The knapsack problem is a classic optimization challenge in computer science and mathematics. Imagine you have a backpack (or knapsack) that can hold a limited weight, and you want to pack it with items that have different weights and values. The goal is to maximize the total value of the items you can carry without exceeding the weight limit. There are different versions of the knapsack problem, but the most common one is the 0/1 knapsack problem, where you can either take an item or leave it behind, but you can't take a fraction of it. This problem is widely studied because it has applications in various fields, such as resource allocation, budgeting, and logistics.