Dynamic Programming: Knapsack - Coin Change II (Count Ways)
Given the dp array after processing coins [1, 2] for amount=5 as dp = [1,1,2,2,3,3], which coin was processed last?
Given the dp array after processing coins [1, 2] for amount=5 as dp = [1,1,2,2,3,3], which coin was processed last?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand dp array meaning
dp[w] counts combinations using processed coins so far.Step 2: Recognize dp after coin 1 only
After coin 1, dp = [1,1,1,1,1,1]; after coin 2, dp updates to given array.Final Answer:
Option A -> Option AQuick Check:
dp matches after processing coin 2 last [OK]
Quick Trick: dp array reflects last processed coin's effect [OK]
Common Mistakes:
MISTAKES- Confusing order of coin processing
- Assuming dp array alone insufficient
Trap Explanation:
PITFALL- Candidates may think dp array alone can't reveal last coin processed, but it can.
Interviewer Note:
CONTEXT- Tests deep understanding of dp state evolution.
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