🪙
Coin Change Challenge
Beginner
Learn dynamic programming through the classic coin change problem. Find the minimum number of coins needed to make exact change.
15-20 min
🪙 Find the Minimum Coins!
🪙 Make Change for $11
Target: $11
Current: $0
Available Coins:
Selected Coins:
No coins selected
DP Table Preview
🧠 How the DP Algorithm Works
1. Base Case:dp[0] = 0 (no coins needed for amount 0)
2. For each amount:Try using each available coin to see if we can make change
3. State Transition:dp[amount] = min(dp[amount - coin] + 1) for all coins
4. Result:dp[target] gives the minimum coins needed
| Amount | Min Coins | Explanation |
|---|---|---|
| 0 | 0 | Base case: no coins needed |
| 1 | ∞ | Not calculated yet |
| 2 | ∞ | Not calculated yet |
| 3 | ∞ | Not calculated yet |
| 4 | ∞ | Not calculated yet |
| 5 | ∞ | Not calculated yet |
| 6 | ∞ | Not calculated yet |
| 7 | ∞ | Not calculated yet |
| 8 | ∞ | Not calculated yet |
| 9 | ∞ | Not calculated yet |
| 10 | ∞ | Not calculated yet |
| 11 | ∞ | Not calculated yet |
Base case (0)
Calculated values
Infinity (impossible)
Current step (animating)
📝 Current Algorithm State
• Available coins: 1, 3, 4
• Target amount: 11
• Current step: Ready to start
• Result: Not yet calculated
🎮 How to Play
• Click on coins to add them to your selection
• Try to make exact change for the target amount
• Use the minimum number of coins possible
• Click "See DP Solution" to watch the algorithm
• The game will check if your solution is optimal
💡 Dynamic Programming Tips
Bottom-up:Build solutions from smaller amounts up
Memoization:Store results to avoid recalculation
Optimal Substructure:Use solutions of smaller subproblems
State Transitions:dp[i] = min(dp[i-coin] + 1) for all coins
🌍 Real-world Uses
• Banking and ATM systems
• Vending machines
• Cash registers
• Game economies
• Resource allocation
⏱️ Algorithm Analysis
Time Complexity:O(amount × coins)
Space Complexity:O(amount)
Approach:Bottom-up DP