Count how many coin combinations can form a target amount.
Use the 2-d dynamic programming pattern to design an efficient solution and explain the tradeoffs in your approach.
Examples
Input: See starter test cases Output: Expected result depends on the selected implementation Explanation: These local prompts are original practice stubs and can be replaced by backend-provided examples later.
Constraints
- Inputs follow the shape implied by the prompt title.
- Prefer an approach that matches the named pattern track.
- Optimize for clarity first, then improve time and space complexity.