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What is the space complexity of the dynamic programming solution for the 0/1 Kna

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Question: What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array?

Options:

  1. O(n)
  2. O(w)
  3. O(n * w)
  4. O(1)

Correct Answer: O(n * w)

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.

What is the space complexity of the dynamic programming solution for the 0/1 Kna

Practice Questions

Q1
What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array?
  1. O(n)
  2. O(w)
  3. O(n * w)
  4. O(1)

Questions & Step-by-Step Solutions

What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem using a 2D array?
  • 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).
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