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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?

Options:

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

Correct Answer: O(n*w)

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.

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

Questions & Step-by-Step Solutions

What is the space complexity of the dynamic programming solution for the 0/1 Knapsack problem?
  • 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).
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