Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest. Introduction to Algorithms
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1 Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest Introduction to Algorithms
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3 Preface xiii 1 Introduction Algorithms Analyzing algorithms Designing algorithms Summary 1 6 I Mathematical Foundations Introduction 21 2 Growth of Functions Asymptotic notation Standard notations and common functions 32 3 Summations Summation formulas and properties Bounding summations 46 4 Recurrences The substitution method The iteration method The master method 6 1 * 4.4 Proof of the master theorem Sets, Etc Sets Relations Functions Graphs Trees 91
4 6 Counting and Probability Counting Probability Discrete random variables The geometric and binomial distributions 115 * 6.5 The tails of the binomial distribution Probabilistic analysis 126 II Sorting and Order Statistics Introduction Heapsort Heaps Maintaining the heap property Building a heap The heapsort algorithm Priority queues Quicksort Description of quicksort Performance of quicksort Randomized versions of quicksort Analysis of quicksort Sorting in Linear Time Lower bounds for sorting Counting sort Radix sort Bucket sort Medians and Order Statistics Minimum and maximum Selection in expected linear time Selection in worst-case linear time 189
5 III Data Structures Introduction Elementary Data Structures Stacks and queues Linked lists Implementing pointers and objects Representing rooted trees Hash Tables Direct-address tables Hash tables Hash functions Open addressing Binary Search Trees What is a binary search tree? Querying a binary search tree Insertion and deletion 25 0 * 13.4 Randomly built binary search trees Red-Black Trees Properties of red-black trees Rotations Insertion Deletion Augmenting Data Structures Dynamic order statistics How to augment a data structure Interval trees 290 IV Advanced Design and Analysis Technique s Introduction Dynamic Programming Matrix-chain multiplication Elements of dynamic programming Longest common subsequence Optimal polygon triangulation 320
6 17 Greedy Algorithms An activity-selection problem Elements of the greedy strategy Huffman codes 33 7 * 17.4 Theoretical foundations for greedy methods 345 * 17.5 A task-scheduling problem Amortized Analysis The aggregate method The accounting method The potential method Dynamic tables 36 7 V Advanced Data Structures Introduction B-Trees Definition of B-trees Basic operations on B-trees Deleting a key from a B-tree Binomial Heaps Binomial trees and binomial heaps Operations on binomial heaps Fibonacci Heaps Structure of Fibonacci heaps Mergeable-heap operations Decreasing a key and deleting a node Bounding the maximum degree Data Structures for Disjoint Sets Disjoint-set operations Linked-list representation of disjoint sets Disjoint-set forests 446 * 22.4 Analysis of union by rank with path compression 450
7 VI Graph Algorithms Introduction Elementary Graph Algorithms Representations of graphs Breadth-first search Depth-first search Topological sort Strongly connected components Minimum Spanning Trees Growing a minimum spanning tree The algorithms of Kruskal and Prim Single-Source Shortest Paths Shortest paths and relaxation Dijkstra's algorithm The Bellman-Ford algorithm Single-source shortest paths in directed acyclic graph s Difference constraints and shortest paths All-Pairs Shortest Paths Shortest paths and matrix multiplication The Floyd-Warshall algorithm Johnson's algorithm for sparse graphs 56 5 * 26.4 A general framework for solving path problems in directed graphs Maximum Flow Flow networks The Ford-Fulkerson method Maximum bipartite matching 600 * 27.4 Preflow-push algorithms 60 5 * 27.5 The lift-to-front algorithm 615
8 VII Selected Topics Introduction Sorting Networks Comparison networks The zero-one principle A bitonic sorting network A merging network A sorting network Arithmetic Circuits Combinational circuits Addition circuits Multiplication circuits Clocked circuits Algorithms for Parallel Computers Pointer jumping CRCW algorithms versus EREW algorithms Brent's theorem and work efficiency 709 * 30.4 Work-efficient parallel prefix computation Deterministic symmetry breaking Matrix Operations Properties of matrices Strassen's algorithm for matrix multiplication 739 * 31.3 Algebraic number systems and boolean matrix multipli - cation Solving systems of linear equations Inverting matrices Symmetric positive-definite matrices and least-square s approximation Polynomials and the FFT Representation of polynomials The DFT,and FFT Efficient FFT implementations Number-Theoretic Algorithms Elementary number-theoretic notions Greatest common divisor Modular arithmetic 814
9 33.4 Solving modular linear equations The Chinese remainder theorem Powers of an element The RSA public-key cryptosystem 83 1 * 33.8 Primality testing 83 7 * 33.9 Integer factorization String Matching The naive string-matching algorithm The Rabin-Karp algorithm String matching with finite automata The Knuth-Morris-Pratt algorithm 86 9 * 34.5 The Boyer-Moore algorithm Computational Geometry Line-segment properties Determining whether any pair of segments intersect s Finding the convex hull Finding the closest pair of points NP-Completeness Polynomial time Polynomial-time verification NP-completeness and reducibility NP-completeness proofs NP-complete problems Approximation Algorithms The vertex-cover problem The traveling-salesman problem The set-covering problem The subset-sum problem 978 Bibliography 98 7 Index 997
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