Dynamic Programming: Knapsack - Coin Change II (Count Ways)
Consider the following Python code for counting the number of ways to make change. What is the output when calling
change(5, [1, 2, 5])?Consider the following Python code for counting the number of ways to make change. What is the output when calling change(5, [1, 2, 5])?
easy🧾 Code Trace Q12 of Q15
Step-by-Step Solution
Solution:
Step 1: Initialize dp array
dp = [1,0,0,0,0,0] since dp[0]=1.Step 2: Update dp for each coin
For coin=1: dp becomes [1,1,1,1,1,1]; for coin=2: dp updates to [1,1,2,2,3,3]; for coin=5: dp updates to [1,1,2,2,3,4].Final Answer:
Option C -> Option CQuick Check:
dp[5] = 4 matches known output [OK]
Quick Trick: Trace dp updates coin by coin [OK]
Common Mistakes:
MISTAKES- Off-by-one in dp indexing
- Confusing permutations with combinations
Trap Explanation:
PITFALL- Counting permutations would yield 6, but this code counts combinations correctly.
Interviewer Note:
CONTEXT- Tests ability to mentally execute DP code and track array updates.
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