Can you explain the 0-1 Knapsack problem and its solution?
The 0-1 Knapsack problem involves selecting items with given weights and values to maximize total value without exceeding a weight capacity.
Why Interviewers Ask This
This is a quintessential dynamic programming problem that tests optimization skills. Interviewers assess your ability to define states and transitions. It also evaluates your understanding of NP-hard problems and approximation strategies.
How to Answer This Question
Define the problem clearly with items, weights, values, and capacity. Explain the recursive relation: max value is either including the item or excluding it. Show how to build a DP table to store results of subproblems. Discuss the time and space complexity and mention space optimization techniques.
Key Points to Cover
- Dynamic programming table
- Include vs exclude decision
- State transition formula
- O(n*W) complexity
Sample Answer
The 0-1 Knapsack problem is solved using dynamic programming. We create a 2D table where dp[i][w] represents the max value using the first i items with capacity w. For each item, we decide whether to include it (if weigh…
Common Mistakes to Avoid
- Confusing with fractional knapsack
- Incorrect base case initialization
- Not handling weight constraints properly
Sound confident on this question in 5 minutes
Answer once and get a 30-second AI critique of your structure, content, and delivery. First attempt is free — no signup needed.