Lec21

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link rel=3DFile-List href=3D"lec21_files/filelist.xml"><link rel=3DPreview href=3D"lec21_files/preview.wmf"><link rel=3DEdit-Time-Data href=3D"lec21_files/editdata.mso"><link rel=3DOLE-Object-Data href=3D"lec21_files/oledata.mso"><title>Priority Queues</title><link rel=3DPresentation-XML href=3D"lec21_files/pres.xml"><meta name=3DDescription content=3D"3/18/2005: Binary Heaps"><meta http-equiv=3Dexpires content=3D0><![if !ppt]><script></script><![endif]></head>

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec21.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\D0F41271\lec21_files\master04.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DRobots content=3DNoIndex><link rel=3DStylesheet href=3D"master04_stylesheet.css"><![if !ppt]><script src=3Dscript.js></script><script></script><![endif]></head>

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<div v:shape=3D"_x0000_s106498" class=3DO style=3D'text-align:center;mso-ch=ar-wrap:1;mso-kinsoku-overflow:1'><span style=3D'font-family:Arial;font-size:50%;mso-field-code:meta15'>‹footer›</span><span style=3D'font-famil=y:Arial;font-size:50%;mso-special-format:lastCR'> </span></div>

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec21.htm"><link rel=3DPreview href=3Dpreview.wmf><title>Priority Queues</title><![if IE]><base href=3D"file:///C:\D0F41271\lec21_files\slide0127.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"3/18/2005: Binary Heaps"><link rel=3DStylesheet href=3D"master04_stylesheet.css"><![if !ppt]><style media=3Dprint></style><script src=3Dscript.js></script><script></script><![endif]><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"165"/></o:shapelayout></head>

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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#CCCCE6;clip:rect(=0%, 101%, 101%, 0%);visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#00007D,#000000,#9999FF,#9999CC,#666699,#CCCCE6" masterhref=3D"master04.xml"> <p:shaperange href=3D"master04.xml#_x0000_s106497"/><![if !ppt]><p:shapera=nge href=3D"master04.xml#_x0000_s106498"/><p:shaperange href=3D"master04.xml#_x0000_s106499"/> <div v:shape=3D"_x0000_s106499" class=3DO style=3D'text-align:right;mso-ch=ar-wrap: 1;mso-kinsoku-overflow:1;position:absolute;top:94.0%;left:72.65%;width:21.=53%; height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-fi=eld-code: meta16'>1</span><span style=3D'font-family:"Arial Black";font-size:50%; mso-special-format:lastCR;display:none'> </span></div> <p:shaperange href=3D"master04.xml#_x0000_s106500"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s106500,_x0000_s106501,_x0000_s106502,_x0000_s106503,_x=0000_s106504,_x0000_s106505,_x0000_s106506,_x0000_s106507,_x0000_s106508,_x=0000_s106509" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master04.xml#_x0000_s106512"/><![endif]><p:shaperange href=3D"master04.xml#_x0000_m106510"/><v:shape id=3D"_x0000_s168962" type==3D"#_x0000_m106510" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:108pt'

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec21.htm"><link rel=3DPreview href=3Dpreview.wmf><title>Priority Queues</title><![if IE]><base href=3D"file:///C:\D0F41271\lec21_files\slide0067.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"3/18/2005: Delete-min in a Heap (2)"><link rel=3DStylesheet href=3D"master04_stylesheet.css"><![if !ppt]><style media=3Dprint></style><style></style><script src=3Dscript.js></script><script></script><script></script><![endif]><o:shapelayout v:ext=3D"edit">

<o:idmap v:ext=3D"edit" data=3D"99"/></o:shapelayout></head>


<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#CCCCE6;clip:rect(=0%, 101%, 101%, 0%);visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#00007D,#000000,#9999FF,#9999CC,#666699,#CCCCE6" masterhref=3D"master04.xml"> <p:shaperange href=3D"master04.xml#_x0000_s106497"/><![if !ppt]><p:shapera=nge href=3D"master04.xml#_x0000_s106498"/><p:shaperange href=3D"master04.xml#_x0000_s106499"/> <div v:shape=3D"_x0000_s106499" class=3DO> <div style=3D'text-align:right;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:94.0%;left:72.65%;width:21.53%;height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-field-code:meta16'>4<=/span><span style=3D'font-family:"Arial Black";font-size:50%;mso-special-format:lastCR; display:none'> </span></div> </div> <p:shaperange href=3D"master04.xml#_x0000_s106500"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s106500,_x0000_s106501,_x0000_s106502,_x0000_s106503,_x=0000_s106504,_x0000_s106505,_x0000_s106506,_x0000_s106507,_x0000_s106508,_x=0000_s106509" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master04.xml#_x0000_s106512"/><![endif]><p:shaperange href=3D"master04.xml#_x0000_m106510"/><v:shape id=3D"_x0000_s101378" type==3D"#_x0000_m106510" style=3D'position:absolute;left:51.75pt;top:43.5pt;width:612pt;height:48.=875pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape> <div v:shape=3D"_x0000_s101378" class=3DT style=3D'position:absolute;top:9=.0%; left:8.23%;width:83.14%;height:7.75%'><span style=3D'font-size:90%'>Delete=-min in a Heap (2)</span></div> <p:shaperange href=3D"master04.xml#_x0000_m106511"/><v:shape id=3D"_x0000_=s101379" type=3D"#_x0000_m106511" style=3D'position:absolute;left:52.875pt;top:95.=375pt; width:612pt;height:122.875pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/><p:animation number=3D"2" de=lay=3D"0" type=3D"text" level=3D"1" effect=3D"cut" direction=3D"noBlack"/></v:shap=e> <div v:shape=3D"_x0000_s101379" class=3DB> <div id=3D"_x0000_s101379_0_47" style=3D'mso-line-spacing:"90 20 0";positi=on:absolute; top:18.25%;left:8.42%;width:94.0%;height:13.25%;white-space:nowrap'><span

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec21.htm"><link rel=3DPreview href=3Dpreview.wmf><link rel=3DOLE-Object-Data href=3Doledata.mso><title>Priority Queues</title><![if IE]><base href=3D"file:///C:\D0F41271\lec21_files\slide0068.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"3/18/2005: Building a heap"><link rel=3DStylesheet href=3D"master04_stylesheet.css"><![if !ppt]><style media=3Dprint></style><style></style><script src=3Dscript.js></script><script></script><![endif]><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"100"/></o:shapelayout></head>


<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#CCCCE6;clip:rect(=0%, 101%, 101%, 0%);visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#00007D,#000000,#9999FF,#9999CC,#666699,#CCCCE6" masterhref=3D"master04.xml"> <p:shaperange href=3D"master04.xml#_x0000_s106497"/><![if !ppt]><p:shapera=nge href=3D"master04.xml#_x0000_s106498"/><p:shaperange href=3D"master04.xml#_x0000_s106499"/> <div v:shape=3D"_x0000_s106499" class=3DO> <div style=3D'text-align:right;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:94.0%;left:72.65%;width:21.53%;height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-field-code:meta16'>5<=/span><span style=3D'font-family:"Arial Black";font-size:50%;mso-special-format:lastCR; display:none'> </span></div> </div> <p:shaperange href=3D"master04.xml#_x0000_s106500"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s106500,_x0000_s106501,_x0000_s106502,_x0000_s106503,_x=0000_s106504,_x0000_s106505,_x0000_s106506,_x0000_s106507,_x0000_s106508,_x=0000_s106509" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master04.xml#_x0000_s106512"/><![endif]><v:line id=3D"_x0000_s102=404" style=3D'position:absolute;flip:x;v-text-anchor:middle' from=3D"609.5pt,4=05.125pt" to=3D"634.375pt,472.625pt" strokecolor=3D"#bf0f18"> <v:shadow color=3D"#00007d [2]"/> </v:line><v:oval id=3D"_x0000_s102442" style=3D'position:absolute;left:590=.875pt; top:459.125pt;width:31.125pt;height:33.875pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"white [0]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><p:shaperange href=3D"master04.xml#_x0000_m106510"/><v:shape id==3D"_x0000_s102402" type=3D"#_x0000_m106510" style=3D'position:absolute;left:36pt;top:36pt;wi=dth:9in; height:58.75pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master04.xml#_x0000_m106511"/><v:shape id=3D"_x0000_s102403" type==3D"#_x0000_m106511" style=3D'position:absolute;left:34.875pt;top:103.375pt;width:542pt;height=:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/>

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href=3D"master04.xml#_x0000_m106510"/><v:shape id=3D"_x0000_s112642" type==3D"#_x0000_m106510" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:59pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master04.xml#_x0000_m106511"/><v:shape id=3D"_x0000_s112643" type==3D"#_x0000_m106511" style=3D'position:absolute;left:18.875pt;top:102.375pt;width:289.125pt; height:385.125pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape><v:line id=3D"_x00=00_s112644" style=3D'position:absolute;flip:x;v-text-anchor:middle' from=3D"623.125pt=,361.75pt" to=3D"9in,429.25pt" strokecolor=3D"#bf0f18"> <v:shadow color=3D"#00007d [2]"/> </v:line><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s112644" src=3D"slide0072_image030.gif" style=3D'position:absolute;top:67.0%;left:8=6.51%; width:3.93%;height:13.0%'><![endif]> <div v:shape=3D"_x0000_s112642" class=3DT style=3D'position:absolute;top:8=.25%; left:5.99%;width:88.2%;height:8.5%'>Heap Sort</div> <div v:shape=3D"_x0000_s112643" class=3DB> <div style=3D'position:absolute;top:20.0%;left:3.55%;width:39.13%;height:6=.75%'><span style=3D'position:absolute;top:0%;left:9.56%;width:90.43%;height:100.0%'><=span class=3DBB style=3D'position:absolute;left:-10.58%;top:.3em'>¨</span>C=reate a heap. </span></div> <span style=3D'position:absolute;top:28.5%;left:7.3%;width:34.64%;height:6=.75%'><span class=3DBB style=3D'position:absolute;left:-10.81%;top:.3em'>¨</span>Do delete-min </span><span style=3D'position:absolute;top:35.75%;left:7.3%; width:34.64%;height:6.75%'>repeatedly till </span><span style=3D'position:=absolute; top:42.75%;left:7.3%;width:35.2%;height:6.75%'>heap becomes </span><span style=3D'position:absolute;top:49.75%;left:7.3%;width:34.64%;height:6.75%'=>empty. </span><span style=3D'position:absolute;top:58.5%;left:7.3%;width:41.01%;height:6.75%'>=<span class=3DBB style=3D'position:absolute;left:-9.13%;top:.3em'>¨</span>To= do an in place </span><span style=3D'position:absolute;top:65.5%;left:7.3%;width=:34.64%; height:6.75%'>sort, we move </span><span style=3D'position:absolute;top:72=.5%; left:7.3%;width:38.01%;height:6.75%'>deleted element </span><span style=3D'position:absolute;top:79.75%;left:7.3%;width:35.76%;height:6.75%'=>to end of heap.</span></div> <v:oval id=3D"_x0000_s112645" style=3D'position:absolute;left:604.5pt;top:=415.75pt; width:31.125pt;height:33.875pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"white [0]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s112645" src=3D"slide0072_image031.gif" style=3D'position:absolute;top:77.0%;left:8=

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<div class=3DN1><span style=3D'font-family:Times;mso-ascii-font-family:Time=s'>Secondlevel </span></div>

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<o:lock v:ext=3D"edit" grouping=3D"t"/> <p:placeholder type=3D"footer" position=3D"4" size=3D"quarter"/></v:shapet=ype>

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------=_NextPart_01C52BA1.54A585B0Content-Location: file:///C:/D0F41271/lec21_files/script.jsContent-Transfer-Encoding: quoted-printableContent-Type: application/javascript; charset="us-ascii"

function LoadSld(){

var sld=3DGetObj("SlideObj")if( !g_supportsPPTHTML ) {

sld.style.visibility=3D"visible"return

}if( MakeNotesVis() ) returnrunAnimations =3D _InitAnimations();if( IsWin("PPTSld") )

parent.SldUpdated(GetSldId())g_origSz=3DparseInt(SlideObj.style.fontSize)g_origH=3Dsld.style.posHeightg_origW=3Dsld.style.posWidthg_scaleHyperlinks=3D(document.all.tags("AREA").length>0)if( g_scaleHyperlinks )

InitHLinkArray()if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) )

document.body.scroll=3D"no"_RSW()if( IsWin("PPTSld") && parent.IsFullScrMode() )

FullScrInit();=09

MakeSldVis();ChkAutoAdv()

if( runAnimations ){

if( document.all("NSPlay") )document.all("NSPlay").autoStart =3D false;

if( sld.filters && sld.filters.revealtrans )setTimeout( "document.body.start()",

sld.filters.revealtrans.duration * =1000 );

elsedocument.body.start();

}}function MakeSldVis(){

var fTrans=3Dg_showAnimation && SldHasTrans()if( fTrans ){

if( g_bgSound ) {idx=3Dg_bgSound.indexOf(",");pptSound.src=3Dg_bgSound.substr( 0, idx );pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1)));

}SlideObj.filters.revealtrans.Apply()

}SlideObj.style.visibility=3D"visible"if( fTrans )

SlideObj.filters.revealtrans.Play()

}function MakeNotesVis(){

if( !IsNts() ) return falseSlideObj.style.display=3D"none"nObj =3D document.all.item("NotesObj")parent.SetHasNts(0)if( nObj ) {

nObj.style.display=3D""parent.SetHasNts(1)

}return 1

}function ChkAutoAdv(){

if(SldHasTrans())SlideObj.onfilterchange=3DAutoAdv

elseAutoAdv()

}function AutoAdv(){

if(!IsWin("PPTSld") || !gUseSldTimings )returnvar sld=3DGetCurSld()if( (sld.mAdvDelay>0) && !parent.IsFramesMode() )

setTimeout("parent.GoToNextSld()",sld.mAdvDelay)}function GetObj(id){

if(g_supportsPPTHTML) return document.all(id);else return document.getElementById(id);

}function SldHasTrans() { return SlideObj.style.getAttribute("filter")!=3D""= }function GetSldId() { return sId=3Dlocation.href.substring(location.href.la=stIndexOf('/')+1) }function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx=tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl=e.display=3D'none'; return true } return false }function IsWin( name ) { return window.name =3D=3D name }function IsNts() { return IsWin("PPTNts") }function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) }function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) }function SupportsPPTHTML(){

var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0if( msie >=3D 0 )

ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) )

elsever=3DparseInt(appVer)

return( ver >=3D 4 && msie >=3D 0 )}function _RSW(){

if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) )

return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6

cltWidth=3Ddocument.body.clientWidth-paddingcltHeight=3Ddocument.body.clientHeight-paddingfactor=3D(1.0*cltWidth)/g_origW

if( cltHeight < g_origH*factor )factor=3D(1.0*cltHeight)/g_origH

newSize =3D g_origSz * factorif( newSize < 1 ) newSize=3D1s=3DSlideObj.styles.fontSize=3DnewSize+"px"s.posWidth=3Dg_origW*factors.posHeight=3Dg_origH*factors.posLeft=3D(cltWidth-s.posWidth+padding)/2s.posTop=3D(cltHeight-s.posHeight+padding)/2if( g_scaleHyperlinks )

ScaleHyperlinks( factor )}function _InitAnimations(){

animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined';isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode();g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !

(isFullSc=reen && parent.IsSldVisited());

if( g_animUseRuntime ) {collSeq =3D document.all.tags("seq");if( collSeq !=3D null ) {

for(ii=3D0;ii<collSeq.length;ii++) {if( collSeq[ii].getAttribute( "p:nodeType" ) =3D=3D

"mainSeq" ) {g_animMainSequence =3D collSeq[ii];break;

}}

}if( g_animItemsToHide ) {

for(jj =3D 0; jj < g_animItemsToHide.length; jj++) {if( hideObj =3D GetObj(g_animItemsToHide[jj]) )

hideObj.runtimeStyle.visibility=3D"hidden";}

}if( g_animInteractiveItems ){

for(jj =3D 0; jj < g_animInteractiveItems.length; jj++) {if( triggerObj =3D GetObj(g_animInteractiveItems[jj]) )

triggerObj.runtimeStyle.cursor=3D"hand";}

}if( gUseSldTimings && ''+g_animSlideTime !=3D 'undefined' ) {

adjustedTime =3D document.body.calculateAutoAdvanceTimes( g_animSlideTim=e, g_animEffectTimings );

if( IsWin("PPTSld") && adjustedTime !=3D g_animSlideTime ) { var sld =3D GetCurSld(); sld.mAdvDelay =3D adjustedTime * 1000;}

}}return g_animUseRuntime;

}gSldJump =3D 0, gSldJumpTrack =3D 0, gSldJumpIdx =3D "";function _KPH(){

if( IsNts() ) return;if( !parent.IsFramesMode() && event.keyCode =3D=3D 27 && !HideMenu() )

parent.window.close( self );else if( event.keyCode =3D=3D 32 ) {

if( window.name =3D=3D "PPTSld" )parent.PPTSld.DocumentOnClick();

elseparent.GoToNextSld();

}CatchNumKeys( parent, event );

}function CatchNumKeys( win, event ) {

if( win.IsFullScrMode() && (48<=3Devent.keyCode) && (event.keyCode<=3D57) =) {

gSldJump =3D 1;gSldJumpIdx +=3D (event.keyCode-48).toString();

}if( win.IsFullScrMode() && gSldJump && event.keyCode =3D=3D 13 ) {

var numSlds =3D parent.GetSldList().mList.lengthif ( gSldJumpIdx > numSlds )

gSldJumpIdx =3D numSlds;if ( gSldJumpIdx >=3D 0 ) {

if ( gSldJumpIdx =3D=3D 0 )gSldJumpIdx =3D 1;

var jumpTo =3D parseInt(gSldJumpIdx);gSldJump =3D 0; gSldJumpIdx =3D "";win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )

}}

}function _KDH(){

if( event.keyCode =3D=3D 8 ) {event.returnValue =3D 0;parent.GoToPrevSld();

}}function DocumentOnClick(){

if( IsNts() || parent.HideMenu() ) return;if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !

parent.IsFrames=Mode() ) ||

(event && event.keyCode=3D=3D32) ) {if( g_animUseRuntime && g_animMainSequence &&

g_animMainSequence.cangonex=t )

return;parent.GoToNextSld();

}}

var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""=, g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser ==3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1;var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w=indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va=r g_animManager =3D null;var g_animUseRuntime =3D false;var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;var g_animMainSequence =3D null;var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram=es", gIsEndShow=3D0, NUM_VIS_SLDS=3D11, SCRIPT_HREF=3D"script.js", FULLSCR_=HREF=3D"fullscreen.htm";var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO=tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D truewindow.gPPTHTML=3DSupportsPPTHTML()var gMainDoc=3Dnew Array(new hrefList("slide0127.htm",1,-1,1),new hrefList(=

"slide0082.htm",1,-1,1),new hrefList("slide0066.htm",1,-1,1),new hrefList("=slide0067.htm",1,-1,1),new hrefList("slide0068.htm",1,-1,1),new hrefList("s=lide0087.htm",1,-1,1),new hrefList("slide0088.htm",1,-1,1),new hrefList("sl=ide0128.htm",1,-1,1),new hrefList("slide0089.htm",1,-1,1),new hrefList("sli=de0072.htm",1,-1,1),new hrefList("slide0129.htm",1,-1,1));function FullScrInit(){

g_allowAdvOnClick =3D GetCurSld().mAdvOnClkdocument.body.style.backgroundColor=3D"black"document.oncontextmenu=3Dparent._CM;document.onkeydown =3D _KDH;document.ondragstart=3DCanceldocument.onselectstart=3DCancelself.focus()

}function Redirect( frmId ){

var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId()if(idx>=3D0) str=3Dstr.substr(1);if( window.name !=3D frmId && ( sId !=3D str) ) {

obj =3D GetObj("Main-File")window.location.href=3Dobj.href+"#"+sIdreturn 1

}return 0

}var MHTMLPrefix =3D CalculateMHTMLPrefix();function CalculateMHTMLPrefix(){

if ( document.location.protocol =3D=3D 'mhtml:') {href=3Dnew String(document.location.href)Start=3Dhref.indexOf('!')+1End=3Dhref.lastIndexOf('/')+1if (End < Start)

return href.substring(0, Start)elsereturn href.substring(0, End)

}return '';

}function GetTags(base,tag){

if(g_supportsPPTHTML) return base.all.tags(tag);else return base.getElementsByTagName(tag);

}function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP=refix+GetHrefObj( gCurSld ).mNtsHref ) }function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }function SetHasNts( fVal ){

if( gHasNts !=3D fVal ) {gHasNts=3DfValUpdNavPane()

}}function ToggleOtlText(){

gOtlTxtExp=3D!gOtlTxtExpUpdOtlPane()

}function ToggleOtlPane(){

frmset=3Ddocument.all("PPTHorizAdjust")frm=3Ddocument.all("PPTOtl")if( gOtlOpen )

frmset.cols=3D"*,100%"else

frmset.cols=3D"25%,*"gOtlOpen=3D!gOtlOpenfrm.noResize=3D!frm.noResizeUpdOtNavPane()

}function ToggleNtsPane(){

frmset=3Ddocument.all("PPTVertAdjust")frm=3Ddocument.all("PPTNts")if( gNtsOpen )

frmset.rows=3D"100%,*"else

frmset.rows=3D"*,20%"gNtsOpen=3D!gNtsOpenUpdNtsPane()

}function ClearMedia(){

if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0;}function FullScreen(){

if ( PPTSld.g_animUseRuntime )PPTSld.document.body.pause();

ClearMedia();var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF

=: FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;

if(PPTNav.event.ctrlKey) {var w =3D (window.screen.availWidth * 1.0) / 2.0var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origWwin =3D

window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top==3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h );

if( PPTSld.g_animUseRuntime )win.document.body.PPTSldFrameset=3Dwindow;

}else{

win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" );if( PPTSld.g_animUseRuntime )

win.document.body.PPTSldFrameset=3Dwindow;}

}function ToggleVNarration(){

rObj=3DPPTSld.document.all("NSPlay")if( rObj && !PPTSld.g_animUseRuntime ) {

if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) )rObj.Play()

else if( rObj.playState =3D=3D 2 )rObj.Pause()

elsereturn;

}else if( PPTSld.g_animUseRuntime ){

narObj =3D PPTSld.document.all("narrationID")if( narObj )

narObj.togglePause()}

}function GetCurSldNum(){

obj=3DGetHrefObj(gCurSld)if( obj.mOrigVis =3D=3D 1 )

return obj.mSldIdxelse

return gCurSld}function GetNumSlds(){

if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )return GetSldList().mNumVisSlds;

elsereturn GetSldList().mList.length

}function GetSldNum( href ){

for(ii=3D0; ii<GetSldList().mList.length; ii++) {if ( GetSldList().mList[ii].mSldHref =3D=3D href )

return ii+1}return 1

}function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] }function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) }function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) }function GoToNextSld(){

ii=3DgCurSld + 1if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) {

if( ii<=3DGetSldList().mList.length ) {obj=3DGetHrefObj(ii)obj.mVis=3D1GoToSldNum(ii)return

}}else {

obj=3DGetHrefObj( ii )while ( obj && ( obj.mOrigVis =3D=3D 0 ) )

obj=3DGetHrefObj(++ii)if( obj && obj.mOrigVis ) {

GoToSldNum(ii)return

}}if( gSldStack.length > 1 )

PopSldList();else if( !IsFramesMode() ) {

if( gLoopCont )GoToFirst()

elseEndShow()

}}function GoToPrevSld(){

ii=3DgCurSld-1if( ii > 0 ) {

obj=3DGetHrefObj(ii)while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )

obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1

GoToSldNum(ii)}

}function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }function GoToLast(){

ii=3DGetSldList().mList.lengthif( ii !=3D gCurSld )

GoToSld( GetHrefObj(ii).mSldHref )}function GoToSldNum( num ){

if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrueobj =3D GetHrefObj( num )obj.mVis=3D1gPrevSld=3DgCurSldgCurSld =3D num;PPTSld.location.replace(MHTMLPrefix+obj.mSldHref)if( IsFramesMode() ) {

UpdNavPane(); UpdOtlPane(); UpdNtsPane()}

}function GoToSld( href ){

if( PPTSld.event ) PPTSld.event.cancelBubble=3DtrueGetHrefObj( GetSldNum(href) ).mVis=3D1PPTSld.location.replace(MHTMLPrefix+href)

}function SldUpdated( id ){

if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) returngPrevSld=3DgCurSldgCurSld=3DGetSldNum(id)if( IsFramesMode() ) {

UpdNavPane(); UpdOtlPane(); UpdNtsPane()}

}function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO=bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }function CloseWindow() {

if( HideMenu() ) return;var event =3D PPTSld.event;if( !IsFramesMode() && event && (event.keyCode=3D=3D27 ||

event.keyCode=3D==3D32 || event.type=3D=3D"click" ) )

window.close( self );CatchNumKeys( self, event );

}function Unload() { gIsEndShow=3D0; }function SetupEndShow() {

gIsEndShow=3D1;PPTSld.document.body.scroll=3D"no";PPTSld.document.onkeypress=3DCloseWindow;PPTSld.document.onclick=3DCloseWindow;PPTSld.document.oncontextmenu=3D_CM;

}function EndShow(){

if( IsFramesMode() ) returnif( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue

doc=3DPPTSld.documentdoc.open()doc.writeln('<html><body bgcolor=3Dblack onload=3Dparent.SetupEndShow()

on=unload=3Dparent.Unload()><center><p><font face=3DTahoma color=3Dwhite size==3D2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></body></html>')

doc.close()}function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue }function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited }function hrefList( sldHref, visible, advDelay, advClk ){

this.mSldHref=3D this.mNtsHref =3D sldHrefthis.mOrigVis=3D this.mVis =3D visiblethis.mVisited=3D falsethis.mAdvDelay=3D advDelaythis.mAdvOnClk=3D advClk

}function SldList(arr,curSld,fEnd){

this.mCurSld =3D curSld;this.mList =3D new Array();var idx =3D 1;for(ii=3D0;ii<arr.length;ii++) {

this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[=ii].mAdvDelay, arr[ii].mAdvOnClk );

if( arr[ii].mOrigVis )this.mList[ii].mSldIdx =3D idx++;

}this.mNumVisSlds =3D idx-1;this.fEndShow =3D fEnd;

}function GetSldList() { return gSldStack[gSldStack.length-1] }function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1]= }gSldStack =3D new Array();gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1)function ViewCustomShow(idx,fEnd){

if( !IsFullScrMode() ) return;var sldList =3D new Array();var custShow =3D custShowList[idx-1];var jj =3D 0;for( ii=3D0;ii<custShow.length;ii++ ) {

if( custShow[ii] <=3D gMainDoc.length )sldList[jj++] =3D gMainDoc[custShow[ii]-1];

}if (sldList.length > 0) {PushSldList(sldList,fEnd);gCurSld =3D 1;}else

if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue}function PushSldList(arr,fEnd) {

var ii =3D gSldStack.length;gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);GoToSld( gSldStack[ii].mList[0].mSldHref );

}function PopSldList() {

if (gSldStack[gSldStack.length-1].fEndShow)EndShow()

else {

gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;gSldStack[gSldStack.length-1] =3D null;gSldStack.length--;var sldList =3D gSldStack[gSldStack.length-1];GoToSld( sldList.mList[gCurSld - 1].mSldHref );}

}var custShowList=3Dnew Array();function ImgBtn( oId,bId,w,action ){

var t=3Dthist.Perform =3D _IBPt.SetActive =3D _IBSetAt.SetInactive=3D _IBSetIt.SetPressed =3D _IBSetPt.SetDisabled=3D _IBSetDt.Enabled =3D _IBSetEt.ChangeIcon =3D nullt.UserAction =3D actiont.ChgState =3D _IBUIt.mObjId =3D oIdt.mBorderId=3D bIdt.mWidth =3D wt.mIsOn =3D t.mCurState =3D 0

}function _IBSetA(){

if( this.mIsOn ) {obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )obj.style.posTop=3D0

}}function _IBSetI(){

if( this.mIsOn ) {obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )obj.style.posTop=3D0

}}function _IBSetP(){

if( this.mIsOn ) {obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )obj.style.posLeft+=3D1; obj.style.posTop+=3D1

}}function _IBSetD(){

obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )obj.style.posTop=3D0

}function _IBSetE( state ){

var t=3DthisGetObj( t.mBorderId ).style.visibility=3D"visible"if( state !=3D t.mIsOn ) {

t.mIsOn=3Dstateif( state )

t.SetInactive()else

t.SetDisabled()}

}function _IBP()

{var t=3Dthisif( t.mIsOn ) {

if( t.UserAction !=3D null )t.UserAction()

if( t.ChangeIcon ) {obj=3DGetObj(t.mObjId)if( t.ChangeIcon() )

obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth

elseobj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-

0)*t.mWidth}t.SetActive()

}}function _IBUI( clr1,clr2,nextState ){

var t=3DthisSetBorder( GetObj( t.mBorderId ),clr1,clr2 )obj=3DGetObj( t.mObjId )obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-

obj=.style.posTop

t.mCurState=3DnextStatereturn obj

}function TxtBtn( oId,oeId,action,chkState ){

var t=3Dthist.Perform =3D _TBPt.SetActive =3D _TBSetAt.SetInactive=3D _TBSetIt.SetPressed =3D _TBSetPt.SetDisabled=3D _TBSetDt.SetEnabled =3D _TBSetEt.GetState =3D chkStatet.UserAction =3D actiont.ChgState =3D _TBUIt.mObjId =3D oIdt.m_elementsId=3D oeIdt.mIsOn =3D 1

}function _TBSetA(){

var t=3Dthisif( t.mIsOn && !t.GetState() )

t.ChgState( gHiliteClr,gShadowClr,0,0 )}function _TBSetI(){

var t=3Dthisif( t.mIsOn && !t.GetState() )

t.ChgState( gFaceClr,gFaceClr,0,0 )}function _TBSetP(){

if( this.mIsOn )this.ChgState( gShadowClr,gHiliteClr,1,1 )

}function _TBSetD(){

this.ChgState( gFaceClr,gFaceClr,0,0 )

this.mIsOn =3D 0}function _TBSetE(){

var t=3Dthisif( !t.GetState() )

t.ChgState( gFaceClr,gFaceClr,0,0 )else

t.ChgState( gShadowClr,gHiliteClr,1,1 )t.mIsOn =3D 1

}function _TBP(){

var t=3Dthisif( t.mIsOn ) {

if( t.UserAction !=3D null )t.UserAction()

if( !t.GetState ) return

if( t.GetState() )t.SetPressed()

elset.SetActive()

}}function _TBUI( clr1,clr2,lOffset,tOffset ){

SetBorder( GetObj( this.mObjId ),clr1,clr2 )Offset( GetObj( this.m_elementsId ),lOffset,tOffset )

}function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=ft }function SetBorder( obj, upperLeft, lowerRight ){

s=3Dobj.style;s.borderStyle =3D "solid"s.borderWidth =3D 1s.borderLeftColor =3D s.borderTopColor =3D upperLefts.borderBottomColor=3D s.borderRightColor =3D lowerRight

}function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }function BtnOnUp(){

b=3DGetBtnObj()if( b !=3D null )

b.Perform()else

Upd()}function GetNtsState(){ return parent.gNtsOpen }function GetOtlState(){ return parent.gOtlOpen }function GetOtlTxtState(){ return parent.gOtlTxtExp }function NtsBtnSetFlag( fVal ){

s=3Ddocument.all.item( this.m_flagId ).styles.display=3D"none"if( fVal )

s.display=3D""else

s.display=3D"none"}

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<table style=3D'position:relative' align=3Dcenter cellpadding=3D0 cellspaci=ng=3D0> <td> <div style=3D'position:absolute;left:-18px;width:24px;height:20px;border-s=tyle: solid;border-width:1px;border-color:threedface' id=3D"nb_otlTxtBorder"> <div style=3D'position:absolute;clip:rect(0px, 22px, 18px, 0px)'><img src=3Dbuttons.gif id=3D"nb_otlTxt" title=3D"Expand/Collapse Outline" style=3D'position:relative;left:-157px'></div> </div> </td></table>

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<table width=3D"100%" style=3D'font-family:Arial;font-size:9pt'> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>1</font></div> </td> <td width=3D"100%"> <div id=3DPPTP1 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0127.htm');" id=3DPPTL1>Binary Heaps</a>=</font></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Delete-min</li> <li>Building a heap in O(n) time</li> <li>Heap Sort</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>2</font></div> </td> <td> <div id=3DPPTP2 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0082.htm');" id=3DPPTL2>Delete-min</a></=font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The minimum element is the one at the top of the heap.</li> <li>We can delete this and move one of its children up to fill the space=.</li> <li>Empty location moves down the tree.</li> <li>Might end up at any position on last level.</li> <li>Resulting tree would not be left filled.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>3</font></div> </td> <td> <div id=3DPPTP3 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0066.htm');" id=3DPPTL3>Delete-min in a =Heap</a></font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>This is not a heap</li> </ul> </font></div> </td> </tr>

<tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>4</font></div> </td> <td> <div id=3DPPTP4 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0067.htm');" id=3DPPTL4>Delete-min in a =Heap (2)</a></font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Replace top element with last element of heap.</li> <li>Heapify(1)</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>5</font></div> </td> <td> <div id=3DPPTP5 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0068.htm');" id=3DPPTL5>Building a heap<=/a></font></div> <div id=3DPPTC5 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>We start from the bottom and move up</li> <li>All leaves are heaps to begin with</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>6</font></div> </td> <td> <div id=3DPPTP6 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0087.htm');" id=3DPPTL6>Building a Heap: Analysis</a></font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Correctness: induction on i, all trees rooted at m > i are heaps<=/li> <li>Running time: n calls to Heapify =3D n O(lg n) =3D O(n lg n)</li> <li>We can provide a better O(n) bound.</li> <ul> <li>Intuition: for most of the time Heapify works on smaller than n ele=ment heaps</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'>

<td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>7</font></div> </td> <td> <div id=3DPPTP7 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0088.htm');" id=3DPPTL7>Building a Heap: Analysis (2)</a></font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>height of node: length of longest path from node to leaf</li> <li>height of tree: height of root</li> <li>time for Heapify(i) =3D O(height of subtree rooted at i)</li> <li>assume n =3D 2<sup>k</sup> – 1 (a complete binary tree)</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>8</font></div> </td> <td> <div id=3DPPTP8 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0128.htm');" id=3DPPTL8>Building a heap: Analysis (3)</a></font></div> <div id=3DPPTC8 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>For the n/2 nodes of height 1, heapify() requires at most 1 swap eac=h.</li> <li>For the n/4 nodes of height 2, heapify() requires at most 2 swaps ea=ch.</li> <li>For the n/2<sup>i</sup> nodes of height i, heapify() requires at mos=t i swaps each.</li> <li>So total number of swaps required is</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>9</font></div> </td> <td> <div id=3DPPTP9 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0089.htm');" id=3DPPTL9>Building a Heap: Analysis (4)</a></font></div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>How? By using the following "trick"</li> <br> <br> <br> <br> <br> <br> <br> <br> <br> <li>Therefore Build-Heap time is O(n)</li>

</ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>10</font></div> </td> <td> <div id=3DPPTP10 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0072.htm');" id=3DPPTL10>Heap Sort</a></=font></div> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Create a heap.</li> <li>Do delete-min repeatedly till heap becomes empty.</li> <li>To do an in place sort, we move deleted element to end of heap.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>11</font></div> </td> <td> <div id=3DPPTP11 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0129.htm');" id=3DPPTL11>Running times o=f heap operations</a></font></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Insert: O(log n)</li> <li>Heapify: O(log n)</li> <li>Find minimum: O(1)</li> <li>Delete-min: O(log n)</li> <li>Building a heap: O(n)</li> <li>Heap Sort: O(nlog n)</li> </ul> </font></div> </td> </tr></table>

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