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If the coin change problem is extended to allow fractional coin denominations (e.g., 0.25, 0.5) and a fractional target amount, which approach is most appropriate to find the minimum number of coins?

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Dynamic Programming: Knapsack - Coin Change (Minimum Coins)

If the coin change problem is extended to allow fractional coin denominations (e.g., 0.25, 0.5) and a fractional target amount, which approach is most appropriate to find the minimum number of coins?

AConvert to integer problem by scaling and apply DP

BUse a greedy algorithm with sorting

CUse standard integer DP without modifications

DApply graph shortest path algorithms directly

Step-by-Step Solution

Solution:

Step 1: Understand fractional denominations
DP requires integer indices; fractional amounts complicate direct DP.
Step 2: Scale problem
Multiply all coin values and amount by a factor (e.g., 100) to convert to integers.
Step 3: Apply integer DP
Use standard DP on scaled integers to find minimum coins.
Final Answer:
Option A -> Option A
Quick Check:
Scaling preserves problem structure for DP [OK]

Quick Trick: Scale fractional amounts to integers before DP [OK]

Common Mistakes:

MISTAKES

Applying DP directly on floats
Assuming greedy always works
Ignoring precision issues

Trap Explanation:

PITFALL

Ignoring scaling leads to incorrect DP indexing and results

Interviewer Note:

CONTEXT

Tests ability to adapt DP solutions to fractional inputs

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