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A further relaxation requiring only a list of the k smallest elements, but without requiring that these be ordered, makes the problem equivalent to partition-based selection; the original partial sorting problem can be solved by such a selection algorithm to obtain an array where the first k elements are the k smallest, and sorting these, at a total cost of O(n + k log k) operations.
The order of inheritance affects the class semantics. Python had to deal with this upon the introduction of new-style classes, all of which have a common ancestor, object. Python creates a list of classes using the C3 linearization (or Method Resolution Order (MRO)) algorithm.
In other words, the output of C3 superclass linearization is a deterministic Method Resolution Order (MRO). In object-oriented systems with multiple inheritance, some mechanism must be used for resolving conflicts when inheriting different definitions of the same property from multiple superclasses.
Related problems include approximate sorting (sorting a sequence to within a certain amount of the correct order), partial sorting (sorting only the k smallest elements of a list, or finding the k smallest elements, but unordered) and selection (computing the kth smallest element). These can be solved inefficiently by a total sort, but more ...
Insertion sort is very similar in that after the kth iteration, the first elements in the array are in sorted order. Insertion sort's advantage is that it only scans as many elements as it needs in order to place the k + 1 {\displaystyle k+1} st element, while selection sort must scan all remaining elements to find the k + 1 {\displaystyle k+1 ...
Python's standard library includes heapq.nsmallest and heapq.nlargest functions for returning the smallest or largest elements from a collection, in sorted order. The implementation maintains a binary heap , limited to holding k {\displaystyle k} elements, and initialized to the first k {\displaystyle k} elements in the collection.
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.
With new-style classes, objects and types were unified, allowing the subclassing of types. Even entirely new types can be defined, complete with custom behavior for infix operators. This allows for many radical things to be done syntactically within Python. A new method resolution order for multiple inheritance was also adopted with Python 2.3 ...