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When the array contains only duplicates of a relatively small number of items, a constant-time perfect hash function can greatly speed up finding where to put an item 1, turning the sort from Θ(n 2) time to Θ(n + k) time, where k is the total number of hashes. The array ends up sorted in the order of the hashes, so choosing a hash function ...
The shuffle sort [6] is a variant of bucket sort that begins by removing the first 1/8 of the n items to be sorted, sorts them recursively, and puts them in an array. This creates n/8 "buckets" to which the remaining 7/8 of the items are distributed. Each "bucket" is then sorted, and the "buckets" are concatenated into a sorted array.
In computer science, smoothsort is a comparison-based sorting algorithm.A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. [1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation), [2] but it is not a stable sort.
One implementation can be described as arranging the data sequence in a two-dimensional array and then sorting the columns of the array using insertion sort. The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from O ( n 2 ) to O ( n 4/3 ) and Θ( n log 2 n ).
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.
As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). [1] Quicksort operates in-place on the data to be sorted.
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed.
The difference between pigeonhole sort and counting sort is that in counting sort, the auxiliary array does not contain lists of input elements, only counts: 3: 1; 4: 0; 5: 2; 6: 0; 7: 0; 8: 1; For arrays where N is much larger than n, bucket sort is a generalization that is more efficient in space and time.