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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"lec9_files/filelist.xml"><link rel=3DPreview href=3D"lec9_files/preview.wmf"><link rel=3DEdit-Time-Data href=3D"lec9_files/editdata.mso"><link rel=3DOLE-Object-Data href=3D"lec9_files/oledata.mso"><title>Searching</title><link rel=3DPresentation-XML href=3D"lec9_files/pres.xml"><meta name=3DDescription content=3D"2/2/2005: Deletion"><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"../lec9.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]><base href=3D"file:///C:\2687A099\lec9_files\master12.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DRobots content=3DNoIndex><link rel=3DStylesheet href=3D"master12_stylesheet.css"><![if !ppt]><script src=3Dscript.js></script><script></script><![endif]></head>

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<div v:shape=3D"_x0000_s132098" class=3DO style=3D'text-align:center;mso-ch=ar-wrap:1;mso-kinsoku-overflow:1'><span style=3D'font-family:Arial;font-size:50%;mso-field-code:meta15'>‹footer›</span><span style=3D'font-famil=y:Arial;font-size:50%;mso-special-format:lastCR'> </span></div>

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<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec9.htm"><link rel=3DPreview href=3Dpreview.wmf><title>Searching</title><![if IE]><base href=3D"file:///C:\2687A099\lec9_files\slide0105.htm"id=3D"webarch_temp_base_tag"><![endif]><meta name=3DDescription content=3D"2/2/2005: Deletion"><link rel=3DStylesheet href=3D"master12_stylesheet.css"><![if !ppt]><style media=3Dprint></style><script src=3Dscript.js></script><script></script><![endif]><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"110"/></o:shapelayout></head>

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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#CCCCE6;clip:rect(=0%, 101%, 101%, 0%);visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#00007D,#000000,#9999FF,#9999CC,#666699,#CCCCE6" masterhref=3D"master12.xml"> <p:shaperange href=3D"master12.xml#_x0000_s132097"/><![if !ppt]><p:shapera=nge href=3D"master12.xml#_x0000_s132098"/><p:shaperange href=3D"master12.xml#_x0000_s132099"/> <div v:shape=3D"_x0000_s132099" class=3DO style=3D'text-align:right;mso-ch=ar-wrap: 1;mso-kinsoku-overflow:1;position:absolute;top:94.0%;left:72.65%;width:21.=53%; height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-fi=eld-code: meta16'>1</span><span style=3D'font-family:"Arial Black";font-size:50%; mso-special-format:lastCR;display:none'> </span></div> <p:shaperange href=3D"master12.xml#_x0000_s132100"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s132100,_x0000_s132101,_x0000_s132102,_x0000_s132103,_x=0000_s132104,_x0000_s132105,_x0000_s132106,_x0000_s132107,_x0000_s132108,_x=0000_s132109" src=3D"master12_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master12.xml#_x0000_s132112"/><![endif]><p:shaperange href=3D"master12.xml#_x0000_m132110"/><v:shape id=3D"_x0000_s112642" type==3D"#_x0000_m132110" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:108pt' 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"master12.xml#_x0000_m132111"/><v:shape id=3D"_x0000_s112643" type==3D"#_x0000_m132111" style=3D'position:absolute;left:36pt;top:156pt;width:9in;height:306pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s112642" class=3DT style=3D'position:absolute;top:1=2.75%; left:5.99%;width:88.2%;height:8.5%'><span lang=3DDA>Deletion</span></div> <div v:shape=3D"_x0000_s112643">

<div class=3DB style=3D'position:absolute;top:30.0%;left:5.99%;width:88.2%; height:6.75%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.=75%; height:100.0%'><span class=3DBB style=3D'position:absolute;left:-4.43%;top=:.3em'>¨</span><span lang=3DDA>Delete node </span><span lang=3DDA><i>x</i></span><span lang=3DD=A> from a tree </span><span lang=3DDA><i>T</i></span><span lang=3DDA style=3D'displa=y:none'> </span></span></div> <div class=3DB style=3D'position:absolute;top:38.5%;left:5.99%;width:88.2%; height:6.75%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.=75%; height:100.0%'><span class=3DBB style=3D'position:absolute;left:-4.43%;top=:.3em'>¨</span><span lang=3DDA>We can distinguish three cases </span></span></div> <div class=3DB1 style=3D'position:absolute;top:46.75%;left:11.04%;width:83=.14%; height:6.0%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17=%; height:100.0%'><span class=3DB1B style=3D'position:absolute;left:-3.74%; top:.3em'>¨</span><span lang=3DDA><i>x </i></span><span lang=3DDA>has =no children </span></span></div> <div class=3DB1 style=3D'position:absolute;top:54.25%;left:11.04%;width:83=.14%; height:6.0%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17=%; height:100.0%'><span class=3DB1B style=3D'position:absolute;left:-3.74%; top:.3em'>¨</span><span lang=3DDA><i>x</i></span><span lang=3DDA> has =one child </span></span></div> <div class=3DB1 style=3D'position:absolute;top:61.75%;left:11.04%;width:83=.14%; height:6.0%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17=%; height:100.0%'><span class=3DB1B style=3D'position:absolute;left:-3.74%; top:.3em'>¨</span><span lang=3DDA><i>x</i></span><span lang=3DDA> has =two children</span></span></div> </div></p:slide></div>

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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#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"master12.xml"> <p:shaperange href=3D"master12.xml#_x0000_s132097"/><![if !ppt]><p:shapera=nge href=3D"master12.xml#_x0000_s132098"/><p:shaperange href=3D"master12.xml#_x0000_s132099"/> <div v:shape=3D"_x0000_s132099" class=3DO> <div style=3D'text-align:right;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:94.0%;left:72.65%;width:21.53%;height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-field-code:meta16'>5<=/span><span style=3D'font-family:"Arial Black";font-size:50%;mso-special-format:lastCR; display:none'> </span></div> </div> <p:shaperange href=3D"master12.xml#_x0000_s132100"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s132100,_x0000_s132101,_x0000_s132102,_x0000_s132103,_x=0000_s132104,_x0000_s132105,_x0000_s132106,_x0000_s132107,_x0000_s132108,_x=0000_s132109" src=3D"master12_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master12.xml#_x0000_s132112"/><![endif]><p:shaperange href=3D"master12.xml#_x0000_m132110"/><v:shape id=3D"_x0000_s116738" type==3D"#_x0000_m132110" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:108pt' 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><v:rect id=3D"_x0000_s116739" st=yle=3D'position:absolute; left:65pt;top:119.75pt;width:571.5pt;height:377.25pt' filled=3D"f" fillco=lor=3D"#99f [4]" stroked=3D"f" strokecolor=3D"black [1]" strokeweight=3D"1pt"> <v:fill color2=3D"white [0]"/> <v:stroke startarrowwidth=3D"narrow" startarrowlength=3D"short" endarroww=idth=3D"narrow" endarrowlength=3D"short"/> <v:shadow color=3D"#00007d [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> </v:rect> <div v:shape=3D"_x0000_s116738" class=3DT style=3D'position:absolute;top:1=2.75%; left:5.99%;width:88.2%;height:8.5%'><span lang=3DDA>Delete Pseudocode</spa=n></div> <div v:shape=3D"_x0000_s116739" class=3DO style=3D'tab-stops:.25in .4722in= .7083in .9444in 1.1805in 1.4166in 1.6527in 1.8906in 2.1267in 2.3628in 2.59=89in'> <div style=3D'text-align:justify;position:absolute;top:23.0%;left:10.11%; width:25.09%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=

ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:83%'><b>TreeDelete</b></span=><span lang=3DEN-GB style=3D'font-family:"Courier New";mso-ascii-font-family:"Cou=rier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:83%'>(T,z) </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:27.0%;left:10.11%; width:55.24%;height:4.5%'><nobr><span style=3D'font-family:"Courier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'>01</span><span style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> </span><span lang=3DDA style=3D'font-family:"Courier =New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> left[z] </span><span lang=3DDA style=3D'font-family:Symbol; mso-ascii-font-family:Symbol;mso-bidi-font-family:"Courier New";mso-hansi-=font-family: Symbol;font-size:75%'>=3D</span><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> NIL or right[z] =3D NI=L</span><span style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Courier New";mso-hansi-font-family:"Courier New"; font-size:75%;display:none'> </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:31.0%;left:10.11%; width:23.59%;height:4.5%'><nobr><span style=3D'font-family:"Courier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'>02</span><span style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> </span><span lang=3DDA style=3D'font-family:"Courier =New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'><span style=3D'mso-spacerun:yes'> </span></span><span lang=3DDA style=3D'f=ont-family: "Courier New";mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Ti=mes New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'><b>then </b></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'>y </span><span style=3D'font-family:Symbol;mso-ascii-font-f=amily: Symbol;mso-bidi-font-family:"Courier New";mso-hansi-font-family:Symbol; font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier N=ew"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> z </span></nobr></=div> <div style=3D'text-align:justify;position:absolute;top:35.0%;left:10.11%; width:45.88%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>03<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA

style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>else</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> y </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> TreeSuccessor(z) </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:39.0%;left:10.11%; width:28.46%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'>04 </span><span lang=3D=DA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Courier New";mso-hansi-font-family:"Courier New"; font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Couri=er New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'> left[y] </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¹</span><sp=an lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> NIL </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:43.0%;left:10.11%; width:32.58%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>05<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>then</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> x </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> left[y] </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:47.0%;left:10.11%; width:34.08%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>06<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>else</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> x </span><span

style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> right[y] </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:51.0%;left:10.11%; width:19.47%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>07 </span><span lang=3D=DA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Couri=er New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> x </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¹</span><sp=an lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> NIL </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:55.0%;left:10.11%; width:32.58%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>08<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>then</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> p[x] </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> p[y] </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:59.5%;left:10.11%; width:23.97%;height:4.0%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>09 </span><span lang=3D=DA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Couri=er New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> p[y] =3D NIL </spa=n></nobr></div> <div style=3D'text-align:justify;position:absolute;top:63.0%;left:10.11%; width:32.58%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>10<span

style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>then</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> root[T] </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> x </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:67.5%;left:10.11%; width:40.44%;height:4.0%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>11<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>else</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> </span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Couri=er New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> y =3D left[p[y]] <=/span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:71.0%;left:10.11%; width:39.88%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>12<span style=3D'mso-spacerun:yes'>     </span></span><span la=ng=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>then</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> left[p[y]] </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> x </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:75.0%;left:10.11%; width:41.38%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>13<span style=3D'mso-spacerun:yes'>     </span></span><span la=ng=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>else</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New";

mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> right[p[y]] </span><sp=an style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> x </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:79.0%;left:10.11%; width:16.47%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>14 </span><span lang=3D=DA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>if</b></span><span lang=3DDA style=3D'font-family:"Couri=er New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> y </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¹</span><sp=an lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> z </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:83.0%;left:10.11%; width:72.84%;height:4.5%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'>15<span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'><b>then</b></span><span lang=3DDA style=3D'font-family:"Cou=rier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Times New Roman"; mso-hansi-font-family:"Courier New";font-size:75%'> key[z] </span><span style=3D'font-family:Symbol;mso-ascii-font-family:Symbol;mso-bidi-font-fam=ily: "Courier New";mso-hansi-font-family:Symbol;font-size:75%'>¬</span><span lang=3DDA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courie=r New"; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:"Courier New"; font-size:75%'> key[y] //copy all fileds of y </span></nobr></div> <div style=3D'text-align:justify;position:absolute;top:87.5%;left:10.11%; width:16.66%;height:4.0%'><nobr><span lang=3DDA style=3D'font-family:"Cour=ier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'>16 </span><span lang=3D=DA style=3D'font-family:"Courier New";mso-ascii-font-family:"Courier New"; mso-bidi-font-family:"Courier New";mso-hansi-font-family:"Courier New"; font-size:75%'><b>return</b></span><span lang=3DDA style=3D'font-family:"C=ourier New"; mso-ascii-font-family:"Courier New";mso-bidi-font-family:"Courier New"; mso-hansi-font-family:"Courier New";font-size:75%'> y</span></nobr></div> </div></p:slide></div>

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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;width:534px;height:400px;font-size:16px;background-color:#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"master12.xml"> <p:shaperange href=3D"master12.xml#_x0000_s132097"/><![if !ppt]><p:shapera=nge href=3D"master12.xml#_x0000_s132098"/><p:shaperange href=3D"master12.xml#_x0000_s132099"/> <div v:shape=3D"_x0000_s132099" class=3DO> <div style=3D'text-align:right;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:94.0%;left:72.65%;width:21.53%;height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-field-code:meta16'>11=</span><span style=3D'font-family:"Arial Black";font-size:50%;mso-special-format:lastCR; display:none'> </span></div> </div> <p:shaperange href=3D"master12.xml#_x0000_s132100"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s132100,_x0000_s132101,_x0000_s132102,_x0000_s132103,_x=0000_s132104,_x0000_s132105,_x0000_s132106,_x0000_s132107,_x0000_s132108,_x=0000_s132109" src=3D"master12_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master12.xml#_x0000_s132112"/><![endif]><p:shaperange href=3D"master12.xml#_x0000_m132110"/><v:shape id=3D"_x0000_s139266" type==3D"#_x0000_m132110" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:108pt' 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"master12.xml#_x0000_m132111"/><v:shape id=3D"_x0000_s139267" type==3D"#_x0000_m132111" style=3D'position:absolute;left:36pt;top:156pt;width:9in;height:306pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s139266" class=3DT><span style=3D'position:absolute; top:9.0%;left:5.99%;width:98.12%;height:7.75%'><span style=3D'font-size:90=%'>Expected insertion time for a random </span></span><span style=3D'position:absolute; top:17.0%;left:5.99%;width:88.2%;height:7.75%'><span style=3D'font-size:90=%'>permutation</span></span></div> <div v:shape=3D"_x0000_s139267" class=3DB> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:29.5%;left:9.73%;width:100.56%;height:6.75%'><span style=3D'mso-specia=

l-format: bullet;color:#9999CC;mso-color-index:5;position:absolute;left:-3.72%; top:.3em;font-family:Wingdings;font-size:75%'>¨</span>We will compute =the average time taken to </span><span style=3D'position:absolute;top:35.75%; left:9.73%;width:98.5%;height:6.75%'>insert keys in the order specified by= the n! </span><span style=3D'position:absolute;top:42.25%;left:9.73%;width:84.=45%; height:6.75%'>permutations. </span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:50.0%;left:9.73%;width:84.45%;height:6.75%'><span style=3D'mso-special=-format: bullet;color:#9999CC;mso-color-index:5;position:absolute;left:-4.43%; top:.3em;font-family:Wingdings;font-size:75%'>¨</span>In other words, =for each of the n! </span><span style=3D'position:absolute;top:56.25%;left:9.7=3%; width:90.44%;height:6.75%'>permutations we will compute the time </span><s=pan style=3D'position:absolute;top:62.75%;left:9.73%;width:98.12%;height:6.75%='>taken to insert keys in that order and then </span><span style=3D'position:absol=ute; top:69.0%;left:9.73%;width:84.45%;height:6.75%'>compute the average. <=/span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:77.0%;left:=5.99%; width:88.2%;height:6.75%'><span style=3D'position:absolute;top:0%;left:4.2=4%; width:95.75%;height:100.0%'><span style=3D'mso-special-format:bullet;color=:#9999CC; mso-color-index:5;position:absolute;left:-4.43%;top:.3em;font-family:Wingd=ings; font-size:75%'>¨</span>Let T(n) denote this quantity.</span></div> </div></p:slide></div>

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<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"master12.xml"> <p:shaperange href=3D"master12.xml#_x0000_s132097"/><![if !ppt]><p:shapera=nge href=3D"master12.xml#_x0000_s132098"/><p:shaperange href=3D"master12.xml#_x0000_s132099"/> <div v:shape=3D"_x0000_s132099" class=3DO> <div style=3D'text-align:right;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:94.0%;left:72.65%;width:21.53%;height:3.5%'><span style=3D'font-family:"Arial Black";font-size:50%;mso-field-code:meta16'>19=</span><span style=3D'font-family:"Arial Black";font-size:50%;mso-special-format:lastCR; display:none'> </span></div> </div> <p:shaperange href=3D"master12.xml#_x0000_s132100"/><![if !vml]><img borde=r=3D0 v:shapes=3D"_x0000_s132100,_x0000_s132101,_x0000_s132102,_x0000_s132103,_x=0000_s132104,_x0000_s132105,_x0000_s132106,_x0000_s132107,_x0000_s132108,_x=0000_s132109" src=3D"master12_image001.gif" style=3D'position:absolute;top:0%;left:0%; width:100.37%;height:8.5%'><![endif]><p:shaperange href=3D"master12.xml#_x0000_s132112"/><![endif]><p:shaperange href=3D"master12.xml#_x0000_m132110"/><v:shape id=3D"_x0000_s147458" type==3D"#_x0000_m132110" style=3D'position:absolute;left:36pt;top:36pt;width:9in;height:1in' 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"master12.xml#_x0000_m132111"/><v:shape id=3D"_x0000_s147459" type==3D"#_x0000_m132111" style=3D'position:absolute;left:30pt;top:108pt;width:9in;height:54pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape><v:line id=3D"_x00=

00_s147460" style=3D'position:absolute;flip:y' from=3D"2in,174pt" to=3D"2in,414pt" 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_s147460" src=3D"slide0123_image022.gif" style=3D'position:absolute;top:32.25%;left:=19.47%; width:1.31%;height:45.0%'><![endif]> <div v:shape=3D"_x0000_s147458" class=3DT style=3D'position:absolute;top:9=.5%; left:5.99%;width:88.38%;height:8.5%'>Summing the harmonic series</div> <div v:shape=3D"_x0000_s147459" class=3DB style=3D'position:absolute;top:2=1.0%; left:5.24%;width:89.51%;height:6.75%'><span style=3D'position:absolute; top:0%;left:4.18%;width:95.81%;height:100.0%'><span class=3DBB style=3D'po=sition: absolute;left:-4.36%;top:.3em'>¨</span>What is the sum ½+ 1/3 + ¼+…1/n?</span></div> <v:line id=3D"_x0000_s147461" style=3D'position:absolute' from=3D"2in,414p=t" to=3D"570pt,414pt" strokecolor=3D"black [1]"> <v:stroke endarrow=3D"block"/> <v:shadow color=3D"#00007d [2]"/> </v:line><v:shape id=3D"_x0000_s147462" style=3D'position:absolute;left:16=8pt; top:174pt;width:408pt;height:234pt' coordsize=3D"3264,1872" path=3D"m,c64=,352,128,704,192,912v64,208,128,248,192,336c448,1336,515,1392,576,1440v61,4=8,109,65,173,97c813,1569,797,1584,960,1632v163,48,384,152,768,192c2112,1864=,2688,1868,3264,1872e" filled=3D"f" fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <v:path arrowok=3D"t"/> </v:shape><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s147461,_x0000_s1=47462" src=3D"slide0123_image023.gif" style=3D'position:absolute;top:32.25%;left:=20.03%; width:60.48%;height:45.5%'><![endif]><v:rect id=3D"_x0000_s147463" style==3D'position:absolute; left:168pt;top:4in;width:24pt;height:126pt;mso-wrap-style:none; v-text-anchor:middle' fillcolor=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"2" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"17408"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147463" src=3D"slide0123_image024.gif" style=3D'positi=on:absolute; top:53.25%;left:23.22%;width:3.74%;height:24.0%'><![endif]> <div id=3D"_x0000_s147463_AllText" v:shape=3D"_x0000_s147463" class=3DO style=3D'position:absolute;top:63.25%;left:22.84%;width:4.3%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/2</span></div> </div> <v:rect id=3D"_x0000_s147464" style=3D'position:absolute;left:192pt;top:33=0pt; width:24pt;height:84pt;mso-wrap-style:none;v-text-anchor:middle' fillcolo=r=3D"#99f [4]" strokecolor=3D"black [1]">

<v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"3" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"17408"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147464" src=3D"slide0123_image025.gif" style=3D'positi=on:absolute; top:61.0%;left:26.59%;width:3.74%;height:16.0%'><![endif]> <div id=3D"_x0000_s147464_AllText" v:shape=3D"_x0000_s147464" class=3DO style=3D'position:absolute;top:67.0%;left:26.21%;width:4.3%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/3</span></div> </div> <v:rect id=3D"_x0000_s147465" style=3D'position:absolute;left:3in;top:354p=t; width:24pt;height:60pt;mso-wrap-style:none;v-text-anchor:middle' fillcolo=r=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"4" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"17408"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147465" src=3D"slide0123_image026.gif" style=3D'positi=on:absolute; top:65.5%;left:29.96%;width:3.74%;height:11.75%'><![endif]> <div id=3D"_x0000_s147465_AllText" v:shape=3D"_x0000_s147465" class=3DO style=3D'position:absolute;top:69.25%;left:29.58%;width:4.3%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/4</span></div> </div> <v:rect id=3D"_x0000_s147466" style=3D'position:absolute;left:240pt;top:37=2pt; width:24pt;height:42pt;mso-wrap-style:none;v-text-anchor:middle' fillcolo=r=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"5" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"17408"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147466" src=3D"slide0123_image027.gif" style=3D'positi=on:absolute; top:68.75%;left:33.33%;width:3.74%;height:8.25%'><![endif]> <div id=3D"_x0000_s147466_AllText" v:shape=3D"_x0000_s147466" class=3DO style=3D'position:absolute;top:71.0%;left:32.95%;width:4.3%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/5</span></div> </div> <v:rect id=3D"_x0000_s147467" style=3D'position:absolute;left:264pt;top:37=8pt; width:24pt;height:36pt;mso-wrap-style:none;v-text-anchor:middle' fillcolo=

r=3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"6" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"17408"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147467" src=3D"slide0123_image028.gif" style=3D'positi=on:absolute; top:70.0%;left:36.7%;width:3.74%;height:7.25%'><![endif]> <div id=3D"_x0000_s147467_AllText" v:shape=3D"_x0000_s147467" class=3DO style=3D'position:absolute;top:71.5%;left:36.14%;width:4.3%;height:4.0%; white-space:nowrap'> <div style=3D'text-align:center;mso-char-wrap:1;mso-kinsoku-overflow:1; position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/6</span></div> </div> <v:shapetype id=3D"_x0000_t202" coordsize=3D"21600,21600" o:spt=3D"202" pa=th=3D"m,l,21600r21600,l21600,xe"> <v:stroke joinstyle=3D"miter"/> <v:path gradientshapeok=3D"t" o:connecttype=3D"rect"/> </v:shapetype><v:shape id=3D"_x0000_s147468" type=3D"#_x0000_t202" style==3D'position:absolute; left:156pt;top:420pt;width:364.5pt;height:28.875pt;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:shape><v:shape id=3D"_x0000_s147469" type=3D"#_x0000_t202" style=3D'po=sition:absolute; left:568.75pt;top:398.875pt;width:23.5pt;height:28.875pt;mso-wrap-style:n=one; 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:shape><v:shape id=3D"_x0000_s147470" type=3D"#_x0000_t202" style=3D'po=sition:absolute; left:124.75pt;top:140.875pt;width:38.5pt;height:28.875pt;mso-wrap-style:n=one; 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:shape> <div v:shape=3D"_x0000_s147468" class=3DO style=3D'mso-char-wrap:1;mso-kin=soku-overflow: 1;position:absolute;top:78.75%;left:22.65%;width:58.61%;height:4.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1<span style=3D'mso-spacerun:yes'>   </span>2<span style=3D'mso-spacerun:yes'>   </span>3<span style=3D'mso-spacerun:yes'> </span>4<span style=3D'mso-spacerun:yes'>   </span>5<span style=3D'mso-spacerun:yes'>   </span>6<span style=3D'mso-spacerun:yes'>       &nbsp=

;            &n=bsp;           &nbsp=;        </span>n </span></div> <div v:shape=3D"_x0000_s147469" class=3DO style=3D'mso-char-wrap:1;mso-kin=soku-overflow: 1;position:absolute;top:74.75%;left:79.96%;width:1.68%;height:4.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>x</span></div> <div v:shape=3D"_x0000_s147470" class=3DO style=3D'mso-char-wrap:1;mso-kin=soku-overflow: 1;position:absolute;top:27.0%;left:18.35%;width:4.11%;height:4.0%'><span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:75%'>1/x</span></div> <v:rect id=3D"_x0000_s147471" style=3D'position:absolute;left:480pt;top:40=8pt; width:24pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' fillcolor==3D"#99f [4]" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <p:animation number=3D"7" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack" flag=3D"16384"/></v:rect><![if !vml]><img border==3D0 v:shapes=3D"_x0000_s147471" src=3D"slide0123_image029.gif" style=3D'positi=on:absolute; top:75.5%;left:66.66%;width:3.74%;height:1.75%'><![endif]><v:shape id=3D"_=x0000_s147472" type=3D"#_x0000_t202" style=3D'position:absolute;left:46.75pt;top:443.125=pt; width:601.25pt;height:74.5pt' filled=3D"f" fillcolor=3D"#99f [4]" stroked==3D"f" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#00007d [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> <p:animation number=3D"9" delay=3D"0" type=3D"object" effect=3D"cut" direction=3D"noBlack"/></v:shape> <div id=3D"_x0000_s147472_AllText" v:shape=3D"_x0000_s147472" class=3DO style=3D'position:absolute;top:83.0%;left:7.49%;width:93.25%;height:12.25%; white-space:nowrap'> <div style=3D'mso-char-wrap:1;mso-kinsoku-overflow:1'><span style=3D'posit=ion: absolute;top:0%;left:0%;width:100.0%;height:48.97%'><span style=3D'font-fa=mily: Arial;mso-ascii-font-family:Arial;mso-bidi-font-family:Arial;font-size:117=%'>It is at most the area under the curve f(x)=3D1/x </span></span><span style=3D'position:absolute;top:51.02%;left:0%;width:87.55%;height:48.97%'>=<span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil=y: Arial;font-size:117%'>between limits 1 and n</span></span></div> </div> <v:shape id=3D"_x0000_s147477" type=3D"#_x0000_t202" style=3D'position:abs=olute; left:468pt;top:378pt;width:39.5pt;height:28.875pt;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]"/>

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

------=_NextPart_01C50927.8AB046F0Content-Location: file:///C:/2687A099/lec9_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=3D22, 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("slide0105.htm",1,-1,1),new hrefList(="slide0106.htm",1,-1,1),new hrefList("slide0107.htm",1,-1,1),new hrefList("=slide0108.htm",1,-1,1),new hrefList("slide0109.htm",1,-1,1),new hrefList("s=lide0112.htm",1,-1,1),new hrefList("slide0110.htm",1,-1,1),new hrefList("sl=ide0111.htm",1,-1,1),new hrefList("slide0113.htm",1,-1,1),new hrefList("sli=de0114.htm",1,-1,1),new hrefList("slide0115.htm",1,-1,1),new hrefList("slid=e0116.htm",1,-1,1),new hrefList("slide0117.htm",1,-1,1),new hrefList("slide=0118.htm",1,-1,1),new hrefList("slide0119.htm",1,-1,1),new hrefList("slide0=120.htm",1,-1,1),new hrefList("slide0121.htm",1,-1,1),new hrefList("slide01=22.htm",1,-1,1),new hrefList("slide0123.htm",1,-1,1),new hrefList("slide012=4.htm",1,-1,1),new hrefList("slide0125.htm",1,-1,1),new hrefList("slide0126=.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('/')+1

if (End < Start)return href.substring(0, Start)

elsereturn href.substring(0, End)

}return '';

}function GetTags(base,tag){

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

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

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

}}function ToggleOtlText(){

gOtlTxtExp=3D!gOtlTxtExpUpdOtlPane()

}function ToggleOtlPane(){

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

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

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

}function ToggleNtsPane(){

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

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

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

}function ClearMedia(){

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

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

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

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

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

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

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

}else{

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

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

}function ToggleVNarration(){

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

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

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

elsereturn;

}else if( PPTSld.g_animUseRuntime ){

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

narObj.togglePause()}

}function GetCurSldNum(){

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

return obj.mSldIdxelse

return gCurSld}function GetNumSlds(){

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

elsereturn GetSldList().mList.length

}function GetSldNum( href ){

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

return ii+1}return 1

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

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

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

}}else {

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

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

GoToSldNum(ii)return

}}if( gSldStack.length > 1 )

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

if( gLoopCont )GoToFirst()

elseEndShow()

}}function GoToPrevSld(){

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

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

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

GoToSldNum(ii)}

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

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

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

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

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

}function GoToSld( href ){

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

}function SldUpdated( id ){

if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return

gPrevSld=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 _TBSetA

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

}function _TBSetA(){

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

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

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

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

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

}function _TBSetD(){

this.ChgState( gFaceClr,gFaceClr,0,0 )this.mIsOn =3D 0

}function _TBSetE(){

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

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

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

}function _TBP(){

var t=3Dthisif( t.mIsOn ) {

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

if( !t.GetState ) return

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

elset.SetActive()

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

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

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

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

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

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

b.Perform()else

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

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

s.display=3D""else

s.display=3D"none"}function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=etActive() }function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=etInactive() }var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=THREEDFACE"var gBtnArr =3D new Array()gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=e,GetOtlState )gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=lPane,GetOtlState )gBtnArr["nb_nts"] =3D new TxtBtn( "nb_nts","nb_ntsElem",parent.ToggleNtsPan=e,GetNtsState )gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToP=revSld )gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToN=extSld )gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=.FullScreen )gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=rent.FullScreen,null )gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=.FullScreen,null )gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;gBtnArr["nb_voice"] =3D new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.=ToggleVNarration )gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent=.ToggleOtlText )gBtnArr["nb_nts"].m_flagId=3D "notes_flag"gBtnArr["nb_nts"].SetFlag =3D NtsBtnSetFlag

gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtStatevar sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"function ShowMenu(){

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

=3DPPTSld.event.clientY+doc.scrollTopm =3D PPTSld.document.all.item("ctxtmenu")m.style.pixelLeft=3Dxif( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )

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

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

}function _CM(){

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

ShowMenu()return false

} elseHideMenu()

}function BuildMenu(){

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

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

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

e.Action()else

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

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

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

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

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

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

}function CreateSeparator( node ){

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

}function CreateItem( node ){

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

}function SetCMBorder( o,ltClr,rbClr ){

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

}

------=_NextPart_01C50927.8AB046F0Content-Location: file:///C:/2687A099/lec9_files/fullscreen.htmContent-Transfer-Encoding: quoted-printableContent-Type: text/html; charset="us-ascii"

<html>

<head><meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"><meta name=3DProgId content=3DPowerPoint.Slide><meta name=3DGenerator content=3D"Microsoft PowerPoint 10"><link id=3DMain-File rel=3DMain-File href=3D"../lec9.htm"><link rel=3DPreview href=3Dpreview.wmf><![if IE]>

<base href=3D"file:///C:\2687A099\lec9_files\fullscreen.htm"id=3D"webarch_temp_base_tag"><![endif]><script src=3Dscript.js></script><script></script></head>

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<table width=3D"100%" style=3D'font-family:Arial;font-size:9pt'> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>1</font></div> </td> <td width=3D"100%"> <div id=3DPPTP1 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0105.htm');" id=3DPPTL1>Deletion</a></fo=nt></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Delete node x from a tree T</li> <li>We can distinguish three cases</li> <ul> <li>x has no children</li> <li>x has one child</li> <li>x has two children</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('slide0106.htm');" id=3DPPTL2>Deletion Case 1<=/a></font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If x has no children – just remove x</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('slide0107.htm');" id=3DPPTL3>Deletion Case 2<=/a></font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If x has exactly one child, then to delete x, simply make p[x] point= to that child</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('slide0108.htm');" id=3DPPTL4>Deletion Case 3<=/a></font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>If x has two children, then to delete it we have to</li> <ul> <li>find its successor (or predecessor) y</li> <li>remove y (note that y has at most one child – why?)</li> <li>replace x with y</li> <br> <br> </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>5</font></div> </td> <td> <div id=3DPPTP5 class=3DPTxt><font size=3D2><a

href=3D"javascript:GoToSld('slide0109.htm');" id=3DPPTL5>Delete Pseudocod=e</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>6</font></div> </td> <td> <div id=3DPPTP6 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0112.htm');" id=3DPPTL6>In order travers=al of a BST</a></font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>ITW can be thought of as a projection of the BST nodes onto a one dimensional interval</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('slide0110.htm');" id=3DPPTL7>BST Sorting</a><=/font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Use TreeInsert and InorderTreeWalk to sort a list of n elements, A</=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('slide0111.htm');" id=3DPPTL8>BST Sorting (2)<=/a></font></div> <div id=3DPPTC8 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Sort the following numbers<br> 5 10 7 1 3 1 8</li> <li>Build a binary search tree</li> <br> <br> <br> <br> <br> <li>Call InorderTreeWalk</li> <br> <br>

<li><span style=3D'mso-spacerun:yes'>      &nbsp=;     </span>1 1 3 5 7 8 10</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('slide0113.htm');" id=3DPPTL9>In what order sh=ould we insert?</a></font></div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>We want to sort numbers {1,2,…,n}</li> <li>Total time taken to insert these numbers equals the sum of the level numbers of the nodes.</li> <li>Thus if numbers were inserted in ascending order we would get a tree= of height n-1 in which there is one node at each level.</li> <li>So total time for insertion in this case is 1+2+3+…+n-1 =3D O(=n<sup>2</sup>).</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('slide0114.htm');" id=3DPPTL10>Inserting a ran=dom permutation</a></font></div> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Suppose we take a random permutation of the keys and inserted them in this order.</li> <li>The total time required for insertion is now a random variable.</li> <li>We want to compute the expected value of this r.v.</li> <li>Recall that the expected value of a r.v. is the average value it tak=es over a large number of trials.</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('slide0115.htm');" id=3DPPTL11>Expected insert=ion time for a random permutation</a></font></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>We will compute the average time taken to insert keys in the order specified by the n! permutations.</li> <li>In other words, for each of the n! permutations we will compute the =time taken to insert keys in that order and then compute the average.</li> <li>Let T(n) denote this quantity.</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>12</font></div> </td> <td> <div id=3DPPTP12 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0116.htm');" id=3DPPTL12>Inserting a ran=dom permutation (2)</a></font></div> <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Of the n! permutations, there are (n-1)! permutations in which the f=irst element is i.</li> <li>The tree formed in these instances has i as the root. The left subtr=ee has keys 1..(i-1) and the right subtree has keys (i+1)..n</li> <li>Consider the ordering of keys 1..(i-1) in the (n-1)! permutations. A=ll (i-1)! permutations appear and each occurs (n-1)!/(i-1)! times.</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('slide0117.htm');" id=3DPPTL13>Inserting a ran=dom permuation(3)</a></font></div> <div id=3DPPTC13 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Recall that if we only had keys 1..(i-1) then average time taken to insert them is T(i-1).</li> <li>The average is taken over all permutations of 1..(i-1).</li> <li>hence total time to insert all (i-1)! permutations is (i-1)!T(i-1).<=/li> <br> <br> </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('slide0118.htm');" id=3DPPTL14>Inserting a ran=dom permutation(4)</a></font></div> <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>When inserting keys 1..(i-1) into the left subtree, each key has to =be compared with the root.</li> <li>This leads to an additional unit cost for each key.</li> <li>So total time to insert all (i-1)! permutations is (i-1)!(T(i-1)+(i-=1)).</li> <li>Since each permutation appears (n-1)!/(i-1)! times, total time to in=sert keys 1..(i-1) is<span style=3D'mso-spacerun:yes'>   &=nbsp; </span>(n-1)!(T(i-1)+(i-1))</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0119.htm');" id=3DPPTL15>Inserting a ran=dom permutation(5)</a></font></div> <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Time to insert keys 1..(i-1) is<span style=3D'mso-spacerun:yes'>      &nbsp=;             </span>(n-1)!(T(i-1)+(i-1))</li> <li>Similarly, time to insert keys (i+1)..n is<span style=3D'mso-spacerun:yes'>     </span>(n-1)!(T(n-i)+(n-i))</li> <li>Total time to insert all n keys in permutations where the first key =is i is<span style=3D'mso-spacerun:yes'>     </span>(=n-1)! (T(i-1)+T(n-i)+ n-1)</li> <li>Total time to insert all n keys in all n! permutations is<span style=3D'mso-spacerun:yes'>      &nbsp=;            &n=bsp;           &nbsp=;        </span>(n-1)! <font face=3DSymbol>å</font><font face=3DArial><=sub>i=3D1</sub><sup>n</sup> (T(i-1)+T(n-i)+ n-1).</font></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('slide0120.htm');" id=3DPPTL16>Building the re=currence</a></font></div> <div id=3DPPTC16 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>We are expressing the value of function T() at point n in terms of t=he value of T() at points 0..n-1. This is called a recurrence relation.=</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>17</font></div> </td> <td> <div id=3DPPTP17 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0121.htm');" id=3DPPTL17>Solving the rec=urrence</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>18</font></div> </td> <td> <div id=3DPPTP18 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0122.htm');" id=3DPPTL18>Solving the recurrence(2)</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>19</font></div> </td> <td> <div id=3DPPTP19 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0123.htm');" id=3DPPTL19>Summing the har=monic series</a></font></div> <div id=3DPPTC19 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>What is the sum ½+ 1/3 + ¼+…1/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>20</font></div> </td> <td> <div id=3DPPTP20 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0124.htm');" id=3DPPTL20>The expected ti=me for insertion</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>21</font></div> </td> <td> <div id=3DPPTP21 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0125.htm');" id=3DPPTL21>Minimum time to= insert n keys</a></font></div> <div id=3DPPTC21 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The time required to insert n keys is minimum when the resulting tree has the smallest possible height.</li> <li>A binary tree on n nodes has height at least log<sub>2</sub> n</li> <li>To insert the n/2 nodes at level log<sub>2</sub> n we require at lea=st (n/2)log<sub>2</sub> n time.</li> <li>Hence inserting n keys requires <font face=3DSymbol>W</font><font face=3DArial>(nlog<sub>2</sub> n) time.</font></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>22</font></div> </td> <td> <div id=3DPPTP22 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0126.htm');" id=3DPPTL22>Summary of Runn=ing times</a></font></div> <div id=3DPPTC22 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>To insert n keys into a binary search tree which is initially empty requires</li> <li>O(n<sup>2</sup>) time in the worst case.</li> <li>O(nlog n) time in the best case.</li> <li>O(nlog n) time in the average case; the average is taken over the n! different orders in which the n keys could be inserted.</li> </ul> </font></div> </td> </tr></table>

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

STxMKoQG8SXxMKkQGsSXxMOkQmgQXxIPkwqhQXxJPEwqhAbxJfEwqRAaxJfEw6RCaBBfEg+TCqFBfEk8TCqEBvEl8TCpEBrEl8TDpEJoEF8SD5MKoUF8STxMKoQG8SXxMKkQGsSXxMOkQmgQXxIPkwqhQXxJPEwqhAbxJfEwqRAaxJfEw6RCaBBfEg+TCqFBfEk8TCqEBvEl8TCpEBrEl8TDpEJoEF8SD5MKoUF8STxMKoQG8SXxMKkQGsSXxMOkQmgQXxIPkwqhQXxJPEwqhAbxJfEwqRAaxJfEw6RCaBBfEg+TCgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC8AEBTEFwAICuILAAQF8QUAgoL4AgBBQXwBgKAgvgBAUBBfACAoiC9RJ+WCsPsI4AxLM7oUYsfwbcPD+4er3xJlIJqwKKNIIV4c2H9A4cP9LVEGogbLMXK4zFmq5DJhbwHAKKzFaFEILl4zF9stiQxEBFZhhKgzcyGLgajBKowKvmQutiwm7G2CZoclGAl8zFzIYiA6sP4iQQ3fFpHFQPRh8YWPSV78zlxKt8QXCBEWX/j4fuRl/HkxYW8iNCmsvJCpdORl997Bni35TCZTfh2AHrakWwr/yOVyA7sGOAoDUYaVFzLVj7wM7hsqBRcFlMLzu3ftnjxpcvHJHvIXiCysvJCZ8JujUnxROlN6vrev1/F58heIFKy8kJnwm6PyOOL4/JSpU/gWCaIJyy5kastfyp93c+4M8QVCgWUXMrXlL729hz8fZZdmyV8gmrDsQqaG/GVw31DhWyQxedJkN98iEV8gFFh2IeM+f8lkMvkt+a6ursKXR+l0WhFnaGiYs3ghsrDsQsZ9/qLI0rezP5fLFeJLS0tLb18vZ/FClGHZhUwNx18G9w6Wzn/Zfm0v+QtEFpZdyNT2/ZGymNKX05y/C5GFlRcytX1/pH+XfznN+bsQTVh5IVNb/pJdli082dLSQv4CkYWVFz7Vc5Dx+UtfX1/pSf2bIy8QWVh84ZNy+v2XwaGhvp39XV1d5d9PK8SUZy59/f18cwRRhsUXCcYfhRncN9Tf368Q43jr5jsj8hcIHRZfJJjwKExttwQXCBfWX1Rw800Qv7wL8YIlGCF8zGIILhAFWIVRoRARfMliCC4QEViIkaA8ItSZxRBcIDqwFsNnfEQofANdw38ngOACkYLlGDJVIsLhKwBc5CwEF4ggrMgwcRkRUhPh6dUAGgYrMjR8DwekMBA1WI7hQCCAZoBVHgLBBRdSGIgUrEVv1H8kNej9n/gC0YG16I3xR1W9Vve9SwCRheXujXriS8OCC1EMIgIL0TO1xZdG7vPEF4gILETP1JDCNH6HJ8RAFGAV1oKn+MKuDk0LS78W3KcwIQYX4hqEDkuwFlzGl3D3cM6FgdBh/dXIhPGFfRuAfaBGqqcw0Qku0ekJNCEsvtqpFF8itUtHqjPQbLD4ascxhYna/hy1/kBTweKrnfHxJZo7czR7Bc0AK68uyuNLZHfjyHYMEg8rry5qOJc3FCLePUgqLLt6iUV8AQgF9op6IYUBqARrri5SYwm7O9WIePcgkbDm6qJ0ZDf68WWEEAMNhwVXO+VfSxNiAMbDaqsR245KfAEYD6utFhyvCSC+ANhgtXmm0gWNcQkxAA2DncEbVcJHXOJLLDoJyYB15oHqu2WMUpjo9xCSAevMLW72ybjEF4DGwJ7gCpchI0bxJRadhLjDIpsY97siH5EAymGRTYDX/TAu8WWEEAPBwwqrRg17YIxSGICgYR+oSM0BIkbxJRadhPiSzOWVmgg3r1B/6zW/QsOISz+hAdS/1zi8pu+9DJfCQBzYf2D4tuEqt9WHrM5djo9IECNKa9XlXuPtxQPqdOMpbLwGYnj/sPvb8ePlS1CIUXyJSz8hCMwu42V/0a2nBZOQheUm+rqJyn7taTGKLyMchWlKXOYsVfYaV60EvRkNoIYYXGdUThhNu+FNSw2ZvmPuP+HKif3CqicG226beTdr5m1vNgrBpTF7TbxXlS+Ziy2LCXubwqFpN7zZ8CVzqX4Ec0xzDdsw3/ExcyGLGSHENAdB7DVVVk5cl5TvmYvLeAwQXxq/18R1X6ryGbJnS37ypMkqoFv9e3DvYOmv+S35lpaW8vNTOpd17h4crO3YePJo2g1vBgLK96tn/bFcTxN+hhy4ZUBl+nb2j/9rb19vKbhkl2U5ClNO0254M+D7kRc3e00s15ObSNzV1bX92l7H50vxRWGonu/2E0kzb3uyqb7XbL92ey7XU0j8C2QyGeX7dR6FieVichOJd+8d1ADZntdHofLh4yiMI8287UnF5ZGXXC5X2kEGh4bIX6rdKlXReCkG92zJF247l3WWhq+vr6+Gz5PNQDNve1Jxec6L9pHSDuLLUZj4rST3x8D7dva3pFt029ffr9vyIy9Tpk6pXreZ97Fm3vak4nKvGRNfyrL+mr9Fit9K8hRZ9SGo9P2RPmGWxk7/5iwYaB7qyV9yuR7yF+dbxRF9Sir8WzlLYeAmT5o84WfLJo8vhYEKuxfgG/XkLy0tLeQvFW/T6fTgvqG+vr7SwLmJx+xdjECSqDl/KTxD/lLxVimMxkgflEoD5+bzJHsXI5AkashftMuUvq4mf6l4q09C5efs6uNSPecjNhUMQmKoLX/ZvWt3dmmW/MVDVO7r768tEjchDEJiqOf4i/mytXnylxHvV1KUTqsz59TVGombE8YhGdR8/GXYOo+stB8lP38ZqelKisJlAduv3V5zJAaIL/XkL6XjlYVAU6mu4y4Ty73Ia/5S+CSpNM9leYJLOYxGMnCz11Q5f3doaHjypMle95pYLp0a8hfdujzywocjG4xGMnCz1zjmL7odHBoqHehNfv4y4vdviJK/QLIphIwqa37gloG+vr7y66dLV+3pY1Hpea/HK+O6I9XwLZKnIy+F0Qx7K6MCoxFfyueuyl4zsGugdKVelVuvxytjvGhqOArj9Zsj9qsSjEPscFy9Qew1VdZGvBeN71mM82dIogzxJVZUWbG1Hbus+ZvWeC+aVBn+Zi6V2mrYpgHUgJtV6u+xy8TGl/LgElDmUqnRoDctmjTztkcfT7PjVxYzcSyre7tCIDWWkbo/VXrdbZp2T2vOrY44ta3GOrMYl43GabmkKlD+1xo+Pda8zzRtlIGIUOcKrDn395Ao1dy5RlIpsozfzsKTLnMWX6JDs0WZptrYyOLjqivtSi5zFk/tRn2tVIksVbazeq0gIkJwUSagDtdMdHrSnDRgpfm4y0R3rTQ4QPhCcJErUtsbqc40D1FbBm6IXHfdpB4RH2V/exjBrY5OT5qESM2+JyLUaZeRJS5j7WM/o7bV0elJ4onUvNdAhLqepOBSwpcOR3Dbo9OTpBKp6a6ZaG1AwoJLiTp7HvfNB08kaaKjtRmJDC4l6tmECI5ApDqTDKI2xfUTuY1JanApUdu2RHAcotOTBBCpmfWRyG1S4uNLgRq2KILjEKnOxJcED2O0Nqw00MkOLiU8bVo0RyNSnYkdUZtN34nKttkGuhmCSwmX2xjNAYlUZ2JE1OYxICKxhY4DHcF9KVDcbGwExyRq/Yk+TTVi4W9nlbFuqpkoUH2To5nCgEuacOLC3NomHG6XVBmZaMaXqPUnakRwyhpDaNvcnMPtCcdFGc0UJlKdiRRRm6kGE86WN/OIe8U2VtGMLzAe5mgklPjCoHvFtlKjGV+i1p8QieDshEVDR4Fxr4fS6EUzhYlUZ8IiapMSOo0bC8bdF1JjCbs7Y4hafxpJBKcjCjRoRBh6f4lsiGlCmIUqBD4ujH4QRDa+RK0/gRLB8Y8awY4Oox8c0fygFKnOBEeTbGb9BDhGTECg2IILK74xMM6eCGSkmIPGMD55icjIR6EPvhORsY0X/o8Xc9AwKn0+Cn1PSNgaCH0844vPo8Y0NJLqx19C3CsSswyILHXi59gxE41nwuO7Ye0hcV8MRBZf8GcEmYywcPkVUuMnKL7rgcXsIz6MI5MRLm7iS3nJBnSp1FzD2vIFIovv1DuaTEnouExhbOWD7lW8YEwCYsyY3nvvvffdd1/1ZyBqeI0v5bWC61WplaCbqBMiS6AcHtl77rlHAz1lypShfUOFZxRcCs/oT+H0DtxRQ3wprxhEl0qvH9yL1wmRpQEcHl/lKbt37VYo6bu5rxBQ9FATcGD/AT2jWBNaH2EiakthbNV971XpxQN65ZohsjQM51FWQNFtz+ae0jSUkhqIJvXEl/JX8LFL5a8cxMvWAJGlwTiPtbIVJS/6ZNS1pqvBHYLaqD++lL+OL10qf01/X7C2PkShG81GxREvfDjSbSN7AxHB373R9mqpqvjVaKXWoZFUHHd9ICocfGlkbyBSBBFlxPBtw8P7hyvd+tgokSV0Ko7+9mu3a2447AL176WlsKK3K5e3kT2WBJ6oOAfpdDqbzfbd3Mf5LzBSxx5rIkvlbMX3XIbIEimcZ+KuO+4qHHwpfGldum1w5yBqeNp7C4Xd5yxVchnf

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k+U2NSTVVKuqNvVEu/XKR6TyGxvUhlSzqkay5S/Jlm/Ilp+dLZcrv1mUj2p7QZHLzjFRtlkq29kQV1Nt+mVbTJSdW6YPV2TLzs+WnacVaijYdzFtXzT0JBrU+cnUcm3nyrVapVrrs7WwBxtFrWW6teYX1UK/MsepSW1Jppbo1log1dqgbbnoYUqrtbhJ75gtlPbBATEmUvN191dUKnu9aGG/ftmYVFZtxPtu0y+7SCrb1Ij33aBfdrFUdrYou0q/bJtUtln0IapfdolUdp543+ZMWTkulopXC+JiviibwCb2JLaLl+Tyy6TyC0U/NmijQLd8u1R+kXh/vDinJ7VNr/xyqXybKI+D1dyT2KZ3zFdI27q0UW1K7Zmnu19WSmXbG5ONqYR+2VVFZfG+2+bp7sPVUp+XNSbRB9Hnjk1627imqLwaEftwYU/HRr3ya4vKxyJiHy7qieqW75DKrxT9QaQu7Uls0NuHcWlb441qS2p/i+5+WSeV7WyMz0nt0S+7vqhsck4qoV92g4myG6Wymxtjzalt+mU3FZWNN6c69ctulspuakyWLNtpouyWorLYvxv0y3ZJZTc2xkqW3Wqi7DYTZbebKLvDRNmdJsomTJRNmti/u0wct90myu4pU1aOz73i1YL43KDlZ1Xt6IlqISPPhldrBSdnw3WNmdlwdQ/2EmbDOY16tfZJtTq02UVVV/V0NIhaEd1a+6Vaa0QtDPYVYpZHrUbdWt1SrVWiFnZJe09Kq6Xq1rpGqrVC1EppeUqb5a9v0Kt1rVSrXZshGtTFPR0RUatHt9YBqdZSbW80qNGejtmi1rW6tXqkWtps1NmgtvYk5oha3bq1rpNqaXPetgYxR84Vtfbp1rpeqhXVZmJRK6XV2qtbKyXVWiBq7Re1OuaJWrt1a2UqTNZqFbUONKize1JaraRurQap1lzteDVgLu9oFbV26tZqlGq1NMawqm9ELSxfUGu7bq0mqdYc0RZqYR2g1dqqWysi1YpokYUh2BNdIGpt0a01W6rVKGq1NqpzexJarc26teZItVRtHIpaHQtFrY26tZqlWtq6s61RndeT0mqt163VItXqEbVWiVodUVErrltrrlTrWlGroxGjN6XVWqtba55Uq1vU6hRtJWKi1mrdWq1SrX3aelrb84tErZW6teZLtfaKWs1NGBsJrdZy7U9XZWstyp0diFdjk7V2i1qtTeL8Ba8nUy3a3tHO4BS57kKpblLb/6IuUkgkmWrVnmfqyr2NSr3dKcq2i7qpJdpZie42xqRa27WjIGp1LBW1Yrq1Fkm1topaG5qwLk9ptRbq1los1dqiHTtRK7FM1JqvW6tNqrVZ1EpoPWwXtebp1loi1dqoHXFtb2i1WnRrLZVqrRe1DmjHbrk2l+nWWibViotaKa2HK7S5TLdWu1RrrTa6IqKHWq1MZio6AxGvFszOq7Xtmod9GI3ptbJCamWlNoJEK9FV2iym6tVaKdVaro2liDhSWq3MzCP3bZXUt2Xa8W0VtbSTXzVbflnuzESUj0+2sgtrezF/YVsWi1b2NGRmprliFtSpv0aqv1PFmUS7qJ9YLKJFi/J2MYsmtAsscrStlaJthxqPpJpF/Y5dov1FajKSyqR6RW67Q2p7mxqbnTogzkw72kTbB7SRI1YLqSa9vsel+lvV5OzsmW2baPu6hsyZbrtYbej0fZ3U9y41NkecpaH9vaL9ueJ5ZrlU1Pf1UttbVJzNtGt1l4i6jfm1WFS37xuK6qvN4qpJo8g0EbF2y60AU416fd8o9b1TxWq0fbaIsnVi2xtUnDElMi3LI3OTNDI7VZwxISOi7+vVnl2pebrjebOcQ0SLbVqLZWp1Wqq1pagW1vutolYK6+fdqbm6tbr0ajVna0VK1doq1dqkxgzU2qZXq0nUim4oXWu7pVo7DNWSM8lOKZNotfYvUNf1dOiu1RN6e++AyFcdZfqWLFELe2/D5PGV+7ZL6ps2KlILcH6U0O3bbr1RpLUS3Vh6FO3RG+f7tS3aqO7dlWrV7dteqW+dIpKaF6prspFYdO4mz8gikvdrfdukbt+VuTpZfO4m1epS43OyW1RQS+7bfqlvWsZqX4hztw7dDNctZYmtWGansBhoyq572xuTWsZVdTLcNVKG2q6qs8Uuw5GNiDXY1SpW+Z1z89lZbvvaopkhc02rQcwk88UV3pg2U+i1fUBqO6HGmkRmxt6ZbPvAXHWB6Iv2DlPr90j1d2MVKM5WtavLaHufqN88T5xrzNY7OtdJR2dOA8rvF9dAOxaI7Kw/Eq6XajWLWnu0K6fa3tavlZJqtYhaCXH9PNOW2qRXK3O+PVlrrqjVOdlD/VoNUq15otaGybYadGs1SrVaRa1Vk23p12qSas0Xtdqze0PMkLq1IlKtBaJWm3Y3QavVpFtrtlRroajVOtmWfq05Uq2oqNWcbaslV6vo/k6jOuU6UEzc7+jU7jYUXQdqEWWTUtmoWK1HtctUcvm5ReWT2XOXjl16fZkn9SUq7thk+1J0/la0tZn7aXjv+WIfzdHdR/OL9qzYAi2StCsCmVrydiyQtkOrpd3dSVyn18rColaS2ghDvLeKvrXo9i1aNFbQSofWinaNo0W3bzGpbwtEW53aFvXotbKoaByjlW1aee2qzVzdvi3Wq5XQ+jZXbNE83VptRbWSWt7BMSpTa0lRfKKtA1oPW7QzXt1aS4tqoS2s1NHDMrWWFWUQcZdV1Ipqtebr1mrXq9WqtdUsai3QrbVcL4O0iVodBbXk47tCOr7rtSys1dqjV36lVH6DKL9N65tu+VVS+Y1a5p0sL2/FamkrNmUz9XxxLQNbEdXdijVSK5uzOTfWE92rV36tVL4zmzfbSmxFh1R+Szb3LcvupaI7SFKmwVp7TmqP/t3JdVLZLQ1Y2yT0y64vKovzqBJ3XjdIZbHTm0uV3SiV3dwg7grpl91kouzmorJYiZa4+9splcV5V0upsltMlO0yUXaribLbisrijKFDv+x2E2V3mCi700R/EybKJk2U3WXiGO82MXb2mCi7t6i/8ZJj/Wqp7LqGeEuurBz3+6S4X9MQbxRxv7Inpd0MKzrjkMovb4g3ifl/eU9UN690S+WXNKgRkbeWlci+1xSVT2or/SUl8ta1ReXRn0TpvHhAKr8UJz9ibkT21S3fU1Q+2Siuf2Eu1W7Syfv+OmnfLxX788BC3X1/vfTebQ2Zu4ItPZlzMLl8Siq/KPsZmdk9HT165bU1f0H5aEM8u05P6JZvkMovaMjcCWzMroQuzZaP5M4DRPktk+W1K+kYDJm5TS7dJJWemy3dpFs6IpVuzpaerVt6tlR6drZ0s27pOVLppmzpubqlm6XSjWJmROlW3dItUmk1+97zdUvPlUpfr2ZKL9QtPU8q3ZMtHdMt3SqVvjZberFu6flS6e5s6SW6pRdIpfdlSy/TLb1QKr03W3q5bumoVHp3tvRK3dIxqXQyW3q1bulFUumd2dJrdUsvlkpvz5aO65Zuk0pvzZbWbvCrV2ZLL8yt0UXplslV4GI1qX3qqTF7JzzVlBmOcr2lUr1Faub8qzH76bpUU1y33jKpXpsaz7XXmG1vnl699pL1otl6cd16y0u315Btr1Wv3oqiekktJyIHaXfrUk2xVr29v1La+204VxZ7f5/usVplqvTqotKqVnq/buk1Uukl2XHQrVt6bdF7Z0pfo1u6Qyq9OFv6Wt3Scal0NLuV+qXXFZXObOUB3dLri0pnepL5JIT8Gd8NorSBzwJvNFhuk8Fymw2W6zRYbovBcl0Gy20tUU58jvsq7Zt452kf4Ra/nT/9t8r2aWeKbwSJ7/tMUzSuhvfBtIJDA/E8gucRPO/C8y4878LzLjzvxfNePO/F8148H8bzYTwfxvNhPB/H83E8H8fzcTyfwPMJPJ/A84m01oSSxvP0feLD5Znm0H4E7UfwxwheiKD9CNqPoP0I2o+g/Qjaj6D9CNqPoP0I2o+g/Qjaj6D9CNqPoP0I2o+g/Qjaj6D9CNqPoP0I2o+gfbFJEbQfQfsRtK9tHtrvQvtdaL8L7Xeh/S6034XCXSjQhfa70H4X2u9C+11ovwvtd6H9LrTfhfa70H4X2u9C+11ovwvtd6H9LrTfhfa70H4X2he7sAvtd6H9LrSv7U6034v2e9F+L9rvRfu9aL8X7fei/V6034v2e1G5FxV60X4v2u9F+71ovxft96L9XrTfi/Z70X4v2u9F+71ovxft96L9XrQvDlkv2u9F+71oXzt8aH8Y7Q+j/WG0P4z2h9H+MNofRvvDaH8Y7Q+j/WG0P4z2h9H+MN5sGG8wjPaH0f4w2h9G+8NofxjtD6P9YbQ/jPaH0f4w2hdDZBjtD6P9YbSvDRe0P472x9H+ONofR/vjaH8c7Y+j/XG0P472x9H+ONofR/vjaH8c7Y+j/XG0P472x/Hm43jDcbQ/jvbH0f442h9H++NofxztiyE5jvbH0f442teGJ9qfQPsTaH8C7U+g/Qm0P4H2J9D+BNqfQPsTaH8C7U+g/Qm0P4H2J9D+BNqfQPsTaH8C7U+g/Qm0P4HGJtDABNqfQPsTaF+EwATan0D7E2hfCwe0n0b74lka7afRfhrtp9F+Gu2n0X4a7afRfhrtp9F+Gu2n0X4a7afRfhrtp9F+Gu2n0X4a7afRfhrtp9F+Gu2n0bj4Rmga7afRfhpPxPc8lkzPfAd2qfbs7GkztG90bJilKl/C8weVHVqWyP1sgeK3BxXxDZHLtPzxz3tmKJ+6QNHM4fKXWAghzsM4JyT4MM4JCT6Mc0KCD+OckODDOCck+DDOCQk+jHNCgo+5OB87PjZybMSZnhBCnMJcnMdisbq6unhn/PTp0w51iBBiO+bi

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1fL3JZZ63bTzaUmSJEVZLX9fYqnP5+GcWpIkSVEWlXXqfPNm59SSJEmKsnqvU082X3Y+LUmSpKirxzp1SqHvX7U/B5IkSVI5arlOXcr82Dm1JEmSoi61ZlzL5/Eo5n2r9McrSZIkVUNqXl3J9ehiru/I935V6mOUJEmSqi19Hlzq83ZUeg7snFqSJEmNKFaCar4v1XrbkiRVUz3uNyUpk+ccSVKjyJwzF3p9pPd1kqrN84wkKap2mz+X+fvOnFtLqibPL5KkKEnNfav1+8+835NUaZ5XJElRkbqWoxa/D63eH6uk5uJ5RZJUb5NdFx2F34smSfl4XpEk1UP6YwyrvS7tOrWkavKcIkmqh1qvS7tOLamaPKdIkmqpXuvSrlNLqibPKZKkWqj3urTr1JKqxfOJJKnaorIu7Tq1pGrxfCJJqqZqPb90ua+9/5NUSZ5TJEnVUO7vO0x/3d7ePmkjI8NF/z7Fen+OJDUPzymSpEqr1HXT/Rv6YpNpaWnxOmpJdeU5RZJUSZW8brpjccek8+k+5txeRy2p3jynSJIqpVLXTY9uG5l0Lh0ItvM6aklR4HlFklSu5Np0ha6bDtadZ8yc4fN8SGoYnlckSeVKXetRifXp4HGGPd3dVX2+D+/7JFWa5xVJUjkqtT4dPF9HumBu3dnZGevv76/oOrX3e5KqwXOLJKlUlVqfTvQmcl4vPX3a9OS/uz4tKao8t0iSSlWp9engOfAm0xJvST4W0fVpSVHk+UWSVIpKrE9nXuuRTzweL/n5PVyfllRtnmMkScWqxPr0yNbh2OCmgdjg4EDyeulEb0/y+ulcuscfs+j6tKQo8jwjSSpGJdanc70O1qGD66aD66fTBX92fVpSVHmekSQVoxLr04WsX2deXz1085Dr05Iiy3ONJKlQ1VyfTn+9fXR0t3XqwcFB16clRZrnG0lSIWqxPp16HVw3nRI8htH1aUlR5vlGklSIWq1PB6+DxywGgt9J7vXTkhqB5xxJ0mQqtT4dzJWD5/XIt+4cPP9HoG9Dn8/vIalheN6RJOVTifXpzOefTj4f3uho1nbB7x8Pnkev1P14nyapHjz3SJImk5pTl7o+nVp3Thdc09E/0J/899HRkYnnpC7n9yN6nyapXjz/SJLyCe4nyr0+uiftsYahc+vxazzK2Y/3Z5LqyXOQJCmXctenU6+DdejUddRBwXXSpT7PtNdNS4oiz0WSpFxq+TwfPq+HpEbluUiSlEstn4fa66YlNTLPSZKkXCpxHXU1XnvfJSlqPC9JknKJ2jq191mSoshzkyQplyhdR+39laQo8xwlScqlUs/34XXTkpqd5ylJUi71Xqf2PkpSI/BcJUnKJ/X7WGp9vbT3T5IaiecsSdJkavW8H94nSWpUnr8kSZOZWKuu0nXSrktLamSevyRJhUrNeyu1Hp15H+R9kqRG5flLklSMWIZi16Hz3e94nySpUXn+kiSVKmuyHKKYt1XN91WSqslzmCQpCrw/ktSoPH9JkqLC+yRJjcrzlyQpCrw/ktTIPIdJkqLA+yNJjcrzlyQpKrxPktSoPH9JkqLA+yNJjcxzmCQpCrw/ktSoPH9JkqLC+yRJjcrzlyQpKrxPktSoPH9JkqLA+yNJjcxzmCQpCrw/ktSoPH9JkqLC+yRJjcrzl6aiWB71ft+kqcrjT1Ij8xymZpc5Z77z9jtj22/bHvra+bVUPx5zkhqV5y81o/Q5cTBX3n779pJeO6+WasvjTVKj8vylZpE+h863Dl3sa+fVUm14nElqZJ7D1OiS8+gS16Fdr5aiw2NMUqPy/KVGNtl10dVYr673xyw1M48xSY3K85caUS3WpcNee7xI1ePxJamReQ5TI6n1urTr1FLteHxJamSew9QI6rUu7Tq1VDseX5IalecvRV2916Vdp5Zqx+NLUqPy/KWoisq6dObzftT78yI1K48vSY3Mc5iiqBrPL12J1x4vUvV4fElqVJ6/FDXl/r7D1Ou+DX2xRG9P3gY3DbhOLUWIx5ekRuX5S1FSqeump0+bHpvMyNYRr6OWIsTjS1Ij8xymKKjUddP9/f2TzqXb29u9jlqKII8xSY3K85eioFLXTS9fsnzS+XRwPYjXUUvR5DEmqVF5/lI9pebS5a5Pj46OJOe7qeujBwcHQl8H25W6H48Vqbo8xiQ1Ms9hqpfgtleJ66aDdecZM2f4PB9Sg/M4k9SoPH+pXiq1Ph1cF51+jXRnZ2dyjl3OerTXUUv14XEmqVEVev6a7PrUar+fai6VWJ8Onq8jn2BuPbptxN+XKDUQjzVJjSrs/JU5NylkvuH8WoWqxPp0cM30ZILn0Ru6ecj1aalBeKxJamSpc9jE/LkC8w/Pi8qlEuvTwXXThUjNqV2fnrr8fr+x+DVSlHj+UDEm5tEVfjyXtz+FSd3Wyvm+Lf35O4K16uD6jly/16Ul3uL69BQ22fdc9X7/lM2vi6LC84cKMTGPrtDjtlyvViGC20K1no+jf/w5PzINbx52fXqKmuz+0PvH6PHroKjw/KHJJOfRVZjPOC/RZFK3vWp9/xY8v0ewXp0uWMN2fXpqKvb+0PvHaPBzryjw/KF8gq9xNecz/n4M5RPcBmrx/Vv68+klehN+HzhFlXt/6P1j/fj5Vr15/lAuwdez1uvSzk+ULnUbrPb3b/0D/RPnsOB5qV2fnpoqfX/o/WPt+PlVvXn+UJjga1evdWnXqXc/Lmuxn2ruo5z9BGNq9f1bSvB81VH//q9qJ2zVVC1uK1OJn9PC1Pt2r8qo9+1IhQm+VvVcl57K69S1Om5qdWyWs59g+3K/Hwt+V0twTXTw/B6Tfd8WXEvt931TV0Xu5IpQ74+3Gfl5Vb14/lCm4OsUhXXpqfpz9FodN7U6NsvZT7B9ud+PxePxiX0H10mHrT8H13gEz6FXzu9JnEq30WZV7v3bZOr98U0Vfq5VD54/lC74mpU6nwjmKcXOR4I1w0Kfn2wq3Z5qdQzV6jgtZz/BuHK+H8t8rungz8F6dXBbDf49mEsHzztd7u9HnEq3z2bl/V9z8HOvevD8oXTB17DYeUQwD0k951jwezMK+fl7d3d3cvtgHhM8B3BqjuN8RZlSt8lSv88bGBjI+TsSx253ibLWpafi93vNyvu/5uHXQ7Xm+UMpwdezmPnD4ODgbs8zFgjWm/ONC+YtqZ+/9zCnTv19S0tL8u+CebnXUStT6rZZzvpx6vcjpprsemqvR5p6vP9rLn6NVEueP5SSnLMUMH8Ifj6eOY9OmWx9OrUundw2bT4TzG9S+vv7nbdoN8HXPQqPi/X7vObm/V9z8WumWvL8oUCh85VgDhz8nuaxtb5E9nw6z/p0cH11uu2joxP/HsyhU4KfzftzdWVK3mYi8vhYr0NqTt7/NR+/jqoVzx8KJOcqRc4jgms3subTedanM3+vc/q/B+PSJX+nhvMXpUndZqKwHu26tNQ4PE4l1Uqh69Nh84lC16czHxOWue6dLt911J4bp65Svu+r5mtvi1L0eZxKqpVS5ymFrk+PbB3O2jbf+nTqmg/Xp5UpKuvU3g6lxuHxKqkWqr0+nbn+PNn69GTvj+fGqSs5n3ZdWlKRPG4lVVM585NC16fTn7+jkPXpQL7fr+F5cWpLvw25Li2pEB67kqqpnHlJoevTYfPpydang+e3dn1a+WR+X+a6tKR8PIYlVUtU16fz/b4Nz4lKqcU6dUq9P1ZJ5fNYllQNrk+r0U18j+bzS0sqgMe1pEqrxfp02PpzMf/u+rQKkev7tXK+T6z3xySp8jy2JVVaau5azfXp4LGFmfKtT0+fNt3n91BZiv3+zDm0NLV4rEuqtMnmG+WuTwevgzlyrvlN5vp0x5IOf/6uisq6sTp/lqY8j39JlZS5Xlzp9eng9fIly3fbNt/6dHC9tc9XJkmqJu9PJFVSLdanM+fMudang3Xs0dER16clSVXnfYqkSqnF+nTwur29PW3uff/zd6Q//0eiN5F3v577JEmV5P2KpEpJrhkXsT7d39+fNZ8O5sX5xo1sHZ64jjq57fjfp+bZLfEWn79MklRT3q9IqpTUNRj51pdHRoaT68ednZ1Zjy9MCf4t3/XPw5uHYy0tLcnx3d3dye0DwfXVo9tGfF4PSVLNef8iqRKKXZ8u93VwbUgw7w4a2jxU8PXa9f48SZKak/cxkiqh1Ouoa/Ha85wkqdoKua8J/eFshlq8r5KiKXXNRy3XqQt97flJklRtYfc1mXPlUh6vX4+PRVL9FHIdda1fey6SJNVK6j4nNReuxLqQ82pp6onSOrXnH0lSLRWzDl3K+pD3a1Jzyjy+o3QdtecdSVKt1Go9yfs2qbnkOqaT55Q6r097vpEk1UL6tR2uF0kqxmTHcj3XqT3PSJJqoZ7rR97XSY2t0GO4ko/HKPR6ac8vkqRaiML1jd7nSY2plGO3Fj8H85wiSaqlqDz+3vs/qbGUc8xOrFVX4TziuUSSVEu1vl7adWqpOVTqWI2lKee84TxaklQPUVmXdp1aaizVOkZjGSa7Lto5tCSpnspZlx4ZGY5tHx0tatzg4GBs6OYhr3uUGlwtj8+sibPzZ0lShJRy3eLQ5qFYZ2dn8v5scNPApNuPjo7Euru7k9u3tLTEZsycEZs+bXos0dsz6f68z5Six+NSkqQxxV6nGMyd29vbd1sfCtab840L1q+DOXQgmFOn/j4ejyf/LpiXex211Dg8JiVJul+h1033bejLmkdPzKcnWZ9OrUuPzb0HJv4+WJtO6R/o9zpqqQF4LEqStLtC1qeD9edgPh28Tp8DF7I+HVxfnW5028jEvw8MDEz8fXD9h9dRS9HmcShJ0u5KuW46uA66mPXp1DXWKen/HoxLF8zZXZ+W

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