: Sorting a list of numbers in ascending order involves comparing pairs and swapping them based on the results of the comparisons. Widespread Usage: Due to their simplicity and versatility, comparison-based sorting algorithms, such as bubble sort, merge sort, quicksort, and heapsort, are widely applied in various data structures and problem-solving scenarios.

Some of the famous comparison-based sorting algorithms are bubble sort, selection sort, insertion sort, merge sort, quick sort, and heap sort. Out of this bubble, selection and insertion are fundamental sorting algorithms based on comparing the adjacent elements with different approaches. Quick Sort and Merge Sort are implemented as an application of the Divide and Conquer Approach. And Heap Sort is based on the concept of Heap-based data structure i.e. how to build a heap, min heap, max heap, and deletion operations for the same.

The most popular comparison-based sorting algorithms are: Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Quick Sort and Heap Sort. However, there are a few other comparison-based sorting algorithms worth mentioning. For example: - Comb Sort: Comb sort is an improvement over bubble sort. It eliminates small values at the end of the list to speed up the sorting process. It works by comparing elements with a gap, which gradually decreases after each iteration. - Odd-Even Sort: Odd-even sort is a variation of bubble sort where adjacent elements are compared and swapped in case of the wrong order, but in alternating odd and even pairs. This allows for parallelization as two adjacent elements can be compared and swapped simultaneously.

Some of the popular comparison-based sorting algorithms are bubble sort, insertion sort, heap sort, selection sort, merge sort, quick sort.

Some of the popular comparison-based sorting algorithms are as bellow: Insertion Sort, Selection Sort, Bubble Sort, Heap Sort (Based on binary heap data structure), Quick Sort (Base on divide and conquer rule), Merge Sort (Base on divide and conquer rule), etc.

A key concept involving the time complexity of comparison based sorting algorithm is understanding it's lower bound. If you consider any comparison based sorting algorithm it cannot do better than nlgn. This stems from the fact that, any comparison based sorting algorithm can be modeled as a decision tree. Since there are n! possible outcomes in the decision tree and the worst case number of comparisons is the height of the decision tree, the lower bound can be derived to be at least nlgn.

Any algorithm is said to be an efficient algorithm when that algorithm has a lower time and space complexity. Among all the listed comparison-based sorting algorithms, the time complexity in the worst case is listed below: 1. Bubble Sort: O(n^2) 2. Selection Sort: O(n^2) 3. Insertion Sort: O(n^2) 4. Merge Sort: O(n log n) 5. Quick Sort: O(n^2) 6. Heap Sort: O(n log n) Interesting Tip: When the array is almost sorted, insertion sort gives the best performance out of the above sorting algorithms by giving time complexity as O(n) and when the array is highly unsorted quick sort gives the best performance by giving time complexity as O(n log n).

One of key factor while selecting an algorithm is to check its efficiency on Time and space complexity. Merge Sort: O(n log n) Quicksort: O(n^2) Selection sort: O(n^2) Heap Sort: O(n log n) Insertion Sort: O(n^2) Bubble Sort: O(n^2)

Any algorithm is said to be an efficient if it has a lower time and space complexity. Algorithms with time complexity in the worst case are listed below: Insertion Sort: O(n^2) Selection Sort: O(n^2) Bubble Sort: O(n^2) Heap Sort: O(n log n) Quick Sort: O(n^2) Merge Sort: O(n log n)

Space complexity talks about how much extra space any algorithm is taking up to sort the data. So, here is a listed comparison sort space complexity: 1. Bubble Sort: O(1) 2. Selection Sort: O(1) 3. Insertion Sort: O(1) 4. Merge Sort: O(n) [Because of extra array(n)+ recursion stack(log n)] 5. Quick Sort: O(log n) [Because of recursion stack] 6. Heap Sort: O(1)

A comparison based sorting algorithm does not have an intrinsic lower bound on space complexity that's stemming from it being comparison-based. I believe this should be noted.

?For smaller data, simpler algorithms like bubble sort, selection sort, and insertion sort may be sufficient due to their simplicity. ?For the almost sorted data, insertion sort gives the best performance with the time complexity as O(n), and Quick Sort gives the worst case performance with the time complexity as O(n^2). ?For the larger data, algorithms with O(n log n) time complexity such as Merge Sort, Quick Sort, or heap sort are preferred due to their efficiency. ?When stability matters (preserving the order of equal elements), then stable algorithms like Merge Sort are a good choice. ?Algorithms that parallelize well, such as merge sort, can be advantageous in environments where distributed computing is feasible.

Real world examples of java collections?? LinkedList uses merge sort as it's internal sorting algorithm, as for linked list, merge step would not need extra space. ArrayList on the other hand would rely on quick sort due to it's continuous memory allocation which allows O(1) time to access an index element.