Lec13

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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"lec13_files/filelist.xml"><link rel=3DPreview href=3D"lec13_files/preview.wmf"><link rel=3DEdit-Time-Data href=3D"lec13_files/editdata.mso"><title>(2,4) Trees</title><link rel=3DPresentation-XML href=3D"lec13_files/pres.xml"><meta name=3DDescription content=3D"2/24/2005: (2,4) Trees"><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"../lec13.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\D0F41253\lec13_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_s21509" class=3DO style=3D'text-align:center;mso-cha=r-wrap:1;mso-kinsoku-overflow:1'><span style=3D'font-family:"Times New Roman";mso-special-format:lastCR'> </span></div>

<div v:shape=3D"_x0000_s21510" class=3DO style=3D'mso-char-wrap:1;mso-kinso=ku-overflow:1'><span style=3D'font-family:"Times New Roman";mso-special-format:lastCR'>= </span></div>

<div v:shape=3D"_x0000_s21511" class=3DO style=3D'mso-char-wrap:1;mso-kinso=ku-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_s21513" class=3DO style=3D'mso-char-wrap:1;mso-kinso=ku-overflow:1'><span style=3D'font-family:Arial;font-size:75%;color:#9999CC;mso-color-i=ndex:5;mso-special-format:lastCR'> </span></div>





<div v:shape=3D"_x0000_m21518" class=3DT>Click to edit Master title style</=div>

<div v:shape=3D"_x0000_m21519">

<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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<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"../lec13.htm"><link rel=3DPreview href=3Dpreview.wmf><title>(2,4) Trees</title><![if IE]><base href=3D"file:///C:\D0F41253\lec13_files\slide0001.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"2/24/2005: (2,4) Trees"><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"2"/></o:shapelayout></head>

<body lang=3DEN-US style=3D'margin:0px;background-color:black'onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()"onkeypress=3D"_KPH()" oa:clockstart=3D"onstart">

<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_s21505"/><![if !ppt]><p:shaperan=ge href=3D"master04.xml#_x0000_s21508"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s21508,_x0000_s21509,_x0000_s21510,_x0000_s21511,_x0000=_s21512,_x0000_s21513,_x0000_s21514,_x0000_s21515,_x0000_s21516,_x0000_s215=17" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><![endif]><p:shaperange href=3D"master04.xml#_x0000_m21518"/><v:shape id=3D"_x0000_s2050" type=3D="#_x0000_m21518" 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> <div v:shape=3D"_x0000_s2050" class=3DT style=3D'position:absolute;top:8.2=5%; left:5.99%;width:88.2%;height:8.5%'><span lang=3DEN-US style=3D'mso-ansi-l=anguage: EN-US'>(2,4) Trees</span></div> <p:shaperange href=3D"master04.xml#_x0000_m21519"/><v:shape id=3D"_x0000_s=2051" type=3D"#_x0000_m21519" style=3D'position:absolute;left:30pt;top:2in;widt=h:621pt; height:324pt' 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" size=3D"half"/><p:animation n=umber=3D"2" delay=3D"0" type=3D"text" level=3D"2" effect=3D"dissolve"/><p:tag name==3D"___PPT2001" type=3D"binary" datasize=3D"36" dataoffset=3D"1"/></v:shape> <div v:shape=3D"_x0000_s2051"> <div id=3D"_x0000_s2051_0_15" class=3DHB style=3D'position:absolute;top:27=.75%; left:5.24%;width:84.45%;height:6.0%;white-space:nowrap'><span style=3D'position:absolute;top:0%;left:4.43%;width:95.56%;height:100.0%'><=span class=3DHBB style=3D'position:absolute;left:-4.64%;top:.3em'>¨</span><=span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>What are they? </span><=

/span></div> <div id=3D"_x0000_s2051_15_67" class=3DHB1 style=3D'position:absolute;top:=35.0%; left:10.11%;width:83.33%;height:10.5%;white-space:nowrap'><span style=3D'position:absolute;top:0%;left:3.82%;width:96.4%;height:50.0%'><sp=an class=3DHB1B style=3D'position:absolute;left:-3.96%;top:.3em'>¨</span>=<span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>They are search Trees (but =not binary search </span></span><span style=3D'position:absolute;top:50.0%; left:3.82%;width:91.46%;height:50.0%'><span lang=3DEN-US style=3D'mso-ansi=-language: EN-US'>trees) </span></span></div> <div id=3D"_x0000_s2051_67_107" class=3DHB1 style=3D'position:absolute;top=:46.5%; left:10.11%;width:79.4%;height:5.25%;white-space:nowrap'><span style=3D'position:absolute;top:0%;left:4.0%;width:95.99%;height:100.0%'><s=pan class=3DHB1B style=3D'position:absolute;left:-4.17%;top:.3em'>¨</span>=<span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>They are also known as 2-4,= 2-3-4 trees</span></span></div> </div> <v:rect id=3D"_x0000_s2054" style=3D'position:absolute;left:270pt;top:202.=5pt; width:14.5pt;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'/> </v:rect> <div v:shape=3D"_x0000_s2054" class=3DO><span style=3D'position:absolute;t=op:38.5%; left:38.57%;width:.18%;height:5.25%'><span lang=3DEN-US style=3D'mso-ansi-=language: EN-US;mso-special-format:lastCR;display:none'> </span></span></div></p:slide></div>

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0000_s19679,_x0000_s19680,_x0000_s19682,_x0000_s19683,_x0000_s19684" src=3D"slide0015_image012.gif" style=3D'position:absolute;top:59.5%;left:1=5.54%; width:78.46%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19662" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.75%;left:84.83%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>35</span></div> <div v:shape=3D"_x0000_s19668" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.5%;left:65.35%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>25</span></div> <div v:shape=3D"_x0000_s19674" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.5%;left:45.5%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>18</span></div> <div v:shape=3D"_x0000_s19680" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.75%;left:16.29%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>3</span></div> <v:oval id=3D"_x0000_s19686" style=3D'position:absolute;left:337.625pt;top=:250pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regroupid=3D"3" fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19686" src=3D"slide0015_image013.gif" style=3D'position:absolute;top:46.25%;left:=46.81%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19686" class=3DO style=3D'text-align:center;positi=on:absolute; top:46.25%;left:46.81%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>13</span></div> <v:rect id=3D"_x0000_s19688" style=3D'position:absolute;left:337pt;top:250=pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regrou=pid=3D"4" filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s19689" style=3D'position:absolute;left:358p=t;top:250pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regrou=pid=3D"4" filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s19690" style=3D'position:absolute;left:379p=t;top:250pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regrou=pid=3D"4" filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:oval id=3D"_x0000_s19691" style=3D'position:absolute;left:380.=625pt; top:250pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19688,_x0000_s19689,_x0000_s19690,_x0000_s19691" src=3D"slide0015_image014.gif" style=3D'position:absolute;top:46.25%;left:=46.81%;

width:9.36%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19691" class=3DO style=3D'text-align:center;positi=on:absolute; top:46.25%;left:52.8%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>32</span></div> <v:oval id=3D"_x0000_s19692" style=3D'position:absolute;left:238.625pt;top=:394pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19692" src=3D"slide0015_image015.gif" style=3D'position:absolute;top:73.0%;left:3=3.14%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19692" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.0%;left:33.14%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>12</span></div> <v:oval id=3D"_x0000_s19693" style=3D'position:absolute;left:154.625pt;top=:323pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19693" src=3D"slide0015_image016.gif" style=3D'position:absolute;top:59.75%;left:=21.34%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19693" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.75%;left:21.34%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>10</span></div> <v:oval id=3D"_x0000_s19694" style=3D'position:absolute;left:133.625pt;top=:323pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19694" src=3D"slide0015_image017.gif" style=3D'position:absolute;top:59.75%;left:=18.53%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19694" class=3DO style=3D'text-align:center;positi=on:absolute; top:59.75%;left:19.28%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>8</span></div> <v:oval id=3D"_x0000_s19695" style=3D'position:absolute;left:116.625pt;top=:396pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s19696" style=3D'position:absolute;left:96.6=25pt; top:396pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s19697" style=3D'position:absolute;left:22.6=25pt; top:395pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19695,_x0000_s19696,_x0000_s19697" src=3D"slide0015_image018.gif" style=3D'position:absolute;top:73.0%;left:3=

.18%; width:16.29%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19695" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.25%;left:16.85%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>6</span></div> <div v:shape=3D"_x0000_s19696" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.25%;left:14.04%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>5</span></div> <div v:shape=3D"_x0000_s19697" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.0%;left:3.74%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>2</span></div> <v:oval id=3D"_x0000_s19698" style=3D'position:absolute;left:142.625pt;top=:126pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19698" src=3D"slide0015_image019.gif" style=3D'position:absolute;top:23.25%;left:=19.85%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19698" class=3DO style=3D'text-align:center;positi=on:absolute; top:23.25%;left:19.66%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>29</span></div> <v:oval id=3D"_x0000_s19703" style=3D'position:absolute;left:106.625pt;top=:127pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19703" src=3D"slide0015_image020.gif" style=3D'position:absolute;top:23.5%;left:1=4.79%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s19703_AllText" v:shape=3D"_x0000_s19703" class=3DO style=3D'position:absolute;top:23.5%;left:14.79%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>40</span></div> </div> <v:oval id=3D"_x0000_s19704" style=3D'position:absolute;left:666.625pt;top=:394pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19704" src=3D"slide0015_image021.gif" style=3D'position:absolute;top:73.0%;left:9=2.5%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s19704" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.0%;left:92.5%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>39</span></div> <v:oval id=3D"_x0000_s19705" style=3D'position:absolute;left:545.625pt;top=:395pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s19705" src=3D"slide0015_image022.gif" style=3D'position:absolute;top:73.0%;left:7=5.65%;

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5%'>18</span></div> <div v:shape=3D"_x0000_s24658" class=3DO style=3D'text-align:center;positi=on:absolute; top:62.0%;left:17.97%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>3</span></div> <v:oval id=3D"_x0000_s24663" style=3D'position:absolute;left:349.625pt;top=:262pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24663" src=3D"slide0016_image037.gif" style=3D'position:absolute;top:48.5%;left:4=8.5%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24663" class=3DO style=3D'text-align:center;positi=on:absolute; top:48.5%;left:48.5%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>13</span></div> <v:rect id=3D"_x0000_s24664" style=3D'position:absolute;left:349pt;top:262=pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s24665" style=3D'position:absolute;left:370p=t;top:262pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s24666" style=3D'position:absolute;left:391p=t;top:262pt; width:21pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:oval id=3D"_x0000_s24667" style=3D'position:absolute;left:392.=625pt; top:262pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24664,_x0000_s24665,_x0000_s24666,_x0000_s24667" src=3D"slide0016_image038.gif" style=3D'position:absolute;top:48.5%;left:4=8.5%; width:9.36%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24667" class=3DO style=3D'text-align:center;positi=on:absolute; top:48.5%;left:54.49%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>32</span></div> <v:oval id=3D"_x0000_s24668" style=3D'position:absolute;left:250.625pt;top=:406pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24668" src=3D"slide0016_image039.gif" style=3D'position:absolute;top:75.0%;left:3=4.83%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24668" class=3DO style=3D'text-align:center;positi=

on:absolute; top:75.0%;left:34.64%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>12</span></div> <v:oval id=3D"_x0000_s24669" style=3D'position:absolute;left:166.625pt;top=:335pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24669" src=3D"slide0016_image040.gif" style=3D'position:absolute;top:62.0%;left:2=3.03%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24669" class=3DO style=3D'text-align:center;positi=on:absolute; top:62.0%;left:23.03%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>10</span></div> <v:oval id=3D"_x0000_s24670" style=3D'position:absolute;left:145.625pt;top=:335pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24670" src=3D"slide0016_image041.gif" style=3D'position:absolute;top:62.0%;left:2=0.22%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24670" class=3DO style=3D'text-align:center;positi=on:absolute; top:62.0%;left:20.97%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>8</span></div> <v:oval id=3D"_x0000_s24671" style=3D'position:absolute;left:128.625pt;top=:408pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s24672" style=3D'position:absolute;left:108.=625pt; top:408pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s24673" style=3D'position:absolute;left:34.6=25pt; top:407pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24671,_x0000_s24672,_x0000_s24673" src=3D"slide0016_image042.gif" style=3D'position:absolute;top:75.25%;left:=4.68%; width:16.29%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24671" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.5%;left:18.53%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>6</span></div> <div v:shape=3D"_x0000_s24672" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.5%;left:15.73%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>5</span></div> <div v:shape=3D"_x0000_s24673" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.25%;left:5.43%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>2</span></div> <v:oval id=3D"_x0000_s24674" style=3D'position:absolute;left:154.625pt;top=

:138pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24674" src=3D"slide0016_image043.gif" style=3D'position:absolute;top:25.5%;left:2=1.34%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s24674_AllText" v:shape=3D"_x0000_s24674" class=3DO style=3D'position:absolute;top:25.5%;left:21.34%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>29</span></div> </div> <v:oval id=3D"_x0000_s24675" style=3D'position:absolute;left:699.625pt;top=:406pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24675" src=3D"slide0016_image044.gif" style=3D'position:absolute;top:75.0%;left:9=7.19%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24675" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.0%;left:97.0%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>40</span></div> <v:oval id=3D"_x0000_s24676" style=3D'position:absolute;left:678.625pt;top=:406pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24676" src=3D"slide0016_image045.gif" style=3D'position:absolute;top:75.0%;left:9=4.19%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24676" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.0%;left:94.19%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>39</span></div> <v:oval id=3D"_x0000_s24677" style=3D'position:absolute;left:557.625pt;top=:407pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24677" src=3D"slide0016_image046.gif" style=3D'position:absolute;top:75.25%;left:=77.34%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s24677_AllText" v:shape=3D"_x0000_s24677" class=3DO style=3D'position:absolute;top:75.25%;left:77.34%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>30</span></div> </div> <v:oval id=3D"_x0000_s24679" style=3D'position:absolute;left:395.625pt;top=:406pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24679" src=3D"slide0016_image047.gif" style=3D'position:absolute;top:75.0%;left:5=

4.86%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24679" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.0%;left:54.86%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>21</span></div> <v:oval id=3D"_x0000_s24680" style=3D'position:absolute;left:188.625pt;top=:137pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24680" src=3D"slide0016_image048.gif" style=3D'position:absolute;top:25.25%;left:=26.21%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24680" class=3DO style=3D'text-align:center;positi=on:absolute; top:25.25%;left:26.77%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>7</span></div> <v:oval id=3D"_x0000_s24681" style=3D'position:absolute;left:443.625pt;top=:408pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24681" src=3D"slide0016_image049.gif" style=3D'position:absolute;top:75.5%;left:6=1.61%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24681" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.5%;left:61.61%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>23</span></div> <v:oval id=3D"_x0000_s24682" style=3D'position:absolute;left:370.625pt;top=:263pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24682" src=3D"slide0016_image050.gif" style=3D'position:absolute;top:48.75%;left:=51.49%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24682" class=3DO style=3D'text-align:center;positi=on:absolute; top:48.75%;left:51.31%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>22</span></div> <v:oval id=3D"_x0000_s24683" style=3D'position:absolute;left:321.625pt;top=:406pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s24683" src=3D"slide0016_image051.gif" style=3D'position:absolute;top:75.0%;left:4=4.56%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s24683" class=3DO style=3D'text-align:center;positi=on:absolute; top:75.0%;left:44.56%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>15</span></div> <v:line id=3D"_x0000_s24684" style=3D'position:absolute;flip:x' from=3D"15=5pt,280pt" to=3D"349pt,334pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><v:line id=3D"_x0000_s24685" style=3D'position:absolute' from=3D"=

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<div id=3D"_x0000_s25694_AllText" v:shape=3D"_x0000_s25694" class=3DO style=3D'position:absolute;top:75.0%;left:16.85%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>6</span></div> </div> <v:oval id=3D"_x0000_s25695" style=3D'position:absolute;left:96.625pt;top:=405pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25695" src=3D"slide0017_image074.gif" style=3D'position:absolute;top:75.0%;left:1=3.29%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s25695_AllText" v:shape=3D"_x0000_s25695" class=3DO style=3D'position:absolute;top:75.0%;left:14.04%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>5</span></div> </div> <v:oval id=3D"_x0000_s25696" style=3D'position:absolute;left:22.625pt;top:=404pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25696" src=3D"slide0017_image075.gif" style=3D'position:absolute;top:74.75%;left:=3.18%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25696" class=3DO style=3D'text-align:center;positi=on:absolute; top:74.75%;left:3.74%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>2</span></div> <v:oval id=3D"_x0000_s25697" style=3D'position:absolute;left:549.625pt;top=:431pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25697" src=3D"slide0017_image076.gif" style=3D'position:absolute;top:79.75%;left:=76.21%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25697" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.75%;left:76.21%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>29</span></div> <v:oval id=3D"_x0000_s25698" style=3D'position:absolute;left:687.625pt;top=:403pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25698" src=3D"slide0017_image077.gif" style=3D'position:absolute;top:74.5%;left:9=5.5%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25698" class=3DO style=3D'text-align:center;positi=on:absolute; top:74.5%;left:95.5%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>40</span></div> <v:oval id=3D"_x0000_s25699" style=3D'position:absolute;left:666.625pt;top=:403pt;

width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25699" src=3D"slide0017_image078.gif" style=3D'position:absolute;top:74.5%;left:9=2.5%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25699" class=3DO style=3D'text-align:center;positi=on:absolute; top:74.5%;left:92.5%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>39</span></div> <v:oval id=3D"_x0000_s25700" style=3D'position:absolute;left:571.625pt;top=:431pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25700" src=3D"slide0017_image079.gif" style=3D'position:absolute;top:79.75%;left:=79.4%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25700" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.75%;left:79.21%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>30</span></div> <v:oval id=3D"_x0000_s25701" style=3D'position:absolute;left:383.625pt;top=:403pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25701" src=3D"slide0017_image080.gif" style=3D'position:absolute;top:74.5%;left:5=3.18%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25701" class=3DO style=3D'text-align:center;positi=on:absolute; top:74.5%;left:53.18%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>21</span></div> <v:oval id=3D"_x0000_s25702" style=3D'position:absolute;left:176.625pt;top=:134pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25702" src=3D"slide0017_image081.gif" style=3D'position:absolute;top:24.75%;left:=24.53%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s25702_AllText" v:shape=3D"_x0000_s25702" class=3DO style=3D'position:absolute;top:24.75%;left:25.28%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>7</span></div> </div> <v:oval id=3D"_x0000_s25703" style=3D'position:absolute;left:431.625pt;top=:405pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s25703" src=3D"slide0017_image082.gif" style=3D'position:absolute;top:75.0%;left:5=9.92%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s25703" class=3DO style=3D'text-align:center;positi=on:absolute;

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<meta name=3DDescription content=3D"2/24/2005: Insertion(4)"><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"26"/> <o:regrouptable v:ext=3D"edit"> <o:entry new=3D"1" old=3D"0"/> </o:regrouptable></o:shapelayout></head>


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height:100.0%'><span style=3D'font-size:75%'>32</span></div> </div> <v:oval id=3D"_x0000_s26704" style=3D'position:absolute;left:238.625pt;top=:445pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26704" src=3D"slide0018_image102.gif" style=3D'position:absolute;top:82.25%;left:=33.14%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s26704" class=3DO style=3D'text-align:center;positi=on:absolute; top:82.25%;left:33.14%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>12</span></div> <v:oval id=3D"_x0000_s26705" style=3D'position:absolute;left:154.625pt;top=:374pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26705" src=3D"slide0018_image103.gif" style=3D'position:absolute;top:69.25%;left:=21.34%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s26705_AllText" v:shape=3D"_x0000_s26705" class=3DO style=3D'position:absolute;top:69.25%;left:21.34%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>10</span></div> </div> <v:oval id=3D"_x0000_s26706" style=3D'position:absolute;left:133.625pt;top=:374pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26706" src=3D"slide0018_image104.gif" style=3D'position:absolute;top:69.25%;left:=18.53%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s26706_AllText" v:shape=3D"_x0000_s26706" class=3DO style=3D'position:absolute;top:69.25%;left:19.28%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>8</span></div> </div> <v:oval id=3D"_x0000_s26707" style=3D'position:absolute;left:108.625pt;top=:475pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26707" src=3D"slide0018_image105.gif" style=3D'position:absolute;top:88.0%;left:1=4.98%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s26707" class=3DO style=3D'text-align:center;positi=on:absolute; top:88.0%;left:15.73%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>6</span></div> <v:oval id=3D"_x0000_s26708" style=3D'position:absolute;left:55.625pt;top:=475pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]">

<v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26708" src=3D"slide0018_image106.gif" style=3D'position:absolute;top:88.0%;left:7=.67%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s26708_AllText" v:shape=3D"_x0000_s26708" class=3DO style=3D'position:absolute;top:88.0%;left:8.42%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>5</span></div> </div> <v:oval id=3D"_x0000_s26709" style=3D'position:absolute;left:22.625pt;top:=446pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26709" src=3D"slide0018_image107.gif" style=3D'position:absolute;top:82.5%;left:3=.18%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s26709" class=3DO style=3D'text-align:center;positi=on:absolute; top:82.5%;left:3.74%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>2</span></div> <v:oval id=3D"_x0000_s26710" style=3D'position:absolute;left:549.625pt;top=:473pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s26711" style=3D'position:absolute;left:571.=625pt; top:473pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26710,_x0000_s267=11" src=3D"slide0018_image108.gif" style=3D'position:absolute;top:87.5%;left:7=6.21%; width:6.36%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s26710" class=3DO style=3D'text-align:center;positi=on:absolute; top:87.5%;left:76.21%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>29</span></div> <div v:shape=3D"_x0000_s26711" class=3DO style=3D'text-align:center;positi=on:absolute; top:87.5%;left:79.21%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>30</span></div> <v:oval id=3D"_x0000_s26712" style=3D'position:absolute;left:383.625pt;top=:445pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s26713" style=3D'position:absolute;left:431.=625pt; top:447pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s26712,_x0000_s267=13" src=3D"slide0018_image109.gif" style=3D'position:absolute;top:82.25%;left:=53.18%;

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style=3D'position:absolute;top:27.5%;left:9.17%;width:84.26%;height:6.0%'>=<span style=3D'font-size:88%'>then it is split. </span></span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:34.25%; left:5.43%;width:88.01%;height:6.0%'><span style=3D'position:absolute; top:0%;left:4.25%;width:95.74%;height:100.0%'><span style=3D'font-size:88%='><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-4.44%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span style=3D'font-size:88%'>In this manner splits can cascade.</span></span></=div> </div></p:slide></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"../lec13.htm"><link rel=3DPreview href=3Dpreview.wmf><title>(2,4) Trees</title><![if IE]><base href=3D"file:///C:\D0F41253\lec13_files\slide0019.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"2/24/2005: Insertion(5)"><link rel=3DStylesheet href=3D"master04_stylesheet.css"><![if !ppt]><style media=3Dprint></style><style></style><script src=3Dscript.js></script><script></script><script><title>(2,4) Trees</title><![if IE]><base href=3D"file:///C:\D0F41253\lec13_files\slide0009.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"2/24/2005: Time for Search and Inserti=on"><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"11,12"/></o:shapelayout>

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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_s21505"/><![if !ppt]><p:shaperan=ge href=3D"master04.xml#_x0000_s21508"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s21508,_x0000_s21509,_x0000_s21510,_x0000_s21511,_x0000=_s21512,_x0000_s21513,_x0000_s21514,_x0000_s21515,_x0000_s21516,_x0000_s215=17" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><![endif]><p:shaperange href=3D"master04.xml#_x0000_m21518"/><v:shape id=3D"_x0000_s11266" type==3D"#_x0000_m21518" style=3D'position:absolute;left:35pt;top:32pt;width:685pt;height:64pt' 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_s11266" class=3DT style=3D'position:absolute;top:8.=0%; left:5.8%;width:93.25%;height:8.5%'><span lang=3DEN-US style=3D'mso-ansi-l=anguage: EN-US'>Time for Search and<span style=3D'mso-spacerun:yes'> </span>Insertion</span></div> <p:shaperange href=3D"master04.xml#_x0000_m21519"/><v:shape id=3D"_x0000_s=11267" type=3D"#_x0000_m21519" style=3D'position:absolute;left:54pt;top:138pt;wi=dth:636pt; height:324pt' 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" size=3D"half"/><p:animation n=umber=3D"2" 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"6"/></v:shape> <div v:shape=3D"_x0000_s11267"> <div class=3DHB1 style=3D'mso-margin-left-alt:576'></div> <div class=3DHB2 style=3D'mso-margin-left-alt:816'></div> <div class=3DHB3 style=3D'mso-margin-left-alt:1080'></div> <div class=3DHB4 style=3D'mso-margin-left-alt:1368'></div> <div id=3D"_x0000_s11267_0_32" class=3DHB style=3D'mso-line-spacing:"90 20= 0"; mso-margin-left-alt:336;position:absolute;top:26.0%;left:8.42%;width:86.51=%; height:5.25%;white-space:nowrap'><span style=3D'position:absolute;top:0%; left:6.92%;width:93.29%;height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-7.42%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:86%;mso-ansi-language:EN-US'>A search visi=ts<span

style=3D'mso-spacerun:yes'> </span>O(log N) nodes </span></span>=</div> <div id=3D"_x0000_s11267_32_75" class=3DHB style=3D'mso-line-spacing:"90 2=0 0"; mso-margin-left-alt:336;position:absolute;top:32.0%;left:8.42%;width:86.51=%; height:5.25%;white-space:nowrap'><span style=3D'position:absolute;top:0%; left:6.92%;width:93.29%;height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-7.42%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:86%;mso-ansi-language:EN-US'>An insertion =requires O(log N) node splits </span></span></div> <div id=3D"_x0000_s11267_75_111" class=3DHB style=3D'mso-line-spacing:"90 =20 0"; mso-margin-left-alt:336;position:absolute;top:37.75%;left:8.42%;width:86.5=1%; height:5.25%;white-space:nowrap'><span style=3D'position:absolute;top:0%; left:6.92%;width:93.29%;height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-7.42%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:86%;mso-ansi-language:EN-US'>Each node spl=it takes constant time </span></span></div> <div id=3D"_x0000_s11267_111_171" class=3DHB style=3D'mso-line-spacing:"90= 20 0"; mso-margin-left-alt:336;position:absolute;top:43.75%;left:8.42%;width:98.3=1%; height:10.0%;white-space:nowrap'><span style=3D'position:absolute;top:0%; left:6.09%;width:94.09%;height:52.5%'><span style=3D'font-size:86%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-6.47%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span lang=3DEN-US style=3D'font-size:86%;mso-ansi-language:EN-US'>Hence, operat=ions Search and Insert each take time </span></span><span style=3D'position:abs=olute; top:47.5%;left:6.09%;width:82.09%;height:52.5%'><span lang=3DEN-US style=3D'font-size:86%;color:#5C69FF;mso-ansi-language:EN-US'>O(log N)</sp=an></span></div> </div></p:slide></div>

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onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()"onkeypress=3D"_KPH()" oa:clockstart=3D"onstart">

<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_s21505"/><![if !ppt]><p:shaperan=ge href=3D"master04.xml#_x0000_s21508"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s21508,_x0000_s21509,_x0000_s21510,_x0000_s21511,_x0000=_s21512,_x0000_s21513,_x0000_s21514,_x0000_s21515,_x0000_s21516,_x0000_s215=17" src=3D"master04_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><![endif]><p:shaperange href=3D"master04.xml#_x0000_m21518"/><v:shape id=3D"_x0000_s28674" type==3D"#_x0000_m21518" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:65pt' 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_m21519"/><v:shape id=3D"_x0000_s28675" type==3D"#_x0000_m21519" style=3D'position:absolute;left:19pt;top:111pt;width:9in;height:87pt' 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:group id=3D"_x0=000_s28676" style=3D'position:absolute;left:47pt;top:429pt;width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s28677" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s28678" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s28679" style=3D'position:absolute;left:576;top:269=6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s28680" style=3D'position:absolute;left:82=4;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s28681" style=3D'position:absolute;left:10=72; top:2696;width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/>

</v:rect></v:group></v:group><v:oval id=3D"_x0000_s28682" style=3D'posit=ion:absolute; left:81.625pt;top:457pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s28676,_x0000_s28677,_x0000_s28679,_x0000_s28680,_x0000=_s28681,_x0000_s28682" src=3D"slide0020_image164.gif" style=3D'position:absolute;top:79.5%;left:6=.55%; width:9.17%;height:9.0%'><![endif]> <div v:shape=3D"_x0000_s28674" class=3DT style=3D'position:absolute;top:8.=75%; left:5.99%;width:88.2%;height:8.5%'>Deletion</div> <div v:shape=3D"_x0000_s28675" class=3DB> <div style=3D'mso-line-spacing:"80 20 0";position:absolute;top:20.75%; left:3.55%;width:88.2%;height:5.25%'><span style=3D'position:absolute; top:0%;left:4.24%;width:95.75%;height:100.0%'><span style=3D'font-size:75%='><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span style=3D'font-size:75%'>Delete 21. </span></span></div> <div style=3D'mso-line-spacing:"80 20 0"'><span style=3D'position:absolute; top:26.0%;left:7.3%;width:100.18%;height:5.25%'><span style=3D'font-size:7=5%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-3.73%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span style=3D'font-size:75%'>No problem if key to be deleted is in a leaf with =at least 2 </span></span><span style=3D'position:absolute;top:30.25%;left:7.3=%; width:84.45%;height:5.25%'><span style=3D'font-size:75%'>keys</span></span=></div> </div> <div v:shape=3D"_x0000_s28677" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.5%;left:7.3%;width:1.68%;height:4.0%'><span style=3D'font-size:75%'=>1</span></div> <div v:shape=3D"_x0000_s28682" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.5%;left:11.98%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>4</span></div> <v:group id=3D"_x0000_s28683" style=3D'position:absolute;left:192pt;top:42=9pt; width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s28684" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s28685" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s28686" style=3D'position:absolute;left:576;top:269=6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/>

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on:absolute; top:79.25%;left:36.51%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>11</span></div> <div v:shape=3D"_x0000_s28696" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.25%;left:46.44%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>14</span></div> <div v:shape=3D"_x0000_s28702" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.25%;left:56.74%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>20</span></div> <div v:shape=3D"_x0000_s28707" class=3DO style=3D'text-align:center;positi=on:absolute; top:79.5%;left:69.47%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>24</span></div> <v:group id=3D"_x0000_s28708" style=3D'position:absolute;left:478pt;top:43=0pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s28709" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s28710" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s28711" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><v:oval id=3D"_x0000_s28712" style=3D'position:absolut=e; left:518.625pt;top:455pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s28708,_x0000_s28709,_x0000_s28710,_x0000_s28711,_x0000=_s28712" src=3D"slide0020_image166.gif" style=3D'position:absolute;top:79.5%;left:6=6.29%; width:9.17%;height:8.5%'><![endif]> <div v:shape=3D"_x0000_s28712" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.25%;left:71.91%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>26</span></div> <v:group id=3D"_x0000_s28725" style=3D'position:absolute;left:518pt;top:35=6pt; width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s28726" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s28727" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240">

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ion:absolute; left:88.625pt;top:495pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29700,_x0000_s29701,_x0000_s29703,_x0000_s29704,_x0000=_s29705,_x0000_s29706" src=3D"slide0021_image188.gif" style=3D'position:absolute;top:86.5%;left:7=.49%; width:9.17%;height:9.0%'><![endif]> <div v:shape=3D"_x0000_s29698" class=3DT style=3D'position:absolute;top:7.=5%; left:5.99%;width:88.2%;height:7.75%'><span style=3D'font-size:90%'>Deletio=n(2)</span></div> <div v:shape=3D"_x0000_s29699" class=3DB> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:17.25%;left:8.98%;width:94.56%;height:6.0%'><span style=3D'font-size:8=8%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-3.96%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span style=3D'font-size:88%'>If key to be deleted is in an internal node then <=/span></span><span style=3D'position:absolute;top:23.0%;left:8.98%;width:92.88%;height:6.0%'>=<span style=3D'font-size:88%'>we swap it with its predecessor (which is in a </s=pan></span><span style=3D'position:absolute;top:28.5%;left:8.98%;width:84.45%;height:6.0%'>=<span style=3D'font-size:88%'>leaf) and then delete it. </span></span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:35.5%;left:=5.24%; width:88.2%;height:6.0%'><span style=3D'position:absolute;top:0%;left:4.24=%; width:95.75%;height:100.0%'><span style=3D'font-size:88%'><span style=3D'mso-special-format:bullet;color:#9999FF;mso-color-index:4;positio=n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>¨</=span></span><span style=3D'font-size:88%'>Delete 25</span></span></div> </div> <div v:shape=3D"_x0000_s29701" class=3DO style=3D'text-align:center;positi=on:absolute; top:86.5%;left:8.23%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>1</span></div> <div v:shape=3D"_x0000_s29706" class=3DO style=3D'text-align:center;positi=on:absolute; top:91.5%;left:12.92%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>4</span></div> <v:group id=3D"_x0000_s29707" style=3D'position:absolute;left:199pt;top:46=7pt; width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s29708" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s29709" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s29710" style=3D'position:absolute;left:576;top:269=6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=

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:394pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regroupid=3D"1" fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29738" src=3D"slide0021_image192.gif" style=3D'position:absolute;top:73.0%;left:7=3.03%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s29738_AllText" v:shape=3D"_x0000_s29738" class=3DO style=3D'position:absolute;top:73.0%;left:72.84%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>25</span></div> </div> <v:group id=3D"_x0000_s29739" style=3D'position:absolute;left:525pt;top:39=4pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240" o:regroupid=3D"1"> <v:rect id=3D"_x0000_s29740" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s29741" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s29742" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><v:group id=3D"_x0000_s29743" style=3D'position:absolu=te; left:382pt;top:394pt;width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s29744" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s29745" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s29746" style=3D'position:absolute;left:576;top:269=6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s29747" style=3D'position:absolute;left:82=4;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/>

<v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s29748" style=3D'position:absolute;left:10=72; top:2696;width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29739,_x0000_s29740,_x0000_s29741,_x0000_s29742,_x0000=_s29743,_x0000_s29744,_x0000_s29746,_x0000_s29747,_x0000_s29748" src=3D"slide0021_image193.gif" style=3D'position:absolute;top:73.0%;left:5=2.99%; width:29.02%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29744" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.0%;left:52.99%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>18</span></div> <v:oval id=3D"_x0000_s29749" style=3D'position:absolute;left:118.625pt;top=:369pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29749" src=3D"slide0021_image194.gif" style=3D'position:absolute;top:68.25%;left:=16.47%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29749" class=3DO style=3D'text-align:center;positi=on:absolute; top:68.25%;left:17.22%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>3</span></div> <v:oval id=3D"_x0000_s29750" style=3D'position:absolute;left:393.625pt;top=:227pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29750" src=3D"slide0021_image195.gif" style=3D'position:absolute;top:42.0%;left:5=4.68%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29750" class=3DO style=3D'text-align:center;positi=on:absolute; top:42.0%;left:54.49%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>13</span></div> <v:oval id=3D"_x0000_s29751" style=3D'position:absolute;left:292.625pt;top=:466pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29751" src=3D"slide0021_image196.gif" style=3D'position:absolute;top:86.25%;left:=40.63%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29751" class=3DO style=3D'text-align:center;positi=on:absolute; top:86.25%;left:40.63%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>12</span></div> <v:oval id=3D"_x0000_s29752" style=3D'position:absolute;left:223.625pt;top=:370pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29752" src=3D"slide0021_image197.gif" style=3D'position:absolute;top:68.5%;left:3=1.08%;

width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29752" class=3DO style=3D'text-align:center;positi=on:absolute; top:68.5%;left:30.89%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>10</span></div> <v:oval id=3D"_x0000_s29753" style=3D'position:absolute;left:202.625pt;top=:369pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29753" src=3D"slide0021_image198.gif" style=3D'position:absolute;top:68.25%;left:=28.08%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29753" class=3DO style=3D'text-align:center;positi=on:absolute; top:68.25%;left:28.83%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>8</span></div> <v:oval id=3D"_x0000_s29754" style=3D'position:absolute;left:162.625pt;top=:496pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29754" src=3D"slide0021_image199.gif" style=3D'position:absolute;top:91.75%;left:=22.47%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29754" class=3DO style=3D'text-align:center;positi=on:absolute; top:91.75%;left:23.22%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>6</span></div> <v:oval id=3D"_x0000_s29755" style=3D'position:absolute;left:328.625pt;top=:290pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29755" src=3D"slide0021_image200.gif" style=3D'position:absolute;top:53.75%;left:=45.5%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29755" class=3DO style=3D'text-align:center;positi=on:absolute; top:53.75%;left:46.25%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>5</span></div> <v:oval id=3D"_x0000_s29756" style=3D'position:absolute;left:76.625pt;top:=467pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s29756" src=3D"slide0021_image201.gif" style=3D'position:absolute;top:86.5%;left:1=0.67%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s29756" class=3DO style=3D'text-align:center;positi=on:absolute; top:86.5%;left:11.23%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>2</span></div> <v:oval id=3D"_x0000_s29757" style=3D'position:absolute;left:603.625pt;top=:494pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s29758" style=3D'position:absolute;left:625.=625pt;

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<v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30751,_x0000_s30752,_x0000_s30753,_x0000_s30754" src=3D"slide0022_image216.gif" style=3D'position:absolute;top:87.0%;left:5=8.05%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s30755" style=3D'p=osition:absolute; left:529.625pt;top:398pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30755" src=3D"slide0022_image217.gif" style=3D'position:absolute;top:73.75%;left:=73.59%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30755" class=3DO style=3D'text-align:center;positi=on:absolute; top:73.75%;left:73.4%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>24</span></div> <v:group id=3D"_x0000_s30756" style=3D'position:absolute;left:489pt;top:47=2pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s30757" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30758" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30759" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><v:oval id=3D"_x0000_s30760" style=3D'position:absolut=e; left:529.625pt;top:497pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30756,_x0000_s30757,_x0000_s30758,_x0000_s30759,_x0000=_s30760" src=3D"slide0022_image218.gif" style=3D'position:absolute;top:87.25%;left:=67.79%; width:9.17%;height:8.5%'><![endif]> <div v:shape=3D"_x0000_s30760" class=3DO style=3D'text-align:center;positi=on:absolute; top:92.0%;left:73.4%;width:3.18%;height:4.0%'><span style=3D'font-size:75%='>26</span></div> <v:group id=3D"_x0000_s30762" style=3D'position:absolute;left:529pt;top:39=8pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s30763" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]">

<v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30764" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30765" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30762,_x0000_s30763,_x0000_s30764,_x0000_s30765" src=3D"slide0022_image219.gif" style=3D'position:absolute;top:73.75%;left:=73.4%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s30767" style=3D'p=osition:absolute; left:386.625pt;top:398pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' o:regroupid=3D"2" fillcolor=3D"#cccce6 [7]" strokec=olor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30767" src=3D"slide0022_image220.gif" style=3D'position:absolute;top:73.75%;left:=53.55%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s30767_AllText" v:shape=3D"_x0000_s30767" class=3DO style=3D'position:absolute;top:73.75%;left:53.55%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>18</span></div> </div> <v:group id=3D"_x0000_s30768" style=3D'position:absolute;left:386pt;top:39=8pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240" o:regroupid=3D"2"> <v:rect id=3D"_x0000_s30769" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30770" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s30771" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30768,_x0000_s30769,_x0000_s30770,_x0000_s30771" src=3D"slide0022_image221.gif" style=3D'position:absolute;top:73.75%;left:=

53.55%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s30772" style=3D'p=osition:absolute; left:122.625pt;top:373pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30772" src=3D"slide0022_image222.gif" style=3D'position:absolute;top:69.0%;left:1=7.04%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30772" class=3DO style=3D'text-align:center;positi=on:absolute; top:69.0%;left:17.6%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>3</span></div> <v:oval id=3D"_x0000_s30773" style=3D'position:absolute;left:397.625pt;top=:231pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30773" src=3D"slide0022_image223.gif" style=3D'position:absolute;top:42.75%;left:=55.24%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30773" class=3DO style=3D'text-align:center;positi=on:absolute; top:42.75%;left:55.05%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>13</span></div> <v:oval id=3D"_x0000_s30774" style=3D'position:absolute;left:296.625pt;top=:470pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30774" src=3D"slide0022_image224.gif" style=3D'position:absolute;top:87.0%;left:4=1.19%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30774" class=3DO style=3D'text-align:center;positi=on:absolute; top:87.0%;left:41.19%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>12</span></div> <v:oval id=3D"_x0000_s30775" style=3D'position:absolute;left:227.625pt;top=:374pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30775" src=3D"slide0022_image225.gif" style=3D'position:absolute;top:69.25%;left:=31.64%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30775" class=3DO style=3D'text-align:center;positi=on:absolute; top:69.25%;left:31.46%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>10</span></div> <v:oval id=3D"_x0000_s30776" style=3D'position:absolute;left:206.625pt;top=:373pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30776" src=3D"slide0022_image226.gif" style=3D'position:absolute;top:69.0%;left:2=8.65%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30776" class=3DO style=3D'text-align:center;positi=on:absolute;

top:69.0%;left:29.4%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>8</span></div> <v:oval id=3D"_x0000_s30777" style=3D'position:absolute;left:166.625pt;top=:500pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30777" src=3D"slide0022_image227.gif" style=3D'position:absolute;top:92.5%;left:2=3.03%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30777" class=3DO style=3D'text-align:center;positi=on:absolute; top:92.5%;left:23.78%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>6</span></div> <v:oval id=3D"_x0000_s30778" style=3D'position:absolute;left:332.625pt;top=:294pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30778" src=3D"slide0022_image228.gif" style=3D'position:absolute;top:54.5%;left:4=6.06%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30778" class=3DO style=3D'text-align:center;positi=on:absolute; top:54.5%;left:46.81%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>5</span></div> <v:oval id=3D"_x0000_s30779" style=3D'position:absolute;left:80.625pt;top:=471pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30779" src=3D"slide0022_image229.gif" style=3D'position:absolute;top:87.25%;left:=11.23%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30779" class=3DO style=3D'text-align:center;positi=on:absolute; top:87.25%;left:11.79%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>2</span></div> <v:oval id=3D"_x0000_s30780" style=3D'position:absolute;left:607.625pt;top=:498pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s30781" style=3D'position:absolute;left:629.=625pt; top:498pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30780,_x0000_s307=81" src=3D"slide0022_image230.gif" style=3D'position:absolute;top:92.25%;left:=84.26%; width:6.36%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30780" class=3DO style=3D'text-align:center;positi=on:absolute; top:92.25%;left:84.26%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>29</span></div> <div v:shape=3D"_x0000_s30781" class=3DO style=3D'text-align:center;positi=on:absolute; top:92.25%;left:87.45%;width:3.18%;height:4.0%'><span style=3D'font-size:7=

5%'>30</span></div> <v:oval id=3D"_x0000_s30782" style=3D'position:absolute;left:489.625pt;top=:472pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30782" src=3D"slide0022_image231.gif" style=3D'position:absolute;top:87.25%;left:=67.97%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30782" class=3DO style=3D'text-align:center;positi=on:absolute; top:87.25%;left:67.97%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>23</span></div> <v:oval id=3D"_x0000_s30783" style=3D'position:absolute;left:460.625pt;top=:295pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30783" src=3D"slide0022_image232.gif" style=3D'position:absolute;top:54.5%;left:6=3.85%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s30783" class=3DO style=3D'text-align:center;positi=on:absolute; top:54.5%;left:63.85%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>22</span></div> <v:oval id=3D"_x0000_s30784" style=3D'position:absolute;left:367.625pt;top=:470pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30784" src=3D"slide0022_image233.gif" style=3D'position:absolute;top:87.0%;left:5=0.93%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s30784_AllText" v:shape=3D"_x0000_s30784" class=3DO style=3D'position:absolute;top:87.0%;left:50.93%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>15</span></div> </div> <v:line id=3D"_x0000_s30785" style=3D'position:absolute;flip:x' from=3D"37=8pt,416pt" to=3D"387pt,470pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><v:line id=3D"_x0000_s30786" style=3D'position:absolute' from=3D"=407pt,416pt" to=3D"451pt,470pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><v:line id=3D"_x0000_s30787" style=3D'position:absolute;flip:x' f=rom=3D"520pt,417pt" to=3D"530pt,472pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s30785,_x0000_s30786,_x0000_s30787" src=3D"slide0022_image234.gif" style=3D'position:absolute;top:77.0%;left:5=2.05%; width:21.91%;height:11.0%'><![endif]><v:group id=3D"_x0000_s30788" style==3D'position:absolute;

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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"

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_s32777,_x0000_s32778" src=3D"slide0024_image275.gif" style=3D'position:absolute;top:84.75%;left:=8.05%; width:9.17%;height:9.0%'><![endif]> <div v:shape=3D"_x0000_s32770" class=3DT style=3D'position:absolute;top:8.=5%; left:5.99%;width:88.2%;height:8.5%'>Delete(5)</div> <div v:shape=3D"_x0000_s32771" class=3DB><span style=3D'position:absolute; top:19.75%;left:9.55%;width:100.18%;height:6.0%'><span style=3D'font-size:=88%'><span class=3DBB style=3D'position:absolute;left:-3.73%;top:.3em'>¨</span></=span><span style=3D'font-size:88%'>Moving a key down from the parent corresponds </sp=an></span><span style=3D'position:absolute;top:26.0%;left:9.55%;width:84.45%;height:6.0%'>=<span style=3D'font-size:88%'>to deletion in the parent node. </span></span> <div style=3D'position:absolute;top:33.5%;left:5.8%;width:98.31%;height:6.=0%'><span style=3D'position:absolute;top:0%;left:3.8%;width:96.19%;height:100.0%'><s=pan style=3D'font-size:88%'><span class=3DBB style=3D'position:absolute;left:-=3.96%; top:.3em'>¨</span></span><span style=3D'font-size:88%'>The procedure i=s the same as for a leaf node. </span></span></div> <div style=3D'position:absolute;top:41.0%;left:5.8%;width:88.2%;height:6.0=%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=span style=3D'font-size:88%'><span class=3DBB style=3D'position:absolute;left:-=4.43%; top:.3em'>¨</span></span><span style=3D'font-size:88%'>Can lead to a c=ascade . </span></span></div> <div style=3D'position:absolute;top:48.5%;left:5.8%;width:88.2%;height:6.0=%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=span style=3D'font-size:88%'><span class=3DBB style=3D'position:absolute;left:-=4.43%; top:.3em'>¨</span></span><span style=3D'font-size:88%'>Delete 18</span=></span></div> </div> <div v:shape=3D"_x0000_s32773" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.75%;left:8.8%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>1</span></div> <div v:shape=3D"_x0000_s32778" class=3DO style=3D'text-align:center;positi=on:absolute; top:90.0%;left:13.48%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>4</span></div> <v:group id=3D"_x0000_s32779" style=3D'position:absolute;left:203pt;top:45=8pt; width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s32780" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s32781" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32782" style=3D'position:absolute;left:576;top:269=

6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32783" style=3D'position:absolute;left:82=4;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32784" style=3D'position:absolute;left:10=72; top:2696;width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group></v:group><v:group id=3D"_x0000_s32785" style=3D'posi=tion:absolute; left:274pt;top:457pt;width:63pt;height:18pt' coordorigin=3D"112,2792" coordsize=3D"600,208"> <v:oval id=3D"_x0000_s32786" style=3D'position:absolute;left:118;top:2792; width:194;height:208;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:group id=3D"_x0000_s32787" style=3D'position:absolute;left:11=2;top:2792; width:600;height:208' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32788" style=3D'position:absolute;left:576;top:269=6; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32789" style=3D'position:absolute;left:82=4;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled==3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32790" style=3D'position:absolute;left:10=72; top:2696;width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32779,_x0000_s32780,_x0000_s32782,_x0000_s32783,_x0000=_s32784,_x0000_s32785,_x0000_s32786,_x0000_s32788,_x0000_s32789,_x0000_s327=90" src=3D"slide0024_image276.gif" style=3D'position:absolute;top:84.5%;left:2=8.08%; width:19.1%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32780" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.75%;left:29.02%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>9</span></div> <div v:shape=3D"_x0000_s32786" class=3DO style=3D'text-align:center;positi=on:absolute;

top:84.5%;left:38.01%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>11</span></div> <v:oval id=3D"_x0000_s32792" style=3D'position:absolute;left:346.625pt;top=:457pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' o:regroupid=3D"1" fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32792" src=3D"slide0024_image277.gif" style=3D'position:absolute;top:84.5%;left:4=8.12%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32792_AllText" v:shape=3D"_x0000_s32792" class=3DO style=3D'position:absolute;top:84.5%;left:48.12%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>14</span></div> </div> <v:group id=3D"_x0000_s32793" style=3D'position:absolute;left:346pt;top:45=7pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240" o:regroupid=3D"1"> <v:rect id=3D"_x0000_s32794" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32795" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32796" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32793,_x0000_s32794,_x0000_s32795,_x0000_s32796" src=3D"slide0024_image278.gif" style=3D'position:absolute;top:84.5%;left:4=7.94%; width:9.17%;height:4.0%'><![endif]><v:group id=3D"_x0000_s32797" style=3D'=position:absolute; left:419pt;top:457pt;width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32798" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32799" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32800" style=3D'position:absolute;left:107=

2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32797,_x0000_s32798,_x0000_s32799,_x0000_s32800" src=3D"slide0024_image279.gif" style=3D'position:absolute;top:84.5%;left:5=8.05%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s32801" style=3D'p=osition:absolute; left:450.625pt;top:495pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32801" src=3D"slide0024_image280.gif" style=3D'position:absolute;top:91.5%;left:6=2.54%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32801" class=3DO style=3D'text-align:center;positi=on:absolute; top:91.5%;left:62.54%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>24</span></div> <v:oval id=3D"_x0000_s32806" style=3D'position:absolute;left:471.625pt;top=:497pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32806" src=3D"slide0024_image281.gif" style=3D'position:absolute;top:92.0%;left:6=5.54%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32806" class=3DO style=3D'text-align:center;positi=on:absolute; top:92.0%;left:65.35%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>26</span></div> <v:group id=3D"_x0000_s32807" style=3D'position:absolute;left:529pt;top:38=5pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32808" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32809" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32810" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32807,_x0000_s32808,_x0000_s32809,_x0000_s32810" src=3D"slide0024_image282.gif" style=3D'position:absolute;top:71.25%;left:=73.4%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s32811" style=3D'p=

osition:absolute; left:419.625pt;top:457pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32811" src=3D"slide0024_image283.gif" style=3D'position:absolute;top:84.5%;left:5=8.23%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32811_AllText" v:shape=3D"_x0000_s32811" class=3DO style=3D'position:absolute;top:84.5%;left:58.23%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>18</span></div> </div> <v:group id=3D"_x0000_s32812" style=3D'position:absolute;left:386pt;top:38=5pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32813" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32814" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32815" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32812,_x0000_s32813,_x0000_s32814,_x0000_s32815" src=3D"slide0024_image284.gif" style=3D'position:absolute;top:71.25%;left:=53.55%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s32816" style=3D'p=osition:absolute; left:122.625pt;top:5in;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32816" src=3D"slide0024_image285.gif" style=3D'position:absolute;top:66.5%;left:1=7.04%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32816" class=3DO style=3D'text-align:center;positi=on:absolute; top:66.5%;left:17.6%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>3</span></div> <v:oval id=3D"_x0000_s32817" style=3D'position:absolute;left:397.625pt;top=:218pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32817" src=3D"slide0024_image286.gif" style=3D'position:absolute;top:40.25%;left:=55.24%; width:3.18%;height:4.0%'><![endif]>

<div id=3D"_x0000_s32817_AllText" v:shape=3D"_x0000_s32817" class=3DO style=3D'position:absolute;top:40.25%;left:55.05%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>13</span></div> </div> <v:oval id=3D"_x0000_s32818" style=3D'position:absolute;left:296.625pt;top=:457pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32818" src=3D"slide0024_image287.gif" style=3D'position:absolute;top:84.5%;left:4=1.19%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32818" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.5%;left:41.19%;width:3.18%;height:4.0%'><span style=3D'font-size:75=%'>12</span></div> <v:oval id=3D"_x0000_s32819" style=3D'position:absolute;left:227.625pt;top=:361pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32819" src=3D"slide0024_image288.gif" style=3D'position:absolute;top:66.75%;left:=31.64%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32819" class=3DO style=3D'text-align:center;positi=on:absolute; top:66.75%;left:31.46%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>10</span></div> <v:oval id=3D"_x0000_s32820" style=3D'position:absolute;left:206.625pt;top=:5in; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32820" src=3D"slide0024_image289.gif" style=3D'position:absolute;top:66.5%;left:2=8.65%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32820" class=3DO style=3D'text-align:center;positi=on:absolute; top:66.5%;left:29.4%;width:1.68%;height:4.0%'><span style=3D'font-size:75%='>8</span></div> <v:oval id=3D"_x0000_s32821" style=3D'position:absolute;left:166.625pt;top=:487pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32821" src=3D"slide0024_image290.gif" style=3D'position:absolute;top:90.0%;left:2=3.03%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32821" class=3DO style=3D'text-align:center;positi=on:absolute; top:90.0%;left:23.78%;width:1.68%;height:4.0%'><span style=3D'font-size:75=%'>6</span></div> <v:oval id=3D"_x0000_s32822" style=3D'position:absolute;left:332.625pt;top=:281pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/>

</v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32822" src=3D"slide0024_image291.gif" style=3D'position:absolute;top:52.0%;left:4=6.06%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32822_AllText" v:shape=3D"_x0000_s32822" class=3DO style=3D'position:absolute;top:52.0%;left:46.81%;width:1.68%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>5</span></div> </div> <v:oval id=3D"_x0000_s32823" style=3D'position:absolute;left:80.625pt;top:=458pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32823" src=3D"slide0024_image292.gif" style=3D'position:absolute;top:84.75%;left:=11.23%; width:3.18%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32823" class=3DO style=3D'text-align:center;positi=on:absolute; top:84.75%;left:11.79%;width:1.68%;height:4.0%'><span style=3D'font-size:7=5%'>2</span></div> <v:oval id=3D"_x0000_s32824" style=3D'position:absolute;left:607.625pt;top=:485pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><v:oval id=3D"_x0000_s32825" style=3D'position:absolute;left:629.=625pt; top:485pt;width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:mi=ddle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32824,_x0000_s328=25" src=3D"slide0024_image293.gif" style=3D'position:absolute;top:89.75%;left:=84.26%; width:6.36%;height:4.0%'><![endif]> <div v:shape=3D"_x0000_s32824" class=3DO style=3D'text-align:center;positi=on:absolute; top:89.75%;left:84.26%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>29</span></div> <div v:shape=3D"_x0000_s32825" class=3DO style=3D'text-align:center;positi=on:absolute; top:89.75%;left:87.45%;width:3.18%;height:4.0%'><span style=3D'font-size:7=5%'>30</span></div> <v:oval id=3D"_x0000_s32827" style=3D'position:absolute;left:460.625pt;top=:282pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32827" src=3D"slide0024_image294.gif" style=3D'position:absolute;top:52.25%;left:=63.85%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32827_AllText" v:shape=3D"_x0000_s32827" class=3DO style=3D'position:absolute;top:52.25%;left:63.85%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>22</span></div> </div>

<v:oval id=3D"_x0000_s32828" style=3D'position:absolute;left:387.625pt;top=:386pt; width:20.375pt;height:18pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32828" src=3D"slide0024_image295.gif" style=3D'position:absolute;top:71.5%;left:5=3.74%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32828_AllText" v:shape=3D"_x0000_s32828" class=3DO style=3D'position:absolute;top:71.5%;left:53.74%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>15</span></div> </div> <v:line id=3D"_x0000_s32829" style=3D'position:absolute;flip:x' from=3D"37=8pt,403pt" to=3D"387pt,457pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32829" src=3D"slide0024_image296.gif" style=3D'position:absolute;top:74.5%;left:5=2.05%; width:2.05%;height:10.75%'><![endif]><v:line id=3D"_x0000_s32830" style=3D='position:absolute' from=3D"407pt,403pt" to=3D"451pt,457pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32830" src=3D"slide0024_image297.gif" style=3D'position:absolute;top:74.5%;left:5=6.55%; width:6.92%;height:11.0%'><![endif]><v:group id=3D"_x0000_s32832" style=3D='position:absolute; left:607pt;top:485pt;width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32833" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32834" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32835" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32832,_x0000_s32833,_x0000_s32834,_x0000_s32835" src=3D"slide0024_image298.gif" style=3D'position:absolute;top:89.75%;left:=84.26%; width:9.17%;height:4.0%'><![endif]><v:oval id=3D"_x0000_s32842" style=3D'p=osition:absolute; left:530.625pt;top:385pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]">

<v:shadow color=3D"#00007d [2]"/> </v:oval><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s32842" src=3D"slide0024_image299.gif" style=3D'position:absolute;top:71.25%;left:=73.59%; width:3.18%;height:4.0%'><![endif]> <div id=3D"_x0000_s32842_AllText" v:shape=3D"_x0000_s32842" class=3DO style=3D'position:absolute;top:71.25%;left:73.59%;width:3.18%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;position:absolute;top:0%;left:0%;width:100=.0%; height:100.0%'><span style=3D'font-size:75%'>28</span></div> </div> <v:group id=3D"_x0000_s32843" style=3D'position:absolute;left:166pt;top:48=8pt; width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32844" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32845" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32846" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><v:group id=3D"_x0000_s32847" style=3D'position:absolu=te; left:91pt;top:487pt;width:63pt;height:18pt' coordorigin=3D"576,2696" coordsize=3D"744,240"> <v:rect id=3D"_x0000_s32848" style=3D'position:absolute;left:576;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32849" style=3D'position:absolute;left:824=;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect><v:rect id=3D"_x0000_s32850" style=3D'position:absolute;left:107=2;top:2696; width:248;height:240;mso-wrap-style:none;v-text-anchor:middle' filled=3D="f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> </v:rect></v:group><v:oval id=3D"_x0000_s32851" style=3D'position:absolut=e; left:188.625pt;top:488pt;width:20.375pt;height:18pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#cccce6 [7]" strokecolor=3D"black [1]"> <v:shadow color=3D"#00007d [2]"/>

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------=_NextPart_01C51A5F.96C81F00Content-Location: file:///C:/D0F41253/lec13_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_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=3D16, 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("slide0001.htm",1,-1,1),new hrefList(="slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("=slide0004.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("s=lide0016.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("sl=ide0018.htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("sli=de0009.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slid=e0021.htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide=0023.htm",1,-1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("slide0=014.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()

else

EndShow()}

}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 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

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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"../lec13.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\D0F41253\lec13_files\outline.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DRobots content=3DNoIndex><script src=3Dscript.js></script><script></script><style></style></head>

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<div id=3DOtlNavObj onload=3D"Load()" onmouseover=3D"BtnOnOver()"onmousedown=3D"BtnOnDown()" onmouseout=3D"BtnOnOut()" onmouseup=3D"BtnOnUp(=)"onkeypress=3D"_KPH()" style=3D'display:none;visibility:hidden'>

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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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<div id=3DOtlObj style=3D'display:none;visibility:hidden;'>

<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('slide0001.htm');" id=3DPPTL1>(2,4) Trees</a><=/font></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>What are they?</li> <ul> <li>They are search Trees (but not binary search trees)</li> <li>They are also known as 2-4, 2-3-4 trees</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>2</font></div> </td> <td> <div id=3DPPTP2 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0002.htm');" id=3DPPTL2>Multi-way Search= Trees</a></font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Each internal node of a multi-way search tree T:</li> <ul> <li>has at least two children</li> <li>stores a collection of items of the form (k, x), where k is a key a=nd x is an element</li> <li>contains d - 1 items, where d is the number of children</li> <li>Has pointers to d children</li> </ul> <li>Children of each internal node are “between” items</li> <li>all keys in the subtree rooted at the child fall between keys of tho=se items.</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('slide0003.htm');" id=3DPPTL3>Multi-way Search=ing</a></font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Similar to binary searching</li> <ul> <li>If search key s<k<sub>1</sub><sub> </sub>search the leftmost chi=ld</li> <li>If s>k<sub>d-1</sub> ,<span style=3D'mso-spacerun:yes'> </span>search the rightmost child</li> </ul> <li>That’s it in a binary tree; what about if d>2?</li> <ul> <li>Find two keys k<sub>i-1</sub> and k<sub>i</sub> between which s fal=ls, and search the child v<sub>i</sub>.</li> </ul> <li>What would an in-order traversal look like?</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('slide0004.htm');" id=3DPPTL4>(2,4) Trees</a><=/font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Properties:</li> <ul> <li>At most 4 children</li> <li>All leaf nodes are at the same level.</li> <li>Height h of (2,4) tree is at least log<sub>4</sub> n and atmost log=<sub>2</sub> n</li> </ul> <li>How is the last fact useful in searching?</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('slide0015.htm');" id=3DPPTL5>Insertion</a></f=ont></div> <div id=3DPPTC5 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>No problem if the node has empty space</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('slide0016.htm');" id=3DPPTL6>Insertion(2)</a>=</font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Nodes get split if there is insufficient space.</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>7</font></div> </td> <td> <div id=3DPPTP7 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0017.htm');" id=3DPPTL7>Insertion(3)</a>=</font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>One key is promoted to parent and inserted in there</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('slide0018.htm');" id=3DPPTL8>Insertion(4)</a>=</font></div> <div id=3DPPTC8 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If parent node does not have sufficient space then it is split.</li> <li>In this manner splits can cascade.</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('slide0019.htm');" id=3DPPTL9>Insertion(5)</a>=</font></div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Eventually we may have to create a new root.</li> <li>This increases the height of the 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>10</font></div> </td> <td> <div id=3DPPTP10 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0009.htm');" id=3DPPTL10>Time for Search and<span style=3D'mso-spacerun:yes'> </span>Insertion</a></font></d=iv> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A search visits<span style=3D'mso-spacerun:yes'> </span>O(log =N) nodes</li> <li>An insertion requires O(log N) node splits</li> <li>Each node split takes constant time</li> <li>Hence, operations Search and Insert each take time O(log 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>11</font></div> </td> <td> <div id=3DPPTP11 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0020.htm');" id=3DPPTL11>Deletion</a></f=ont></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Delete 21.</li> <li>No problem if key to be deleted is in a leaf with at least 2 keys</l=i> </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>12</font></div> </td> <td>

<div id=3DPPTP12 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0021.htm');" id=3DPPTL12>Deletion(2)</a>=</font></div> <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If key to be deleted is in an internal node then we swap it with its predecessor (which is in a leaf) and then delete it.</li> <li>Delete 25</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>13</font></div> </td> <td> <div id=3DPPTP13 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0022.htm');" id=3DPPTL13>Deletion(3)</a>=</font></div> <div id=3DPPTC13 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If after deleting a key a node becomes empty then we borrow a key fr=om its sibling.</li> <li>Delete 20</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>14</font></div> </td> <td> <div id=3DPPTP14 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0023.htm');" id=3DPPTL14>Deletion(4)</a>=</font></div> <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If sibling has only one key then we merge with it.</li> <li>The key in the parent node separating these two siblings moves down =into the merged node.</li> <li>Delete 23</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>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0024.htm');" id=3DPPTL15>Delete(5)</a></=font></div> <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2>

<ul> <li>Moving a key down from the parent corresponds to deletion in the par=ent node.</li> <li>The procedure is the same as for a leaf node.</li> <li>Can lead to a cascade .</li> <li>Delete 18</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>16</font></div> </td> <td> <div id=3DPPTP16 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0014.htm');" id=3DPPTL16>(2,4) Conclusio=n</a></font></div> <div id=3DPPTC16 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The height of a (2,4) tree is O(log n).</li> <li>Split, transfer, and merge each take O(1).</li> <li>Search, insertion and deletion each take O(log n) .</li> <li>Why are we doing this?</li> <ul> <li>(2,4) trees are fun! Why else would we do it?</li> <li>Well, there’s another reason, too.</li> <li>They’re pretty fundamental to the idea of Red-Black trees as well.</li> </ul> <li></li> </ul> </font></div> </td> </tr></table>

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