Cormen T.H., Leiserson C.E., Rivest R.L., Stein C. Introduction to Algorithms

The MIT Press, 2001. — 1180 p. — ISBN 0262032937.This book provides a comprehensive introduction to the modern study of computer algorithms. It presents many algorithms and covers them in considerable depth, yet makes their design and analysis accessible to all levels of readers. We have tried to keep explanations elementary without sacrificing depth of coverage or mathematical rigor. Each chapter presents an algorithm, a design technique, an application area, or a related topic. Algorithms are described in English and in a "pseudocode" designed to be readable by anyone who has done a little programming. The book contains over 230 figures illustrating how the algorithms work. Since we emphasize efficiency as a design criterion, we include careful analyses of the running times of all our algorithms. The text is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Because it discusses engineering issues in algorithm design, as well as mathematical aspects, it is equally well suited for self-study by technical professionals. In this, the second edition, we have updated the entire book. The changes range from the addition of new chapters to the rewriting of individual sentences.Foundations.
The Role of Algorithms in Computing.
Getting Started.
Growth of Functions.
Recurrences.
Probabilistic Analysis and Randomized Algorithms.
Sorting and Order Statistics.
Heapsort.
Quicksort.
Sorting in Linear Time.
Medians and Order Statistics.
Data Structures.
Elementary Data Structures.
Hash Tables.
Binary Search Trees.
Red-Black Trees.
Augmenting Data Structures.
Advanced Design and Analysis Techniques.
Dynamic Programming.
Greedy Algorithms.
Amortized Analysis.
Advanced Data Structures.
B-Trees.
Binomial Heaps.
Fibonacci Heaps.
Data Structures for Disjoint Sets.
Graph Algorithms.
Elementary Graph Algorithms.
Minimum Spanning Trees.
Single-Source Shortest Paths.
All-Pairs Shortest Paths.
Maximum Flow.
Selected Topics.
Sorting Networks.
Matrix Operations.
Linear Programming.
Polynomials and the FFT.
Number-Theoretic Algorithms.
String Matching.
Computational Geometry.
NP-Completeness.
Approximation Algorithms.
Appendix: Mathematical Background.
Summations.
Sets, Etc..
Counting and Probability.