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Radix sort is an algorithm that sorts numbers by processing individual digits. n numbers consisting of k digits each are sorted in O(n · k) time. Radix sort can process digits of each number either starting from the least significant digit (LSD) or starting from the most significant digit (MSD). The LSD algorithm first sorts the list by the ...
Then, sorting a subset of is equivalent to convert it into an increasing sequence. The lexicographic order on the resulting sequences induces thus an order on the subsets, which is also called the lexicographical order. In this context, one generally prefer to sort first the subsets by cardinality, such as in the shortlex order. Therefore, in ...
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
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. The algorithm finds subsequences of the data that are already ordered (runs) and uses them to sort the ...
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})
The basic definition of a dictionary does not mandate an order. To guarantee a fixed order of enumeration, ordered versions of the associative array are often used. There are two senses of an ordered dictionary: The order of enumeration is always deterministic for a given set of keys by sorting.
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.
In computer programming, the Schwartzian transform is a technique used to improve the efficiency of sorting a list of items. This idiom [1] is appropriate for comparison-based sorting when the ordering is actually based on the ordering of a certain property (the key) of the elements, where computing that property is an intensive operation that should be performed a minimal number of times.