AgentSkillsCN

recurrence-solver

采用主定理、生成函数等多种方法求解递推关系

SKILL.md
--- frontmatter
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

  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