Computational Theory Questions
The knapsack problem is a classic optimization problem in computer science and mathematics. It involves selecting a subset of items from a given set, each with a certain value and weight, in order to maximize the total value while keeping the total weight within a given limit (the capacity of the knapsack). The problem is known to be NP-hard, meaning that there is no known efficient algorithm to solve it exactly for large instances. Various algorithms and heuristics have been developed to approximate the optimal solution or find good solutions within a reasonable amount of time.