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The problem is then to produce an array such that all "bottom" elements come before (have an index less than the index of) all "middle" elements, which come before all "top" elements. One algorithm is to have the top group grow down from the top of the array, the bottom group grow up from the bottom, and keep the middle group just above the ...
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 ).
A bidirectional variant of selection sort (called double selection sort or sometimes cocktail sort due to its similarity to cocktail shaker sort) finds both the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the ...
Take an array of numbers "5 1 4 2 8", and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required; First Pass ( 5 1 4 2 8 ) → ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1.
The average case is also quadratic, [4] which makes insertion sort impractical for sorting large arrays. However, insertion sort is one of the fastest algorithms for sorting very small arrays, even faster than quicksort; indeed, good quicksort implementations use insertion sort for arrays smaller than a certain threshold, also when arising as ...
The complexity of the cocktail shaker sort in big O notation is () for both the worst case and the average case, but it becomes closer to () if the list is mostly ordered before applying the sorting algorithm. For example, if every element is at a position that differs by at most k (k ≥ 1) from the position it is going to end up in, the ...
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 ...
If the sort key values are totally ordered, the sort key defines a weak order of the items: items with the same sort key are equivalent with respect to sorting. See also stable sorting. If different items have different sort key values then this defines a unique order of the items. Workers sorting parcels in a postal facility