Knapsack problem

The knapsack problem is problem in [applied mathmatics]?. Given a set of items, each with a cost and a value, determine the number of each item to include in a collection so that the total cost is less than some given cost and the total value is as large as possible.

The 0/1 knapsack problem restricts the number of each items to zero or one.

Such constraint satisfaction problems are often solved using [dynamic programming]?. The general knapsack problem is NP-hard?, and this has led to attempts to use it as the basis for [public-key encryption]? systems. Several such attempts failed because the knapsack problems they produced were in fact solvable by [polynomial-time algorithms]?.

---

Based on material from FOLDOC, used with permission.