Merge Sort in a sentence

Comparison with other sort algorithms Although heapsort has the same time bounds as merge sort, it requires only Θ(1) auxiliary space instead of merge sort's Θ(n).

Insertion sort is widely used for small data sets, while for large data sets an asymptotically efficient sort is used, primarily heap sort, merge sort, or quicksort.

An example for merge sort An example merge sort is given above.

In terms of moves, merge sort's worst case complexity is (n log n)—the same complexity as quicksort's best case, and merge sort's best case takes about half as many iterations as the worst case.

Merge sort main Merge sort takes advantage of the ease of merging already sorted lists into a new sorted list.

In the typical case, the natural merge sort may not need as many passes because there are fewer runs to merge.

Analysis A recursive merge sort algorithm used to sort an array of 7 integer values.

Efficient sorts Practical general sorting algorithms are almost always based on an algorithm with average time complexity (and generally worst-case complexity) O(n log n), of which the most common are heap sort, merge sort, and quicksort.

On the other hand, merge sort is a stable sort and is more efficient at handling slow-to-access sequential media.

Thus more sophisticated algorithms are often employed, such as Timsort (based on merge sort) or introsort (based on quicksort, falling back to heap sort).

Unlike some (efficient) implementations of quicksort, merge sort is a stable sort.

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.

Each has advantages and drawbacks, with the most significant being that simple implementation of merge sort uses O(n) additional space, and simple implementation of quicksort has O(n 2 ) worst-case complexity.

For example, consider a bottom-up merge sort.

For example, the tiled merge sort algorithm stops partitioning subarrays when subarrays of size S are reached, where S is the number of data items fitting into a CPU's cache.

In the bottom up merge sort, the starting point assumes each run is one item long.

One drawback of merge sort, when implemented on arrays, is its O(n) working memory requirement.

The algorithm takes little more average time than standard merge sort algorithms, free to exploit O(n) temporary extra memory cells, by less than a factor of two.

These are the steps a human would take to emulate merge sort (top-down).

This is a standard sorting technique, not restricted to merge sort.