The knapsack problem is a classic optimization problem in computer science, mathematics, and operations research. It is a problem of combinatorial optimization, where the goal is to optimize a function subject to a set of constraints. The problem is framed in terms of a knapsack, which is a container with a limited capacity. A set of items is given, each with a weight and a value. The objective is to select a subset of items that maximizes the value, subject to the constraint that the sum of the weights of the selected items does not exceed the capacity of the knapsack. Fig 1: Knapsack Problem The problem can be formulated mathematically as follows: Maximize ∑ vi xi Subject to ∑ wi xi ≤ W xi ∈ {0, 1} where vi is the value of the i-th item, wi is its weight, W is the capacity of the knapsack, and xi is a bin...