Which dynamic programming approach is used to solve the 0/1 Knapsack problem?
Practice Questions
1 question
Q1
Which dynamic programming approach is used to solve the 0/1 Knapsack problem?
Top-down approach with memoization
Bottom-up approach with tabulation
Greedy approach
Brute force approach
The 0/1 Knapsack problem can be solved using a bottom-up dynamic programming approach with tabulation, which builds up solutions to subproblems.
Questions & Step-by-step Solutions
1 item
Q
Q: Which dynamic programming approach is used to solve the 0/1 Knapsack problem?
Solution: The 0/1 Knapsack problem can be solved using a bottom-up dynamic programming approach with tabulation, which builds up solutions to subproblems.
Steps: 7
Step 1: Understand the 0/1 Knapsack problem. It involves selecting items with given weights and values to maximize value without exceeding a weight limit.
Step 2: Identify that we need to solve smaller problems first. This means we will look at combinations of items and their weights/values.
Step 3: Use a table (2D array) to store solutions to these smaller problems. The rows represent items, and the columns represent weight limits.
Step 4: Fill in the table using a bottom-up approach. Start with the smallest weight limits and build up to the maximum weight limit.
Step 5: For each item, decide whether to include it in the knapsack or not based on its weight and value compared to the current weight limit.
Step 6: Continue filling the table until all items and weight limits are considered.
Step 7: The final cell in the table will contain the maximum value that can be achieved with the given weight limit.
