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The maximum coverage problem is a classical question in computer science, computational complexity theory, and operations research. It is a problem that is widely taught in approximation algorithms. As input you are given several sets and a number . The sets may have some elements in common.
As it is only a necessary condition but not a sufficient one, it can be used in checking if a given triple of numbers is not a Pythagorean triple. For example, the triples {6, 12, 18} and {1, 8, 9} each pass the test that ( c − a )( c − b )/2 is a perfect square, but neither is a Pythagorean triple.
The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence. When a circle is cut n times to produce the maximum number of pieces, represented as p = f (n), the n th cut must be considered; the number of pieces before the last cut is f (n − 1), while the number of pieces added by the last cut is n.
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
The problem is to select the maximum number of activities that can be performed by a single person or machine, assuming that a person can only work on a single activity at a time. The activity selection problem is also known as the Interval scheduling maximization problem (ISMP) , which is a special type of the more general Interval Scheduling ...
The soft satisfiability problem (soft-SAT), given a set of SAT problems, asks for the maximum number of those problems which can be satisfied by any assignment. [16] The minimum satisfiability problem. The MAX-SAT problem can be extended to the case where the variables of the constraint satisfaction problem belong to the set of reals.
If a set of numbers is empty, then there is no highest number. Assume the first number in the set is the largest. For each remaining number in the set: if this number is greater than the current largest, it becomes the new largest. When there are no unchecked numbers left in the set, consider the current largest number to be the largest in the set.
The maximum subarray problem was proposed by Ulf Grenander in 1977 as a simplified model for maximum likelihood estimation of patterns in digitized images. [5] Grenander was looking to find a rectangular subarray with maximum sum, in a two-dimensional array of real numbers.