Algorithm Design Prompt

Help me design an algorithm for this problem.

Problem statement: [Describe what you need to solve]

Input: [What data you're working with]
Output: [What the result should be]
Constraints: [Any limitations - time, space, etc.]

Example:
- Input: [Sample input]
- Expected output: [Sample output]

Please help me:

1. Problem Analysis
   - Break down the problem
   - Identify sub-problems
   - Edge cases and constraints

2. Approach Brainstorm
   - Multiple solution approaches
   - Pros and cons of each
   - Which is best and why

3. Algorithm Design
   - Step-by-step algorithm
   - Pseudocode
   - Visual representation if helpful

4. Complexity Analysis
   - Time complexity
   - Space complexity
   - Best/worst/average cases

5. Implementation Tips
   - Language-specific considerations
   - Data structure recommendations
   - Implementation order

6. Optimization
   - Performance improvements
   - Memory optimization
   - Readability vs efficiency trade-offs

7. Testing
   - Test cases to validate
   - Edge cases to cover
   - Performance benchmarks

Language: [Programming language]
Experience level: [Beginner/Intermediate/Advanced]