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Timsort is a hybrid, stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data.It was implemented by Tim Peters in 2002 for use in the Python programming language.
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 ).
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.
In the bingo sort variant, items are sorted by repeatedly looking through the remaining items to find the greatest value and moving all items with that value to their final location. [2] Like counting sort , this is an efficient variant if there are many duplicate values: selection sort does one pass through the remaining items for each item ...
The best case input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., O(n)). During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array. The simplest worst case input is an array sorted in reverse order.
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 ...
For this reason, it is sometimes called partition-exchange sort. [4] The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is ...
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.