Dynamic Programming: Knapsack - Target Sum
What is the time complexity of the bottom-up DP solution for the Target Sum problem with input array length n and total sum W = sum(nums)?
What is the time complexity of the bottom-up DP solution for the Target Sum problem with input array length n and total sum W = sum(nums)?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify DP dimensions
The DP table iterates over n items and sums from -W to W, total 2W+1 states.Step 2: Calculate complexity
Each of the n iterations updates O(W) states, resulting in O(n * W) time complexity.Final Answer:
Option D -> Option DQuick Check:
DP over n items and sum range W -> O(n * W) [OK]
Quick Trick: DP time depends on n and sum W -> O(n * W) [OK]
Common Mistakes:
MISTAKES- Confusing with O(2^n) brute force
- Assuming quadratic in n only
Trap Explanation:
PITFALL- Candidates often mistake exponential brute force for DP time or ignore sum dimension W.
Interviewer Note:
CONTEXT- Tests understanding of DP time complexity with sum dimension.
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