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In the merge sort algorithm, this subroutine is typically used to merge two sub-arrays A[lo..mid], A[mid+1..hi] of a single array A. This can be done by copying the sub-arrays into a temporary array, then applying the merge algorithm above. [1] The allocation of a temporary array can be avoided, but at the expense of speed and programming ease.
The k-way merge problem consists of merging k sorted arrays to produce a single sorted array with the same elements.Denote by n the total number of elements. n is equal to the size of the output array and the sum of the sizes of the k input arrays.
In Java, the Arrays.sort() methods use merge sort or a tuned quicksort depending on the datatypes and for implementation efficiency switch to insertion sort when fewer than seven array elements are being sorted. [29]
For instance, the array might be subdivided into chunks of a size that will fit in RAM, the contents of each chunk sorted using an efficient algorithm (such as quicksort), and the results merged using a k-way merge similar to that used in merge sort. This is faster than performing either merge sort or quicksort over the entire list. [40] [41]
The outer loop of block sort is identical to a bottom-up merge sort, where each level of the sort merges pairs of subarrays, A and B, in sizes of 1, then 2, then 4, 8, 16, and so on, until both subarrays combined are the array itself.
Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network.The algorithm was devised by Ken Batcher.The resulting sorting networks consist of ( ()) comparators and have a delay of ( ()), where is the number of items to be sorted. [1]
Merge-insertion sort performs the following steps, on an input of elements: [6] Group the elements of X {\displaystyle X} into ⌊ n / 2 ⌋ {\displaystyle \lfloor n/2\rfloor } pairs of elements, arbitrarily, leaving one element unpaired if there is an odd number of elements.
To merge, Timsort copies the elements of the smaller array (X in this illustration) to temporary memory, then sorts and fills elements in final order into the combined space of X and Y. The original merge sort implementation is not in-place and it has a space overhead of N (data size).