Dynamic Programming: Knapsack - Last Stone Weight II
What is the time complexity of the space-optimized bottom-up DP solution for Last Stone Weight II, where n is the number of stones and sum is the total weight of all stones?
What is the time complexity of the space-optimized bottom-up DP solution for Last Stone Weight II, where n is the number of stones and sum is the total weight of all stones?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify loops in the code
Outer loop runs n times (for each stone), inner loop runs up to half the total sum (sum/2).Step 2: Calculate total operations
Each iteration updates dp array, so total operations ≈ n * (sum/2) -> O(n * sum).Final Answer:
Option D -> Option DQuick Check:
DP complexity depends on n and sum, not n squared or log factors [OK]
Quick Trick: DP loops over stones and sums -> O(n * sum) [OK]
Common Mistakes:
MISTAKES- Confusing n with sum leading to O(n^2)
- Assuming logarithmic factor due to sorting
- Ignoring that dp array size depends on sum
Trap Explanation:
PITFALL- O(n^2) looks plausible if candidate confuses n and sum; sum can be large, so complexity depends on sum.
Interviewer Note:
CONTEXT- Checks if candidate understands DP complexity depends on sum dimension, not just input size n.
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