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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.
Algorithm design is a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as divide-and-conquer or dynamic programming within operation research .
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.
Does linear programming admit a strongly polynomial-time algorithm? (This is problem #9 in Smale's list of problems.) How many queries are required for envy-free cake-cutting? What is the algorithmic complexity of the minimum spanning tree problem? Equivalently, what is the decision tree complexity of the MST problem?
In theoretical computer science, a computational problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n." is a computational problem that has a solution, as there are many known integer factorization algorithms.
This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory. However, there are intermediate methods that, for example, use theory to guide the method, an approach known as guided empiricism. [citation needed]
The quantum algorithm solving Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. [1] Both problems are special cases of the abelian hidden subgroup problem , which is now known to have efficient quantum algorithms.
Classic combinatorial search problems include solving the eight queens puzzle or evaluating moves in games with a large game tree, such as reversi or chess. A study of computational complexity theory helps to motivate combinatorial search. Combinatorial search algorithms are typically concerned with problems that are NP-hard. Such problems are ...