Coin Change
Find the fewest coins needed to make an amount, or −1 if it cannot be made.
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Lesson notes
Try it before you watch
Restate the problem in your own words, list the edge cases, and sketch a solution with its running time. Then play the video and compare.
Reveal the key idea
Bottom-up DP: dp[a] is 1 + the minimum of dp[a − coin] over all coins that fit.
Pattern: Dynamic programming. Define a state, write the recurrence between states, and compute each state only once.
Complexity
| Measure | Bound |
|---|---|
| Time | O(amount · number of coins) |
| Extra space | O(amount) |
Walkthroughs often start from a simpler approach first; aim to reach these bounds. New to Big-O? Read understanding algorithmic complexity.