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Greedy algorithms determine the minimum number of coins to give while making change. These are the steps most people would take to emulate a greedy algorithm to represent 36 cents using only coins with values {1, 5, 10, 20}. The coin of the highest value, less than the remaining change owed, is the local optimum.
Pages in category "Greedy algorithms" ... out of 9 total. ... Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; ...
In computer science, greedy number partitioning is a class of greedy algorithms for multiway number partitioning. The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers ...
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions , such as 5 / 6 = 1 / 2 + 1 / 3 .
A greedy algorithm is optimal for every R-compatible linear objective function over a greedoid. The intuition behind this proposition is that, during the iterative process, each optimal exchange of minimum weight is made possible by the exchange property, and optimal results are obtainable from the feasible sets in the underlying greedoid.
Zaker (2006) defines a sequence of graphs called t-atoms, with the property that a graph has Grundy number at least t if and only if it contains a t-atom.Each t-atom is formed from an independent set and a (t − 1)-atom, by adding one edge from each vertex of the (t − 1)-atom to a vertex of the independent set, in such a way that each member of the independent set has at least one edge ...
The Complete Greedy Algorithm (CGA) considers all partitions by constructing a k-ary tree. Each level in the tree corresponds to an input number, where the root corresponds to the largest number, the level below to the next-largest number, etc. Each of the k branches corresponds to a different set in which the current number can be put.
However, the odd greedy expansion is more typically long, with large denominators. For instance, as Wagon discovered, [4] the odd greedy expansion for 3/179 has 19 terms, the largest of which is approximately 1.415×10 439491. Curiously, the numerators of the fractions to be expanded in each step of the algorithm form a sequence of consecutive ...