Knapsack problem is a fundamental combinatorial optimization problem that investigates the optimal selection of items from a given set, each with an associated weight and value, to be included in a container (the "knapsack") with a fixed weight capacity. The objective is to maximize the total value of the items selected while ensuring their collective weight does not exceed the knapsack's capacity. This concept is significant as a classical example of an NP-hard problem, extensively studied in theoretical computer science and operations research, serving as a benchmark for algorithm design and a model for resource allocation challenges across various disciplines.