# merge sort

(algorithm)

Definition: A sort algorithm that splits the items to be sorted into two groups, recursively sorts each group, and merges them into a final, sorted sequence. Run time is Θ(n log n).

Generalization (I am a kind of ...)
sort.

Specialization (... is a kind of me.)
k-way merge sort, balanced k-way merge sort, polyphase merge sort.

Aggregate child (... is a part of or used in me.)
divide and conquer.

See also external sort, bitonic sort, strand sort.

Note: There seem to be some references to linear-time in-place merging; look for papers by Geffert, Katajainen & Pasanen.

Author: PEB

## Implementation

(Python). (C) that needs list merge (C) or array merge (C), (Pascal) that needs list merge (Pascal) or array merge (Pascal); Worst-case behavior annotated for real time (WOOP/ADA), including bibliography. Siegfried Sielaff's description and code of an in-place, stable variant he calls Swap Sort (C) (click the British flag for an English translation). Other implementations may be available through the Stony Brook Algorithm Repository, Sorting. Alexander Georgiev's merge sort (Java) implemented as part of a linked-list package. Includes a parallel merge sort, too. Flower Brackets (Java).

Comparison of quicksort, heapsort, and merge sort on modern processors.

Merge sort illustrated.

Merge sort vs. quick sort race. First a random permutation, then a near-worst case for merge sort.

Heap sort vs. merge sort race.

Merge sort illustrated through a Transylvanian-saxon (German) folk dance. Created at Sapientia University.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 6 April 2023.
HTML page formatted Thu Apr 6 11:44:03 2023.

Cite this as:
Paul E. Black, "merge sort", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 6 April 2023. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/mergesort.html