3.获取表的描述
part1basicconceptsandintroductiontoalgorithms1chapter1basicconceptsinalgorithmicanalysis51.1introduction.............................51.2historicalbackground.......................61.3binarysearch............................81.3.1analysisofthebinarysearchalgorithm.........101.4mergingtwosortedlists.....................121.5selectionsort............................141.6insertionsort............................151.7bottomj.jpmergesorting.....................171.7.1analysisofbottom-upmergesorting...........191.8timecomplexity..........................201.8.1orderofgrowth......................211.8.2theo-notation.......................251.8.3theΩ-notation.......................261.8.4theΘ-notation.......................271.8.5examples..........................291.8.6complexityclassesandtheenotation..........311.9spacecomplexity.........................321.10optimalalgorithms........................341.11howtoestimatetherunningtimeofanalgorithm......351.11.1countingthenumberofiterations............351.11.2countingthefrequencyofbasicoperations...381.11.3usingrecurrencerelations.................411.12worstcaseandaveragecaseanalysis..............421.12.1worstcaseanalysis.....................441.12.2averagecaseanalysis...................461.13amortizedanalysis.........................471.14inputsizeandprobleminstance.................501.15exercises..............................521.16bibliographicnotes.........................59chapter2mathematicalpreliminaries612.1sets,relationsandfunctions...................622.1.1sets.............................622.1.2relations..........................632.1.2.1equivalencerelations..............642.1.3functions..........................642.2proofmethods...........................652.2.1directproof.........................652.2.2indirectproof........................662.2.3proofbycontradiction...................662.2.4proofbycounterexampie.................672.2.5mathematicinduction..................682.3logarithms.............................692.4floorandceilingfunctions....................702.5factorialandbinomialcoefficients................712.5.1factorials..........................712.5.2binomialcoefficients..................732.6thepigeonholeprinciple......................752.7summations.............................762.7.1approximationofsummationsbyintegration......782.8recurrencerelations.......................822.8.1solutionoflinearhomogeneousrecurrences.......832.8.2solutionofinhomogeneousrecurrences..........852.8.3solutionofdivide-and-conquerrecurrences......872.8.3.1expandingtherecurrence...........872.8.3.2substitution...................912.8.3.3changeofvariables...............952.9exercises..............................98chapter3datastructures1033.1introduction.............................1033.2linkedlists.............................1033.2.1stacksandqueues.....................1043.3graphs...............................1043.3.1representationofgraphs.................1063.3.2planargraphs........................1073.4trees.................................1083.5rootedtyees............................1083.5.1treetraversals.......................1093.6binarytrees............................1093.6.1somequantitativeaspectsofbinarytrees........1113.6.2binarysearchtrees.....................1123.7exercises..............................1123.8bibliographicnotes.........................114chapter4heapsandthedisjointsetsdatastructures1154.1introduction.............................1154.2heaps................................1154.2.1operationsonheaps....................1164.2.2creatingaheap......................1204.2.3heapsort..........................1244.2.4minandmaxheaps....................1254.3disjointsetsdatastructures...................1254.3.1theunionbyrankheuristic................1274.3.2pathcompression....................1294.3.3theunion-findalgorithms.................1304.3.4analysisoftheunion-findalgorithms...........1324.4exercises..............................1344.5bibliographicnotes.........................137part2techniquesbasedonrecursion139chapter5induction............................1435.1introduction.............................1435.2twosimpleexamples.......................1445.2.1selectionsort........................1445.2.2insertionsort........................1455.3radixsort.............................1455.4integerexponentiation.......................1485.5evaluatingpolynomials.............1495.6generatingpermutations.....................1505.6.1thefirstalgorithm.....................1505.6.2thesecondalgorithm...................1525.7findingthemajorityelement...................1545.8bibliographicnotes.........................1585.9exercises..............................158chapter6divideandconquer1616.1introduction.............................1616.2binarysearch............................1636.3mergesort..............................1656.3.1howthealgorithmworks.................1666.3.2analysisofthemergesortalgorithm...........1676.4selection:findingthemedianandthekthsmallestelement.1696.5thedivideandconquerparadigm................1726.5.1analysisoftheselectionalgorithm............1756.6quicksort..............................1776.6.1apartitioningalgorithm..................1776.6.2thesortingalgorithm...................1796.6.3analysisofthequicksortalgorithm............1816.6.3.1theworstcasebehavior............1816.6.3.2theaveragecasebehavior...........1846.6.4comparisonofsortingalgorithms.............1866.7multiplicationoflargeintegers..................1876.8matrixmultiplication.......................1886.8.1thetraditionalalgorithm.................1886.8.2recursiveversion......................1886.8.3strassen’salgorithm....................1906.8.4comparisonsofthethreealgorithms...........1916.9theclosestpairproblem.....................1926.9.1timecomplexity......................1946.10exercises..............................1956.11bibliographicnotes.........................202chapter7dynamicprogramming2037.1introduction.............................2037.2thelongestcommonsubsequenceproblem..........2057.3matrixchainmultiplication....................2087.4thedynamicprogrammingparadigm..............2147.5theall-pairsshortestpathproblem...............2157.7exercises..............................2177.6theknapsackproblem......................2207.8bibliographicnotes.........................226part3first-cuttechniques227chapter8thegreedyapproach2318.1introduction.............................2318.2theshortestpathproblem....................2328.2.1alineartimealgorithmfordensegraphs........2378.3minimumcostspanningtrees.....2398.4minimumcostspanningtrees.......2428.4.1alineartimealgorithmfordensegraphs........2468.5filecompression..........................2488.6exercises..............................2518.7bibliographicnotes.........................255chapter9graphtraversal2579.1introduction.............................2579.2depth-firstsearch.........................2579.2.1timecomplexityofdepth-firstsearch..........2619.3applicationsofdepth-firstsearch................2629.3.1graphacyclicity......................2629.3.2topologicalsorting.....................2629.3.3findingarticulationpointsinagraph..........2639.3.4stronglyconnectedcomponents..............2669.4breadth-firstsearch........................2679.5applicationsofbreadth-firstsearch...............2699.6exercises..............................2709.7bibliographicnotes.........................273part4complexityofproblems275chapter10np-completeproblems27910.1introduction.............................27910.2theclassp.............................28210.3theclassnp............................28310.4np-completeproblems.......................28510.4.1thesatisfiabilityproblem.................28510.4.2vertexcover,independentsetandcliqueproblems...28810.4.3morenp-completeproblems...............29110.5theclassco-np..........................29210.6theclassnpi...........................29410.7therelationshipsbetweenthefourclasses...........29510.8exercises..............................29610.9bibliographicnotes.........................298chapter11introductiontocomputationalcomplexity29911.1introduction.............................29911.2modelofcomputation:theturingmachine...........29911.3k-tapeturingmachinesandtimecomplexity..........30011.4off-lineturingmachinesandspacecomplexity........30311.5tapecompressionandlinearspeed-up.............30511.6relationshipsbetweencomplexityclasses............30611.6.1spaceandtimehierarchytheorems............30911.6.2paddingarguments.....................31111.7reductions.............................31311.8completeness............................31811.8.1nlogspace-completeproblems............31811.8.2pspace-completeproblems...............31911.8.3p-completeproblems....................32111.8.4someconclusionsofcompleteness.............32311.9thepolynomialtimehierarchy.................32411.10exercises..............................32811.11bibliographicnotes.........................332chapter12lowerbounds33512.1introduction.............................33512.2triviallowerbounds.......................33512.3thedecisiontreemodel.....................33612.3.1thesearchproblem....................33612.3.2thesortingproblem....................33712.4thealgebraicdecisiontreemodel................33912.4.1theelementuniquenessproblem.............34112.5lineartimereductions......................34212.5.1theconvexhullproblem.................34212.5.2theclosestpairproblem.................34312.5.3theeuclideanminimumspanningtreeproblem.....34412.6exercises..............................34512.7bibliographicnotes.........................346part5copingwithhardness349chapter13backtracking35313.1introduction.............................35313.2the3-coloringproblem......................35313.3the8-queensproblem.......................35713.4thegeneralbacktrackingmethod................36013.5branchandbound.........................36213.6exercises..............................36713.7bibliographicnotes.........................369chapter14randomizedalgorithms37114.1introduction.............................37114.2lasvegasandmontecarloalgorithms.............37214.3randomizedquicksort.......................37314.4randomizedselection.......................37414.5testingstringequality......................37714.6patternmatching..........................37914.7randomsampling.........................38114.8primalitytesting..........................38414.9exercises..............................39014.10bibliographicnotes.........................392chapter15approximationalgorithms...................39315.1introduction.............................39315.2basicdefinitions..........................39315.3differencebounds.........................39415.3.1planargraphcoloring...................39515.3.2hardnessresult:theknapsackproblem.........39515.4relativeperformancebounds...................39615.4.1thebinpackingproblem.................39715.4.2theeuclideantravelingsalesmanproblem.......39915.4.3thevertexcoverproblem.................40115.4.4hardnessresult:thetravelingsalesmanproblem....40215.5polynomialapproximationschemes...............40415.5.1theknapsackproblem...................40415.6fullypolynomialapproximationschemes............40715.6.1thesubset-sumproblem..................40815.7exercises..............................41015.8bibliographicnotes.........................413part6iterativeimprovementfordomain-specificproblems415chapter16networkflow41916.1introduction.............................41916.2preliminaries............................41916.3theford-fulkersonmethod....................42316.4maximumcapacityaugmentation................42416.5shortestpathaugmentation...................42616.6dinic’salgorithm..........................42916.7thempmalgorithm.......................43116.8exercises..............................43416.9bibliographicnotes.........................436chapter17matching.............................43717.1introduction.............................43717.2preliminaries............................43717.3thenetworkflowmethod....................44017.4thehungariantreemethodforbipartitegraphs.......44117.5maximummatchingingeneralgraphs.............44317.6anoalgorithmforbipartitegraphs...........45017.7exercises..............................45517.8bibliographicnotes.........................457part7techniquesincomputationalgeometry459chapter18geometricsweeping46318.1introduction.............................46318.2geometricpreliminaries......................46518.3computingtheintersectionsoflinesegments.........46718.4theconvexhullproblem.....................47118.5computingthediameterofasetofpoints...........47418.6exercises..............................47818.7bibliographicnotes.........................480chapter19voronoidiagrams48119.1introduction.............................48119.2nearest-pointvoronoidiagram..................48119.2.1delaunaytriangulation..................484constructionofthevoronoidiagram...........48619.3applicationsofthevoronoidiagram...............48919.3.1computingtheconvexhull................48919.3.2allnearestneiors....................49019.3.3theeuclideanminimumspanningtree..........49119.4farthest-pointvoronoidiagram.................49219.4.1constructionofthefarthest-pointvoronoidiagram...49319.5applicationsofthefarthest-pointvoronoidiagram......49619.5.1allfarthestneiors...................49619.5.2smallestenclosingcircle..................49719.6exercises..............................49719.7bibliographicnotes.........................499bibliography.........................501index.........................511'pageviews',{name=>'info',data_block_encoding=>'none',bloomfilter=>'row',',min_versions=>'0',ttl=>'forever',keep_deleted_cells=>'false',
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