http://wiki.karljones.com/index.php?action=history&feed=atom&title=Knapsack_problem 2026-10-23T17:12:34Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Knapsack_problem&diff=15387&oldid=prev 2016-05-14T01:19:52Z

<p>Created page with &quot;The &#039;&#039;&#039;knapsack problem&#039;&#039;&#039; or &#039;&#039;&#039;rucksack problem&#039;&#039;&#039; is a problem in <a href="/index.php/Combinatorial_optimization" title="Combinatorial optimization">combinatorial optimization</a>: Given a set of items, each with a weight and a value, determine the number...&quot;</p> <p><b>New page</b></p><div>The '''knapsack problem''' or '''rucksack problem''' is a problem in [[combinatorial optimization]]: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.<br /> <br /> == Description ==<br /> <br /> 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.<br /> <br /> The problem often arises in resource allocation where there are financial constraints and is studied in fields such as [[combinatorics]], [[computer science]], [[complexity theory]], [[cryptography]], [[applied mathematics,]] and daily fantasy sports.<br /> <br /> The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.<br /> <br /> The name &quot;knapsack problem&quot; dates back to the early works of mathematician [[Tobias Dantzig ]](1884–1956), and refers to the commonplace problem of packing your most valuable or useful items without overloading your luggage.<br /> <br /> == See also ==<br /> <br /> * [[Change-making problem]]<br /> * [[Combinatorial auction]]<br /> * [[Combinatorial optimization]]<br /> * [[Continuous knapsack problem]]<br /> * [[Cutting stock problem]]<br /> * [[List of knapsack problems]]<br /> * [[Packing problem]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Knapsack_problem Knapsack problem] @ Wikipedia<br /> <br /> <br /> <br /> [[Category:Mathematics]]</div>

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