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List comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
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.
External sorting algorithms generally fall into two types, distribution sorting, which resembles quicksort, and external merge sort, which resembles merge sort. External merge sort typically uses a hybrid sort-merge strategy. In the sorting phase, chunks of data small enough to fit in main memory are read, sorted, and written out to a temporary ...
A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements. The single list is the sorted list. The merge algorithm is used repeatedly in the merge sort algorithm. An example merge sort is given in the illustration.
The canonical 2-way merge algorithm [1] stores indices i, j, and k into A, B, and C respectively. Initially, these indices refer to the first element, i.e., are 1. If A[i] < B[j], then the algorithm copies A[i] into C[k] and increases i and k. Otherwise, the algorithm copies B[j] into C[k] and increases j and k.
It then merges each of the resulting lists of two into lists of four, then merges those lists of four, and so on; until at last two lists are merged into the final sorted list. [24] Of the algorithms described here, this is the first that scales well to very large lists, because its worst-case running time is O( n log n ).
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
In the most balanced case, each time we perform a partition we divide the list into two nearly equal pieces. This means each recursive call processes a list of half the size. Consequently, we can make only log 2 n nested calls before we reach a list of size 1. This means that the depth of the call tree is log 2 n.