Dynamic Programming: Knapsack - Coin Change II (Count Ways)
What is the output of the following code when called with change(0, [1])?
What is the output of the following code when called with change(0, [1])?
medium🧾 Code Trace Q4 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze dp initialization for amount=0
dp array size is 1, dp[0]=1 means one way to make amount zero (empty set).Step 2: Loop does not run as coin=1 > amount=0
Return dp[0] which is 1.Final Answer:
Option B -> Option BQuick Check:
One way to make zero amount (empty combination) [OK]
Quick Trick: Amount zero always has 1 way (empty set) [OK]
Common Mistakes:
MISTAKES- Assuming zero ways for zero amount
- Index errors with zero-length dp
Trap Explanation:
PITFALL- Candidates forget dp[0]=1 base case means one valid way for zero amount.
Interviewer Note:
CONTEXT- Checks understanding of base case and edge input handling in DP.
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