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AiTechWorlds
AiTechWorlds
Watch the minimum-coins DP table build up for a target amount, with synced multi-language code.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|---|
| min coins | 0 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
def coin_change(coins, amount):
dp = [float('inf')] * (amount + 1)
dp[0] = 0
for a in range(1, amount + 1):
for c in coins:
if a - c >= 0:
dp[a] = min(dp[a], dp[a - c] + 1)
return -1 if dp[amount] == float('inf') else dp[amount]Coin Change computes the minimum number of coins needed to make a target amount, building up dp[a] = 1 + min over coins of dp[a − coin].
| Time | O(amount × coins) |
| Space | O(amount) |
The Coin Change Visualizer animates the dynamic programming solution for the minimum number of coins needed to make a target amount. dp[a] = 1 + min over each coin c of dp[a − c]. It runs in O(amount × coins) time and O(amount) space. Watch the table build up from dp[0] = 0.
Press Play
Watch dp[a] computed from smaller amounts for each coin.
Step through
Use Step Forward/Back or the timeline to follow each coin choice.
Read the code
View the Coin Change DP in C++, Java, Python, or JavaScript and copy it.
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Last reviewed on June 14, 2026 by the AiTechWorlds Tools Team. All processing runs locally in your browser.