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Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [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.
The initial input is a set P of points. The algorithm selects one point p randomly and uniformly from P, and recursively finds the minimal circle containing P – {p}, i.e. all of the other points in P except p. If the returned circle also encloses p, it is the minimal circle for the whole of P and is returned.
Input = a set S of n points Assume that there are at least 2 points in the input set S of points function QuickHull(S) is // Find convex hull from the set S of n points Convex Hull := {} Find left and right most points, say A & B, and add A & B to convex hull Segment AB divides the remaining (n − 2) points into 2 groups S1 and S2 where S1 are points in S that are on the right side of the ...
Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol. 3 of The Art of Computer Programming (1973) called it the post-office problem , referring to an application of assigning to a residence the nearest post ...
It is a density-based clustering non-parametric algorithm: given a set of points in some space, it groups together points that are closely packed (points with many nearby neighbors), and marks as outliers points that lie alone in low-density regions (those whose nearest neighbors are too far away). DBSCAN is one of the most commonly used and ...
When this is the case, one obtains a linear-time or near-linear time approximation scheme, based on the idea of finding a coreset and then applying an exact optimization algorithm to the coreset. Regardless of how slow the exact optimization algorithm is, for any fixed choice of ε , the running time of this approximation scheme will be O (1 ...
Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original algorithm in 1972. [1] The algorithm finds all vertices of the convex hull ordered along its boundary.