What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array?
Practice Questions
1 question
Q1
What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array?
O(n)
O(w)
O(n * w)
O(1)
The space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array is O(n * w), where n is the number of items and w is the maximum weight.
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 using a 2D array?
Solution: The space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array is O(n * w), where n is the number of items and w is the maximum weight.
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: In a dynamic programming solution, we use a table (2D array) to store results of subproblems.
Step 3: The table has 'n' rows, where 'n' is the number of items.
Step 4: The table has 'w' columns, where 'w' is the maximum weight capacity of the knapsack.
Step 5: Each cell in the table represents the maximum value that can be achieved with a certain number of items and a certain weight limit.
Step 6: Therefore, the total number of cells in the table is n * w.
Step 7: Since each cell requires a constant amount of space, the overall space complexity is O(n * w).
