Introduction

These days technology is amazing. Generative AI understands your questions. Instagram knows what you’ll like next. Google autocomplete predicts what we’re typing after just a few letters. Your iPhone unlocks instantly with Face ID. But here’s the secret: it’s not magic. It’s mathematics—specifically, algorithms that computer scientists developed between 1946 and the early 2000s, now applied in ways their creators never imagined.

The platform

When Apple’s Swift language debuted in 2014, it was the answer to modern iOS development. Ten years later, Swift has evolved into something far more powerful—a full-stack language that spans far beyond the iPhone. Swift Package Manager lets you share your algorithm implementations as reusable libraries. Swift Testing provides modern, expressive test suites that verify your algorithms work correctly at scale. And solutions like Vapor take Swift to the server, allowing you to create backend APIs that power websites, online services, and cloud-based applications. You can build your iOS app and its backend API in the same language, sharing the same algorithm implementations.

The algorithm lineage

Understanding modern technology means understanding the classical algorithms that power it. Binary search, invented in 1946 for dictionary lookups, now powers vector database indexes in modern AI search systems. Tries, developed in 1968 for efficient string storage, became the foundation for Google’s autocomplete in 2004 and every modern suggestion system. PageRank, Larry Page’s 1998 breakthrough for ranking web pages, evolved into the attention mechanisms that power today’s transformer-based AI models. Hash tables from the 1960s, originally used for compiler symbol tables, now enable real-time session management in web applications.

What we’ll learn

This book teaches fundamental algorithms and data structures through production Swift code. We’ll understand not just how algorithms work, but why they matter and where they’re used in modern development.

We’ll start with searching and sorting algorithms in Chapters 3-5, building intuition for algorithm design and performance analysis. Chapter 7 introduces Swift generics, showing how one algorithm can work with any data type—the foundation for every data structure in this book. Chapter 8 provides comprehensive performance analysis and Big O notation. Chapters 9-16 cover essential data structures: linked lists, stacks, queues, binary search trees, graphs, tries, hash tables, and heaps. Each chapter shows both the theory and the production implementation.

The advanced chapters demonstrate how these fundamentals power modern systems. Chapter 18 teaches dynamic programming, the optimization technique behind route planning and recommendation systems. Chapter 19 covers PageRank, Google’s original algorithm that revolutionized web search and influenced modern AI architectures. Chapters 20-22 introduce vectors, matrices, and transformations with the Quiver framework, and Chapter 23 covers similarity operations—dot products, cosine similarity, and vector arithmetic—the same techniques that power AI-driven search and recommendations.

Audience

This book is designed for developers comfortable with programming fundamentals, whether from Swift, Python, Java, or similar modern languages. We should understand core concepts: variables, functions, classes, arrays, and dictionaries. The ability to read code and follow program logic is more important than mastery of any specific language.