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In computer science, merge sort (also commonly spelled as mergesort and as merge-sort[ 2 ]) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output.
The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform . [1]
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that occur in the analysis of divide-and-conquer algorithms. The approach was first presented by Jon Bentley, Dorothea Blostein (née Haken), and James B. Saxe in 1980, where it was described as a ...
Recursion: Some algorithms are either recursive or non-recursive, while others may be both (e.g., merge sort). Stability: stable sorting algorithms maintain the relative order of records with equal keys (i.e., values). Whether or not they are a comparison sort. A comparison sort examines the data only by comparing two elements with a comparison ...
In computer science, merge-insertion sort or the Ford–Johnson algorithm is a comparison sorting algorithm published in 1959 by L. R. Ford Jr. and Selmer M. Johnson. [1][2][3][4] It uses fewer comparisons in the worst case than the best previously known algorithms, binary insertion sort and merge sort, [1] and for 20 years it was the sorting ...
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
The main disadvantage of merge sort is that it is an out-of-place algorithm, so when operating on arrays, efficient implementations require O(n) auxiliary space (vs. O(log n) for quicksort with in-place partitioning and tail recursion, or O(1) for heapsort). Merge sort works very well on linked lists, requiring only a small, constant amount of ...
Batcher's odd–even mergesort[1] is a generic construction devised by Ken Batcher for sorting networks of size O (n (log n) 2) and depth O ( (log n) 2), where n is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in 1998, with respect to the AKS network that "Batcher's method is much better, unless n ...