Agent skill

advanced-topics

Explore advanced CS topics including advanced data structures, parallel computing, security, functional programming, and quantum computing.

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npx add-skill https://github.com/pluginagentmarketplace/custom-plugin-computer-science/tree/main/skills/advanced

SKILL.md

Advanced Topics Skill

Skill Metadata

yaml
skill_config:
  version: "1.0.0"
  category: advanced
  prerequisites: [cs-foundations, algorithms, data-structures, complexity-analysis]
  estimated_time: "12-16 weeks"
  difficulty: expert

  parameter_validation:
    topic:
      type: string
      enum: [advanced-ds, parallel, security, functional, quantum, ml-theory]
      required: true

  retry_config:
    max_attempts: 3
    backoff_strategy: exponential
    initial_delay_ms: 500

  observability:
    log_level: INFO
    metrics: [topic_usage, depth_level]

Advanced Data Structures

Segment Trees

  • Range minimum/maximum queries
  • Range updates
  • Time: O(log n) per operation

Fenwick Trees (Binary Indexed Trees)

  • Prefix sum queries and updates
  • Time: O(log n) per operation
  • Space: O(n)

Suffix Trees & Arrays

  • Fast string pattern matching
  • Linear time construction

Disjoint Set Union (Union-Find)

  • Merging sets efficiently
  • Path compression + union by rank: nearly O(1)

Persistent Data Structures

  • Maintain all historical versions
  • Immutable updates

Parallel Computing

Parallelism Concepts

  • Threads vs processes
  • Shared memory vs message passing
  • Race conditions and synchronization
  • Deadlock and livelock

Parallel Algorithms

  • Reduction operations
  • Prefix sums in parallel
  • Sorting networks

GPU Computing

  • CUDA/OpenCL
  • Massive parallelism
  • Memory hierarchy

Security & Cryptography

Cryptographic Primitives

  • Symmetric encryption: AES
  • Asymmetric encryption: RSA
  • Hash functions: SHA-256
  • Digital signatures

Security Protocols

  • TLS/SSL handshake
  • Key exchange: Diffie-Hellman
  • Authentication: certificates

Advanced Algorithms

Network Flows

  • Max flow problem
  • Ford-Fulkerson algorithm
  • Min-cost max-flow

Linear Programming

  • Simplex algorithm
  • Interior point methods
  • Integer programming (NP-hard)

Approximation Algorithms

  • Approximation ratios
  • PTAS and FPTAS

Randomized Algorithms

  • Monte Carlo vs Las Vegas
  • Quicksort randomization

Quantum Computing

Quantum Concepts

  • Qubits and superposition
  • Entanglement
  • Quantum gates

Quantum Algorithms

  • Shor's algorithm (factoring)
  • Grover's search
  • Quantum simulation

Troubleshooting

Issue Root Cause Resolution
Parallel race condition Missing synchronization Add locks or use atomic ops
Segment tree wrong answer Off-by-one in ranges Verify range boundaries
Crypto implementation weak Timing attack vulnerability Use constant-time operations

Competitive Programming

Advanced Techniques

  • Bit manipulation tricks
  • Coordinate compression
  • Offline algorithms
  • Meet in the middle
  • Small to large merging

Practice Platforms

  • Codeforces: 1000+ problems
  • TopCoder: Advanced competitions
  • ICPC: Team programming contests

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