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Identify the subtle bug that causes incorrect results on some inputs.

medium🐞 Bug Identification Q7 of Q15
Dynamic Programming: Knapsack - Ones and Zeroes (2D Knapsack)
Examine the following code snippet attempting to solve the Ones and Zeroes problem. Identify the subtle bug that causes incorrect results on some inputs. ```python def findMaxForm(strs, m, n): dp = [[0] * (n + 1) for _ in range(m + 1)] for s in strs: zeros = s.count('0') ones = len(s) - zeros for i in range(zeros, m + 1): # Forward iteration for j in range(ones, n + 1): # Forward iteration dp[i][j] = max(dp[i][j], 1 + dp[i - zeros][j - ones]) return dp[m][n] ```
AIncorrect counting of zeros and ones in strings
BIterating dp array forwards causes counting strings multiple times
CNot initializing dp array with zeros
DMissing base case for recursion
Step-by-Step Solution
Solution:
  1. Step 1: Analyze iteration order

    Forward iteration over dp causes reuse of updated states within the same iteration, counting strings multiple times.
  2. Step 2: Correct approach is backward iteration

    Backward iteration prevents double counting by using only states from previous iteration.
  3. Final Answer:

    Option B -> Option B
  4. Quick Check:

    Forward iteration -> multiple counting bug [OK]
Quick Trick: DP knapsack requires backward iteration to avoid reuse [OK]
Common Mistakes:
MISTAKES
  • Iterating forwards in knapsack DP
  • Assuming order doesn't matter
Trap Explanation:
PITFALL
  • Candidates often overlook iteration direction causing subtle bugs.
Interviewer Note:
CONTEXT
  • Tests subtle DP update order bugs.
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