Foundations of Algorithms

Algorithm design is not just a matter of writing steps that work—it also means choosing an approach suited to the problem and understanding the cost of that choice. In Foundations of Algorithms, Richard E. Neapolitan builds that reasoning through clear pseudocode, worked examples, and detailed mathematical explanations, with a presentation designed to be approachable without setting rigor aside.

Learn to choose an algorithmic strategy

The book is organized largely by design technique, helping readers compare ways to tackle problems rather than treating each algorithm as an isolated recipe. It covers divide-and-conquer, dynamic programming, greedy methods, backtracking, and branch-and-bound. Examples revisit familiar challenges through different approaches, making the trade-offs between techniques part of the learning.

Connect performance to the problem

Alongside algorithm analysis, Neapolitan introduces computational complexity: the study of the problems themselves and the limits of efficient solutions. Chapters on sorting and searching lead into intractability, the sets P and NP, NP-complete problems, and approximation algorithms. The emphasis on explanation and formal proof gives readers a way to follow not only what an algorithm does, but why its performance matters.

From genetic algorithms to parallel computing

The fifth edition extends the range of techniques with coverage of genetic algorithms and genetic programming, including theory and applications. Further chapters introduce number-theoretic algorithms, including Euclid’s algorithm, and parallel algorithms, architectures, and the PRAM model.

A mathematically considerate textbook

Rather than relying on one programming language’s syntax, the text uses pseudocode intended to be readable across high-level languages. It assumes college algebra, finite or discrete mathematics, and prior study of data structures; an appendix reviews mathematics used in the book, and another covers recurrence-solving methods. Neapolitan also presents concepts such as order of growth with substantial English explanation and detailed proofs, while identifying material that requires calculus.

Designed for upper-level undergraduate and graduate study, this edition offers a systematic route through core algorithmic ideas—from selecting a design method to analyzing efficiency and recognizing computational limits.