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Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithmics theory and practical applications of algorithms in software engineering. [1]
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
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.
There are several broadly recognized algorithmic techniques that offer a proven method or process for designing and constructing algorithms. Different techniques may be used depending on the objective, which may include searching, sorting, mathematical optimization, constraint satisfaction, categorization, analysis, and prediction.
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, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process. For maximum efficiency it is desirable to minimize resource usage.
For looking up a given entry in a given ordered list, both the binary and the linear search algorithm (which ignores ordering) can be used. The analysis of the former and the latter algorithm shows that it takes at most log 2 n and n check steps, respectively, for a list of size n.
Best explored is functional correctness, which refers to the input-output behavior of the algorithm: for each input it produces an output satisfying the specification. [ 1 ] Within the latter notion, partial correctness , requiring that if an answer is returned it will be correct, is distinguished from total correctness , which additionally ...