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What is meant by knapsack problem?
The knapsack 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.
What is the complexity of knapsack problem?
The dynamic programming algorithm for the knapsack problem has a time complexity of O(nW) where n is the number of items and W is the capacity of the knapsack.
Why is the knapsack problem important?
It is easily the most important problem in logistics. In the knapsack problem, the given items have two attributes at minimum – an item’s value, which affects its importance, and an item’s weight or volume, which is its limitation aspect.
Which is the best method to solve knapsack problem?
So this Knapsack problem can be solved by using these following methods: Greedy method. Dynamic Programming method. Back Tracking method.
What is the optimal solution for knapsack problem?
After selecting item A, no more item will be selected. Hence, for this given set of items total profit is 24. Whereas, the optimal solution can be achieved by selecting items, B and C, where the total profit is 18 + 18 = 36.
Is the knapsack problem a weakly NP-complete problem?
However, since this runtime is pseudopolynomial, this makes the (decision version of the) knapsack problem a weakly NP-complete problem . A similar dynamic programming solution for the 0-1 knapsack problem also runs in pseudo-polynomial time.
How is the knapsack problem a resource allocation problem?
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.
How is the knapsack problem used in combinatorial optimization?
The knapsack 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.
What is the problem of an unbounded knapsack?
The Unbounded Knapsack Problem – You have an unbounded quantity of each item type, instead of a bounded quantity. Some set of M types of items, each item type m having unbounded quantity and associated with weight w [m] and profit p [m] A maximum weight W .