Fewest-coins DP animated — including the classic case where greedy fails (coins 1, 4, 5 for amount 8) and the table finds 4+4 instead.
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Coin Change Visualizer is a free, browser-based tool that helps you turn raw numbers into clear charts. Fewest-coins DP animated — including the classic case where greedy fails (coins 1, 4, 5 for amount 8) and the table finds 4+4 instead. It's built for speed and privacy: Everything runs locally in your browser — your data is never uploaded to a server. No sign-up, no installs, and no daily limits.
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Open tool| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|---|---|
| min# | 0 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
1Fewest coins from {1, 4, 5} for amount 8. dp[a] = min coins for amount a; dp[0] = 0. (Greedy fails here: greedy for 8 gives 5+1+1+1 = 4 coins, DP finds 4+4 = 2.)
dp[0] = 0; dp[a] = ∞for a = 1..amount:dp[a] = 1 + min(dp[a-c] for c in coins)return dp[amount]
Fewest coins for an amount. With coins {1,4,5}, greedy fails (8 → 5+1+1+1) where DP finds 4+4 — the classic greedy-counterexample.
