The polyphase merge found a way to use the idle drives.It can sort using just three sequential files rather than the four required by merge sort.…

The two buffers must then be redistributed back into the array using the opposite process that was used to create them.After repeating these steps for every level of the bottom-up merge sort, the block sort is completed.…

The two buffers must then be redistributed back into the array using the opposite process that was used to create them.After repeating these steps for every level of the bottom-up merge sort, the block sort is completed.…

Like the standard merge sort, in-place merge sort is also a stable sort.

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.In the bottom up merge sort, the starting point assumes each run is one item long.In practice, random input data will have many short runs that just happen to be sorted.…

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.In the bottom up merge sort, the starting point assumes each run is one item long.In practice, random input data will have many short runs that just happen to be sorted.…

Next it must extract two internal buffers for each level of the merge sort.

External merge sort is not the only external sorting algorithm; there are also distribution sorts, which work by partitioning the unsorted values into smaller "buckets" that can be sorted in main memory.Like merge sort, external distribution sort also has a main-memory sibling; see bucket sort.There is a duality, or fundamental similarity, between merge- and distribution-based algorithms that can aid in thinking about sorting and other external memory algorithms.…

In a sorting algorithm the first comparisons made satisfies the randomness condition, but as the sort progresses the keys compared are clearly not randomly chosen anymore.For example, consider a bottom-up merge sort.The first pass will compare pairs of random keys, but the last pass will compare keys that are very close in the sorting order.…

In a sorting algorithm the first comparisons made satisfies the randomness condition, but as the sort progresses the keys compared are clearly not randomly chosen anymore.For example, consider a bottom-up merge sort.The first pass will compare pairs of random keys, but the last pass will compare keys that are very close in the sorting order.…

For example, if the target position of two elements is calculated before they are moved into the right position, the number of swaps can be reduced by about 25% for random data.In the extreme case, this variant works similar to merge sort.To avoid having to make a series of swaps for each insertion, the input could be stored in a linked list, which allows elements to be spliced into or out of the list in constant-time when the position in the list is known.…

As previously stated, the outer loop of a block sort is identical to a bottom-up merge sort.

As previously stated, the outer loop of a block sort is identical to a bottom-up merge sort.

One variant of block sort allows it to use any amount of additional memory provided to it, by using this external buffer for merging an A subarray or A block with B whenever A fits into it.In this situation it would be identical to a merge sort.…

At each iteration, the same level/phase of merge occurs -- a file is either completely read or completely written during an iteration.If the four files were on four separate tape drives, watching an ordinary merge sort would show some interesting details.On the first iteration, only one input drive is used -- the other input file is empty.…

In practice, random input data will have many short runs that just happen to be sorted.In the typical case, the natural merge sort may not need as many passes because there are fewer runs to merge.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.…

Also, many applications of external sorting use a form of merge sorting where the input get split up to a higher number of sublists, ideally to a number for which merging them still makes the currently processed set of pages fit into main memory.Merge sort parallelizes well due to use of the divide-and-conquer method.A parallel implementation is shown in pseudo-code in the third edition of Cormen, Leiserson, Rivest, and Stein's Introduction to Algorithms.…

An iteration (or pass) in ordinary merge sort involves reading and writing the entire file.An iteration in a polyphase sort does not read or write the entire file, so a typical polyphase iteration will take less time than a merge sort iteration.…

Typically, a merge sort splits items into sorted runs and then recursively merges each run into larger runs.When there's only one run left, that is the sorted result.…

On typical modern architectures, efficient quicksort implementations generally outperform mergesort for sorting RAM-based arrays.On the other hand, merge sort is a stable sort and is more efficient at handling slow-to-access sequential media.…