Longest Increasing Path in a Matrix

Find the longest path of strictly increasing values through adjacent cells.

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.