Introduction to Algorithms - 3rd Edition - by Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein - ISBN 9780262033848
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Introduction to Algorithms
3rd Edition
Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
ISBN: 9780262033848

Solutions for Introduction to Algorithms

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Chapter 4 - Divide-and-conquerChapter 4.1 - The Maximum-subarray ProblemChapter 4.2 - Strassen’s Algorithm For Matrix MultiplicationChapter 4.3 - The Substitution Method For Solving RecurrencesChapter 4.4 - The Recursion-tree Method For Solving RecurrencesChapter 4.5 - The Master Method For Solving RecurrencesChapter 4.6 - Proof Of The Master TheoremChapter 5 - Probabilistic Analysis And RandomizedalgorithmsChapter 5.1 - The Hiring ProblemChapter 5.2 - Indicator Random VariablesChapter 5.3 - Randomized AlgorithmsChapter 5.4 - Probabilistic Analysis And Further Uses Of Indicator Random VariablesChapter 6 - HeapsortChapter 6.1 - HeapsChapter 6.2 - Maintaining The Heap PropertyChapter 6.3 - Building A HeapChapter 6.4 - The Heapsort AlgorithmChapter 6.5 - Priority QueuesChapter 7 - QuicksortChapter 7.1 - Description Of QuicksortChapter 7.2 - Performance Of QuicksortChapter 7.3 - A Randomized Version Of QuicksortChapter 7.4 - Analysis Of QuicksortChapter 8 - Sorting In Linear TimeChapter 8.1 - Lower Bounds For SortingChapter 8.2 - Counting SortChapter 8.3 - Radix SortChapter 8.4 - Bucket SortChapter 9 - Medians And Order StatisticsChapter 9.1 - Minimum And MaximumChapter 9.2 - Selection In Expected Linear TimeChapter 9.3 - Selection In Worst-case Linear TimeChapter 10 - Elementary Data StructuresChapter 10.1 - Stacks And QueuesChapter 10.2 - Linked ListsChapter 10.3 - Implementing Pointers And ObjectsChapter 10.4 - Representing Rooted TreesChapter 11 - Hash TablesChapter 11.1 - Direct-address TablesChapter 11.2 - Hash TablesChapter 11.3 - Hash FunctionsChapter 11.4 - Open AddressingChapter 11.5 - Perfect HashingChapter 12 - Binary Search TreesChapter 12.1 - What Is A Binary Search Tree?Chapter 12.2 - Querying A Binary Search TreeChapter 12.3 - Insertion And DeletionChapter 12.4 - Randomly Built Binary Search TreesChapter 13 - Red-black TreesChapter 13.1 - Properties Of Red-black TreesChapter 13.2 - RotationsChapter 13.3 - InsertionChapter 13.4 - DeletionChapter 14 - Ugmenting Data StructuresChapter 14.1 - Dynamic Order StatisticsChapter 14.2 - How To Augment A Data StructureChapter 14.3 - Interval TreesChapter 15 - Dynamic ProgrammingChapter 15.1 - Rod CuttingChapter 15.2 - Matrix-chain MultiplicationChapter 15.3 - Elements Of Dynamic ProgrammingChapter 15.4 - Longest Common SubsequenceChapter 15.5 - Optimal Binary Search TreesChapter 16 - Greedy AlgorithmsChapter 16.1 - An Activity-selection ProblemChapter 16.2 - Elements Of The Greedy StrategyChapter 16.3 - Huffman CodesChapter 16.4 - Matroids And Greedy MethodsChapter 16.5 - A Task-scheduling Problem As A MatroidChapter 17 - Amortized AnalysisChapter 17.1 - Aggregate AnalysisChapter 17.2 - The Accounting MethodChapter 17.3 - The Potential MethodChapter 17.4 - Dynamic TablesChapter 18 - TreesChapter 18.1 - Definition Of B-treesChapter 18.2 - Basic Operations On B-treesChapter 18.3 - Deleting A Key From A B-treeChapter 19 - Fibonacci HeapsChapter 19.2 - Mergeable-heap OperationsChapter 19.3 - Decreasing A Key And Deleting A NodeChapter 19.4 - Bounding The Maximum DegreeChapter 20 - Van Emde Boas TreesChapter 20.1 - Preliminary ApproachesChapter 20.2 - A Recursive StructureChapter 20.3 - The Van Emde Boas TreeChapter 21 - Data Structures For Disjoint SetsChapter 21.1 - Disjoint-set OperationsChapter 21.2 - Linked-list Representation Of Disjoint SetsChapter 21.3 - Disjoint-set ForestsChapter 21.4 - Analysis Of Union By Rank With Path CompressionChapter 22 - Elementary Graph AlgorithmsChapter 22.1 - Representations Of GraphsChapter 22.2 - Breadth-first SearchChapter 22.3 - Depth-first SearchChapter 22.4 - Topological SortChapter 22.5 - Strongly Connected ComponentsChapter 23 - Minimum Spanning TreesChapter 23.1 - Growing A Minimum Spanning TreeChapter 23.2 - The Algorithms Of Kruskal And PrimChapter 24 - Single-source Shortest PathsChapter 24.1 - The Bellman-ford AlgorithmChapter 24.2 - Single-source Shortest Paths In Directed Acyclic GraphsChapter 24.3 - Dijkstra’s AlgorithmChapter 24.4 - Difference Constraints And Shortest PathsChapter 24.5 - Proofs Of Shortest-paths PropertiesChapter 25 - All-pairs Shortest PathsChapter 25.1 - Shortest Paths And Matrix MultiplicationChapter 25.2 - The Floyd-warshall AlgorithmChapter 25.3 - Johnson’s Algorithm For Sparse GraphsChapter 26 - Maximum FlowChapter 26.1 - Flow NetworksChapter 26.2 - The Ford-fulkerson MethodChapter 26.3 - Maximum Bipartite MatchingChapter 26.4 - Push-relabel AlgorithmsChapter 26.5 - The Relabel-to-front AlgorithmChapter 27 - Multithreaded AlgorithmsChapter 27.1 - The Basics Of Dynamic MultithreadingChapter 27.2 - Multithreaded Matrix MultiplicationChapter 27.3 - Multithreaded Merge SortChapter 28 - Matrix OperationsChapter 28.1 - Solving Systems Of Linear EquationsChapter 28.2 - Inverting MatricesChapter 28.3 - Symmetric Positive-definite Matrices And Least-squares ApproximationChapter 29 - Linear ProgrammingChapter 29.1 - Standard And Slack FormsChapter 29.2 - Formulating Problems As Linear ProgramsChapter 29.3 - The Simplex AlgorithmChapter 29.4 - DualityChapter 29.5 - The Initial Basic Feasible SolutionChapter 30 - Polynomials And The FftChapter 30.1 - Representing PolynomialsChapter 30.2 - The Dft And FftChapter 30.3 - Efficient Fft ImplementationsChapter 31 - Number-theoretic AlgorithmsChapter 31.1 - Elementary Number-theoretic NotionsChapter 31.2 - Greatest Common DivisorChapter 31.3 - Modular ArithmeticChapter 31.4 - Solving Modular Linear EquationsChapter 31.5 - The Chinese Remainder TheoremChapter 31.6 - Powers Of An ElementChapter 31.7 - The Rsa Public-key CryptosystemChapter 31.8 - Primality TestingChapter 31.9 - Integer FactorizationChapter 32 - String MatchingChapter 32.1 - The Naive String-matching AlgorithmChapter 32.2 - The Rabin-karp AlgorithmChapter 32.3 - String Matching With Finite AutomataChapter 32.4 - The Knuth-morris-pratt AlgorithmChapter 33 - Computational GeometryChapter 33.1 - Line-segment PropertiesChapter 33.2 - Determining Whether Any Pair Of Segments IntersectsChapter 33.3 - Finding The Convex HullChapter 33.4 - Finding The Closest Pair Of PointsChapter 34 - Np-completenessChapter 34.1 - Polynomial TimeChapter 34.2 - Polynomial-time VerificationChapter 34.3 - Np-completeness And ReducibilityChapter 34.4 - Np-completeness ProofsChapter 34.5 - Np-complete ProblemsChapter 35 - Approximation AlgorithmsChapter 35.1 - The Vertex-cover ProblemChapter 35.2 - The Traveling-salesman ProblemChapter 35.3 - The Set-covering ProblemChapter 35.4 - Randomization And Linear ProgrammingChapter 35.5 - The Subset-sum ProblemChapter A - SummationsChapter A.1 - Summation Formulas And PropertiesChapter A.2 - Bounding SummationsChapter B - B Sets, Etc.Chapter B.1 - SetsChapter B.2 - RelationsChapter B.3 - FunctionsChapter B.4 - GraphsChapter B.5 - TreesChapter C - C Counting And ProbabilityChapter C.1 - CountingChapter C.2 - ProbabilityChapter C.3 - Discrete Random VariablesChapter C.4 - The Geometric And Binomial DistributionsChapter C.5 - The Tails Of The Binomial DistributionChapter D - D MatricesChapter D.1 - Matrices And Matrix OperationsChapter D.2 - Basic Matrix Properties

Book Details

Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called "Divide-and-Conquer"). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition.

Sample Solutions for this Textbook

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