Introduction to Algorithms - 3rd Edition

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Introduction to Algorithms - 3rd Edition\r\n\r\n\r\nAuthor: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein\r\nISBN: ISBN 978-0-262-03384-8 (hardcover : alk. paper) - ISBN 978-0-262-53305-8 (pbk. : alk. paper)\r\nFormat: PDF\r\nPages: 1313\r\nPublisher: The MIT Press\r\nPub. Date: 2009\r\n\r\n\r\n::Description::\r\n\r\nI Foundations\r\n	\r\n	Introduction 3\r\n\r\n	1 The Role of Algorithms in Computing 5\r\n	1.1 Algorithms 5\r\n	1.2 Algorithms as a technology 11\r\n	\r\n	2 Getting Started 16\r\n	2.1 Insertion sort 16\r\n	2.2 Analyzing algorithms 23\r\n	2.3 Designing algorithms 29\r\n	\r\n	3 Growth of Functions 43\r\n	3.1 Asymptotic notation 43\r\n	3.2 Standard notations and common functions 53\r\n	\r\n	4 Divide-and-Conquer 65\r\n	4.1 The maximum-subarray problem 68\r\n	4.2 Strassen’s algorithm for matrix multiplication 75\r\n	4.3 The substitution method for solving recurrences 83\r\n	4.4 The recursion-tree method for solving recurrences 88\r\n	4.5 The master method for solving recurrences 93\r\n	4.6 Proof of the master theorem 97\r\n	\r\n	5 Probabilistic Analysis and Randomized Algorithms 114\r\n	5.1 The hiring problem 114\r\n	5.2 Indicator random variables 118\r\n	5.3 Randomized algorithms 122\r\n	5.4 Probabilistic analysis and further uses of indicator random variables 130\r\n\r\n\r\nII Sorting and Order Statistics\r\n	Introduction 147\r\n\r\n	6 Heapsort 151\r\n	6.1 Heaps 151\r\n	6.2 Maintaining the heap property 154\r\n	6.3 Building a heap 156\r\n	6.4 The heapsort algorithm 159\r\n	6.5 Priority queues 162\r\n\r\n	7 Quicksort 170\r\n	7.1 Description of quicksort 170\r\n	7.2 Performance of quicksort 174\r\n	7.3 A randomized version of quicksort 179\r\n	7.4 Analysis of quicksort 180\r\n\r\n	8 Sorting in Linear Time 191\r\n	8.1 Lower bounds for sorting 191\r\n	8.2 Counting sort 194\r\n	8.3 Radix sort 197\r\n	8.4 Bucket sort 200\r\n\r\n	9 Medians and Order Statistics 213\r\n	9.1 Minimum and maximum 214\r\n	9.2 Selection in expected linear time 215\r\n	9.3 Selection in worst-case linear time 220\r\n\r\n\r\nIII Data Structures\r\n	Introduction 229\r\n\r\n	10 Elementary Data Structures 232\r\n	10.1 Stacks and queues 232\r\n	10.2 Linked lists 236\r\n	10.3 Implementing pointers and objects 241\r\n	10.4 Representing rooted trees 246\r\n\r\n	11 Hash Tables 253\r\n	11.1 Direct-address tables 254\r\n	11.2 Hash tables 256\r\n	11.3 Hash functions 262\r\n	11.4 Open addressing 269\r\n	11.5 Perfect hashing 277\r\n\r\n	12 Binary Search Trees 286\r\n	12.1 What is a binary search tree? 286\r\n	12.2 Querying a binary search tree 289\r\n	12.3 Insertion and deletion 294\r\n	12.4 Randomly built binary search trees 299\r\n\r\n	13 Red-Black Trees 308\r\n	13.1 Properties of red-black trees 308\r\n	13.2 Rotations 312\r\n	13.3 Insertion 315\r\n	13.4 Deletion 323\r\n\r\n	14 Augmenting Data Structures 339\r\n	14.1 Dynamic order statistics 339\r\n	14.2 How to augment a data structure 345\r\n	14.3 Interval trees 348\r\n\r\n\r\nIV Advanced Design and Analysis Techniques\r\n	Introduction 357\r\n\r\n	15 Dynamic Programming 359\r\n	15.1 Rod cutting 360\r\n	15.2 Matrix-chain multiplication 370\r\n	15.3 Elements of dynamic programming 378\r\n	15.4 Longest common subsequence 390\r\n	15.5 Optimal binary search trees 397\r\n\r\n	16 Greedy Algorithms 414\r\n	16.1 An activity-selection problem 415\r\n	16.2 Elements of the greedy strategy 423\r\n	16.3 Huffman codes 428\r\n	16.4 Matroids and greedy methods 437\r\n	16.5 A task-scheduling problem as a matroid 443\r\n\r\n	17 Amortized Analysis 451\r\n	17.1 Aggregate analysis 452\r\n	17.2 The accounting method 456\r\n	17.3 The potential method 459\r\n	17.4 Dynamic tables 463\r\n\r\n\r\nV Advanced Data Structures\r\n	Introduction 481\r\n\r\n	18 B-Trees 484\r\n	18.1 Definition of B-trees 488\r\n	18.2 Basic operations on B-trees 491\r\n	18.3 Deleting a key from a B-tree 499\r\n\r\n	19 Fibonacci Heaps 505\r\n	19.1 Structure of Fibonacci heaps 507\r\n	19.2 Mergeable-heap operations 510\r\n	19.3 Decreasing a key and deleting a node 518\r\n	19.4 Bounding the maximum degree 523\r\n\r\n	20 van Emde Boas Trees 531\r\n	20.1 Preliminary approaches 532\r\n	20.2 A recursive structure 536\r\n	20.3 The van Emde Boas tree 545\r\n\r\n	21 Data Structures for Disjoint Sets 561\r\n	21.1 Disjoint-set operations 561\r\n	21.2 Linked-list representation of disjoint sets 564\r\n	21.3 Disjoint-set forests 568\r\n	21.4 Analysis of union by rank with path compression 573\r\n\r\n\r\nVI Graph Algorithms\r\n	Introduction 587\r\n\r\n	22 Elementary Graph Algorithms 589\r\n	22.1 Representations of graphs 589\r\n	22.2 Breadth-first search 594\r\n	22.3 Depth-first search 603\r\n	22.4 Topological sort 612\r\n	22.5 Strongly connected components 615\r\n\r\n	23 Minimum Spanning Trees 624\r\n	23.1 Growing a minimum spanning tree 625\r\n	23.2 The algorithms of Kruskal and Prim 631\r\n	24 Single-Source Shortest Paths 643\r\n	24.1 The Bellman-Ford algorithm 651\r\n	24.2 Single-source shortest paths in directed acyclic graphs 655\r\n	24.3 Dijkstra’s algorithm 658\r\n	24.4 Difference constraints and shortest paths 664\r\n	24.5 Proofs of shortest-paths properties 671\r\n\r\n	25 All-Pairs Shortest Paths 684\r\n	25.1 Shortest paths and matrix multiplication 686\r\n	25.2 The Floyd-Warshall algorithm 693\r\n	25.3 Johnson’s algorithm for sparse graphs 700\r\n\r\n	26 Maximum Flow 708\r\n	26.1 Flow networks 709\r\n	26.2 The Ford-Fulkerson method 714\r\n	26.3 Maximum bipartite matching 732\r\n	26.4 Push-relabel algorithms 736\r\n	26.5 The relabel-to-front algorithm 748\r\n\r\n\r\nVII Selected Topics\r\n	Introduction 769\r\n\r\n	27 Multithreaded Algorithms 772\r\n	27.1 The basics of dynamic multithreading 774\r\n	27.2 Multithreaded matrix multiplication 792\r\n	27.3 Multithreaded merge sort 797\r\n\r\n	28 Matrix Operations 813\r\n	28.1 Solving systems of linear equations 813\r\n	28.2 Inverting matrices 827\r\n	28.3 Symmetric positive-definite matrices and least-squares approximation 832\r\n\r\n	29 Linear Programming 843\r\n	29.1 Standard and slack forms 850\r\n	29.2 Formulating problems as linear programs 859\r\n	29.3 The simplex algorithm 864\r\n	29.4 Duality 879\r\n	29.5 The initial basic feasible solution 886\r\n\r\n	30 Polynomials and the FFT 898\r\n	30.1 Representing polynomials 900\r\n	30.2 The DFT and FFT 906\r\n	30.3 Efficient FFT implementations 915\r\n\r\n	31 Number-Theoretic Algorithms 926\r\n	31.1 Elementary number-theoretic notions 927\r\n	31.2 Greatest common divisor 933\r\n	31.3 Modular arithmetic 939\r\n	31.4 Solving modular linear equations 946\r\n	31.5 The Chinese remainder theorem 950\r\n	31.6 Powers of an element 954\r\n	31.7 The RSA public-key cryptosystem 958\r\n	31.8 Primality testing 965\r\n	31.9 Integer factorization 975\r\n\r\n	32 String Matching 985\r\n	32.1 The naive string-matching algorithm 988\r\n	32.2 The Rabin-Karp algorithm 990\r\n	32.3 String matching with finite automata 995\r\n	32.4 The Knuth-Morris-Pratt algorithm 1002\r\n\r\n	33 Computational Geometry 1014\r\n	33.1 Line-segment properties 1015\r\n	33.2 Determining whether any pair of segments intersects 1021\r\n	33.3 Finding the convex hull 1029\r\n	33.4 Finding the closest pair of points 1039\r\n\r\n	34 NP-Completeness 1048\r\n	34.1 Polynomial time 1053\r\n	34.2 Polynomial-time verification 1061\r\n	34.3 NP-completeness and reducibility 1067\r\n	34.4 NP-completeness proofs 1078\r\n	34.5 NP-complete problems 1086\r\n\r\n	35 Approximation Algorithms 1106\r\n	35.1 The vertex-cover problem 1108\r\n	35.2 The traveling-salesman problem 1111\r\n	35.3 The set-covering problem 1117\r\n	35.4 Randomization and linear programming 1123\r\n	35.5 The subset-sum problem 1128\r\n\r\n\r\nVIII Appendix: Mathematical Background\r\n	Introduction 1143\r\n\r\n	A Summations 1145\r\n	A.1 Summation formulas and properties 1145\r\n	A.2 Bounding summations 1149\r\n\r\n	B Sets, Etc. 1158\r\n	B.1 Sets 1158\r\n	B.2 Relations 1163\r\n	B.3 Functions 1166\r\n	B.4 Graphs 1168\r\n	B.5 Trees 1173\r\n\r\n	C Counting and Probability 1183\r\n	C.1 Counting 1183\r\n	C.2 Probability 1189\r\n	C.3 Discrete random variables 1196\r\n	C.4 The geometric and binomial distributions 1201\r\n	? C.5 The tails of the binomial distribution 1208\r\n\r\n	D Matrices 1217\r\n	D.1 Matrices and matrix operations 1217\r\n	D.2 Basic matrix properties 1222\r\n\r\n	Bibliography 1231\r\n\r\n	Index 1251\r\n\r\n\r\n\r\n\r\nMy other torrents can be found here -                        \r\n\r\n\r\nHappy Reading\r\nAmit Verma\r\n
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