Data Structures and Algorithms

Data structures and algorithms is the course that decides who finishes the computer science degree — the point where you stop asking whether the program works and start asking what it costs, where a solution that returns the right answer can still be wrong because it returns it in a year. This is a complete treatment of that subject, built to do three jobs at once: it is a standalone textbook for the gateway course, opening with the machine underneath and the meaning of a step before it asks anyone to count one; it is a field guide for working engineers, because every chapter carries a complexity table, a debugging index organized by symptom rather than by cause, and a survey of where the structure actually runs in production systems — the Linux kernel's scheduler, PostgreSQL's indexes, Redis's sorted sets, the JVM's collections, Git's object store; and it is a preparation manual for technical interviews, with a pattern catalog organized by recognition trigger, because the failure in a real interview is almost never that the candidate did not know what a heap is. Fifty-four chapters, with the difficulty ramp explicitly marked. Early chapters assume you can write a loop and nothing else: memory and pointers, abstract data types, loop invariants, and asymptotic notation with the constants written out rather than waved away. The middle is the canonical curriculum — dynamic arrays, linked lists, stacks and queues, the full sorting catalog with the comparison lower bound proved, hash tables in depth across three chapters, binary search trees and every standard balancing scheme, B-trees, tries, Fenwick and segment trees, the whole of graph algorithms from traversal through network flow, and the design paradigms: greedy with its exchange arguments and matroid characterization, dynamic programming across two long chapters, backtracking, and divide and conquer through Karatsuba and the Fast Fourier Transform. Then it keeps going, past where the undergraduate course stops. Sections marked Going Deeper carry graduate material that can be skipped without losing the thread and found again when it is wanted: NP-completeness and the standard reduction chain, approximation algorithms with proved ratios, parameterized complexity, online algorithms and competitive analysis, streaming and sublinear algorithms, and fine-grained complexity — the theory that explains why, for problems like edit distance, quadratic time is probably the best anyone will ever do, and lets you say so conditionally rather than merely suspect it. There are chapters on what real hardware charges for a memory access, on cache-oblivious structures and succinct encodings that approach the information-theoretic minimum, on learned index structures as a live research frontier, and on the concurrent and persistent structures that a correct sequential implementation turns into silently the moment a second thread arrives. Every algorithm is given four things and not three: the idea in plain language before any code appears, the implementation, the invariant that makes it correct, and the cost together with the reasoning that produces the cost. The invariant is the part usually left out, and it is the difference between a book you can pass a course with and a book you can only look things up in. The interview part is current rather than traditional. Technical hiring changed materially in 2025 and 2026 — assistant-enabled coding rounds became standard rather than experimental, proctoring hardened, and the thing being scored moved from producing a correct solution to reasoning aloud, justifying a design, and surviving follow-up questions. The argument this book makes — and labels as an argument — is that the material became more valuable rather than less: if a machine drafts the code and a human reviews it, the reviewer's job is precisely this subject — knowing which structure is right, knowing what it costs, knowing how it fails, and being able to say why. Fifty-four chapters, a graded exercise set in every one with full solutions, and a closing field guide that collects the reference tables, a decision procedure for choosing a structure, a study plan for the course and a separate one for interviews, and a catalog of canonical problems indexed by the technique each one teaches.



Al-generated content disclosure: This work was created with the help and usage of artificial intelligence. All sources are cited in the bibliography section.