Optimal Algorithmic Approach
Bottom-up DP with 1D array.
Core Invariants & Edge Cases
- dp[i] = min coins to make amount i
- dp[0] = 0; dp[i] = min(dp[i - coin] + 1) for each coin ≤ i
- If dp[amount] == INT_MAX, return -1
Dynamic Programming•Pattern: Unbounded Knapsack / DP•Medium
Coin change — minimum coins to make amount
Problem Intuition & Objective
Find the fewest coins needed to make up a given amount.
Time ComplexityO(amount × coins)
Space ComplexityO(amount)
System Design & Architecture Roadmap
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