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The following code attempts to count combinations to make change. Which line contains a subtle bug that causes incorrect counting?

medium🐞 Bug Identification Q7 of Q15
Dynamic Programming: Knapsack - Coin Change II (Count Ways)
The following code attempts to count combinations to make change. Which line contains a subtle bug that causes incorrect counting?
AThe dp array size is amount + 1
BThe inner loop iterates backwards over amounts
CThe outer loop iterates over coins
Ddp[0] is initialized to 1
Step-by-Step Solution
Solution:

  1. Step 1: Understand iteration order impact

    Iterating amounts backwards causes counting permutations, not combinations.

  2. Step 2: Correct iteration order

    Amounts must be iterated forwards to count combinations correctly.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Backward iteration -> permutation count bug [OK]
Quick Trick: Forward iteration over amounts counts combinations [OK]
Common Mistakes:
MISTAKES
  • Using backward iteration causing overcount
  • Misunderstanding iteration order effect
Trap Explanation:
PITFALL
  • Many candidates use backward iteration from 0/1 knapsack, causing wrong counts here.
Interviewer Note:
CONTEXT
  • Tests candidate's knowledge of iteration order in unbounded knapsack DP.
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