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A sorting algorithm using weak heaps, weak-heapsort, uses a number of comparisons that is close to the theoretical lower bound on the number of comparisons required to sort a list, so is particularly useful when comparison is expensive, such as when comparing strings using the full Unicode collation algorithm.
Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide-and-conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average ...
Sorting a set of unlabelled weights by weight using only a balance scale requires a comparison sort algorithm. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.
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.
External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead they must reside in the slower external memory (usually a hard drive). k-way merge algorithms usually take place in the second stage of external sorting algorithms, much like they do for merge sort.
The lower bound on worst-case running time of output-sensitive convex hull algorithms was established to be Ω(n log h) in the planar case. [1] There are several algorithms which attain this optimal time complexity. The earliest one was introduced by Kirkpatrick and Seidel in 1986 (who called it "the ultimate convex hull algorithm").
For these models, an algorithm based on comparison sort solves the problem within a constant factor of the best possible number of comparisons. The same lower bound applies as well to the expected number of comparisons in the randomized algebraic decision tree model. [3] [4]
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 ...