recurrence-solver

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}
graph	{"domains":["domain:computer-science"],"specializations":["specialization:theoretical-computer-science"],"skillAreas":["skill-area:np-hard-heuristics","skill-area:mathematical-reasoning","skill-area:dynamic-programming"],"workflows":["workflow:research-grant-lifecycle"],"roles":["role:computational-scientist","role:research-engineer"]}

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

1. Recognition: Identify recurrence structure and applicable methods
2. Master Theorem: Check and apply Master Theorem cases
3. Substitution: Formulate and verify guess for complex cases
4. Tree Analysis: Build recursion tree for intuition
5. Verification: Validate solutions with base cases

Tools/Libraries

• SymPy
• Visualization libraries
• Symbolic algebra systems