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Complexities below assume n items to be sorted, with keys of size k, digit size d, and r the range of numbers to be sorted. Many of them are based on the assumption that the key size is large enough that all entries have unique key values, and hence that n ≪ 2 k, where ≪ means "much less than".
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
Most languages provide a generic sort function that implements a sort algorithm that will sort arbitrary objects. This function usually accepts an arbitrary function that determines how to compare whether two elements are equal or if one is greater or less than the other. Consider this Python code sorting a list of strings by length of the string:
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. See also stable sorting. If different items have different sort key ...
In computer science, radix sort is a non-comparative sorting algorithm.It avoids comparison by creating and distributing elements into buckets according to their radix.For elements with more than one significant digit, this bucketing process is repeated for each digit, while preserving the ordering of the prior step, until all digits have been considered.
Example: The following table shows the steps for sorting the sequence {3, 7, 4, 9, 5, 2, 6, 1}. In each step, the key under consideration is underlined. The key that was moved (or left in place because it was the biggest yet considered) in the previous step is marked with an asterisk.
The most frequently used general-purpose implementation of an associative array is with a hash table: an array combined with a hash function that separates each key into a separate "bucket" of the array. The basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})