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In the merge sort algorithm, this subroutine is typically used to merge two sub-arrays A[lo..mid], A[mid+1..hi] of a single array A. This can be done by copying the sub-arrays into a temporary array, then applying the merge algorithm above. [1] The allocation of a temporary array can be avoided, but at the expense of speed and programming ease.
Suppose that such an algorithm existed, then we could construct a comparison-based sorting algorithm with running time O(n f(n)) as follows: Chop the input array into n arrays of size 1. Merge these n arrays with the k-way merge algorithm. The resulting array is sorted and the algorithm has a running time in O(n f(n)).
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 outer loop of block sort is identical to a bottom-up merge sort, where each level of the sort merges pairs of subarrays, A and B, in sizes of 1, then 2, then 4, 8, 16, and so on, until both subarrays combined are the array itself.
Modern C++ compilers are tuned to minimize abstraction penalties arising from heavy use of the STL. The STL was created as the first library of generic algorithms and data structures for C++, with four ideas in mind: generic programming, abstractness without loss of efficiency, the Von Neumann computation model, [2] and value semantics.
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 ...
In-place can have slightly different meanings. In its strictest form, the algorithm can only have a constant amount of extra space, counting everything including function calls and pointers. However, this form is very limited as simply having an index to a length n array requires O(log n) bits. More broadly, in-place means that the algorithm ...
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.