La nueva alianza / The New Alliance: Metamorfosis de la ciencia / Metamorphosis of Science (Alianza Universidad) (Spanish Edition)

The latest edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow. Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor. The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, substantial additions to the chapter on recurrence (now called “Divide-and-Conquer”), and an appendix on matrices. It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many exercises and problems have been added for this edition. The international paperback edition is no longer available; the hardcover is available worldwide. Cover Title Page Copyright Page Table of Contents Preface I Foundations Introduction 1 The Role of Algorithms in Computing 1.1 Algorithms 1.2 Algorithms as a technology 2 Getting Started 2.1 Insertion sort 2.2 Analyzing algorithms 2.3 Designing algorithms 3 Growth of Functions 3.1 Asymptotic notation 3.2 Standard notations and common functions 4 Divide-and-Conquer 4.1 The maximum-subarray problem 4.2 Strassen’s algorithm for matrix multiplication 4.3 The substitution method for solving recurrences 4.4 The recursion-tree method for solving recurrences 4.5 The master method for solving recurrences 4.6 Proof of the master theorem 5 Probabilistic Analysis and Randomized Algorithms 5.1 The hiring problem 5.2 Indicator random variables 5.3 Randomized algorithms 5.4 Probabilistic analysis and further uses of indicator random variables II Sorting and Order Statistics Introduction 6 Heapsort 6.1 Heaps 6.2 Maintaining the heap property 6.3 Building a heap 6.4 The heapsort algorithm 6.5 Priority queues 7 Quicksort 7.1 Description of quicksort 7.2 Performance of quicksort 7.3 A randomized version of quicksort 7.4 Analysis of quicksort 8 Sorting in Linear Time 8.1 Lower bounds for sorting 8.2 Counting sort 8.3 Radix sort 8.4 Bucket sort 9 Medians and Order Statistics 9.1 Minimum and maximum 9.2 Selection in expected linear time 9.3 Selection in worst-case linear time III Data Structures Introduction 10 Elementary Data Structures 10.1 Stacks and queues 10.2 Linked lists 10.3 Implementing pointers and objects 10.4 Representing rooted trees 11 Hash Tables 11.1 Direct-address tables 11.2 Hash tables 11.3 Hash functions 11.4 Open addressing 11.5 Perfect hashing 12 Binary Search Trees 12.1 What is a binary search tree? 12.2 Querying a binary search tree 12.3 Insertion and deletion 12.4 Randomly built binary search trees 13 Red-Black Trees 13.1 Properties of red-black trees 13.2 Rotations 13.3 Insertion 13.4 Deletion 14 Augmenting Data Structures 14.1 Dynamic order statistics 14.2 How to augment a data structure 14.3 Interval trees IV Advanced Design and Analysis Techniques Introduction 15 Dynamic Programming 15.1 Rod cutting 15.2 Matrix-chain multiplication 15.3 Elements of dynamic programming 15.4 Longest common subsequence 15.5 Optimal binary search trees 16 Greedy Algorithms 16.1 An activity-selection problem 16.2 Elements of the greedy strategy 16.3 Huffman codes 16.4 Matroids and greedy methods 16.5 A task-scheduling problem as a matroid 17 Amortized Analysis 17.1 Aggregate analysis 17.2 The accounting method 17.3 The potential method 17.4 Dynamic tables V Advanced Data Structures Introduction 18 B-Trees 18.1 Definition of B-trees 18.2 Basic operations on B-trees 18.3 Deleting a key from a B-tree 19 Fibonacci Heaps 19.1 Structure of Fibonacci heaps 19.2 Mergeable-heap operations 19.3 Decreasing a key and deleting a node 19.4 Bounding the maximum degree 20 van Emde Boas Trees 20.1 Preliminary approaches 20.2 A recursive structure 20.3 The van Emde Boas tree 21 Data Structures for Disjoint Sets 21.1 Disjoint-set operations 21.2 Linked-list representation of disjoint sets 21.3 Disjoint-set forests 21.4 Analysis of union by rank with path compression VI Graph Algorithms Introduction 22 Elementary Graph Algorithms 22.1 Representations of graphs 22.2 Breadth-first search 22.3 Depth-first search 22.4 Topological sort 22.5 Strongly connected components 23 Minimum Spanning Trees 23.1 Growing a minimum spanning tree 23.2 The algorithms of Kruskal and Prim 24 Single-Source Shortest Paths 24.1 The Bellman-Ford algorithm 24.2 Single-source shortest paths in directed acyclic graphs 24.3 Dijkstra’s algorithm 24.4 Difference constraints and shortest paths 24.5 Proofs of shortest-paths properties 25 All-Pairs Shortest Paths 25.1 Shortest paths and matrix multiplication 25.2 The Floyd-Warshall algorithm 25.3 Johnson’s algorithm for sparse graphs 26 Maximum Flow 26.1 Flow networks 26.2 The Ford-Fulkerson method 26.3 Maximum bipartite matching 26.4 Push-relabel algorithms 26.5 The relabel-to-front algorithm VII Selected Topics Introduction 27 Multithreaded Algorithms 27.1 The basics of dynamic multithreading 27.2 Multithreaded matrix multipication 27.3 Multithreaded merge sort 28 Matrix Operations 28.1 Solving systems of linear equations 28.2 Inverting matrices 28.3 Symmetric positive-definite matrices and least-squares approximation 29 Linear Programming 29.1 Standard and slack forms 29.2 Formulating problems as linear programs 29.3 The simplex algorithm 29.4 Duality 29.5 The initial basic feasible solution 30 Polynomials and the FFT 30.1 Representing polynomials 30.2 The DFT and FFT 30.3 Efficient FFT implementations 31 Number-Theoretic Algorithms 31.1 Elementary number-theoretic notions 31.2 Greatest common divisor 31.3 Modular arithmetic 31.4 Solving modular linear equations 31.5 The Chinese remainder theorem 31.6 Powers of an element 31.7 The RSA public-key cryptosystem 31.8 Primality testing 31.9 Integer factorization 32 String Matching 32.1 The naive string-matching algorithm 32.2 The Rabin-Karp algorithm 32.3 String matching with finite automata 32.4 The Knuth-Morris-Pratt algorithm 33 Computational Geometry 33.1 Line-segment properties 33.2 Determining whether any pair of segments intersects 33.3 Finding the convex hull 33.4 Finding the closest pair of points 34 NP-Completeness 34.1 Polynomial time 34.2 Polynomial-time verification 34.3 NP-completeness and reducibility 34.4 NP-completeness proofs 34.5 NP-complete problems 35 Approximation Algorithms 35.1 The vertex-cover problem 35.2 The traveling-salesman problem 35.3 The set-covering problem 35.4 Randomization and linear programming 35.5 The subset-sum problem VIII Appendix: Mathematical Background Introduction A Summations A.1 Summation formulas and properties A.2 Bounding summations B Sets, Etc. B.1 Sets B.2 Relations B.3 Functions B.4 Graphs B.5 Trees C Counting and Probability C.1 Counting C.2 Probability C.3 Discrete random variables C.4 The geometric and binomial distributions C.5 The tails of the binomial distribution D Matrices D.1 Matrices and matrix operations D.2 Basic matrix properties Bibliography Index This Edition Has Been Revised And Updated Throughout. It Includes Some New Chapters. It Features Improved Treatment Of Dynamic Programming And Greedy Algorithms As Well As A New Notion Of Edge-based Flow In The Material On Flow Networks.--[book Cover]. I. Foundations. The Role Of Algorithms In Computing -- Getting Started -- Growth Of Functions -- Divide-and-conquer -- Probabilistic Analysis And Randomized Algorithms -- Ii. Sorting And Order Statistics. Heapsort -- Quicksort -- Sorting In Linear Time -- Medians And Order Statistics -- Iii. Data Structures. Elementary Data Structures -- Hash Tables -- Binary Search Trees -- Red-black Trees -- Augmenting Data Structures -- Iv. Advanced Design And Analysis Techniques. Dynamic Programming -- Greedy Algorithms -- Amortized Analysis -- V. Advanced Data Structures. B-trees -- Fibonacci Heaps -- Van Emde Boas Trees -- Data Structures For Disjoint Sets -- Vi. Graph Algorithms. Elementary Graph Algorithms -- Minimum Spanning Trees -- Single-source Shortest Paths -- All-pairs Shortest Paths -- Maximun Flow -- Vii. Selected Topics. Multithreaded Algorithms -- Matrix Operations -- Linear Programming -- Polynomials And The Fft -- Number-theoretic Algorithms -- String Matching -- Computational Geometry -- Np-completeness -- Approximation Algorithms -- Viii. Appendix: Mathematical Background. Summations -- Sets, Etc. -- Counting And Probability -- Matrices. Thomas H. Cormen ... [et Al.]. Includes Bibliographical References (p. [1231]-1249) And Index. Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor. - The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called "Divide-and-Conquer"). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition 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 260 figrues 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. -- A new edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-base flow