What is the bounded knapsack problem?

What is the bounded knapsack problem?

The bounded knapsack problem is a variation of the knapsack problem where each item has a limited quantity. You need to maximize the total value in the knapsack without exceeding its capacity.

Can you give me an example of how it works?

Sure! Imagine you have a knapsack that can hold 10 kg. You have three items: 2 kg worth $10, 3 kg worth $20, and 5 kg worth $30. If you can only take 1 of each item, the best combination would be the 3 kg and 5 kg items for a total value of $50.

How do I solve it using dynamic programming?

To solve it using dynamic programming, you create a table where each entry represents the maximum value for a given weight limit. You iterate through each item and update the table based on whether including the item increases the total value.

What are some real-world applications of this problem?

Real-world applications include resource allocation, budget management, and cargo loading, where you need to maximize value within constraints.