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Knapsack problem - Wikipedia, the free encyclopedia
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List of knapsack problems - Wikipedia, the free encyclopedia
The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalisations have been examined. ...
en.wikipedia.org/wiki/List_of_knapsack_problems |
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The point is, however, that the Knapsack Problem represents many real-life problems that are not at all "Knapsack Problems" as such. We use the term "Knapsack Problem" as shorthand for the above mathematical model and in that context it is perfectly OK to allow the wjs to be negative.
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The Knapsack Problem can be described as follows: We nave an empty bag with (weight) capacity C, along with n items. The items have weights w(i) and values v(i), for i=1,2,...,n. There is only one of each item. Which items should we take to maximize the total value, while not exceeding the bag capacity?
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The 0-1 Knapsack Problem (AKA The Discrete Knapsack Problem) is a famous problem solvable by dynamic-programming. In this article, I describe the problem, the most common algorithm used to solve it and then provide a sample implementation in C.
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In this article, I describe the greedy algorithm for solving the Fractional Knapsack Problem and give an implementation in C. ... The Fractional Knapsack Problem usually sounds like this:
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