Dynamic Programming: Knapsack - Number of Ways to Make Change
What is the output of the space-optimized code when coins = [3] and amount = 0?
What is the output of the space-optimized code when coins = [3] and amount = 0?
medium🧾 Code Trace Q4 of Q15
Step-by-Step Solution
Solution:
Step 1: Initialize dp array
dp = [1] since amount=0, dp[0]=1 means one way to make amount 0 (empty set).Step 2: Loop over coins and amounts
Since amount=0, inner loop does not run. dp remains [1].Final Answer:
Option B -> Option BQuick Check:
One way to make amount 0: use no coins -> dp[0]=1 [OK]
Quick Trick: Amount zero always has 1 way (empty set) [OK]
Common Mistakes:
MISTAKES- Returning 0 for amount=0
- Looping incorrectly over dp array
- Misunderstanding base case
Trap Explanation:
PITFALL- Candidates often forget dp[0]=1 base case, leading to zero count for amount=0.
Interviewer Note:
CONTEXT- Tests handling of edge cases and base conditions in DP.
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