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In computer science, smoothsort is a comparison-based sorting algorithm.A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. [1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation), [2] but it is not a stable sort.
Insertion sort is widely used for small data sets, while for large data sets an asymptotically efficient sort is used, primarily heapsort, merge sort, or quicksort. Efficient implementations generally use a hybrid algorithm , combining an asymptotically efficient algorithm for the overall sort with insertion sort for small lists at the bottom ...
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.
Heapsort has been described as "nothing but an implementation of selection sort using the right data structure." [1] It greatly improves the basic algorithm by using an implicit heap data structure to find and remove each lowest element in () time, instead of normal selection sort's () inner loop, reducing the total running time to ().
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.
The next pass, 3-sorting, performs insertion sort on the three subarrays (a 1, a 4, a 7, a 10), (a 2, a 5, a 8, a 11), (a 3, a 6, a 9, a 12). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (a 1,..., a 12). As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer ...
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons.It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.
The main disadvantage of merge sort is that it is an out-of-place algorithm, so when operating on arrays, efficient implementations require O(n) auxiliary space (vs. O(log n) for quicksort with in-place partitioning and tail recursion, or O(1) for heapsort). Merge sort works very well on linked lists, requiring only a small, constant amount of ...