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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 ...
If each item to be sorted is itself an integer, and used as key as well, then the second and third loops of counting sort can be combined; in the second loop, instead of computing the position where items with key i should be placed in the output, simply append Count[i] copies of the number i to the output.
Insertion sort is a simple sorting algorithm that is relatively efficient for small lists and mostly sorted lists, and is often used as part of more sophisticated algorithms. It works by taking elements from the list one by one and inserting them in their correct position into a new sorted list similar to how one puts money in their wallet. [22]
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.
A hash table may use linked lists to store the chains of items that hash to the same position in the hash table. A heap shares some of the ordering properties of a linked list, but is almost always implemented using an array. Instead of references from node to node, the next and previous data indexes are calculated using the current data's index.
If the items are stored in a linked list, then the list can be sorted with O(1) additional space. The algorithm starts with an initially empty (and therefore trivially sorted) list. The input items are taken off the list one at a time, and then inserted in the proper place in the sorted list.
When many values have to be searched in the same list, it often pays to pre-process the list in order to use a faster method. For example, one may sort the list and use binary search, or build an efficient search data structure from it. Should the content of the list change frequently, repeated re-organization may be more trouble than it is worth.
Used in Python 2.3 and up, and Java SE 7. Insertion sorts Insertion sort: determine where the current item belongs in the list of sorted ones, and insert it there; Library sort; Patience sorting; Shell sort: an attempt to improve insertion sort; Tree sort (binary tree sort): build binary tree, then traverse it to create sorted list