How do you solve the 0/1 Knapsack Problem using dynamic programming?
This problem asks to maximize value given weight constraints where items cannot be split. It tests classic DP table filling.
Why Interviewers Ask This
Interviewers ask this to test fundamental DP understanding. They want to see if you can define the state transition for including or excluding items. It demonstrates resource allocation logic.
How to Answer This Question
Define dp[i][w] as max value using first i items with capacity w. For each item, decide to include it (if weight allows) or exclude it. Take the maximum of these two choices. Fill the table iteratively. Discuss space optimization to O(W) if needed.
Key Points to Cover
- State definition
- Include/exclude decision
- Table filling order
- Optimization possibilities
Sample Answer
I define a 2D DP table where dp[i][w] represents the maximum value achievable using the first i items with a weight limit of w. For each item, I have two choices: include it if its weight is less than or equal to w, or e…
Common Mistakes to Avoid
- Incorrect recurrence relation
- Confusing 0/1 with fractional knapsack
- Ignoring weight constraints
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