knapsack problem

knapsack problem [′nap‚sak ‚präb·ləm]

(mathematics)

The problem, given a set of integers {A₁,A₂, …,A_n} and a target integerB, of determining whether a subset of theA_ican be selected without repetition so that their sum is the targetB.

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(application, mathematics)

knapsack problem - 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.