What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem?
Practice Questions
1 question
Q1
What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem?
O(1)
O(n)
O(w)
O(n*w)
The space 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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem?
Solution: The space 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.
Steps: 6
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 the variables involved. Let 'n' be the number of items and 'w' be the maximum weight capacity of the knapsack.
Step 3: Recognize that the dynamic programming solution uses a table to store results. This table has dimensions based on the number of items and the weight capacity.
Step 4: The table will have 'n' rows (for each item) and 'w' columns (for each weight from 0 to w).
Step 5: Calculate the total number of entries in the table. It is 'n' multiplied by 'w', which gives us n * w.
Step 6: Conclude that the space complexity, which measures how much memory is used, is O(n * w).
