622
Index
Completebinarytrees,247,254
Completegraphs,380
Compoundinterestrulein
recursion,11
Compression
file,453
path,360–371
Computationalgeometry
individeandconquerstrategy,
468
turnpikereconstruction,
506–511
Computationalmodels,54
computeAdjacentWords
function,
178–180
Congruentialgenerators,496,
499
Connectedgraphs,380
Connectivity
biconnectedgraphs,421
electrical,351
undirectedgraphs,420–421
Consecutivestatementsinrunning
time,58
const
keyword,18
const_iterators
,83–86,92–93,
96–97
Constantgrowthrate,53
Constantmemberfunctions,
15–16
Constantreference
parameterpassingby,26
returningvaluesby,25
Constructors,13
copy,31,141
defaultparameters,13
explicit,15
foriterators,82–83
formatrices,44–45
Containers,80–81,83.Seealso
Lists;Queues;Stacks
contains
function
forbinarysearchtrees,135
forbinarysearches,68
forhashtables,196,200,
205–206
fortop-downsplaytrees,563
continue
reservedword,132
Contradiction,proofsby,7–8
Convergentseries,4
Conversions
infixtopostfix,108–110
type,14
Convexhulls,523
Convexpolygons,523
Cook,S.,436,446
Cook’stheorem,436
Copiesforvectors,89
Coppersmith,D.,529
copy-and-swapidiom,34
Copyassignmentoperators,31–33
forbinarysearchtrees,141
formatrices,46
Copyconstructors,24
foriterators,77
formatrices,39
copy
function,45
Copying
matrices,45
shallowanddeep,32–33
Costs,graphedges,379
Counterexample,proofsby,7
Countersinmergesorts,304–305
Countingradixsort,332–336
countingRadixSort
method,334
Crane,C.A.,288,289
createSuffixArray
routines,
593–599
Criticalpaths,404
Crossedges,429
Cryptography
gcdalgorithmin,71
primenumbersfor,503–504
Cubicgrowthrate,53
Cuckoohashing,215–217,
222–224,226
CuckooHashTable
class,221–227
Culberson,J.,189,190
Culik,K.,190
Currentnodesforlists,92
Cuttingnodesinleftistheaps,
542–544
D
d-heaps,260–261
DAGs(directedacyclicgraphs),
379–380
Datamembersformatrices,44–45
Day,A.C.,613
Deapqueues,288
Decisiontrees
forlowerbounds,323–325
referencesfor,348
Declaring
objects,18
pointers,21
decltype,86,294
decreaseKey
function
forbinaryheaps,254
forbinomialqueues,278
forDijkstra’salgorithm,399
forFibonacciheaps,542–544,
548–551
forpairingheaps,602–606
Deepcopies
vs.shallow,32
forvectors,87
Defaults
forconstructorparameters,
13–14
problemswith,33–35
Definitions,recursionin,9
delete
function
forbinarysearchtrees,141
forlists,100
Deleteoperations
2-dtrees,549–552
AVLtrees,144–158
binaryheaps,247–257
binarysearchtrees,67–68,126,
132–144
binomialqueues,271–281,535
d-heaps,260–261
destructorswith,23–24
Fibonacciheaps,399–400
hashtables,194–196
heapsorts,273–274
leftistheaps,261–268,543
linkedlists,73–74
lists,72,85,87,92–93
multiwaymerges,338–339
pairingheaps,258,553–559,
563
pointers,19–20
priorityqueues,245–283
red-blacktrees,566–576
sets,165–166
skewheaps,269–271
skiplists,459–461
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Index
623
splaytrees,158–166
treaps,576–579
vectors,28,86–91
deleteKey
function,254
deleteMax
function,300,301,303
deleteMin
function
binaryheaps,251–253
binomialqueues,271–276
d-heaps,260–261
Dijkstra’salgorithm,391–400
Fibonacciheaps,548–549
heapsorts,273–274
Huffmanalgorithm,453–459
Kruskal’salgorithm,417–419
leftistheaps,261–268,543
multiwaymerges,338–339
pairingheaps,258,553–559,
563
priorityqueues,245–283
skewheaps,269–271
Demers,A.,529
Densegraphs,404,417,491
Deo,N.,446
Depth-firstsearches,419–420
biconnectedgraphs,421–425
directedgraphs,429–430
Eulercircuits,425–429
forstrongcomponents,431–432
undirectedgraphs,420–421
Depthoftrees,122
Dequeswithheaporder,557
Dequeue operations,113,
115,245
Dereferencingpointers,398
Descendantsintrees,122
Designruleinrecursion,11
Destructors,30–31
forbinarysearchtrees,139–140
formatrices,46
Devroye,L.,242
dfs
function,420
Diamonddequeues,288
Dictionaries,recursionin,10
Dietzfelbinger,M.,243
Digraphs,379
all-pairsshortestpathsin,
491–494
depth-firstsearches,429–430
representationof,380–382
Dijkstra,E.W.,48
dijkstra
function,398–399
Dijkstra’salgorithm,391–400
forall-pairsshortestpaths,
491–494
andPrim’salgorithm,414–417
timeboundimprovementsfor,
541–542
Dimensionsfork-dtrees,602
Diminishingincrementsorts.
SeeShellsort
Ding,Y.,289,613
Dinic,E.A.,446
Directedacyclicgraphs(DAGs),
379–380
Directededges,121
Directedgraphs,379–380
all-pairsshortestpaths in,
491–494
depth-firstsearches,429–430
representationof,380–382
Directories
inextendiblehashing,233–236
treesfor,123,125
Disjointsets,351–374
dynamicequivalenceproblem
in,352–353
equivalencerelationsin,351
formazegeneration,372–374
pathcompressionfor,360–371
referencesfor,376–377
smartunionalgorithmsfor,
357–359
structureof,353–357
worstcase analysis for
union-by-rankapproach,
361–372
DisjSets
class,355–356,359,361,
419
DiskI/Ooperations
inextendiblehashing,233–236
andrunningtimes,57–70
insorting,291
Distances,closestpointsproblem,
470–475
Divideandconquerstrategy,305,
467–482
closestpointsproblem,470–475
components,427–428
integermultiplication,478–480
matrixmultiplication,480–482
maximumsubsequencesum,
60–66
inmergesorts,304–309
quicksort.SeeQuicksort
runningtimeof,468–470
selectionproblem,475–478
Dor,D.348,529
Dosa,G.,529
Doublehashing,207–208
Doublerotationoperations,
149–158
doubleWithLeftChild
function,
155,157
Doublylinkedlists,80–81,91–93,
100–101,117,128,196
Doyle,J.,377
drand48
function,499
Dreyfus,S.E.,528
Driscoll,J.R.,289
Du,H.C.,243
Due,M.W.,289
Dumey,A.I.,243
dumpContents
function,282
Duplicateelementsinquicksorts,
295
Dynamicequivalenceproblem,
352–353
Dynamicobjects,22
Dynamicprogramming,482–494
all-pairsshortestpath,491–494
optimalbinarysearchtrees,
487–491
orderingmatrixmultiplications,
485–487
referencesfor,527
tablesvs.recursion,483–485
E
Eckel,B.,48
Edelsbrunner,H.,529
Edges
indepth-firstsearches,
429–430
graph,379–380
tree,121
Edmonds,J.,446
Eightqueensproblem,525
Eisenbath,B.,190
Electricalconnectivity,351
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624
Index
Employee
class,198–199,239
empty
function
forcontainers,81
formaps,174
forpriorityqueues,282
forsets,173
forvectors,91–92
Emptylists,78
Enbody,R.J.,243
end
function
foriterators,82,85–86,90
forlists,94
formaps,174
forsets,173
#endif
preprocessor,16,18,45,
616
Enqueueoperations,113–115
Eppinger,J.L.,190
Eppstein,D.,529
Equivalenceindisjointsets,
352–353
erase
function
foriterators,83
forlists,93,95,100–101
formaps,174
Eraseoperations.SeeDelete
operations
Eriksson,P.,290
Euclideandistance,470
Euclid’salgorithmrunningtime,
68–69
Eulercircuits,425–429
Euler’sconstant,5,189,321
eval
function,526–527
Even,S.,446
Event-nodegraphs,402
Eventsimulation,259–260
Explicitconstructors,15
Explicitinstantiation,616–618
Exponentialgrowthrate,52,
60
Exponentsandexponentiation
formulasfor,3
runningtimefor,69–70
Expressiontrees,128–131
Extendiblehashing,233–236
Externalsorting,336–341
algorithm,336,337–338
modelfor,336
needfor,336
referencesfor,348
replacementselectionin,
340–341
F
Factorials,recursionfor,59
Fagin,R.,243
Farach,M.,613
Fermat’slessertheorem,504
fib
function,483
fibonacci
function,483
Fibonacciheaps,399–400
cuttingnodesinleftistheaps,
542–544
forDijkstra’salgorithm,400
lazymergingforbinomial
queues,544–548
operations,548–549
forpriorityqueues,288
timeboundprooffor,549–551
Fibonaccinumbers
inpolyphasemerges,340
proofsfor,6
recursionfor,59–60,482–485
Filecompression,453
Fileservers,115
Findoperations.SeealsoSearches
biconnectedgraphs,421–425
binaryheaps,249–257
binarysearchtrees,175–176
binomialqueues,271–281
disjointsets,351–374
hashtables,205–206
lists,78–79
maps,174
shortest-pathalgorithms,
365–366
top-downsplaytrees,563
findArt
function,425
findChain
function,406
findCompMove
function,513,
515–516
findHumanMove
function,513,515
findKth
operations,79
findMax
function,22
forbinarysearchtrees,132–133,
136–137
forfunctionobjects,41–43
templatefor,37–38
fortop-downsplaytrees,563
findMin
function,135–136,193,
249
forbinaryheaps,248–249
forbinarysearchtrees,137
forbinomialqueues,277
forleftistheaps,265
fortop-downsplaytrees,563
findMinIndex
function,277,
280–281
findNewVertexOfIndegreeZero
function,383–384
findPos
function,204,206,220
Firstfitalgorithm,462–463
Firstfitdecreasingalgorithm,
464–465
Fischer,M.J.,377,531
Flajolet,P.,190,243,613
Flamig,B.,613
flip
function,521
Floyd,R.W.,289,348,529
forloopsinrunningtime,67,515
Ford,L.R.,348,446
Forests
forbinomialqueues,271
indepth-firstspanning,422
fordisjointsets,354
forKruskal’salgorithm,416
Forwardedges,429
Fotakis,D.,243
Fredman,M.L.,243,289,377,
446,529,558,612,613
Friedman,J.H.,613
frienddeclarations,96
Frieze,A.,243
front
function,81,93
Fulkerson,D.R.,446
Fullnodes,183–184
Fulltrees,455
Fuller,S.H.,191
Functionobjects,41–42
Functiontemplates,37–38
Functionsandfunctioncalls
member,12
recursive,8–9,484
stacksfor,111–114
Fussenegger,F.,348
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Index
625
G
Gabow,H.N.,289,348,377,446
Gajewska,H.,558
Galambos,G.,528
Galil,Z.,446,528,529
Galler,B.A.,377
Games,511
alpha-betapruning,513–517
hashtablesfor,237
minimaxalgorithm,511–514
Garbagecollection,22
Garey,M.R.,446,529
gcd
(greatestcommondivisor)
function,51,68
General-purpose sorting
algorithms,291,309,331
Geometricseries,4
getChainFromPrevMap
function,406
getName
function,199
Giancarlo,R.,529
Globaloptimums,449
Godbole,S.,529
Goldberg,A.V.,446
Golin,M.,348
Gonnet,G.H.,190,243,289,348
Graham,R.L.,48,529
Grandchildrenintrees,122
Grandparentsintrees,122
Graph
class,398–399
Graphs,379–437
bipartite,439
breadth-firstsearches,389
coloring,436
definitionsfor,379–382
depth-firstsearches.See
Depth-firstsearches
k-colorable,442
minimumspanningtree,
413–419
multigraphs,442
network flowproblems,
406–413
NP-completeness,432–436
planar,400
referencesfor,445–448
representationof,380–382
shortest-pathalgorithmsfor
acyclicgraph,400–404
allpairs,404
Dijkstra’salgorithm,391–400
example,404–405
negativeedgecosts,400
singlesource,385–387
unweighted,388–393
topologicalsortsfor,382–385
travelingsalesman,522
Greatestcommondivisor(GCD)
function,51,68
Greedyalgorithms,449–467
approximatebinpacking.See
Approximatebinpacking
forcoinchangingproblem,451
Dijkstra’salgorithm,392
Huffmancodes,453–459
Kruskal’salgorithm,416–418
maximum-flowalgorithms,409
minimumspanningtree,
413–419
processorscheduling,450–453
Gries,D.,48
Growthrateoffunctions,52–54
Gudes,E.,190
Guibas,L.J.,191,243,613
Gupta,R.,529
Gusfield,D.,613
H
.h
files,16
Hagerup,T.,446
Haken,D.,528
Haltingproblems,433
Hamiltoniancycle,429,434–436
Han,Y.,529
handleReorient
function,570
Harary,F.,446
Harmonicnumbers,5
Harries,R.,243
hash
classtemplate,197–199
hash
function,194–196
hash_map
function,233
hash_set
function,233
Hashtables,193
Carter-Wegmantrick,233
cuckoohashing,215–217,
222–224,226
doublehashingin,207–208
extendiblehashing,233–236
hashfunction,194–196
hopscotchhashing,227–230
linearprobingin,201–203
overview,193–195
perfecthashing,213–215
quadraticprobingin,202–206
referencesfor,242–243
rehashingfor,208–210
separatechainingfor,196–200
inStandardLibrary,210–212
universalhashing,230–233
Hasham,A.,289
HashEntry
class,204–205
HashTable
class,197,205–206,
222,241
headerfiles,16–17
Headerinformation,compilation
of,616
Headernodesforlists,92,563
Heaporder,dequeswith,557
Heap-orderproperty,248–249
Heaps
2-d,610
binary.SeeBinaryheaps
leftist.SeeLeftistheaps
pairing,602–606
priority.SeePriorityqueues
skew,269–271
Heapsort
analysis,303–305
comparing,306
implementation,300–303
referencesfor,347
heapsort
function,302–303
Heavynodesinskewheaps,540
Heightoftrees,122
AVL,154
binarytreetraversals,167
completebinary,247
Hibbard,T.H.,191,348
Hibbard’sincrements,298–299
Hidinginformation,12
Hirschberg,D.S.,530
Hoare,C.A.R.,348,475
Hoey,D.,531
Homometricpointsets,521,528
Hopcroft,J.E.,76,190,377,445,
446,447
Hopscotchhashing,227–230
Horvath,E.C.,348
Hu,T.C.,529
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626
Index
Huang,B.,348
Huffman,D.A.,529
Huffmancodes,453–459
Hulls,convex,523
Hutchinson,J.P.,48
Hypothesesininduction,6–7
I
if/elsestatementsinrunning
time,59
Implementation/interface
separation,16–18
Implicittypeconversions
withconstructors,15
Impossibleproblems,433
Incerpi,J.,348
#include
preprocessor,16
increaseKey
function,254
IncrementsequencesinShellsorts,
296–300
Indegreesofvertices,382–383
Inductiveproofs
process,6–7
recursionin,10–11
Infiniteloop-checkingprograms,
433
Infixtopostfixconversion,
108–110
Informationhiding,12
Information-theoreticlower
bounds,325
Inheritanceforlists,93
init
function,95,98–99
Initializationlistforconstructors,
14
Inordertraversal,129,166
Inputsizeinrunningtime,56–58
insert
functionandinsert
operations
2-dtrees,599–601
AVLtrees,144–158
doublerotation,149–158
singlerotation,158–160
B-trees,168–173
binaryheaps,249–257
binarysearchtrees,132–135,
137–138
binarysearches,68
binomialqueues,273–275,277,
534–539
d-heaps,260–261
extendiblehashing,22
Fibonacciheaps,547,551
hashtables,196–197,199,207
Huffmanalgorithm,459
iterators,83
leftistheaps,262–263,265
linkedlists,79–80
lists,78,92,93,100–101
maps,174
multiwaymerges,338
pairingheaps,602,605
priorityqueues,245–246
red-blacktrees,567–568,
574–575
sets,173–174
skewheaps,253,541
skiplists,502–503
splaytrees,161–163,563,565
treaps,576–579
Insertionsorts,292–295
algorithm,292–293
analysis,294–295
implementation,293–294
insertionSort
function,293–294,
317,322,343
Instantiation,explicit,616–618
IntCell
class
constructorsfor,12–15
defaultsfor,31–34
interface/implementation
separationin,15–17
pointersin,21–23
Integers
greatestcommondivisorsof,
69–70
multiplying,478–479
Interface/implementation
separation,16–18
Internalpathlengths,141
Inversioninarrays,295–296
isActive
function,204
isEmpty
function
forbinaryheaps,248
forbinarysearchtrees,133
forbinomialqueues,277
forleftistheaps,265
fortop-downsplaytrees,563
isLessThan
function,41
Isomorphictrees,188
isPrime
function,505
Iteratedlogarithm,362
Iterators,82
const_iterator
,84–86
forcontaineroperations,83
erase
,84
getting,82
forlists,82–83
formaps,174–175
methodsfor,82–83
forsets,173–174
stale,118
Iyengar,S.S.,613
J
Janson,S.,349
Jiang,T.,349
Johnson,D.B.,289,447
Johnson,D.S.,446,529
Johnson,S.M.,348
Jonassen,A.T.,191
Jones,D.W.,614
Josephusproblem,117
K
k-colorablegraphs,442
k-dtrees,596–601
Kaas,R.,290
Kaehler,E.B.,191
Kahn,A.B.,447
Kane,D.,242
Karatsuba,A.,529
Karger,D.R.,447,529
Karlin,A.R.,242
Karlton,P.L.,191
Karp,R.M.,243,377,446,447
Kärkkäinen,J.,614
Karzanov,A.V.,447
Kasai,T.,614
Kayal,N.,528
Kernighan,B.W.,48,447
KevinBaconGame,444
Keys
inhashing,193–196
formaps,174–178
Khoong,C.M.,289,558
King,V.,447
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Index
627
Kirsch,A.,243
Kishimoto,A.,531
Kittenpuzzle,534
Klein,P.N.,447
Knapsackproblem,436
Knight’stour,525
Knuth,D.E.,48,49,76,191,243,
289,349,377,447,530
Ko,P.,614
Komlos,J.,243
Korsh,J.,529
Kruskal,J.B.,Jr.,447
kruskal
function,418–419
Kruskal’salgorithm,417–419
Kuhn,H.W.,447
Kurtz,S.,613
L
Labelsforclassmembers,12
Ladner,R.E.,289
Lajoie,J.,49
Lake,R.,531
LaMarca,A.,289
Landau,G.M.,530
Landis,E.M.,144,190
Langston,M.,348
LaPoutre,J.A.,377
Larmore,L.L.,530
Lastin,firstout(LIFO)lists.See
Stacks
Lawler,E.L.,447
Lazybinomialqueues,545–546
Lazydeletion
AVLtrees,156
binarysearchtrees,140
hashtables,204
leftistheaps,286
lists,118–119
Lazymerging,542
binomialqueues,544–548
Fibonacciheaps,542
Leavesintrees,122
Lee,C.C.,531
Lee,D.T.,531,614
Lee,G.,614
Lee,K.,530
leftChild
function,277–278,281,
302,304,604–606
Leftistheaps,261–268,543
cuttingnodesin,542–544
mergingwith,266–267
pathlengthsin,261–262
referencesfor,287
skewheaps,266–270
LeftistHeap
class,265–266
LeftistNode
structure,265
Lehmer,D.,496
Lelewer,D.A.,530
Lemke,P.,531
Lempel,A.,531
Length
inbinarysearchtrees,141
graphpaths,379
treepaths,122
Lenstra,H.W.,Jr.,530
Leong,H.W.,289,558
Level-ordertraversal,168
Lewis,T.G.,243
L’Hôpital’srule,53
Li,M.,349
Liang,F.M.,530
LIFO(lastin,firstout)lists.See
Stacks
Lightnodesinskewheaps,540
Limitsoffunctiongrowth,53
Lin,S.,447
Linearcongruentialgenerators,
496,499–500
Linear-expected-timeselection
algorithm,321–323
Lineargrowthrate,53–54
Linearprobing,201–202,209
Linearworst-casetimeinselection
problem,475
Linkedlists,79–80
circular,119
priorityqueues,246
skiplists,499–501
stacks,104
Lippman,S.B.,49
List
class,91–94
listAll
function,124
Lists,78
adjacency,381
arraysfor,78–79
implementationof,91–102
linked.SeeLinkedlists
queues.SeeQueues
skip,500–503
stacks.SeeStacks
inSTL,80–81
vectorsfor.SeeVectors
Loadfactorofhashtables,203
Localoptimums,449
Log-squaredgrowthrate,53
Logarithmicgrowthrate,53
Logarithmicrunningtime,66
forbinarysearches,66–68
forEuclid’salgorithm,70–71
forexponentiation,69–70
Logarithms,formulasfor,3,
66–70,362
Longestcommonprefix(LCP),
581–586,594
Longestcommonsubsequence
problem,529
Longestincreasingsubsequence
problem,524
Look-aheadfactorsingames,514
Loops
graph,379
inrunningtime,56
Lowerbounds,323–328
offunctiongrowth,52
maximumandminimum,
328–331
selection,325–328
forsorting,295–296
Lu,P.,531
Lueker,G.,243
lvalue,23–24,26–29,31
lvaluereference,23–24,26,28
M
M-arysearchtrees,169
Mahajan,S.,530
Mainmemory,sortingin,291
Majorityproblem,75
makeEmpty
function
forbinaryheaps,248
forbinarysearchtrees,133,
140–141
forbinomialqueues,277
forhashtables,196,200,206
forleftistheaps,265
forlists,78
fortop-downsplaytrees,563,
566
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628
Index
makeLCPArray
,609
Manacher,G.K.,349
Manber,U.,614
map
class,121
Maps
example,176–181
forhashtables,193–194
implementation,175–176
operations,174–175
Margalit,O.,528
Marsaglia,G.,530
Martin,W.A.,614
Mathematicsreview,2–8
foralgorithmanalysis,51–54
exponents,3
logarithms,3
modulararithmetic,5–6
proofs,6–8
recursion,7–11
series,4–5
Matrices,44
adjacency,380–381
datamembers,constructors,and
accessorsfor,44
destructors,copyassignment,
andcopyconstructorsfor,
46
multiplying,379–382,
484–487
operator[]
for,44–46
matrix
class,44–45,89
Matsumoto,M.,530
Maurer,W.D.,243
max-heaps,300–301
Maximumandminimum,
328–331, 345,
348,557
Maximum-flowalgorithms,
408–413
Maximumsubsequencesum
problem
analyzing,54–56
runningtimeof,60–68
MAXITgame,526–527
Mazegeneration,372–374
McCreight,E.M.,190,614
McDiarmid,C.J.H.,289
McElroy,M.D.,348
McKenzie,B.J.,243
Median-of-median-of-five
partitioning,476–477,
519
Median-of-threepartitioning,313,
316
median3
function,316–317,322
Medians
samplesof,475
inselectionproblem,258
Melhorn,K.,190,191,242,
445,447
Melsted,P.,243
Memberfunctions,12
constant,15
signaturesfor,16
Memory
address-ofoperatorfor,23
incomputationalmodels,54
sortingin,291
forvectors,87
Memoryleaks,22,33,36
MemoryCell
class
compilationof,615–618
templatefor,37–38
merge
functionandmerge
operations
binomialqueues,277–280,
534–539
d-heaps,260
Fibonacciheaps,542,550
leftistheaps,261–267
mergesorts,307
pairingheaps,602–604
skewheaps,539–541
mergeSort
function,306
analysisof,306–309
externalsorting,337–340
implementationof,303–305
multiway,338–339
polyphase,339–340
referencesfor,347
MersenneTwister,500
Methods,12
Meyers,S.,49
Miller,G.L.,530
Miller,K.W.,530
Min-costflowproblems,
413,445
min-heaps,283
Min-maxheaps,285,288
Minimaxalgorithm,511–514
Minimumspanningtrees,
412–413,522
Kruskal’salgorithm,416–417
Prim’salgorithm,414–417
referencesfor,444
Mitzenmacher,M.,242,243
Modulararithmetic,5–6
Moffat,A.,558
Molodowitch,M.,243
Monier,L.,530
Moore,J.S.,242
Moore,R.W.,530
Moret,B.M.E.,447,614
Morin,P.,242
Morris,J.H.,243
Motwani,R.,530
moveassignmentoperator,30–31,
33,35
moveconstructor,30–32,34–35,
87
Müller,M.,531
Mulmuley,K.,530
Multigraphs,442
Multiplying
integers,478–479
matrices,479–482,484–487
Multiprocessorsinscheduling
problem,451–452
Multiwaymerges,338–339
Munro,J.I.,190,289,529
Musser,D.R.,49,349
Mutatorfunctions,15
Myers,G.,614
myHash
function,198,220
N
Naor,M.,242
Negative-costcycles,386–387
Negativeedgecosts,400
Ness,D.N.,614
Nestedloops inrunning
time,58
Networkflow,406–413
maximum-flowalgorithm,
408–413
referencesfor,444
Networks,queuesfor,115
new
operator
Index
629
forpointers,21–22
forvectors,87
Newlinecharacters,454–455
Nextfitalgorithm,461–462
Nievergelt,J.,191,243,614
Nishimura,T.,530
Node
classforlists,92–93,96
Nodes
binarysearchtrees,132–133
binomialtrees,534
decisiontrees,323
expressiontrees,128
leftistheaps,262–264,542–544
linkedlists,79–80
lists,91–92
pairingheaps,600
red-blacktrees,567
skewheaps,540–541
splaytrees,551,560
treaps,576
trees,121–122
Nondeterministicalgorithms,408
Nondeterminism,434
Nonpreemptivescheduling,450
Nonprintablecharacters,453
Nonterminatingrecursive
functions,9
NP-completeness,432
easyvs.hard,433–434
NPclass,434
referencesfor,445
traveling salesman
problem,434-436
Nullpathsinleftistheaps,
261–262,264
nullptr
,132
Null-terminatorcharacters,36
numcols
function,46
numrows
function,46
O
Objecttype,174
Objects,12
declaring,18
dynamic,21–22
function,41–43
passing,23–24
Odlyzko,A.,190
Off-linealgorithms
approximatebinpacking,
464–467
disjointsets,352
Ofman,Y.,529
Ohlebush,E.,613
On-linealgorithms
approximatebinpacking,
460–461
definition,65
disjointsets,352
One-dimensionalcirclepacking
problem,522
One-parametersetoperations,
173–174
oneCharOff
function,178–179
Operandsinexpressiontrees,128
Operators
inexpressiontrees,128–131
operator!=
function
hashtables,199–200
lists,96–97
operator()
function,41–43
operator
*
function
lists,96–98
matrices,479–480
operator++
function,96–98
operator<
function
in
Comparable
type,39
in
Square
,39–40
sets,174
operator<<
function,39–40
operator=
function,31–33
binarysearchtrees,133,
141–142
binomialqueues,277
in
Employee
,39
iterators,82
leftistheaps,265
lists,98–99
red-blacktrees,571
top-downsplaytrees,563
vectors,87–88
operator==
function
hashtables,199–200
lists,96–97
operator[]
function
lists,81
maps,174–175
matrices,44–46
vectors,81,87,90
overloading,39,41
Optimalbinarysearchtrees,
487–491
optMatrix
function,488
Order
binaryheaps,247–248
matrixmultiplications,
485–487
Orlin,J.B.,445,447
O’Rourke,J.,530
Orthogonalrangequeries,598,
612
Othellogame,527
Ottman,T.,190
Overflow
inB-trees,172
inhashfunction,196
stack,111–112
Overloadingoperators,40–41,44,
82–83,85,96
Overmars,M.H.,378,614
P
Pagh,R.,243
pair
class
formaps,174
forsets,164
Pairingheaps,288,602–606,
611
Pan,V.,530
Papadakis,T.,565
Papadimitriou,C.H.,447
Papernov,A.A.,349
Paragraphs,right-justifying,
523–524
Parameters
default,12–13
passing,23–24
template,36
Parentheses
[( )]
balancing,104–105
forpostfixconversions,108–110
Parentsintrees,121–123
Park,K.,614
Park,S.K.,530
Parsetrees,181
Partialfind,364
Partialmatchqueries,598
partialSum
function,27–29,58
630
Index
Partitions
in2-dtrees,611
inquicksorts,311,313–316
inselectionproblem,476–478
Passingparameters,25–26
Patashnik,O.,48
Paths
augmenting,408–413
binarysearchtrees,141
compression,360–371
indirectorystructures,123–127
graph,379
halving,376
leftistheaps,261–262,263
shortest.SeeShortestpath
algorithms
intrees,122
P˘atra¸scu,M.,243
Patternmatchingproblem,
524–525
percDown
function,302
percolateDown
function,255–257
Percolationstrategies
forbinaryheaps,249–257
forheapsorts,302
Perfecthashing,213–215
Perlis,A.J.,191
Peterson,W.W.,244
Pettie,S.,530,614
PhasesinShellsorts,295–296
Pippenger,N.,243
Pivotsinquicksorts,311–313,476
place
function,510–511
Planargraphs,441,445
Planepartitionsin2-dtrees,611
Plauger,P.J.,48
Plaxton,C.G.,349
Plies,514
Poblete,P.V.,289
Pohl,I.,349
Pointers,22–23
inbinarysearchtrees,132–133
forlists,91
operationsfor,22–23
Points,closest,470–475
Polygons,convex,523
Polyphasemerges,339–340
Poonen,B.,349
pop
function
forpriorityqueues,283
forstacks,102–104
pop_back
function
forlists,81,96
forstacks,104
forvectors,81,87,90–91
pop_front
function
forlists,81,93,98
forvectors,81
Port,G.,558
Positionoflistelements,78
Positive-costcycles,402
Postfixexpressions,105–107
infixconversionto,108–110
stacksfor,105–107
Postordertraversal,125–126,129,
166–167,431
Potentialfunctions,537–539
costsof,555
forsplaytrees,553
pow
(power)functions,69–70
Pratt,V.R.,243,349,529
Prefixcodes,455
Preordertraversal,124,129,167
Preparata,F.P.,531
Preprocessorcommands,16–18
Prim,R.C.,447
Prim’salgorithm,414–417
Primaryclusteringinhashtables,
201,202,207
Primenumbers
probabilityof,70–71
proofsfor,8
SieveofEratosthenesfor,74
testsfor,503–506
Primetablesizeforhashtables,
204
print
function
in
Square
,39–40
foriterators,84–85
Printablecharacters,453
printCollection
function,173
printHighChangeables
function,
212
Printing
queuesfor,115
recursionfor,10,110–111
printList
function,79
printOut
function,10
printPath
function,398
printRange
function,601
printTree
function
forbinarysearchtrees,133
forbinarytrees,166–167
forred-blacktrees,570–571
fortop-downsplaytrees,563
priority_queue
class,282–283
Priorityqueues,245–283
binaryheapsfor.SeeBinary
heaps
d-heaps,260–261
forDijkstra’salgorithm,399
forheapsorts,299–303
inHuffmanalgorithm,459
implementationsof,246
leftistheaps,261–268
modelfor,245–246
referencesfor,288
forselectionproblem,258–259
forsimulation,259–260
skewheaps,269–271
inStandardLibrary,282–283
Prioritysearchtrees,612
private
labels,12
Probabilitydistributionfunctions,
116,259,502
Probinginhashtables
linear,201–202
quadratic,202–207
Processorschedulingproblem,
450–453
Progressinrecursion,9,11
Proofs,6–7,10–11
Properancestorsintrees,122
Properdescendantsintrees,
122
Pruning
alpha-beta,514–518
inbacktrackingalgorithms,504
Pseudorandomnumbers,495
public
labels,12
Puech,C.,613
Pugh,W.,531
Puglisi,S.J.,614
push
functions
forpriorityqueues,282
forstacks,103–105
push_back
function
forlists,81,93
forstacks,104
forvectors,81,87,90–91
Index
631
push_front
function
forlists,81,93
forvectors,81
Q
Quadtrees,611
Quadrangleinequality,520
Quadraticgrowthrate,53
Quadraticprobing
inhashtables,203,206–207
forrehashing,210–211
Queriesfor2-dtrees,600–601
Queueingtheory,116
Queues
applications,115–116
arrayimplementation,113–115
binomial.SeeBinomialqueues
forbreadth-firstsearches,391
forlevel-ordertraversal,167
modelfor,113
priority.SeeBinaryheaps;
Priorityqueues
simulating,259–260
fortopologicalsorts,384–385
Quickselect algorithm
implementation,321–322
runningtime,475–476
Quicksort
algorithm,309–310
analysis,318–321
arraysize,315–316
partitionsin,313–315
pivotsin,311–313
referencesfor,348
routinesfor,315–316
forselectionproblem,321–322
quicksort
function,317–318
R
Rabin,M.O.,243,531
Radixsort,331–336
radixSort
method333,335
Raghavan,P.,530
Ramachandran,V.,530
Ramanan,P.,531
Random
class,498–499
Randomcollisionsinhashtables,
202
Randomnumbergenerators
creating,495–499
referencesfor,527–528
Randompermutationgenerators,
78,339
Randompivotselections,313,
318,495
random0_1
function,498
randomInt
function,28,184,
498–499,578
Randomizedalgorithms,494–506
primalitytests,503–506
randomnumbergenerators,
495–500
skiplists,500–503
range
for
loop,21,25,177
Rangequeries,598
Ranks
binomialtreenodes,534
forFibonacciheaps,550
inpathcompression,361–367
forsplaytrees,552,554
Rao,S.,446,447
Ratesoffunctiongrowth,52–54
read
function
in
IntCell
,12–13,18
in
MemoryCell
,39
reclaimMemory
function
forleftistheaps,265
fortop-downsplaytrees,563
Recurrencerelations
inmergesorts,306–309
inquicksorts,318–321
Recursion,8–11
binarysearchtrees,134
depth-firstsearches,420
divideandconquerstrategy.
SeeDivideandconquer
strategy
exponentiation,69–70
induction,11–12
leftistheaps,263
maximumsubsequencesum
problem,63–67
mergesorts,305–309
pathcompression,360–361
printing,10,111–112
quicksort,315
red-blacktrees,570
runningtime,59–60
selectionproblem,475–478
skewheaps,269–271
stackoverflowfrom,111–112
vs.tables,482–484
treedefinitions,121
treetraversals,166–167
Recursivelyundecidableproblems,
433
Red-blacktrees,566–576
bottom-upinsertion,567–568
referencesfor,189
top-downdeletion,568–570
top-downinsertion,570–576
RedBlackTree
class,570
Reed,B.A.,289
Reference
parameterpassingby,23
returningvaluesby,24
Referencevariables,24–25,198
Reflexiverelations,351
Regionsin2-dtrees,611
Registersforvariables,110
rehash
function,199,220,224
Rehashing,208–210,225
Reingold,E.M.,191,614
Relationsindisjointsets,351
Relativegrowthratesoffunctions,
53
Relativeprimenumbers,
probabilityof,70–71
Relaxedheaps,288
Remainderfunction,5
remove
function
binaryheaps,254
binarysearchtrees,132,
134–135,138–139
binomialqueues,278
Fibonacciheaps,542
hashtables,197,198,205,207
SplayTree,566
top-downsplaytrees,563
treaps,597
Removeoperations.SeeDelete
operations
removeEveryOtherItem
function,84
Replacementselectioninexternal
sorting,340–341
reserve
function,81,87–88,89
Residualedges,408
Residualgraphs,408
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