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Introduction to Algorithms, Third Edition
    ¡¤ ÁöÀºÀÌ | ¿Å±äÀÌ:Thomas H. Cormen|Charles E. Leiserson|Ronald L. Rivest
    ¡¤ ÃâÆÇ»ç:MITPRESS
    ¡¤ ÃâÆdz⵵:20090930
    ¡¤ Ã¥»óÅÂ:³«¼­¾ø´Â »ó±Þ / 1312ÂÊ / 202*228mm / 9780262533058(0262533057)
    ¡¤ ISBN:9780262533058
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This International Student Edition is not available in the USA or Canada. 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 recurrence (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. As of the third edition, this textbook is published exclusively by the MIT Press.


Preface

I Foundations 

Introduction 3

1 The Role of Algorithms in Computing 5

1.1 Algorithms 5

1.2 Algorithms as a technology 11

2 Getting Started 16

2.1 Insertion sort 16

2.2 Analyzing algorithms 23

2.3 Designing algorithms 29

3 Growth of Functions 43

3.1 Asymptotic notation 43

3.2 Standard notations and common functions 53

4 Divide-and-Conquer 65

4.1 The maximum-subarray problem 68

4.2 Strassen's algorithm for matrix multiplication 75

4.3 The substitution method for solving recurrences 83

4.4 The recursion-tree method for solving recurrences 88

4.5 The master method for solving recurrences 93

4.6 Proof of the master theorem 97

5 Probabilistic Analysis and Randomized Algorithms 114

5.1 The hiring problem 114

5.2 Indicator random variables 118

5.3 Randomized algorithms 122

5.4 Probabilistic analysis and further uses of indicator random variables 130


II Sorting and Order Statistics 

Introduction 147

6 Heapsort 151

6.1 Heaps 151

6.2 Maintaining the heap property 154

6.3 Building a heap 156

6.4 The heapsort algorithm 159

6.5 Priority queues 162

7 Quicksort 170

7.1 Description of quicksort 170

7.2 Performance of quicksort 174

7.3 A randomized version of quicksort 179

7.4 Analysis of quicksort 180

8 Sorting in Linear Time 191

8.1 Lower bounds for sorting 191

8.2 Counting sort 194

8.3 Radix sort 197

8.4 Bucket sort 200

9 Medians and Order Statistics 213

9.1 Minimum and maximum 214

9.2 Selection in expected linear time 215

9.3 Selection in worst-case linear time 220


III Data Structures 

Introduction 229

10 Elementary Data Structures 232

10.1 Stacks and queues 232

10.2 Linked lists 236

10.3 Implementing pointers and objects 241

10.4 Representing rooted trees 246

11 Hash Tables 253

11.1 Direct-address tables 254

11.2 Hash tables 256

11.3 Hash functions 262

11.4 Open addressing 269

11.5 Perfect hashing 277

12 Binary Search Trees 286

12.1 What is a binary search tree? 286

12.2 Querying a binary search tree 289

12.3 Insertion and deletion 294

12.4 Randomly built binary search trees 299

13 Red-Black Trees 308

13.1 Properties of red-black trees 308

13.2 Rotations 312

13.3 Insertion 315

13.4 Deletion 323

14 Augmenting Data Structures 339

14.1 Dynamic order statistics 339

14.2 How to augment a data structure 345

14.3 Interval trees 348

IV Advanced Design and Analysis Techniques 

Introduction 357

15 Dynamic Programming 359

15.1 Rod cutting 360

15.2 Matrix-chain multiplication 370

15.3 Elements of dynamic programming 378

15.4 Longest common subsequence 390

15.5 Optimal binary search trees 397

16 Greedy Algorithms 414

16.1 An activity-selection problem 415

16.2 Elements of the greedy strategy 423

16.3 Huffman codes 428

16.4 Matroids and greedy methods 437

16.5 A task-scheduling problem as a matroid 443

17 Amortized Analysis 451

17.1 Aggregate analysis 452

17.2 The accounting method 456

17.3 The potential method 459

17.4 Dynamic tables 463

V Advanced Data Structures 

Introduction 481

18 B-Trees 484

18.1 Definition of B-trees 488

18.2 Basic operations on B-trees 491

18.3 Deleting a key from a B-tree 499

19 Fibonacci Heaps 505

19.1 Structure of Fibonacci heaps 507

19.2 Mergeable-heap operations 510

19.3 Decreasing a key and deleting a node 518

19.4 Bounding the maximum degree 523

20 van Emde Boas Trees 531

20.1 Preliminary approaches 532

20.2 A recursive structure 536

20.3 The van Emde Boas tree 545

21 Data Structures for Disjoint Sets 561

21.1 Disjoint-set operations 561

21.2 Linked-list representation of disjoint sets 564

21.3 Disjoint-set forests 568

21.4 Analysis of union by rank with path compression 573


VI Graph Algorithms 

Introduction 587

22 Elementary Graph Algorithms 589

22.1 Representations of graphs 589

22.2 Breadth-first search 594

22.3 Depth-first search 603

22.4 Topological sort 612

22.5 Strongly connected components 615

23 Minimum Spanning Trees 624

23.1 Growing a minimum spanning tree 625

23.2 The algorithms of Kruskal and Prim 631

24 Single-Source Shortest Paths 643

24.1 The Bellman-Ford algorithm 651

24.2 Single-source shortest paths in directed acyclic graphs 655

24.3 Dijkstra's algorithm 658

24.4 Difference constraints and shortest paths 664

24.5 Proofs of shortest-paths properties 671

25 All-Pairs Shortest Paths 684

25.1 Shortest paths and matrix multiplication 686

25.2 The Floyd-Warshall algorithm 693

25.3 Johnson's algorithm for sparse graphs 700

26 Maximum Flow 708

26.1 Flow networks 709

26.2 The Ford-Fulkerson method 714

26.3 Maximum bipartite matching 732

26.4 Push-relabel algorithms 736

26.5 The relabel-to-front algorithm 748


VII Selected Topics 

Introduction 769

27 Multithreaded Algorithms

27.1 The basics of dynamic multithreading 774

27.2 Multithreaded matrix multiplication 792

27.3 Multithreaded merge sort 797

28 Matrix Operations 813

28.1 Solving systems of linear equations 813

28.2 Inverting matrices 827

28.3 Symmetric positive-definite matrices and least-squares approximation 832

29 Linear Programming 843

29.1 Standard and slack forms 850

29.2 Formulating problems as linear programs 859

29.3 The simplex algorithm 864

29.4 Duality 879

29.5 The initial basic feasible solution 886

30 Polynomials and the FFT 898

30.1 Representing polynomials 900

30.2 The DFT and FFT 906

30.3 Efficient FFT implementations 915

31 Number-Theoretic Algorithms 926

31.1 Elementary number-theoretic notions 927

31.2 Greatest common divisor 933

31.3 Modular arithmetic 939

31.4 Solving modular linear equations 946

31.5 The Chinese remainder theorem 950

31.6 Powers of an element 954

31.7 The RSA public-key cryptosystem 958

31.8 Primality testing 965

31.9 Integer factorization 975

32 String Matching 985

32.1 The naive string-matching algorithm 988

32.2 The Rabin-Karp algorithm 990

32.3 String matching with finite automata 995

32.4 The Knuth-Morris-Pratt algorithm 1002

33 Computational Geometry 1014

33.1 Line-segment properties 1015

33.2 Determining whether any pair of segments intersects 1021

33.3 Finding the convex hull 1029

33.4 Finding the closest pair of points 1039

34 NP-Completeness 1048

34.1 Polynomial time 1053

34.2 Polynomial-time verification 1061

34.3 NP-completeness and reducibility 1067

34.4 NP-completeness proofs 1078

34.5 NP-complete problems 1086

35 Approximation Algorithms 1106

35.1 The vertex-cover problem 1108

35.2 The traveling-salesman problem 1111

35.3 The set-covering problem 1117

35.4 Randomization and linear programming 1123

35.5 The subset-sum problem 1128


VIII Appendix: Mathematical Background 

Introduction 1143

A Summations 1145

A.1 Summation formulas and properties 1145

A.2 Bounding summations 1149

B Sets, Etc. 1158

B.1 Sets 1158

B.2 Relations 1163

B.3 Functions 1166

B.4 Graphs 1168

B.5 Trees 1173

C Counting and Probability 1183

C.1 Counting 1183

C.2 Probability 1189

C.3 Discrete random variables 1196

C.4 The geometric and binomial distributions 1201

C.5 The tails of the binomial distribution 1208

D Matrices 1217

D.1 Matrices and matrix operations 1217

D.2 Basic matrix properties 1222

Bibliography 1231

Index


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