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Array.sort is now guaranteed to be stable, meaning that elements with equal sorting keys will not change relative order before and after the sort operation. Array.prototype.flat(depth=1) flattens an array to a specified depth, meaning that all subarray elements (up to the specified depth) are concatenated recursively.
A sorting algorithm that checks if the array is sorted until a miracle occurs. It continually checks the array until it is sorted, never changing the order of the array. [10] Because the order is never altered, the algorithm has a hypothetical time complexity of O(∞), but it can still sort through events such as miracles or single-event upsets.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
The value should be selected in such a way that it is guaranteed to be distinct from all legal data values since otherwise, the presence of such values would prematurely signal the end of the data (the semipredicate problem). A sentinel value is sometimes known as an "Elephant in Cairo", due to a joke where this is used as a physical sentinel.
As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). [1] Quicksort operates in-place on the data to be sorted.
Afterward, the counting array is looped through to arrange all of the inputs in order. This sorting algorithm often cannot be used because S needs to be reasonably small for the algorithm to be efficient, but it is extremely fast and demonstrates great asymptotic behavior as n increases.
Block sort, or block merge sort, is a sorting algorithm combining at least two merge operations with an insertion sort to arrive at O(n log n) (see Big O notation) in-place stable sorting time.
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.