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Most implementations of merge sort are stable, which means that the relative order of equal elements is the same between the input and output Recursively sort the larger elements from each pair, creating a sorted sequence of of the input. Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements
The single list is the sorted list Perform comparisons, one per pair, to determine the larger of the two elements in each pair The merge algorithm is used repeatedly in the merge sort algorithm
An example merge sort is given in the illustration
It starts with an unsorted array of 7 integers. Problems of sufficient simplicity are solved directly For example, to sort a given list of n natural numbers, split it into two lists of about n /2 numbers each, sort each of them in turn, and interleave both results appropriately to obtain the sorted version of the given list (see the picture) This approach is known as the merge sort algorithm.
Merge sort in computer science, a sorting algorithm is an algorithm that puts elements of a list into an order The most frequently used orders are numerical order and lexicographical order, and either ascending or descending Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. It was implemented by tim peters in 2002 for use in the python programming language
The algorithm finds subsequences of the data that are already ordered (runs) and uses them to sort the remainder more efficiently
This is done by merging runs. An example of such is the classic merge that appears frequently in merge sort examples. Bitonic sorting networks (bitonic merge sort) a bitonic sorting network is created by using several bitonic sorters These bitonic sorters are recursively used to create two monotonic sequences, one decreasing and one increasing, which are then put into the next stage.
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 exceeds the total memory capacity of all. It gets its name from the observation that merging two sorted lists, a and b, is equivalent to breaking a into evenly sized blocks, inserting each a block into b under special rules, and merging ab. [6] group the elements of into pairs of elements, arbitrarily, leaving one element unpaired if there is an odd number of elements
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