---
name: recurrence-solver-656758cc48f3
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


---
Source attribution: a5c-ai
Original project: https://github.com/a5c-ai/babysitter
License: MIT
License information: https://opensource.org/license/mit
Original upstream instructions; downloaded from Mega AI Hub.

## Upstream license notice

MIT License

Copyright (c) 2026 Gabriel Moreira

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



# Mega AI Hub resource metadata

Creator / publisher: a5c-ai
Original project: https://github.com/a5c-ai/babysitter
Attribution basis: Upstream repository explicitly recorded in package mirror path

Fields of work: Data & Analytics, Development & Engineering, Education & Research, Product Management
Roles: Data Scientist, ML / AI Engineer, Product Manager, Researcher, Technical Product Manager
Specialties: API, Backend, Cross Platform
Tools: Sympy
Country applicability: Country not specified
Classification basis: Source catalog labels
Instruction SHA-256: bef82b71d50f85739d9283e3981d338d81bd904c0f158e4b06abb23ee9bec67c