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Unlike some efficient implementations of quicksort, merge sort is a stable sort. Variants[ edit ] Variants of merge sort are primarily concerned with reducing the space complexity and the cost of copying.
With this version it is better to allocate the temporary space outside the merge routine, so that only one allocation is needed. The excessive copying mentioned previously is also mitigated, since the last pair of lines before the return result statement function merge in the pseudo code above become superfluous.
One drawback of merge sort, when implemented on arrays, is its O n working memory requirement. Several in-place variants have been suggested: They achieve an O n log n time bound with small constants, but their algorithm is not stable.
In this case, the notion of "in-place" can be relaxed to mean "taking logarithmic stack space", because standard merge sort requires that amount of space for its own stack usage.
It was shown by Geffert et al. Bing-Chao Huang and Michael A. Langston  presented a straightforward linear time algorithm practical in-place merge to merge a sorted list using fixed amount of additional space.
They both have used the work of Kronrod and others. It merges in linear time and constant extra space. 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.
Though the algorithm is much faster in practical way but it is unstable also for some list. But using similar concept they have been able to solve this problem. A modern stable linear and in-place merging is block merge sort An alternative to reduce the copying into multiple lists is to associate a new field of information with each key the elements in m are called keys.
This field will be used to link the keys and any associated information together in a sorted list a key and its related information is called a record.
Then the merging of the sorted lists proceeds by changing the link values; no records need to be moved at all. A field which contains only a link will generally be smaller than an entire record so less space will also be used.
This is a standard sorting technique, not restricted to merge sort. Use with tape drives[ edit ] Merge sort type algorithms allowed large data sets to be sorted on early computers that had small random access memories by modern standards. Records were stored on magnetic tape and processed on banks of magnetic tape drives, such as these IBM s.
An external merge sort is practical to run using disk or tape drives when the data to be sorted is too large to fit into memory.
External sorting explains how merge sort is implemented with disk drives. A typical tape drive sort uses four tape drives.So the Merge Sort algorithm is a recursive algorithm, and again, that means that a program which calls itself and it calls itself on smaller sub problems of the same form, okay?
So the Merge Sort is its purpose in life is to sort the given input array. A Simple Merge Sort Its easier to understand merge sort if you try to write a simple code on how you'd merge two sorted arrays into a new array which needs to be in sorted order.
Lets try to code that first Now lets try to implement merge sort algorithm in the simplest possible way as explained above. Merge sort is a sorting technique based on divide and conquer technique. With the worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.
C++ Example – Merge Sort Algorithm August 25, admin C++ 0. Merge sort. Merge sort algorithm is one of two important divide-and-conquer sorting algorithms (the other one is quick sort).Merge In this lesson we will learn how to write a source code in C++ programming language for doing simple Merge sort using array in ascending order.
A Simple Merge Sort Its easier to understand merge sort if you try to write a simple code on how you'd merge two sorted arrays into a new array which needs to be in sorted order. Lets try to code that first Now lets try to implement merge sort algorithm in the simplest possible way as explained above.
If the running time of merge sort for a list of length n is T(n), then the recurrence T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists).