Dynamic Programming: Knapsack - Coin Change (Minimum Coins)
You have an infinite number of coins of given denominations and need to find the minimum coins to make a target amount. Which technique is most suitable to solve this problem efficiently?
You have an infinite number of coins of given denominations and need to find the minimum coins to make a target amount. Which technique is most suitable to solve this problem efficiently?
easy💻 Programming Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify overlapping subproblems
The problem can be broken down into smaller subproblems of finding minimum coins for smaller amounts.Step 2: Use optimal substructure
The minimum coins for amount A depends on minimum coins for amounts A - coin for each coin denomination.Final Answer:
Option B -> Option BQuick Check:
Greedy fails for some coin sets, DP always finds optimal [OK]
Quick Trick: DP handles overlapping subproblems optimally [OK]
Common Mistakes:
MISTAKES- Assuming greedy always works
- Using DFS without memoization
- Ignoring subproblem reuse
Trap Explanation:
PITFALL- Greedy looks simpler but fails for non-canonical coin sets
Interviewer Note:
CONTEXT- Tests understanding of algorithmic paradigms suitable for coin change
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