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In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V1, V2, ..., Vn taking y as an argument representing the state of the system at times i from 1 to n .
Introduction to Algorithms is a book on computer programming by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.The book has been widely used as the textbook for algorithms courses at many universities and is commonly cited as a reference for algorithms in published papers, with over 10,000 citations documented on CiteSeerX, and over 67,000 citation on Google ...
Algorithm. Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm ( / ˈælɡərɪðəm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Branch and bound. Branch and bound ( BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as ...
Data structure. Finite-state machine of strings. In computer science, the Aho—Corasick algorithm is a string-searching algorithm invented by Alfred V. Aho and Margaret J. Corasick in 1975. [1] It is a kind of dictionary-matching algorithm that locates elements of a finite set of strings (the "dictionary") within an input text.
Gauss–Legendre algorithm: computes the digits of pi. Chudnovsky algorithm: a fast method for calculating the digits of π. Bailey–Borwein–Plouffe formula: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π. Division algorithms: for computing quotient and/or remainder of two numbers.
Computer programming or coding is the composition of sequences of instructions, called programs, that computers can follow to perform tasks. [1] [2] It involves designing and implementing algorithms, step-by-step specifications of procedures, by writing code in one or more programming languages. Programmers typically use high-level programming ...
A system of linear inequalities defines a polytope as a feasible region. The simplex algorithm begins at a starting vertex and moves along the edges of the polytope until it reaches the vertex of the optimal solution. Polyhedron of simplex algorithm in 3D. The simplex algorithm operates on linear programs in the canonical form.