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This popular sorting algorithm has an average-case performance of O(n log(n)), which contributes to making it a very fast algorithm in practice. But given a worst-case input, its performance degrades to O(n 2). Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)).
The worstsort algorithm is based on a bad sorting algorithm, badsort. The badsort algorithm accepts two parameters: L , which is the list to be sorted, and k , which is a recursion depth. At recursion level k = 0 , badsort merely uses a common sorting algorithm, such as bubblesort , to sort its inputs and return the sorted list.
Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide-and-conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average ...
Bubble sort has a worst-case and average complexity of (), where is the number of items being sorted. Most practical sorting algorithms have substantially better worst-case or average complexity, often ().
Among quadratic sorting algorithms (sorting algorithms with a simple average-case of Θ(n 2)), selection sort almost always outperforms bubble sort and gnome sort. Insertion sort is very similar in that after the kth iteration, the first elements in the array are in sorted order.
The number of comparisons made by merge sort in the worst case is given by the sorting numbers. These numbers are equal to or slightly smaller than (n ⌈lg n⌉ − 2 ⌈lg n⌉ + 1), which is between (n lg n − n + 1) and (n lg n + n + O(lg n)). [6] Merge sort's best case takes about half as many iterations as its worst case. [7]
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold.
The worst-case scenario occurs when all the elements are placed in a single bucket. The overall performance would then be dominated by the algorithm used to sort each bucket, for example () insertion sort or ( ()) comparison sort algorithms, such as merge sort.