Lec23

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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"lec23_files/filelist.xml"><link rel=3DPreview href=3D"lec23_files/preview.wmf"><link rel=3DEdit-Time-Data href=3D"lec23_files/editdata.mso"><link rel=3DOLE-Object-Data href=3D"lec23_files/oledata.mso"><title>Priority Queues</title><link rel=3DPresentation-XML href=3D"lec23_files/pres.xml"><meta name=3DDescription content=3D"3/18/2005: More Sorting"><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"../lec23.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\D0F41273\lec23_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_s106503" class=3DO style=3D'mso-char-wrap:1;mso-kins=oku-overflow:1'><span style=3D'font-family:Arial;font-size:75%;color:#666699;mso-color-i=ndex:6;mso-special-format:lastCR'> </span></div>


<div v:shape=3D"_x0000_s106505" class=3DO style=3D'mso-char-wrap:1;mso-kins=oku-overflow:1'><span style=3D'font-family:Arial;font-size:75%;color:#9999CC;mso-color-i=ndex:5;mso-special-format:lastCR'> </span></div>



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1'><span style=3D'font-family:Arial;font-size:75%;color:#9999CC;mso-color-i=ndex:5;mso-special-format:lastCR'> </span></div>

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<div v:shape=3D"_x0000_m106510" class=3DT>Click to edit Master title style<=/div>

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<div class=3DB>Click to edit Master text styles </div>

<div class=3DB1>Second level </div>

<div class=3DB2>Third level </div>

<div class=3DB3>Fourth level </div>

<div class=3DB4>Fifth level</div>

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<div v:shape=3D"_x0000_s106512" class=3DO style=3D'mso-char-wrap:1;mso-kins=oku-overflow:1'><span lang=3DEN-US style=3D'font-family:Arial;font-size:50%;mso-field-co=de:meta0'>‹date/time›</span><spanstyle=3D'font-family:Arial;font-size:50%;mso-special-format:lastCR'> </=span></div>

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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:white;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'>13=</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_s180226" type==3D"#_x0000_m106510" style=3D'position:absolute;left:48pt;top:36pt;width:612pt;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"/> <p:placeholder type=3D"title"/></v:shape> <div v:shape=3D"_x0000_s180226" class=3DT style=3D'position:absolute;top:1=1.5%; left:7.67%;width:83.14%;height:7.75%'><span lang=3DEN-US style=3D'font-siz=e:90%; mso-ansi-language:EN-US'>Bucket Sort</span></div> <v:rect id=3D"_x0000_s180227" style=3D'position:absolute;left:24pt;top:168=pt; width:378pt;height:179.75pt' filled=3D"f" fillcolor=3D"#99f [4]" stroked==3D"f" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> <p:animation number=3D"1" delay=3D"0" type=3D"text" level=3D"2" effect=3D="dissolve" afterbuild=3D"dim" dimcolor=3D"rgb(217,87,193)"/><p:tag name=3D"___PPT20=01" type=3D"binary" datasize=3D"36" dataoffset=3D"31"/></v:rect> <div v:shape=3D"_x0000_s180227"> <div id=3D"_x0000_s180227_0_8" class=3DO style=3D'position:absolute;top:32=.0%; left:4.3%;width:50.74%;height:5.25%;white-space:nowrap'><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'><b>BASICS</b></span><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>: </span></div> <div id=3D"_x0000_s180227_8_18" class=3DO1 style=3D'position:absolute;top:=37.5%; left:9.36%;width:45.69%;height:5.25%;white-space:nowrap'><span lang=3DEN-US style=3D'color:#E63B32;mso-ansi-language:EN-US'><b>n numbers </b></spa=

n></div> <div id=3D"_x0000_s180227_18_49" class=3DO1 style=3D'position:absolute;top=:42.25%; left:9.36%;width:50.74%;height:5.75%;white-space:nowrap'><span lang=3DEN-US style=3D'color:#E63B32;mso-ansi-language:EN-US'><b>Each number </b></span>=<span lang=3DEN-US style=3D'font-family:Symbol;color:#E63B32;mso-ansi-language:E=N-US; mso-char-type:symbol'><b>Î</b></span><span lang=3DEN-US style=3D'col=or:#E63B32; mso-ansi-language:EN-US'><b> {1, 2, 3, ... m} </b></span></div> <div id=3D"_x0000_s180227_49_56" class=3DO1 style=3D'position:absolute;top=:48.0%; left:9.36%;width:45.69%;height:5.25%;white-space:nowrap'><span lang=3DEN-US style=3D'color:#E63B32;mso-ansi-language:EN-US'><b>Stable </b></span><=/div> <div id=3D"_x0000_s180227_56_73" class=3DO1 style=3D'position:absolute;top=:53.5%; left:9.36%;width:45.69%;height:5.25%;white-space:nowrap'><span lang=3DEN-US style=3D'color:#E63B32;mso-ansi-language:EN-US'><b>Time:<span style=3D'mso-spacerun:yes'> </span>O (n + m) </b></span></div> <div id=3D"_x0000_s180227_73_110" class=3DO style=3D'position:absolute;top=:58.75%; left:4.3%;width:58.8%;height:5.25%;white-space:nowrap'><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>For example, m =3D 3 and our array is:</=span></div> </div> <v:rect id=3D"_x0000_s180228" style=3D'position:absolute;left:18pt;top:390=pt; width:424.625pt;height:36pt;mso-wrap-style:none;v-text-anchor:top-baselin=e' filled=3D"f" fillcolor=3D"#99f [4]" stroked=3D"f" strokecolor=3D"black [1=]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> <p:animation number=3D"4" delay=3D"0" type=3D"text" level=3D"1" effect=3D="dissolve"/><p:tag name=3D"___PPT2001" type=3D"binary" datasize=3D"36" dataoffset=3D"32"/><=/v:rect> <div id=3D"_x0000_s180228_0_44" v:shape=3D"_x0000_s180228" class=3DO style=3D'position:absolute;top:73.25%;left:3.55%;width:68.53%;height:5.25%; white-space:nowrap'><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>(=note that there are two “2”s and two “1”s)</span></div> <v:rect id=3D"_x0000_s180229" style=3D'position:absolute;left:204pt;top:44=4pt; width:289.5pt;height:36pt;mso-wrap-style:none;v-text-anchor:top-baseline' filled=3D"f" fillcolor=3D"#99f [4]" stroked=3D"f" strokecolor=3D"black [1=]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> <p:animation number=3D"5" delay=3D"0" type=3D"text" level=3D"1" effect=3D="dissolve"/><p:tag name=3D"___PPT2001" type=3D"binary" datasize=3D"36" dataoffset=3D"33"/><=/v:rect> <div id=3D"_x0000_s180229_0_29" v:shape=3D"_x0000_s180229" class=3DO style=3D'position:absolute;top:83.25%;left:29.4%;width:46.06%;height:5.25%; white-space:nowrap'><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>F=irst, we create M “buckets”</span></div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok=

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<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'>19=</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_s186370" type==3D"#_x0000_m106510" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:60pt' 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_s186371" type==3D"#_x0000_m106511" style=3D'position:absolute;left:29pt;top:112pt;width:691pt;height:370pt' 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> <div v:shape=3D"_x0000_s186370" class=3DT style=3D'position:absolute;top:8=.75%; left:5.99%;width:88.2%;height:7.75%'><span lang=3DEN-US style=3D'font-size=:90%; mso-ansi-language:EN-US'>How Fast Can We Sort? (2)</span><span style=3D'font-size:90%;mso-special-format:lastCR;display:none'> </span=></div> <div v:shape=3D"_x0000_s186371" class=3DB> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:21.25%;left:8.8%;width:90.44%;height:6.0%'><span style=3D'font-size:88=%'><span style=3D'mso-special-format:bullet;color:#9999CC;mso-color-index:5;positio=n: absolute;left:-4.14%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>Each internal= node of T is associated with a </span></span><span style=3D'position:absolute; top:26.75%;left:8.8%;width:98.12%;height:6.0%'><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>comparison that establishe=s the ordering of two </span></span><span style=3D'position:absolute;top:32.5%; left:8.8%;width:90.44%;height:6.0%'><span lang=3DEN-US style=3D'font-size:=88%; mso-ansi-language:EN-US'>elements of S. </span></span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:39.25%;left:8.8%;width:92.88%;height:6.0%'><span style=3D'font-size:88=%'><span

style=3D'mso-special-format:bullet;color:#9999CC;mso-color-index:5;positio=n: absolute;left:-4.03%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>Each external= node of T represents a distinct </span></span><span style=3D'position:absolute; top:45.0%;left:8.8%;width:90.44%;height:6.0%'><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>permutation of the element=s of S. </span></span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:51.75%;left:8.8%;width:107.49%;height:6.0%'><span style=3D'font-size:8=8%'><span style=3D'mso-special-format:bullet;color:#9999CC;mso-color-index:5;positio=n: absolute;left:-3.48%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>Hence T must =have at least n! external nodes which </span></span><span style=3D'position:absolu=te; top:57.25%;left:8.8%;width:94.56%;height:6.0%'><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>again implies T has a heig=ht of at least log(n!) </span></span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:64.25%;left:8.8%;width:106.74%;height:6.0%'><span style=3D'font-size:8=8%'><span style=3D'mso-special-format:bullet;color:#9999CC;mso-color-index:5;positio=n: absolute;left:-3.5%;top:.3em;font-family:Wingdings;font-size:75%'>¨</s=pan></span><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>Since n! has =at least n/2 terms that are greater than </span></span><span style=3D'position:abso=lute; top:69.75%;left:8.8%;width:97.94%;height:6.0%'><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>or equal to n/2, we have: log(n!) ≥ (n/2) log(n/2) </span></span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:76.25%; left:5.05%;width:94.19%;height:6.5%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.02%;height:100.0%'><span style=3D'font-size:88%; color:#E63B32'><span style=3D'mso-special-format:bullet;color:#9999CC; mso-color-index:5;position:absolute;left:-4.14%;top:.3em;font-family:Wingd=ings; font-size:75%'>¨</span></span><span lang=3DEN-US style=3D'font-size:88=%; color:#E63B32;mso-ansi-language:EN-US'>Total Time Complexity</span><span lang=3DEN-US style=3D'font-size:88%;mso-ansi-language:EN-US'>: </span><span lang=3DEN-US style=3D'font-family:Symbol;font-size:88%;mso-ansi-language:E=N-US; mso-char-type:symbol'>W</span><span lang=3DEN-US style=3D'font-size:88%; mso-ansi-language:EN-US'>(n log n). </span></span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:83.5%;left:=5.05%; width:94.19%;height:6.0%'><span style=3D'position:absolute;top:0%;left:3.9=7%; width:96.02%;height:100.0%'><span style=3D'font-size:88%;visibility:hidden='><span style=3D'mso-special-format:bullet;color:#9999CC;mso-color-index:5;positio=n: absolute;left:-4.14%;font-family:Wingdings;font-size:75%'>¨</span></sp=an><span

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

------=_NextPart_01C52BD2.9856D080Content-Location: file:///C:/D0F41273/lec23_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 );

else

document.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_origWif( cltHeight < g_origH*factor )

factor=3D(1.0*cltHeight)/g_origHnewSize =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=3D19, 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("slide0126.htm",1,-1,1),new hrefList(="slide0127.htm",1,-1,1),new hrefList("slide0128.htm",1,-1,1),new hrefList("=slide0129.htm",1,-1,1),new hrefList("slide0130.htm",1,-1,1),new hrefList("s=lide0131.htm",1,-1,1),new hrefList("slide0132.htm",1,-1,1),new hrefList("sl=ide0133.htm",1,-1,1),new hrefList("slide0134.htm",1,-1,1),new hrefList("sli=de0135.htm",1,-1,1),new hrefList("slide0136.htm",1,-1,1),new hrefList("slid=e0137.htm",1,-1,1),new hrefList("slide0138.htm",1,-1,1),new hrefList("slide=0139.htm",1,-1,1),new hrefList("slide0140.htm",1,-1,1),new hrefList("slide0=141.htm",1,-1,1),new hrefList("slide0142.htm",1,-1,1),new hrefList("slide01=43.htm",1,-1,1),new hrefList("slide0144.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=3Dtruedoc=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 oeId

t.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"}function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=etActive() }function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=etInactive() }var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=THREEDFACE"var gBtnArr =3D new Array()gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=e,GetOtlState )gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=lPane,GetOtlState )gBtnArr["nb_nts"] =3D new TxtBtn( "nb_nts","nb_ntsElem",parent.ToggleNtsPan=e,GetNtsState )gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToP=revSld )gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToN=extSld )gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=.FullScreen )gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=rent.FullScreen,null )gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=.FullScreen,null )gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;gBtnArr["nb_voice"] =3D new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.=ToggleVNarration )gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent=.ToggleOtlText )gBtnArr["nb_nts"].m_flagId=3D "notes_flag"gBtnArr["nb_nts"].SetFlag =3D NtsBtnSetFlaggBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtStatevar sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"function ShowMenu(){

BuildMenu();var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=

=3DPPTSld.event.clientY+doc.scrollTopm =3D PPTSld.document.all.item("ctxtmenu")

m.style.pixelLeft=3Dxif( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )

m.style.pixelLeft=3Dx-m.scrollWidthm.style.pixelTop=3Dyif( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )

m.style.pixelTop=3Dy-m.scrollHeightm.style.display=3D""

}function _CM(){

if( !parent.IsFullScrMode() ) return;if(!PPTSld.event.ctrlKey) {

ShowMenu()return false

} elseHideMenu()

}function BuildMenu(){

if( PPTSld.document.all.item("ctxtmenu") ) returnvar mObj=3DCreateItem( PPTSld.document.body )mObj.id=3D"ctxtmenu"mObj.style.visibility=3D"hidden"var s=3DmObj.styles.position=3D"absolute"s.cursor=3D"default"s.width=3D"120px"SetCMBorder(mObj,"menu","black")var iObj=3DCreateItem( mObj )SetCMBorder( iObj, "threedhighlight","threedshadow" )iObj.style.padding=3D2CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )CreateSeparator( iObj )CreateMenuItem( iObj,sEnd,M_End,M_True )mObj.style.visibility=3D"visible"

}function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa=lue=3Dfalse }function Highlight() { ChangeClr("activecaption","threedhighlight") }function Deselect() { ChangeClr("threedface","menutext") }function Perform(){

e=3DPPTSld.event.srcElementif( e.type=3D=3D"menuitem" && e.IsActive() )

e.Action()else

PPTSld.event.cancelBubble=3Dtrue}function ChangeClr( bg,clr ){

e=3DPPTSld.event.srcElementif( e.type=3D=3D"menuitem" && e.IsActive() ) {

e.style.backgroundColor=3Dbge.style.color=3Dclr

}}function M_HasPrevSld() { return( parent.HasPrevSld() ) }function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }function M_GoPrevSld() { if( gIsEndShow ) { history.back(); PPTSld.event.ca=ncelBubble=3Dtrue; } else GoToPrevSld() }function M_True() { return true }function M_End() { window.close( self ) }function CreateMenuItem( node,text,action,eval )

{var e=3DCreateItem( node )e.type=3D"menuitem"e.Action=3Dactione.IsActive=3Devale.innerHTML=3Dtextif( !e.IsActive() )

e.style.color=3D"threedshadow"e.onclick=3DPerforme.onmouseover=3DHighlighte.onmouseout=3DDeselects=3De.style;s.fontFamily=3DsFonts.fontSize=3D"9pt"s.paddingLeft=3D2

}function CreateSeparator( node ){

var sObj=3DCreateItem( node )SetCMBorder(sObj,"menu","menu")var s=3DsObj.styles.borderTopColor=3D"threedshadow"s.borderBottomColor=3D"threedhighlight"s.height=3D1s.fontSize=3D"0px"

}function CreateItem( node ){

var elem=3DPPTSld.document.createElement("DIV")node.insertBefore( elem )return elem

}function SetCMBorder( o,ltClr,rbClr ){

var s=3Do.styles.backgroundColor=3D"menu"s.borderStyle=3D"solid"s.borderWidth=3D1s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr

}

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<html>

<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"../lec23.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\D0F41273\lec23_files\fullscreen.htm"id=3D"webarch_temp_base_tag"><![endif]><script src=3Dscript.js></script><script></script></head>

<frameset rows=3D"*" frameborder=3D0 onload=3D"Load()" onunload=3D"Unload()="> <frame name=3DPPTSld></frameset>

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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('slide0126.htm');" id=3DPPTL1>More Sorting</a>=</font></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <br> <li>radix sort</li> <li>bucket sort</li> <li>in-place sorting</li> <li>how fast can we 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('slide0127.htm');" id=3DPPTL2>Radix Sort</a></=font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Unlike other sorting methods, radix sort considers the structure of =the keys</li>

<li>Assume keys are represented in a base M number system (M =3D radix),= i.e., if M =3D 2, the keys are represented in binary</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('slide0128.htm');" id=3DPPTL3>Radix Exchange S=ort</a></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('slide0129.htm');" id=3DPPTL4>Radix Exchange S=ort</a></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('slide0130.htm');" id=3DPPTL5>Radix Exchange S=ort</a></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('slide0131.htm');" id=3DPPTL6>Radix Exchange S=ort vs. Quicksort</a></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('slide0132.htm');" id=3DPPTL7>Straight Radix S=ort</a></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('slide0133.htm');" id=3DPPTL8>What is “s=ort in a stable way”!!!</a></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('slide0134.htm');" id=3DPPTL9>The Algorithm is= Correct (right?)</a></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('slide0135.htm');" id=3DPPTL10>For Instance,</=a></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('slide0136.htm');" id=3DPPTL11>Radix sorting a=pplied to decimal numbers</a></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>12</font></div> </td> <td> <div id=3DPPTP12 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0137.htm');" id=3DPPTL12>Straight Radix =

Sort Time Complexity</a></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>13</font></div> </td> <td> <div id=3DPPTP13 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0138.htm');" id=3DPPTL13>Bucket Sort</a>=</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>14</font></div> </td> <td> <div id=3DPPTP14 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0139.htm');" id=3DPPTL14>Bucket Sort</a>=</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>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0140.htm');" id=3DPPTL15>Bucket Sort</a>=</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>16</font></div> </td> <td> <div id=3DPPTP16 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0141.htm');" id=3DPPTL16>In-Place Sortin=g</a></font></div> <div id=3DPPTC16 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A sorting algorithm is said to be in-place if</li> <ul> <li><span style=3D'mso-spacerun:yes'> </span>it uses no auxiliary =data structures (however, O(1) auxiliary variables are allowed)</li> <li>it updates the input sequence only by means of operations replaceEl=ement and swapElements</li> </ul> <li>Which sorting algorithms seen can be made to work in place?</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>17</font></div> </td> <td> <div id=3DPPTP17 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0142.htm');" id=3DPPTL17>Lower Bd. for Comparison Based Sorting</a></font></div> <div id=3DPPTC17 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>internal node: comparison</li> <li>external node: permutation</li> <li>algorithm execution: root-to-leaf path</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>18</font></div> </td> <td> <div id=3DPPTP18 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0143.htm');" id=3DPPTL18>How Fast Can We= Sort?</a></font></div> <div id=3DPPTC18 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>How Fast Can We Sort?</li> <li>Proposition: The running time of any comparison-based algorithm for sorting an n-element sequence S is <font face=3DSymbol>W</font><font face=3DArial>(n log n).</font></li> <li>Justification: The running time of a comparison-based sorting algori=thm must be equal to or greater than the depth of the decision tree T associated with this algorithm.</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>19</font></div> </td> <td> <div id=3DPPTP19 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0144.htm');" id=3DPPTL19>How Fast Can We= Sort? (2)</a></font></div> <div id=3DPPTC19 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Each internal node of T is associated with a comparison that establi=shes the ordering of two elements of S.</li> <li>Each external node of T represents a distinct permutation of the elements of S.</li> <li>Hence T must have at least n! external nodes which again implies T h=

as a height of at least log(n!)</li> <li>Since n! has at least n/2 terms that are greater than or equal to n/=2, we have: log(n!) ≥ (n/2) log(n/2)</li> <li>Total Time Complexity: <font face=3DSymbol>W</font><font face=3DAria=l>(n log n).</font></li> <br> <br> </ul> </font></div> </td> </tr></table>

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