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What is the time complexity of the dynamic programming solution for the 0/1 Knap

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Question: What is the time complexity of the dynamic programming solution for the 0/1 Knapsack problem?

Options:

  1. O(n)
  2. O(n^2)
  3. O(n * W)
  4. O(2^n)

Correct Answer: O(n * W)

Solution: 

The time 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 time complexity of the dynamic programming solution for the 0/1 Knap

Practice Questions

Q1
What is the time complexity of the dynamic programming solution for the 0/1 Knapsack problem?
  1. O(n)
  2. O(n^2)
  3. O(n * W)
  4. O(2^n)

Questions & Step-by-Step Solutions

What is the time 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 approach uses a table to store solutions to subproblems. The table has dimensions (n+1) x (W+1).
  • Step 4: Realize that filling this table requires iterating through each item (n) and each weight capacity (W).
  • Step 5: Calculate the total number of operations. For each item, you check all weight capacities, leading to n * W operations.
  • Step 6: Conclude that the time complexity of the dynamic programming solution is O(n * W).
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