Introduction to algorithms Thomas H. Cormen ... [et al.].

Includes bibliographical references (p. [1231]-1250) and index.

Introduction 3
The Role of Algorithms in Computing 5
1.1 Algorithms 5
1.2 Algorithms as a technology 7 /
Getting Started 16
2.1 Insertion sort 76
2.2 Analyzing algorithms 23
2.3 Designing algorithms 29
Growth of Functions 43
3.1 Asymptotic notation 43
3.2 Standard notations and common functions S3
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
Probabilistic Analysis and Randomized Algorithms 114
5.1 The hiring problem 114
5.2 Indicator random variables 118
5.3 Randomized algorithms 722
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 properly 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 quick.sort 174
7.3 A randomized version of quicksort 179
lA Analysis of quick.sort IHO
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
III Data Structures
9.1 Minimum and maximum 214
9.2 Selection in expected linear time 215
9.3 Selection in worst-case linear time 220
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 TYees 286
12.1 What is a binary search tree? 286
12.2 Querying a binary .search tree 289
12..^ 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 m.ethod 456
17.3 The potential method 459
17.4 Dynamic tables 463
V Advanced Data Structures
Introduction 481
18 B-Trees 484
18.1 Delinilion of B-trees 4H8
18.2 Basic operations on B-trees 491
18.3 Deleting a key from a B-trec 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 56/
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 I'atlis 643
24.1 The Bcilman-Forcl aljzorilhm 65/
24.2 Single-source shortest jxiths in directed acyclic graphs 6.s5
24.3 Dijkstra's algorithm 6.5(S'
24.4 DilTerence constraints and shortest paths 664
24.5 Proofs of shortest-paths properties 67/
25 All-Pairs Shorte.st Paths 6H4
25.1 Shortest paths and matri.x multiplication 6.S'6
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 7/4
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 Greate.st common divisor 933
31.3 Modular arithmetic 939
31.4 Solving modular linear equations 946
31.5 The Chine.se 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 I0I5
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