name: recurrence-solver description: Solve recurrence relations using multiple methods including Master Theorem and generating functions allowed-tools:
- Bash
- Read
- Write
- Edit
- Glob
- Grep metadata: specialization: computer-science domain: science category: algorithm-analysis phase: 6
Recurrence Solver
Purpose
Provides expert guidance on solving recurrence relations arising from divide-and-conquer and recursive algorithm analysis.
Capabilities
- Apply Master Theorem (all three cases)
- Substitution method with guess verification
- Recursion tree analysis with visualization
- Generating functions for complex recurrences
- Akra-Bazzi method for generalized recurrences
- Handle non-standard recurrence forms
Usage Guidelines
- Recognition: Identify recurrence structure and applicable methods
- Master Theorem: Check and apply Master Theorem cases
- Substitution: Formulate and verify guess for complex cases
- Tree Analysis: Build recursion tree for intuition
- Verification: Validate solutions with base cases
Tools/Libraries
- SymPy
- Visualization libraries
- Symbolic algebra systems