What is the knapsack problem in dynamic programming?

What is the knapsack problem in dynamic programming?

The knapsack problem is a classic optimization problem where you have to maximize the total value of items you can carry in a knapsack without exceeding its weight capacity.

Can you explain the different types of knapsack problems?

Sure! The main types are the 0/1 knapsack, fractional knapsack, and unbounded knapsack. Each has different constraints on how items can be selected.

How do you solve the 0/1 knapsack problem using dynamic programming?

To solve the 0/1 knapsack problem using dynamic programming, you create a table where each cell represents the maximum value that can be achieved with a given weight limit and number of items.

What is the time complexity of the dynamic programming solution?

The time complexity of the dynamic programming solution for the 0/1 knapsack problem is O(n * W), where n is the number of items and W is the maximum weight capacity.