Examples of using Merge sort in English and their translations into Hungarian
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Parallel merge sort.
Merge sort with parallel recursion.
Optimizing merge sort.
Merge sort with parallel merging. .
These are the steps a human would take to emulate merge sort(top-down).
Tiled merge sort applied to an array of random integers.
External sorting explains how merge sort is implemented with disk drives.
Merge sort parallelizes well due to the use of the divide-and-conquer method.
Unlike some(efficient) implementations of quicksort, merge sort is a stable sort. .
A recursive merge sort algorithm used to sort an array of 7 integer values.
In the best case, the input is already sorted(i.e., is one run),so the natural merge sort need only make one pass through the data.
In sorting n objects, merge sort has an average and worst-case performance of O(n log n).
An intuitive approach is the parallelization of those recursive calls.[12]Following pseudocode describes the merge sort with parallel recursion using the fork and join keywords.
In the worst case, merge sort does about 39% fewer comparisons than quicksort does in the average case.
In this case, the notion of"in-place" can be relaxed to mean"taking logarithmic stack space",because standard merge sort requires that amount of space for its own stack usage.
In the typical case, the natural merge sort may not need as many passes because there are fewer runs to merge. .
Each of these subarrays is sorted with an in-place sorting algorithm such as insertion sort, to discourage memory swaps,and normal merge sort is then completed in the standard recursive fashion.
A more sophisticated merge sort that optimizes tape(and disk) drive usage is the polyphase merge sort.
Other in-place algorithms include SymMerge, which takes O((n+ m) log(n+ m)) time in total and is stable.[10]Plugging such an algorithm into merge sort increases its complexity to the non-linearithmic, but still quasilinear, O(n(log n)2).
A natural merge sort is similar to a bottom-up merge sort except that any naturally occurring runs(sorted sequences) in the input are exploited.
Both monotonic and bitonic(alternating up/down) runs may be exploited, with lists(or equivalently tapes or files) being convenient data structures(used as FIFO queues or LIFO stacks).[4]In the bottom-up merge sort, the starting point assumes each run is one item long.
It seems arbitrary to restrict the merge sort algorithms to a binary merge method, since there are usually p> 2 processors available.
Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945.[2] A detailed description and analysis of bottom-up mergesort appeared in a report by Goldstine and von Neumann as early as 1948.[3].
Example C-like code using indices for top-down merge sort algorithm that recursively splits the list(called runs in this example) into sublists until sublist size is 1, then merges those sublists to produce a sorted list.
Merge sort is more efficient than quicksort for some types of lists if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common.
Example C-like code using indices for bottom-up merge sort algorithm which treats the list as an array of n sublists(called runs in this example) of size 1, and iteratively merges sub-lists back and forth between two buffers.
Some parallel merge sort algorithms are strongly related to the sequential top-down merge algorithm while others have a different general structure and use the K-way merge method.
Cache-aware versions of the merge sort algorithm, whose operations have been specifically chosen to minimize the movement of pages in and out of a machine's memory cache, have been proposed.
Pseudocode for top-down merge sort algorithm which recursively divides the input list into smaller sublists until the sublists are trivially sorted, and then merges the sublists while returning up the call chain.
Pseudocode for bottom-up merge sort algorithm which uses a small fixed size array of references to nodes, where array[i] is either a reference to a list of size 2i or nil. node is a reference or pointer to a node.