Introduction to Algorithms - 3rd Edition

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Introduction to Algorithms - 3rd Edition


Author: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
ISBN: ISBN 978-0-262-03384-8 (hardcover : alk. paper) - ISBN 978-0-262-53305-8 (pbk. : alk. paper)
Format: PDF
Pages: 1313
Publisher: The MIT Press
Pub. Date: 2009


::Description::

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 772
	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 1251


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