Dynamic Programming: Knapsack - Last Stone Weight II
Given the final dp array from the space-optimized lastStoneWeightII function for stones = [2, 3, 5], where dp = [True, False, True, True, False, True], what is the total sum of stones?
Given the final dp array from the space-optimized lastStoneWeightII function for stones = [2, 3, 5], where dp = [True, False, True, True, False, True], what is the total sum of stones?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze dp array length
dp length is 6, so half = 5 (index max), total sum = 2 * half or 2 * half + 1Step 2: Sum stones
Given stones = [2,3,5], sum = 10Step 3: Confirm dp matches sums
dp[2], dp[3], dp[5] are True, consistent with subset sums from stonesFinal Answer:
Option A -> Option AQuick Check:
dp length 6 -> half=5 -> total sum=10 [OK]
Quick Trick: dp length = half+1 -> total sum = 2*half or 2*half+1 [OK]
Common Mistakes:
MISTAKES- Confusing dp length with total sum
- Ignoring half calculation
- Misreading dp True indices
Trap Explanation:
PITFALL- Candidates often misinterpret dp array length as total sum directly.
Interviewer Note:
CONTEXT- Tests ability to reverse engineer input from DP state
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