Back مسألة حقيبة الظهر Arabic Задача за раницата Bulgarian Problema de la motxilla Catalan Problém batohu Czech Rygsækproblem Danish Rucksackproblem German Problema de la mochila Spanish Bizkar-zorroaren buruketa Basque مسئله کولهپشتی Persian Problème du sac à dos French
(Solution: if any number of each book is available, then three yellow books and three grey books; if only the shown books are available, then all except for the green book.)
The knapsack problem is the following problem in combinatorial optimization:
- Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.
The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.[1]
- ^ Mathews, G. B. (25 June 1897). "On the partition of numbers" (PDF). Proceedings of the London Mathematical Society. 28: 486–490. doi:10.1112/plms/s1-28.1.486.
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