| 目 录 Preface PART1BasicConceptsandIntroductionto Algorithms Chapter1BasicConceptsinAlgorithmicAnalysis 1.1Introduction l.2HistoricalBaCkground 1.3BinarySearch 1.3.1Analysisofthebinarysearchalgorithm 1.4MergingTwoSortedLists 1.5SelectinnSort 1.6InsertionSort 1.7Bottom-UpMergeSorting 1.7.1Analysisofbottom-upmergesorting 1.8TimeComplexity 1.8.1Orderofgrowth 1.8.2TheO-notation 1.8.3Thefl-notation l.8.4Thee-notation 1.8.5MamPles 1.8.6Complekityclassesandtheo-notation 1.9SpaceComplexity 1.10OptimalAlgorithms 1.1lHowtoBstimatetheRunningTimeofanAlgorithm 1.l1.1Coulitingthenumberofforrations l.1l.2Countingthefrequencyofbasicoperatha 1.1l.3Usingrecurrencerelations 1.l2Worstcaseandaveragecaseanalysis l.12.1Wofstcaseanalysis 1.12.2Averagecaseanalysis l.13AmedisedAnalyais 1.14InputSiseandProblemInstance 1.15Exercises 1.16BibiographicNotes Chapter2MathematicalPreliminaries 2.1Sots,ReationsandAnnctions 2.1.1sets 2.1.2ffelations 2.1.2.lEquivalencerelations 2.1.3Thnctions 2.2ProofMehods 2.2.1Directproof 2.2.2Indirectproof 2.2.3Proofbycolltradiction 2.2.4Proofbycotillterexample 2.2.5Mathematicalinduction 2.3Logarithms 2.4FloorandCeilingTunctions 2.5FactorialandBinomialCoefficients 2.5.1Factorials 2.5.2Bintalalcoefficients 2.6ThePigeonholePrinciple 2.7Summations 2.7.1Approkimationofsummationsbyintegration 2.8RecurrenceRelations 2.8.1Solutionoflinearhomogeneousrecurrences 2.8.2Solutionofinhomogeneousrecurrences 2.8.3Solationofdivide-and-conquerrecurrence 2.8.3.1Expandingtherecurrence 2.8.3.2Sutistitution 2.8.3.3Changeofvariables 2.9Exercises Chapter3DataStructures 3.1Introdction 3.2LinkedLists 3.2.1Stacksanaqueues 3.3Graphs 3.3.1Representationofgraphs 3.3.2planargraphs 3.4Trees 3.5RootedTrees 3.5.1Treetraversals 3.6BinaryTrees 3.6.lSomequantitativeaspectsofbinarytrees 3.6.2Binarysearchtrees 3.7Exercises 3.8BlbliographicNotes Chapter4HeapsandtheDisjointSetsDataStructure 4.lIotroduction 4.2Heaps 4.2.1Operationsonheaps 4.2.2Creatingaheap 4.2.3Heapsort 4.2.4Minandmaxheaps 4.3DisjointSetsDataStructures 4.3.1Theunionbyrankheuristic 4.3.2Pathcompression 4.3.3Theunion-findalgorithms 4.3.4Analysisoftheuninn-findalgorithms 4.4Exercises 4.5BibliographicNotes PART2TechniquesBasedonRecursion Chapter5Induction 5.1Introduction 5.2TwoSimpleExamples 5.2.1Selectionsort 5.2.2Insertionsort 5.3TadixSort 5.4IntegerExponentiation 5.5EvaluatingPolynomials(Horner'sRule) 5.6GeneratingPermutations 5.6.1Thefirstalgorithm 5.6.2Thesecondalgorithm 5.7FindingtheMajorityElement 5.8Exercises 5.9BibliographicNotes Chapter6DivideandConquer 6.1Introduction 6.2BinarySearch 6.3Mergesort 6.3.1Howthealgorithmworks 6.3.2Analysisofthemergesortalgorithm 6.4TheDivideandConquerParadigm 6.5Selection:FindingtheMedianandthekthSmallestElement 6.5.lAnalysisoftheselectionalgorithm 6.6Quicksort 6.6.1Apartitinningalgorithm. 6.6.2Thesortingalgorithm 6.6.3Analysisofthequicksortalgorithm 6.6.3.1Theworstcasebehavior 6.6.3.2Theaveragecasebehavior 6.6.4Comparisonofsortingalgorithms 6.7MultiplicationofLargeIntegers 6.8MatrinMultiplication 6.8.1Thetraditionalalgorithm 6.8.2Recursiveversion 6.8.3Strass |
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