Dynamic Programming: Knapsack - Coin Change (Minimum Coins)
Given the bottom-up DP approach for minimum coins with coins = [1, 3, 4] and amount = 7, what is the value of dp[7] after completion?
Given the bottom-up DP approach for minimum coins with coins = [1, 3, 4] and amount = 7, what is the value of dp[7] after completion?
easy🧾 Trace Q3 of Q15
Step-by-Step Solution
Solution:
Step 1: Initialize dp array
dp[0] = 0, others set to infinity initially.Step 2: Calculate dp values up to 7
For dp[7], minimum coins can be dp[7-4] + 1 = dp[3] + 1.Step 3: Calculate dp[3]
dp[3] = 1 (using coin 3), so dp[7] = 1 + 1 = 2.Final Answer:
Option B -> Option BQuick Check:
Check dp[7] with coins 4+3 = 2 coins [OK]
Quick Trick: Use dp[amount - coin] + 1 to find minimum coins [OK]
Common Mistakes:
MISTAKES- Not updating dp array correctly
- Confusing dp indices
- Ignoring smaller coin combinations
Trap Explanation:
PITFALL- Miscomputing dp values leads to wrong minimum coin count
Interviewer Note:
CONTEXT- Tests ability to trace DP array updates for coin change
Master "Coin Change (Minimum Coins)" in Dynamic Programming: Knapsack
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