Free Algorithms Book
This free book, named Algorithms,
contains algorithm topics carefully selected and clustered. Instead of
dwelling on formal proofs the authors distilled in each
case the crisp mathematical idea that makes the algorithm work. In
other words, they emphasized rigor over formalism.
There
are four parts to this Algorithms books:
Part I of
the book starts at the historical beginning: numbers, primality, and
factoring,
and also includes the RSA cryptosystem, and divide-and-conquer
algorithms for integer multiplication, sorting and median finding, as
well as the fast Fourier transform.
Part
II, the most traditional section of the book, concentrates on data
structures and graphs; the contrast here is between the intricate
structure of the underlying problems and the short and crisp pieces of
pseudocode that solve them.
Part III deals with the
"sledgehammers" of the trade, techniques that are powerful and general:
dynamic programming (a novel approach helps clarify this traditional
stumbling block for students) and linear programming (a clean and
intuitive treatment of the simplex algorithm, duality, and reductions
to the basic problem).
Part IV is about ways of
dealing with
hard problems: NP-completeness, various heuristics, as well as quantum
algorithms, perhaps the most advanced and modern topic. As it happens,
we end the story exactly where we started it, with Shor's quantum
algorithm for factoring.
Each chapter is a pdf file,
and the whole
book is also available as a pdf.
Table
of contents
Preface
Chapter 0: Prologue
Chapter 1: Algorithms
with numbers
Chapter 2: Divide-and-conquer
algorithms
Chapter 3: Decompositions
of graphs
Chapter 4: Paths
in graphs
Chapter 5: Greedy
algorithms
Chapter 6: Dynamic
programming
Chapter 7: Linear
programming
Chapter 8: NP-complete
problems
Chapter 9: Coping
with NP-completeness
Chapter 10: Quantum
algorithms
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