Dynamic Programming: Knapsack - Coin Change II (Count Ways)
If the Coin Change II problem is modified so that coins can have fractional values (e.g., 0.5, 1.5) and the amount is also fractional, which approach is best to solve it?
If the Coin Change II problem is modified so that coins can have fractional values (e.g., 0.5, 1.5) and the amount is also fractional, which approach is best to solve it?
hard🎤 Interviewer Follow-up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Recognize fractional weights break integer DP indexing
DP array indexing by amount is not feasible with fractional values.Step 2: Model problem as shortest path in graph
Each state is an amount; edges represent adding a coin; Dijkstra's algorithm finds minimal paths.Step 3: Greedy and rounding approaches fail to guarantee correctness
Greedy misses combinations; rounding loses precision.Final Answer:
Option B -> Option BQuick Check:
Fractional weights -> graph shortest path approach [OK]
Quick Trick: Fractional weights -> graph shortest path, not DP [OK]
Common Mistakes:
MISTAKES- Trying DP with fractional indices
- Using greedy which fails correctness
Trap Explanation:
PITFALL- Candidates try to force DP on fractional amounts, ignoring indexing issues.
Interviewer Note:
CONTEXT- Tests ability to adapt approach to problem variants beyond standard DP.
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