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Heapsort maps the binary tree to the array using a top-down breadth-first traversal of the tree; the array begins with the root of the tree, then its two children, then four grandchildren, and so on. Every element has a well-defined depth below the root of the tree, and every element except the root has its parent earlier in the array.
For example, if every element is at a position that differs by at most k (k ≥ 1) from the position it is going to end up in, the complexity of cocktail shaker sort becomes (). The cocktail shaker sort is also briefly discussed in the book The Art of Computer Programming , along with similar refinements of bubble sort.
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.
The following list contains syntax examples of how a range of element of an array can be accessed. In the following table: first – the index of the first element in the slice; last – the index of the last element in the slice; end – one more than the index of last element in the slice; len – the length of the slice (= end - first)
The simplest worst case input is an array sorted in reverse order. The set of all worst case inputs consists of all arrays where each element is the smallest or second-smallest of the elements before it. In these cases every iteration of the inner loop will scan and shift the entire sorted subsection of the array before inserting the next element.
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the ...
In computer science, selection sort is an in-place comparison sorting algorithm.It has a O(n 2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort.
A typical alternative for dense array storage is to use Iliffe vectors, which typically store pointers to elements in the same row contiguously (like row-major order), but not the rows themselves. They are used in (ordered by age): Java, [14] C#/CLI/.Net, Scala, [15] and Swift.