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In the following buggy code for lastStoneWeightII, which line causes incorrect results?

medium🐞 Bug Identification Q7 of Q15
Dynamic Programming: Knapsack - Last Stone Weight II
In the following buggy code for lastStoneWeightII, which line causes incorrect results? ```python def lastStoneWeightII(stones): total = sum(stones) half = total // 2 dp = [False] * (half + 1) # dp[0] = True is missing for stone in stones: for j in range(half, stone - 1, -1): dp[j] = dp[j] or dp[j - stone] for j in range(half, -1, -1): if dp[j]: return total - 2 * j ```
AReturning total - 2 * j instead of total + 2 * j
BLoop iterating forward instead of backward
CIncorrect calculation of half as total // 2
DLine missing dp[0] = True initialization
Step-by-Step Solution
Solution:
  1. Step 1: Identify dp initialization

    dp[0] must be True to represent sum zero achievable
  2. Step 2: Check loops

    Loops iterate backward correctly to avoid reuse in same iteration
  3. Step 3: Validate calculations

    half calculation and return statement are correct
  4. Final Answer:

    Option D -> Option D
  5. Quick Check:

    dp[0] initialization is essential [OK]
Quick Trick: dp[0] must be True to start subset sums [OK]
Common Mistakes:
MISTAKES
  • Forgetting dp[0] initialization
  • Iterating dp array forward causing reuse
  • Miscomputing half sum
Trap Explanation:
PITFALL
  • Missing dp[0] initialization looks minor but breaks subset sum logic.
Interviewer Note:
CONTEXT
  • Tests debugging skills and understanding of DP base cases.
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