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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 ...
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 ).
This occurs for example in searching for the maximum element of a set, using the first element as the pivot, and having sorted data. However, for randomly chosen pivots, this worst case is very unlikely: the probability of using more than C n {\displaystyle Cn} comparisons, for any sufficiently large constant C {\displaystyle C} , is ...
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.
The previous example is a two-pass sort: first sort, then merge. The sort ends with a single k -way merge, rather than a series of two-way merge passes as in a typical in-memory merge sort. This is because each merge pass reads and writes every value from and to disk, so reducing the number of passes more than compensates for the additional ...
Instead, using selection sort with a bucket queue gives a form of pigeonhole sort, and using van Emde Boas trees or other integer priority queues leads to other fast integer sorting algorithms. [7] Instead of using an integer priority queue in a sorting algorithm, it is possible to go the other direction, and use integer sorting algorithms as ...
For example, addresses could be sorted using the city as primary sort key, and the street as secondary sort key. 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.