📔 Algorithm Engineering

A Handbook for Theory, Performance, and Production

"Academic Computer Science teaches you how to implement QuickSort. Algorithm Engineering teaches you why QuickSort crashed your production server."

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🦅 Why This Book?

Most algorithm textbooks stop at the whiteboard. They teach you the logic, the Big-O notation, and the pseudo-code, then declare the job done.

In the real world, the job is just beginning.

Algorithm Engineering is the discipline of bridging the gap between mathematical theory and industrial reality. It is not enough to know how an algorithm works; you must understand how it interacts with memory hierarchies, CPU caches, and modern constraints.

This handbook is written for two audiences: 1. The Student: Who wants to move beyond "passing the exam" to "building the system." 2. The Professional: Who needs a reference for high-performance logic in Python.

📚 Syllabus & Structure

This book runs in parallel with the Arprax Algorithms video series.

Part I: The Engineering Foundation

• Ch 1: The Anatomy of an Algorithm
  • Theory: Defining correctness and termination.
  • Production: Type hinting, Pydantic, and Clean Code standards.
• Ch 2: The Profiling Mindset
  • Theory: Asymptotic Analysis (Big O).
  • Production: Wall-clock profiling, memory tracing, and the ArpraxProfiler.

Part II: Linear Data Structures

• Ch 3: Dynamic Arrays & Linked Lists
  • Focus: Memory locality and cache performance of Python Lists.
• Ch 4: Stacks, Queues, & Deques
  • Focus: Managing state in real-world applications (Undo/Redo).

Part III: The Pillars of Order

• Ch 5: Quadratic Sorts
  • Focus: Why \(O(N^2)\) is sometimes faster than \(O(N \log N)\) for small \(N\).
• Ch 6: Divide & Conquer
  • Focus: Merge Sort stability vs. Quick Sort raw speed.
• Ch 7: Searching & Hashing
  • Focus: Collision resolution strategies and industrial hash map design.

Part IV: Hierarchical Structures

• Ch 8: Binary Search Trees
  • Focus: The cost of imbalance and the need for self-balancing logic.
• Ch 9: Graph Theory
  • Focus: Modeling real-world networks (social, road, dependency).
• Ch 10: Pathfinding
  • Focus: A* and Dijkstra for navigation systems.

Part V: Optimization Patterns

• Ch 11: Dynamic Programming
  • Focus: Trading memory for time (Memoization vs Tabulation).
• Ch 12: Greedy Algorithms
  • Focus: Huffman coding and compression.

Part VI: Production Readiness

• Ch 13: The Production Pipeline
  • Focus: Unit testing (pytest), packaging (Poetry), and documentation (MkDocs).
• Ch 14: Conclusion
  • Focus: The future of algorithms in an AI-driven world.

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🎓 For Instructors

This material is designed to serve as a primary or supplementary text for courses in Applied Algorithms, Software Engineering, or Advanced Data Structures.

• Prerequisites: Python fluency.
• Tools: Uses the open-source arprax-algorithms library for benchmarking.