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AlgoPath gives competitive programmers progressive hints and instant AI code review. Learn the idea, then solve it yourself.
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Build the answer from smaller subproblems — the minimum for every amount below the target.
Let dp[i] be the min coins for amount i; reuse solved subproblems.
Reveal once you've spent time on hint 2.
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Drop a LeetCode, Codeforces, or USACO link. AlgoPath pulls the statement and samples.
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Three hints unlock in order — each moves your thinking forward without handing over the answer.
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Hints that teach, never spoil
Think about building the answer from smaller subproblems. If you knew the minimum coins for every amount below the target, how would that answer the original question?
Define dp[i] as the minimum coins for amount i. For each amount, subtract every coin and take the best already-solved subproblem.
Reveal after you've spent real time on hint 2.
Feedback the moment you submit
def coinChange(coins, amount): dp = [float("inf")] * (amount + 1) dp[0] = 0 for i in range(1, amount + 1): for c in coins: if c <= i: dp[i] = min(dp[i], dp[i - c] + 1) return dp[amount] if dp[amount] != float("inf") else -1O(n·m) time, O(n) space. Standard bottom-up DP — optimal for this approach.
Clean recurrence, handles the impossible case, idiomatic bottom-up pattern.
Inner loop can break early once dp[i] == 1. A minor win — the solution is already correct.
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