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Recursively divide the list into sublists of (roughly) equal length, until each sublist contains only one element, or in the case of iterative (bottom up) merge sort, consider a list of n elements as n sub-lists of size 1. A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist ...
An example of such is the classic merge that appears frequently in merge sort examples. The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
Example C-like code using indices for top-down merge sort algorithm that recursively splits the list (called runs in this example) into sublists until sublist size is 1, then merges those sublists to produce a sorted list. The copy back step is avoided with alternating the direction of the merge with each level of recursion (except for an ...
Timsort was designed to take advantage of runs of consecutive ordered elements that already exist in most real-world data, natural runs. It iterates over the data collecting elements into runs and simultaneously putting those runs in a stack. Whenever the runs on the top of the stack match a merge criterion, they are merged. This goes on until ...
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.
Merge-insertion sort performs the following steps, on an input of elements: [6] Group the elements of X {\displaystyle X} into ⌊ n / 2 ⌋ {\displaystyle \lfloor n/2\rfloor } pairs of elements, arbitrarily, leaving one element unpaired if there is an odd number of elements.
Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network.The algorithm was devised by Ken Batcher.The resulting sorting networks consist of ( ()) comparators and have a delay of ( ()), where is the number of items to be sorted. [1]