AVLTREES文档格式.docx

AVLTREES文档格式.docx

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balanceFactor=height（right-subtree）-height（left-subtree）

IfbalanceFactorisnegative,thenodeis"

heavyontheleft"

sincetheheightoftheleftsubtreeisgreaterthantheheightoftherightsubtree.WithbalanceFactorpositive,thenodeis"

heavyontheright."

AbalancednodehasbalanceFactor=0.

Figure2describesthreeAVLtreeswithtags-1,0,or+1oneachnodetoindicateitsbalance-factor（relativeheightoftheleftandrightsubtrees）.

-1:

heightoftheleftsubtreeisonegreaterthantherightsubtree.

0:

heightoftheleftandrightsubtreesareequal.

+1:

heightoftherightsubtreeisonegreaterthantheleftsubtree.

FIGURE2

AVLtreeswithbalance-factorofeachnodeinparentheses

TheavlTreeNodeclassissimilartothetnodeclassforbinarysearchtrees.Fourpublicdatamembersincludethedatavalue,theleftandrightpointers,andthebalancefactor.TheconstructorisusedtocreateanodeforanAVLtreeandinitializethedatamembers.

DECLARATION:

avlTreeNodeCLASS

//declaresatreenodeobjectforabinarytree

template<

typenameT>

classavlTreeNode

{

public:

//datainthenode

TnodeValue;

//pointerstotheleftandrightchildrenofthenode

avlTreeNode<

T>

*left;

*right;

intbalanceFactor;

//CONSTRUCTOR

avlTreeNode（constT&

item,avlTreeNode<

*lptr=NULL,

avlTreeNode<

*rptr=NULL,intbal=0）:

nodeValue（item）,left（lptr）,right（rptr）,balanceFactor（bal）

{}

};

2TheavlTreeClass

TheavlTreeclasswiththesameprogrammer-interfaceusedbythestree.Theclasshasbothconstantandnon-constantiterators,whichcanbeusedtoscanthelistofelements.Anon-constantversionissuppliedsothataprogramcanusethedeferenceoperator*toupdatethedatavalueofanode.ThisfeaturecanbeusedwhentheAVLtreesstoresrecordswithakeyandotherdatavaluesandtheupdatemodifiesonlythedatavalues.Anattempttoupdatethekeycoulddestroythestructureofthetree.

LikeBinSTreeiterators,AVLiteratorsareforwarditeratorsbutwithanimportantlimitation.Sinceatreemayneedtoberebalancedwhenanitemisaddedorremoved,theinsert（）anderase（）operationsinvalidatealliterators.Tobeusedagain,theiteratorsmustberesettothestartofthelistwithbegin（）.

Thefollowingisadeclarationoftheprogrammer-interfacefortheavlTreeclass.Weimplementonlytheinsert（）methodanddonotdiscusstheerase（）methods.Themethodclear（）isaddedtoremoveallofthenodesinthetree.Inthestreeclass,clearisexecutedbycallingerase（）withtheiteratorrange[begin（）,end（））.ThememorymanagementfunctionsarenotincludedWewillexpandthedeclarationtoincludetheprivatememberfunctionswhenwediscusstheimplementationoftheclass.

avlTreeCLASS（Programmer-Interface

classavlTree

//CONSTRUCTORS,DESTRUCTOR,ASSIGNMENT

//constructor.initializeroottoNULLandsizeto0

avlTree（）;

//constructor.insertnelementsfromrangeofT*pointers

avlTree（T*first,T*last）;

//searchforitem.iffound,returnaniteratorpointing

//atitinthetree;

otherwise,returnend（）

iteratorfind（constT&

item）;

const_iteratorfind（constT&

item）const;

//indicatewhetherthetreeisempty

intempty（）const;

//returnthenumberofdataitemsinthetree

intsize（）const;

//giveaverticaldisplayofthetree.

voiddisplayTree（intmaxCharacters）const;

//insertitemintothetree

//pair<

iterator,bool>

insert（constT&

//insertanewnodeusingthebasicListoperationandformat

pair<

//deleteallthenodesinthetree

voidclear（）;

//constantversions

iteratorbegin（）;

iteratorend（）;

const_iteratorbegin（）const;

const_iteratorend（）const;

ThefunctiondisplayTree（）issimilartodisplayTree（）inthestreeclass.Itincludesboththelabelandthebalance-factorforeachnodeintheformat<

label>

:

<

balanceFactor>

EXAMPLE1

TheexampleillustratestheuseoftheavlTreeoperations.

1.DeclareanavlTreeobjectavltreeAthatstoresintegersandanobjectavlTreeBthatstoresrealnumberswithinitialvaluesfromarrayarrB.

//avlTreeAisemptytreeofintegers

avlTree<

int>

avlTreeA;

//avlTreeBisatreeofrealswith6initialvalues

doublearrB[6]={2.8,3.9,-2.0,4.9,8.6,-12.8};

avlTree<

double>

avltreeB（arrB,arrB+6）;

2.AloopinitializesavlTreeAwithintegers0to9.ThetreeisdisplayedwithdisplayTree（）

for（i=1;

i<

10;

i++）

avlTreeA.insert（i）;

avlTreeA.displayTree

（2）;

3:

1

1:

07:

02:

05:

08:

4:

06:

09:

3.Determinewhether8.6and1.6areelementsinavlTreeB.

avlTree<

:

iteratordblIter;

if（（dblIter=avlTreeB.find（8.6））!

=avlTreeB.end（））

cout<

<

"

Element"

*dblIter

isanelementinAVLtree"

endl;

if（（dblIter=avlTreeB.find（1.6））==avlTreeB.end（））

Element1.6isnotanelementinAVLtree"

Solution:

Element8.6isanelementinAVLtree

Element1.6isnotanelementinAVLtree

3Application:

UpdatingCharacterCounts

AnAVLtreeismosteffectiveinsituationswherethedatastaticallyresidesinthetreeandtheapplicationprimarilysearchesforitemsandupdatestheirvalue.AsimpleexampledeclaresobjectsoftypecharCountthatcontainacharacteranditsfrequency（count）asdatamembers.Theclasshasaconstructorthatwithacharargumentthatinitializesthedatamemberandsetsthecountto1.Theclassalsoprovidesoverloadedversionsofthecomparisonoperators<

and==alongwithoverloadedversionofthe<

operator.ThecomparisonoperatorsallowcharCounttobeusedasthetemplatetypeforavlTreeobjectsandtheirimplementationcomparesonlyatthecharvalueoftheoperands.The<

operatoroutputsthecharacteranditscountintheform<

char>

（<

count>

）.

Intheexample,wecountthenumberofoccurrencesoftheletters'

a'

to'

z'

inthe25000+worddictionary"

words.dat"

.Foreachcharacterinthedictionary,wesearchforthecorrespondingcharCountobjectandupdatethecountusingthememberfunctionincCount（）.

charCountCLASS

//objectcontainscharacteranditsfrequency（count）

classcharCount

//initializecharacterandcountwithcount=1

charCount（charch）;

//overloadedcomparisonoperators

friendbooloperator<

（constcharCount&

a,constcharCount&

b）;

friendbooloperator==（constcharCount&

//overloadedoutputandincrementoperators

friendostream&

operator<

（ostream&

ostr,constcharCount&

cc）;

//incrementthecountmemberoftheobject

voidincCount（）;

private:

charcharacter;

intcount;

PROGRAM1COUNTINGLETTERS

TheprogramillustratestheAVLtreesearchefficiencybydeclaringanavlTree<

charCount>

objectandaniterator.Aloopinputswordsinthedictionary"

charct.dat"

asst