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详细说明： 算法导论，英文 【本书目录】 I Foundations Introduction 3 l The Role of Algorithms in Computing 5 l.l Algorithms 5 l.2 Algorithms as a technology 10 2 Getting Started I5 2.l Insertion sort 15 2.2 Analyzing algorithms 21 2.3 Designing algorithms 27 3 Growth of Functions 41 3.l Asymptotic notation 41 3.2 Standard notations and common functions 51 4 Recurrences 62 4.l The substitution method 63 4.2 The recursion-tree method 67 4.3 The master method 73 4.4 Proof of the master theorem 76 5 Probabilistic Analysis and Randomized Algorithms 5.l The h iring problem 91 5.2 Indicator random variables 94 5.3 Randomized algorithms 99 5.4 Probabi1istic analysis and further uses of indicator 106 II Sorting and Order Statistics Introduction 123 6 Heapsort 127 6.l Heaps I27 6.2 Maintaining the heap property 130 6.3 Building a heap 132 6.4 The heapsort algorithm 135 6.5 Priority queues 138 7 Quicksort 145 7.l Description of quicksort 145 7.2 Performance ofquicksort 149 7.3 A randomized version of quicksort 153 7.4 Analysis ofquicksort 55 8 Sorting in Linear Time 165 8.l Lower bounds for sorting 165 8.2 Counting sort i68 8.3 Radix sort 170 8.4 Bucket sort 174 9 Medians and Order Statistics 183 9.1 Minimum and maximum 184 9.2 Selection in expected linear time 185 9.3 Selection in worst-case linear time 189 III Data Structures Introduction 197 10 Elementary Data Structures 200 l0.l Stacks and queues 200 l0.2 Linked lists 204 l0.3 Implementing pointers and objects 209 l0.4 Representing rooted trees 214 11 Hash Tables 221 ll.l Direct-address tables 222 11.2 Hash tables 224 ll.3 Hash functions 229 ll.4 Open addressing 237 ll.5 Perfect hashing 24S l2 Binary Search Trees 253 l2.l What is a binary search tree? 2S3 l2.2 Querying a binary search tree 2S6 l2.3 Insertion and deletion 261 l2.4 Randoinly built binary search trees 265 13 Red-Black Thees 273 l3.l Properties of red-black trees 273 l3.2 Rotations 277 l3.3 Insertion 280 l3.4 Deletion 288 14 Augmenting Data Structures 302 l4.l Dynamic order statistics 302 l4.2 How to augment a data structure 308 l4.3 Interval trees 311 IV Advanced Desthe and Analysis Techniques Introduction 321 15 Dynamic Programming J2J l5.l Assembly--line scheduling 324 l5.2 Matrix-chain multiplication 331 l5.3 Elements of dynamic programming 339 15.4 Longest common subsequence 350 l5.5 Optimal binary search trees 356 l6 Greedy Algorithms 370 l6.l An activity-selection problem 371 l6.2 Elements of the greedy strategy 379 l6.3 Huffman codes 385 l6.4 Theoretical foundations for greedy methods 393 16.5 A task-scheduling problem 399 17 Amortized Analysis 405 l7.1 Aggregate analysis 406 17.2 The accounting method 410 17.3 The potential method 412 l7.4 Dynamic tables 416 V Advanced Data Structures Introduction 431 18 B-Trees 434 18.l Definition of B--trees 438 l8.2 Basic operations on B-trees 44j l8.3 Deleting a key from a B--tree 449 19 Binomial Heaps 455 l9.l Binomial trees and binomial heaps 457 19.2 Operations on binomial heaps 461 20 Fibonacci Heaps 476 20.l Structure of Fibonacci heaps 477 20.2 Mergeable-heap operations 479 20.3 Decreasing a key and deleting a node 489 20.4 Bounding the maximum degree 493 21 Data Structures for Disjoint Sets 498 2l.l Disjoint--set operations 498 2l.2 Linked-list representation of disjoint sets 501 2l.3 Disjoint--set forests 505 2l.4 Analysis of union by rank with path compression 50 VI Graph Algorithms Introduction 525 22 Elementary Graph Algorithms 527 22.l Representations of graphs 527 22.2 Breadth-first search 531 22.3 Depth-first search 540 22.4 Topological sort 549 22.5 Strongly connected components 552 23 Minimum Spanning Trees 561 23.l Growing a minimum spanning tree 562 23.2 The algorithms of Kruskal and Prim 567 24 Single-Source Shortest Paths 580 24.l The Bellman-Ford algorithm 588 24.2 Single-source shortest paths in directed acyclic graphs 24.3 Dijkstra's algorithm 595 24.4 Difference constraints and shortest paths 601 24.5 Proofs of shortest-paths properties 607 25 All-Pairs Shortest Paths 620 25.l Shortest paths and matrix multiplication 622 25.2 The Floyd-Warshall a1gorithm 629 25.3 Johnson's algorithm for sparse graphs 636 26 Maximum Flow d43 26.l Flow networks 644 26.2 The Ford-Fulkerson method 651 26.3 Maximum bipartite matching 664 26.4 Push--relabel algorithms 669 26.5 The relabel--to-front a1gorithm 68I VII Selected Topics Introduction 701 27 Sorting Networks 704 27.l Comparison networks 704 27.2 The zero-one principle 709 27.3 A bitonic sorting network 712 27.4 A merging network 716 27.5 A sorting network 719 28 Matrix Operations 725 28.l Properties of matrices 725 28.2 Strassen's algorithm for matrix multiplication 735 28.3 Solving systems of linear equations 742 28.4 Inverting matrices 7S5 28.5 Symmetric positive-definite matrices and least-squares approximation760 29 Linear Programming 770 29.1 Standard and slack forms 777 29.2 Formulating problems as linear programs 785 29.3 The simplex algorithm 790 29.4 Duality 804 29.5 The initial basic feasible solution 811 30 Polynomials and the FFT 822 30.l Representation of polynomials 824 30.2 The DFT and FFT 830 30.3 Efficient FFT implementations 839 31 Number-Theoretic Algorithms 849 3l.l E1ementary numbertheoretic notions 850 31.2 Greatest common divisor 856 3l.3 Modular arithmetic 862 3l.4 Solving modular linear equations 869 3l.5 The Chinese remainder theorem 873 3l.6 Powers of an element 876 3l.7 The RSA public-key cryptosystem 881 3l.8 Primality testing 887 3l.9 Integer factorization 896 32 String Matching 906 32.l The naive string-matching algorithm 909 32.2 The Rabin-Karp algorithm 911 32.3 String matching with finite automata 916 32.4 The Knuth-Morris-Pratt algorithm 923 33 Computational Geometry 933 33.l Line--segment properties 934 33.2 Determining whether any pair of segments intersects 940 33.3 Finding the convex hull 947 33.4 Finding the c1osest pair of points 957 34 NP-Completeness 966 34.1 Polynomial time 971 34.2 Polynomial-time verification 979 34.3 NP-completeness and reducibility 984 34.4 NP--completeness proofs 995 34.5 NP-complete problems 1003 35 Approximation Algorithms 1022 35.l The vertex-cover problem 1024 35.2 The traveling-salesman problem 1027 35.3 The set-covering problem 1033 35.4 Randomization and linear programming ]039 35.5 The subset-sum problem 1043 VH APPendir: Mathematical Background Introduction 1057 A Summations 1058 A.l Summation formulas and properties 1058 A.2 Bounding summations 1062 B Sets, Etc. 1070 B.1 Sets 1070 B.2 Relations 1075 B.3 Functions 1077 B.4 Graphs 1080 B.5 Trees 1085 C Counting and Probability 1094 C.l Counting 1094 C.2 Probability 1100 C.3 Discrete random variables 1106 C.4 The geometric and binomial distributions 1112 C.5 The tails of the binomial distribution 1118 Bibliography 1127 Index 1145 ...展开收缩
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