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For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures. This list of terms was originally derived from the index of that document, and is in the public domain, as it was compiled by a Federal Government employee as part of a Federal Government work. Some of the terms defined are:
The divide-and-conquer paradigm is often used to find an optimal solution of a problem. Its basic idea is to decompose a given problem into two or more similar, but simpler, subproblems, to solve them in turn, and to compose their solutions to solve the given problem. Problems of sufficient simplicity are solved directly.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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.
Merge sorting is an example of divide and conquer, where an unordered list can be divided into segments containing one item and sorting of entire list can be obtained by merging the segments. A simpler variant of divide and conquer is called a decrease-and-conquer algorithm , which solves one smaller instance of itself, and uses the solution to ...
Merging two sorted lists into one can be done in linear time and linear or constant space (depending on the data access model). The following pseudocode demonstrates an algorithm that merges input lists (either linked lists or arrays) A and B into a new list C.
House Republicans are scrambling to find a way to avoid a government shutdown after their second funding proposal was rejected, and are now planning to vote on a third proposal soon.
Each piece of work will be divided repeatedly until the "amount" of work is as small as it can possibly be, at which point the algorithm will do that work very quickly. The algorithm then "reverses" and reassembles the pieces into a complete whole. The classic example of recursion is in list-sorting algorithms, such as merge sort. The merge ...