Dynamic Programming: Knapsack - Coin Change II (Count Ways)
The following code attempts to count the number of combinations to make change. Which line contains a subtle bug that causes it to count permutations instead of combinations?
The following code attempts to count the number of combinations to make change. Which line contains a subtle bug that causes it to count permutations instead of combinations?
medium🐞 Bug Identification Q14 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand iteration order effect
Iterating amounts backwards causes dp to count permutations, not combinations.Step 2: Identify bug line
Line 5 iterates w from amount down to coin, which breaks combination counting logic.Final Answer:
Option A -> Option AQuick Check:
Forward iteration over amounts is required to count combinations correctly [OK]
Quick Trick: Check direction of inner loop iteration [OK]
Common Mistakes:
MISTAKES- Using backward iteration in 1D dp
- Misplacing dp[0] initialization
Trap Explanation:
PITFALL- Backward iteration looks correct for 0/1 knapsack but breaks unbounded knapsack combination counting.
Interviewer Note:
CONTEXT- Tests if candidate knows subtle iteration order impact on counting combinations vs permutations.
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