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Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science.. In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities.
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.
A problem exemplifying the concepts of online algorithms is the Canadian traveller problem.The goal of this problem is to minimize the cost of reaching a target in a weighted graph where some of the edges are unreliable and may have been removed from the graph.
The Euclidean algorithm calculates the greatest common divisor (GCD) of two natural numbers a and b.The greatest common divisor g is the largest natural number that divides both a and b without leaving a remainder.
The problem that we are trying to solve is: given an odd composite number, find its integer factors. To achieve this, Shor's algorithm consists of two parts: A classical reduction of the factoring problem to the problem of order-finding.
In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
The book outlines five approaches of machine learning: inductive reasoning, connectionism, evolutionary computation, Bayes' theorem and analogical modelling.The author explains these tribes to the reader by referring to more understandable processes of logic, connections made in the brain, natural selection, probability and similarity judgments.