ÿþ<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=Content-Type content="text/html; charset=unicode"> <meta name=ProgId content=Word.Document> <meta name=Generator content="Microsoft Word 12"> <meta name=Originator content="Microsoft Word 12"> <link rel=File-List href="cmp251april_files/filelist.xml"> <link rel=Preview href="cmp251april_files/preview.wmf"> <link rel=Edit-Time-Data href="cmp251april_files/editdata.mso"> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} </style> <![endif]--> <title>Class notes for CMP251</title> <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author>Sher</o:Author> <o:LastAuthor>David B. 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link=blue vlink=purple style='tab-interval:.5in'> <div class=Section1> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/2<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Thursday, April 02, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>4:02 PM<o:p></o:p></span></p> </div> <div style='margin-top:22.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Show each enqueue and dequeue when heapsorting <o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>c,u,r,i,o,u,s<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>c<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>uc<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u cr<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u ir c<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u or ci<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u ou ci r<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u ou ci rs<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u os ci r:u<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>s or ci :uu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>r oi c :suu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>o ci :rsuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>i c :orsuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>ciorsuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </div> <div style='margin-top:22.9pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Interface Hashable implements Comparable<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>{<br> <span style='mso-spacerun:yes'>      </span>int hash();<span style='mso-spacerun:yes'>    </span>// returns the hash code<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>} // end Hashable<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>class HashTable<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>{<br> <span style='mso-spacerun:yes'>     </span>public void insert(Hashable toInsert)<br> <span style='mso-spacerun:yes'>     </span>{table[toInsert.hash()%table.length].insert(toInsert);}<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>}<o:p></o:p></span></p> </div> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=239 style='width:179.0pt;margin-left:99.0pt;border-collapse:collapse;mso-yfti-tbllook: 1184;mso-padding-alt:0in 0in 0in 0in' cols=3> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: .75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=135 valign=top style='width:101.25pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=21 valign=top style='width:15.6pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=83 valign=top style='width:62.0pt;padding:0in 0in 0in 0in; height:.75pt'></td> </tr> <tr style='mso-yfti-irow:1;height:20.1pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 20.1pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=135 rowspan=2 valign=top style='width:101.25pt;padding:0in 0in 0in 0in; height:20.1pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:101.25pt;height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image001.png" o:title="image001"/> </v:shape><![endif]--><![if !vml]><img width=135 height=40 src="cmp251april_files/image002.gif" v:shapes="Picture_x0020_1"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=21 valign=top style='width:15.6pt;padding:0in 0in 0in 0in; height:20.1pt'></td> <td width=83 valign=top style='width:62.0pt;padding:0in 0in 0in 0in; height:20.1pt'></td> </tr> <tr style='mso-yfti-irow:2;height:9.65pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 9.65pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=21 valign=top style='width:15.6pt;padding:0in 0in 0in 0in; height:9.65pt'></td> <td width=83 rowspan=2 valign=top style='width:61.9pt;padding:0in 0in 0in 0in; height:9.65pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3;mso-yfti-lastrow:yes;height:4.55pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 4.55pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=135 valign=top style='width:101.25pt;padding:0in 0in 0in 0in; height:4.55pt'></td> <td width=21 valign=top style='width:15.6pt;padding:0in 0in 0in 0in; height:4.55pt'></td> </tr> </table> <div style='margin-left:2.0in;margin-top:1.5pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:134.25pt;height:70.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image003.png" o:title="image002"/> </v:shape><![endif]--><![if !vml]><img width=179 height=94 src="cmp251april_files/image004.gif" v:shapes="Picture_x0020_2"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:159.7pt;margin-top:1.5pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1076" type="#_x0000_t75" style='width:109.5pt;height:34.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image005.png" o:title="image003"/> </v:shape><![endif]--><![if !vml]><img width=146 height=46 src="cmp251april_files/image006.gif" v:shapes="Picture_x0020_3"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:21.75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4" o:spid="_x0000_i1075" type="#_x0000_t75" style='width:525pt;height:691.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image007.png" o:title="image004"/> </v:shape><![endif]--><![if !vml]><img width=700 height=922 src="cmp251april_files/image008.gif" v:shapes="Picture_x0020_4"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:17.95pt;margin-top:7.0pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1074" type="#_x0000_t75" style='width:470.25pt;height:267pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image009.png" o:title="image005"/> </v:shape><![endif]--><![if !vml]><img width=627 height=356 src="cmp251april_files/image010.gif" v:shapes="Picture_x0020_5"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:12.55pt;margin-top:6.7pt'> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:18.0pt'>Proof Without Words: Partial Sums of a Harmonic Sequence<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>David B. Sher</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>Math/Computer Science/Information Technology Department</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>Nassau Community College</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>1 Education Dr.</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>Garden City NY 11530</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><a href="mailto:sherd@ncc.edu">sherd@ncc.edu</a></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6" o:spid="_x0000_i1073" type="#_x0000_t75" style='width:228pt; height:60pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image011.gif" o:title="image006"/> </v:shape><![endif]--><![if !vml]><img border=0 width=304 height=80 src="cmp251april_files/image011.gif" v:shapes="Picture_x0020_6"><![endif]></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:140.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7" o:spid="_x0000_i1072" type="#_x0000_t75" style='width:143.25pt; height:28.5pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image012.gif" o:title="image007"/> </v:shape><![endif]--><![if !vml]><img border=0 width=191 height=38 src="cmp251april_files/image012.gif" v:shapes="Picture_x0020_7"><![endif]></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:140.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:167.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1071" type="#_x0000_t75" style='width:37.5pt; height:27.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image013.gif" o:title="image008"/> </v:shape><![endif]--><![if !vml]><img border=0 width=50 height=37 src="cmp251april_files/image013.gif" v:shapes="Picture_x0020_8"><![endif]></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:167.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:32.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1070" type="#_x0000_t75" style='width:72.75pt; height:71.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image014.gif" o:title="image009"/> </v:shape><![endif]--><![if !vml]><img border=0 width=97 height=95 src="cmp251april_files/image014.gif" v:shapes="Picture_x0020_9"><![endif]></span></p> <div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='margin-left:29.35pt;border-collapse:collapse;border:none;mso-border-alt: solid #A3A3A3 .25pt;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td width=207 valign=top style='width:155.1pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1069" type="#_x0000_t75" style='width:139.5pt; height:1in;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image015.gif" o:title="image010"/> </v:shape><![endif]--><![if !vml]><img border=0 width=186 height=96 src="cmp251april_files/image015.gif" v:shapes="Picture_x0020_10"><![endif]></span></p> </td> </tr> </table> </div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='margin-left:29.35pt;border-collapse:collapse;border:none;mso-border-alt: solid #A3A3A3 .25pt;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td width=102 valign=top style='width:76.3pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11" o:spid="_x0000_i1068" type="#_x0000_t75" style='width:60.75pt; height:35.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image016.gif" o:title="image011"/> </v:shape><![endif]--><![if !vml]><img border=0 width=81 height=47 src="cmp251april_files/image016.gif" v:shapes="Picture_x0020_11"><![endif]></span></p> </td> </tr> </table> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:59.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1067" type="#_x0000_t75" style='width:50.25pt; height:30.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image017.gif" o:title="image012"/> </v:shape><![endif]--><![if !vml]><img border=0 width=67 height=41 src="cmp251april_files/image017.gif" v:shapes="Picture_x0020_12"><![endif]></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:59.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1066" type="#_x0000_t75" style='width:494.25pt; height:279.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image018.jpg" o:title="image013"/> </v:shape><![endif]--><![if !vml]><img border=0 width=659 height=373 src="cmp251april_files/image018.jpg" v:shapes="Picture_x0020_13"><![endif]></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='margin-left:5.35pt;border-collapse:collapse;border:none;mso-border-alt: solid #A3A3A3 .25pt;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=64 valign=top style='width:48.0pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=382 valign=top style='width:286.5pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td width=64 valign=top style='width:48.0pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=382 valign=top style='width:286.5pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1065" type="#_x0000_t75" style='width:80.25pt; height:38.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image019.gif" o:title="image014"/> </v:shape><![endif]--><![if !vml]><img border=0 width=107 height=51 src="cmp251april_files/image019.gif" v:shapes="Picture_x0020_14"><![endif]></span></p> </td> <td width=69 valign=top style='width:51.55pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:2'> <td width=64 valign=top style='width:48.0pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=382 valign=top style='width:286.5pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3;mso-yfti-lastrow:yes'> <td width=64 valign=top style='width:48.0pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=382 valign=top style='width:286.5pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1064" type="#_x0000_t75" style='width:274.5pt; height:80.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image020.gif" o:title="image015"/> </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=107 src="cmp251april_files/image020.gif" v:shapes="Picture_x0020_15"><![endif]></span></p> </td> <td width=69 valign=top style='width:51.55pt;border:none;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> </table> </div> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'>&nbsp;</p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:8.0pt;font-family:"Tahoma","sans-serif"; color:#666666'>Pasted from &lt;<a href="file:///J:\My%20Documents\Proof%20Without%20Words.docx">file:///J:\My%20Documents\Proof%20Without%20Words.docx</a>&gt; <o:p></o:p></span></p> <p style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:5.35pt; margin-bottom:.0001pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </div> <div style='margin-left:.25in;margin-top:51.55pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Avf(n) = average time for a failed search in a tree<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1+<o:p></o:p></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div style='margin-left:5.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/14<o:p></o:p></span></p> </div> <div style='margin-left:5.4pt;margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Tuesday, April 14, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>3:55 PM<o:p></o:p></span></p> </div> <div style='margin-left:5.4pt;margin-top:22.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>d<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>da<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>tad<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(ad)a<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(sd)aa<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(st)(aa)d<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(st)(aa)(dr)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(tt)(sa)(dr)a<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(tt)(sa)(dr)(ac)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(tt)(st)(dr)(ac)a<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(ut)(st)(dr)(ac)(at)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(ut)(st)(rr)(ac)(at)d<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(ut)(st)(rr)(ac)(at)(de)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(ut)(st)(rs)(ac)(at)(de)r<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>u(tt)(st)(rs)(ac)(ar)(de):u<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(ts)(st)(re)(ac)(ar)d:uu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(ts)(sd)(re)(ac)(ar):tuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>t(ss)(rd)(re)(ac)a:ttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>s(sr)(rd)(ae)(ac):tttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>s(rr)(cd)(ae)a:stttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>r(re)(cd)(aa):sstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>r(de)(cd)a:rsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>e(da)(cd):rrsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>d(da)c:errsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>d(ca):derrsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>ca:derrsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>acderrsstttuu<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </div> <div style='margin-left:21.9pt;margin-top:22.25pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16" o:spid="_x0000_i1063" type="#_x0000_t75" style='width:171pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image021.gif" o:title="image016"/> </v:shape><![endif]--><![if !vml]><img border=0 width=228 height=40 src="cmp251april_files/image021.gif" v:shapes="Picture_x0020_16"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1062" type="#_x0000_t75" style='width:131.25pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image022.gif" o:title="image017"/> </v:shape><![endif]--><![if !vml]><img border=0 width=175 height=40 src="cmp251april_files/image022.gif" v:shapes="Picture_x0020_17"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:197.25pt; height:39.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image023.gif" o:title="image018"/> </v:shape><![endif]--><![if !vml]><img border=0 width=263 height=53 src="cmp251april_files/image023.gif" v:shapes="Picture_x0020_18"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:207.75pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image024.gif" o:title="image019"/> </v:shape><![endif]--><![if !vml]><img border=0 width=277 height=40 src="cmp251april_files/image024.gif" v:shapes="Picture_x0020_19"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:277.5pt; height:30.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image025.gif" o:title="image020"/> </v:shape><![endif]--><![if !vml]><img border=0 width=370 height=41 src="cmp251april_files/image025.gif" v:shapes="Picture_x0020_20"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Each time we lose another ln(n) on the denominator<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>After 5 or 6 more l hospitol s the denominator and numerator are the same and <o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>The limit will be 1<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:171pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image021.gif" o:title="image016"/> </v:shape><![endif]--><![if !vml]><img border=0 width=228 height=40 src="cmp251april_files/image021.gif" v:shapes="Picture_x0020_21"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:131.25pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image022.gif" o:title="image017"/> </v:shape><![endif]--><![if !vml]><img border=0 width=175 height=40 src="cmp251april_files/image022.gif" v:shapes="Picture_x0020_22"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:197.25pt; height:39.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image023.gif" o:title="image018"/> </v:shape><![endif]--><![if !vml]><img border=0 width=263 height=53 src="cmp251april_files/image023.gif" v:shapes="Picture_x0020_23"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_24" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:207.75pt; height:30pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image024.gif" o:title="image019"/> </v:shape><![endif]--><![if !vml]><img border=0 width=277 height=40 src="cmp251april_files/image024.gif" v:shapes="Picture_x0020_24"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:277.5pt; height:30.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image025.gif" o:title="image020"/> </v:shape><![endif]--><![if !vml]><img border=0 width=370 height=41 src="cmp251april_files/image025.gif" v:shapes="Picture_x0020_25"><![endif]></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Each time we lose another ln(n) on the denominator<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>After 5 or 6 more l hospitol s the denominator and numerator are the same and <o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>The limit will be 1<o:p></o:p></span></p> </div> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=520 style='width:390.15pt;margin-left:.25in;border-collapse:collapse;mso-yfti-tbllook: 1184;mso-padding-alt:0in 0in 0in 0in' cols=3> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: .75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=205 valign=top style='width:153.8pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=42 valign=top style='width:31.45pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=273 valign=top style='width:204.85pt;padding:0in 0in 0in 0in; height:.75pt'></td> </tr> <tr style='mso-yfti-irow:1;height:2.0in'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 2.0in'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=205 rowspan=2 valign=top style='width:153.8pt;padding:0in 0in 0in 0in; height:2.0in'> <div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;border:none;mso-border-alt:solid #A3A3A3 1.0pt; mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>0hpx<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-left:none;mso-border-left-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border:solid #A3A3A3 1.0pt; border-left:none;mso-border-left-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3*0<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1aiqy<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>a<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4*1<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:2'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2bjrz<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>r<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4*1<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3cks<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>cs<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1*1+2*2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:4'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4dlt<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>td<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1*1+2*2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:5'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>5emu<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>eu<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1*1+2*2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:6'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>6fnv<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3*0<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:7;mso-yfti-lastrow:yes'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>7gow<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=77 valign=top style='width:.8in;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3*0<o:p></o:p></span></p> </td> </tr> </table> </div> </td> <td width=42 valign=top style='width:31.45pt;padding:0in 0in 0in 0in; height:2.0in'></td> <td width=273 valign=top style='width:204.85pt;padding:0in 0in 0in 0in; height:2.0in'></td> </tr> <tr style='mso-yfti-irow:2;height:6.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 6.75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=42 valign=top style='width:31.45pt;padding:0in 0in 0in 0in; height:6.75pt'></td> <td width=273 rowspan=2 valign=top style='width:204.85pt;padding:0in 0in 0in 0in; height:6.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>(0+4+4+5+5+5+0+0)/26 = 0.8846 <o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3;mso-yfti-lastrow:yes;height:7.25pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 7.25pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=205 valign=top style='width:153.8pt;padding:0in 0in 0in 0in; height:7.25pt'></td> <td width=42 valign=top style='width:31.45pt;padding:0in 0in 0in 0in; height:7.25pt'></td> </tr> </table> <div style='margin-left:62.3pt;margin-top:14.85pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:120.75pt;height:129.75pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image026.png" o:title="image021"/> </v:shape><![endif]--><![if !vml]><img border=0 width=161 height=173 src="cmp251april_files/image027.gif" v:shapes="Picture_x0020_26"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:21.1pt'> <div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;border:none;mso-border-alt:solid #A3A3A3 1.0pt; mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>a<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-left:none;mso-border-left-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>2<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border:solid #A3A3A3 1.0pt; border-left:none;mso-border-left-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>b<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:2'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>c<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>d<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>1<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:4'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>e<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:5'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>f<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:6'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>g<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:7'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>h<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:8'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>i<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:9'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>j<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:10'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>k<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:11'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>l<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:12'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>m<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:13'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>n<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:14'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>o<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:15'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>p<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:16'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>q<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>5<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:17'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>r<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>4<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:18'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>s<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:19'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>t<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>2<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:20'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>u<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:21'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>v<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:22'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>w<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:23'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>x<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:24'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>y<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:25'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>z<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:26'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>101<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p align=right style='margin:0in;margin-bottom:.0001pt;text-align:right'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>3.884615<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:27;mso-yfti-lastrow:yes'> <td width=64 valign=top style='width:48.0pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=64 valign=top style='width:48.0pt;border-top:none;border-left:none; border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> <td width=81 valign=top style='width:60.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </td> </tr> </table> </div> </div> <div style='margin-left:23.4pt;margin-top:20.95pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Project 4<span style='mso-spacerun:yes'>  </span>due 4/30<o:p></o:p></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/21<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Tuesday, April 21, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>4:02 PM<o:p></o:p></span></p> </div> <div style='margin-top:4.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Put m,c,g,l,o,n,e into a search tree.<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>What is the average search time for the tree?<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'><span style='mso-spacerun:yes'> </span><o:p></o:p></span></p> </div> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=440 style='width:330.05pt;border-collapse:collapse;mso-yfti-tbllook:1184; mso-padding-alt:0in 0in 0in 0in' cols=5> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: .75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=12 valign=top style='width:9.0pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=156 valign=top style='width:117.3pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=39 valign=top style='width:28.95pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=159 valign=top style='width:119.45pt;padding:0in 0in 0in 0in; height:.75pt'></td> </tr> <tr style='mso-yfti-irow:1;height:6.85pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 6.85pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=12 valign=top style='width:9.0pt;padding:0in 0in 0in 0in; height:6.85pt'></td> <td width=195 colspan=2 rowspan=2 valign=top style='width:146.25pt; padding:0in 0in 0in 0in;height:6.85pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:146.25pt; height:112.5pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image028.png" o:title="image022"/> </v:shape><![endif]--><![if !vml]><img border=0 width=195 height=150 src="cmp251april_files/image029.gif" v:shapes="Picture_x0020_27"><![endif]></span></p> </td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:6.85pt'></td> <td width=159 valign=top style='width:119.45pt;padding:0in 0in 0in 0in; height:6.85pt'></td> </tr> <tr style='mso-yfti-irow:2;height:105.6pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 105.6pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=12 valign=top style='width:9.0pt;padding:0in 0in 0in 0in; height:105.6pt'></td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:105.6pt'></td> <td width=159 rowspan=4 valign=top style='width:119.45pt;padding:0in 0in 0in 0in; height:105.6pt'> <div> <table class=MsoNormalTable border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;border:none;mso-border-alt:solid #A3A3A3 1.0pt; mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>a<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border:solid #A3A3A3 1.0pt; border-left:none;mso-border-left-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>b<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:2'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>c<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>d<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:4'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>e<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:5'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>f<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:6'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>g<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:7'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>h<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:8'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>i<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:9'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>j<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:10'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>k<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:11'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>l<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>4<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:12'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>m<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>1<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:13'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>n<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>3<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:14'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>o<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:15;mso-yfti-lastrow:yes'> <td width=90 valign=top style='width:67.75pt;border:solid #A3A3A3 1.0pt; border-top:none;mso-border-top-alt:solid #A3A3A3 1.0pt;padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Pqrstuvwxyz<o:p></o:p></span></p> </td> <td width=69 valign=top style='width:51.55pt;border-top:none;border-left: none;border-bottom:solid #A3A3A3 1.0pt;border-right:solid #A3A3A3 1.0pt; mso-border-top-alt:solid #A3A3A3 1.0pt;mso-border-left-alt:solid #A3A3A3 1.0pt; padding:1.95pt 3.0pt 1.95pt 3.0pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>2<o:p></o:p></span></p> </td> </tr> </table> </div> </td> </tr> <tr style='mso-yfti-irow:3;height:56.25pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 56.25pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=12 valign=top style='width:9.0pt;padding:0in 0in 0in 0in; height:56.25pt'></td> <td width=156 valign=top style='width:117.3pt;padding:0in 0in 0in 0in; height:56.25pt'></td> <td width=39 valign=top style='width:28.95pt;padding:0in 0in 0in 0in; height:56.25pt'></td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:56.25pt'></td> </tr> <tr style='mso-yfti-irow:4;height:14.2pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 14.2pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=168 colspan=2 valign=top style='width:126.3pt;padding:0in 0in 0in 0in; height:14.2pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>69/26 = 2.6538 <o:p></o:p></span></p> </td> <td width=39 valign=top style='width:28.95pt;padding:0in 0in 0in 0in; height:14.2pt'></td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:14.2pt'></td> </tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:135.2pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 135.2pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=12 valign=top style='width:9.0pt;padding:0in 0in 0in 0in; height:135.2pt'></td> <td width=156 valign=top style='width:117.3pt;padding:0in 0in 0in 0in; height:135.2pt'></td> <td width=39 valign=top style='width:28.95pt;padding:0in 0in 0in 0in; height:135.2pt'></td> <td width=74 valign=top style='width:55.3pt;padding:0in 0in 0in 0in; height:135.2pt'></td> </tr> </table> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/23<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Thursday, April 23, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>4:57 PM<o:p></o:p></span></p> </div> <div style='margin-left:48.75pt;margin-top:8.8pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:291.75pt;height:147.75pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image030.png" o:title="image023"/> </v:shape><![endif]--><![if !vml]><img border=0 width=389 height=197 src="cmp251april_files/image031.gif" v:shapes="Picture_x0020_28"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:63.85pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:468pt;height:242.25pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image032.png" o:title="image024"/> </v:shape><![endif]--><![if !vml]><img border=0 width=624 height=323 src="cmp251april_files/image033.gif" v:shapes="Picture_x0020_29"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:2.0in;margin-top:45.8pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Left rotation<o:p></o:p></span></p> </div> <div style='margin-left:.25in;margin-top:21.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Read 13.4,13.5,13.6<o:p></o:p></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>Talk: 5/3 MAA NY Metro<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Monday, April 27, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>10:57 PM<o:p></o:p></span></p> </div> <div style='margin-top:9.8pt'><nobr> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:1415.25pt;height:10in;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image034.png" o:title="image025"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1887 height=960 src="cmp251april_files/image035.gif" v:shapes="Picture_x0020_30"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:1415.25pt;height:10in; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image036.png" o:title="image026"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1887 height=960 src="cmp251april_files/image037.gif" v:shapes="Picture_x0020_31"><![endif]></span><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:1415.25pt;height:10in; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image038.png" o:title="image027"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1887 height=960 src="cmp251april_files/image039.gif" v:shapes="Picture_x0020_32"><![endif]></span><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:1415.25pt;height:10in; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image040.png" o:title="image028"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1887 height=960 src="cmp251april_files/image041.gif" v:shapes="Picture_x0020_33"><![endif]></span><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:1415.25pt;height:275.25pt; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image042.png" o:title="image029"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1887 height=367 src="cmp251april_files/image043.gif" v:shapes="Picture_x0020_34"><![endif]></span><br style='mso-special-character:line-break'> <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> <![endif]><o:p></o:p></span></p> </div> </nobr> <div style='margin-left:900.65pt;margin-top:3.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:405pt; height:134.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image044.png" o:title="image030"/> </v:shape><![endif]--><![if !vml]><img border=0 width=540 height=179 src="cmp251april_files/image045.gif" v:shapes="Picture_x0020_35"><![endif]></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/28<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Tuesday, April 28, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>4:11 PM<o:p></o:p></span></p> </div> <div style='margin-top:22.4pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:462.75pt;height:149.25pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image046.png" o:title="image031"/> </v:shape><![endif]--><![if !vml]><img border=0 width=617 height=199 src="cmp251april_files/image047.gif" v:shapes="Picture_x0020_36"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:30.9pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>AVL rule: Two brothers can differ in max depth by at most 1<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Every node has 2 children (one of them could be empty)<o:p></o:p></span></p> </div> <div style='margin-top:44.3pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Algorithm keeps the tree balanced (with rotations) according to this rule when new nodes are inserted.<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>If the new node doesn't unbalance we do nothing (except maybe update max depths)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Each node will track the max depth of its tree (each node is the root of its tree)<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Only need to rebalance the lowest out of balance node.<o:p></o:p></span></p> </div> <div style='margin-top:35.5pt'><nobr> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:470.25pt;height:10in;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image048.png" o:title="image032"/> </v:shape><![endif]--><![if !vml]><img border=0 width=627 height=960 src="cmp251april_files/image049.gif" v:shapes="Picture_x0020_37"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:470.25pt;height:238.5pt; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image050.png" o:title="image033"/> </v:shape><![endif]--><![if !vml]><img border=0 width=627 height=318 src="cmp251april_files/image051.gif" v:shapes="Picture_x0020_38"><![endif]></span><br style='mso-special-character:line-break'> <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> <![endif]><o:p></o:p></span></p> </div> </nobr> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=639 style='width:479.25pt;margin-left:.25in;border-collapse:collapse;mso-yfti-tbllook: 1184;mso-padding-alt:0in 0in 0in 0in' cols=7> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: .75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=297 valign=top style='width:222.75pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=120 valign=top style='width:1.25in;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: .75pt'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=6 valign=top style='width:4.45pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in; height:.75pt'></td> </tr> <tr style='mso-yfti-irow:1;height:4.4pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 4.4pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=297 valign=top style='width:222.75pt;padding:0in 0in 0in 0in; height:4.4pt'></td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:4.4pt'></td> <td width=120 valign=top style='width:1.25in;padding:0in 0in 0in 0in; height:4.4pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: 4.4pt'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in; height:4.4pt'></td> <td width=6 rowspan=3 valign=top style='width:4.55pt;padding:0in 0in 0in 0in; height:4.4pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:4.5pt;height:4.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image052.png" o:title="image034"/> </v:shape><![endif]--><![if !vml]><img border=0 width=6 height=6 src="cmp251april_files/image053.gif" v:shapes="Picture_x0020_39"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in; height:4.4pt'></td> </tr> <tr style='mso-yfti-irow:2'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=297 rowspan=6 valign=top style='width:222.75pt;padding:0in 0in 0in 0in'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:222.75pt;height:110.25pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image054.png" o:title="image035"/> </v:shape><![endif]--><![if !vml]><img border=0 width=297 height=147 src="cmp251april_files/image055.gif" v:shapes="Picture_x0020_40"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in'></td> <td width=120 valign=top style='width:1.25in;padding:0in 0in 0in 0in'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in'></td> </tr> <tr style='mso-yfti-irow:3'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in'></td> <td width=120 rowspan=4 valign=top style='width:1.25in;padding:0in 0in 0in 0in'> <p style='margin:0in;margin-bottom:.0001pt'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:90pt; height:98.25pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image056.png" o:title="image036"/> </v:shape><![endif]--><![if !vml]><img border=0 width=120 height=131 src="cmp251april_files/image057.gif" v:shapes="Picture_x0020_41"><![endif]></span></p> </td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in'></td> </tr> <tr style='mso-yfti-irow:4;height:14.9pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 14.9pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:14.9pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: 14.9pt'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in; height:14.9pt'></td> <td width=6 valign=top style='width:4.45pt;padding:0in 0in 0in 0in; height:14.9pt'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in; height:14.9pt'></td> </tr> <tr style='mso-yfti-irow:5;height:58.55pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 58.55pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:58.55pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: 58.55pt'></td> <td width=198 colspan=3 valign=top style='width:148.55pt;padding:0in 0in 0in 0in; height:58.55pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:148.5pt;height:58.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image058.png" o:title="image037"/> </v:shape><![endif]--><![if !vml]><img border=0 width=198 height=78 src="cmp251april_files/image059.gif" v:shapes="Picture_x0020_42"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:6;height:24.7pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 24.7pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:24.7pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: 24.7pt'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in; height:24.7pt'></td> <td width=6 valign=top style='width:4.45pt;padding:0in 0in 0in 0in; height:24.7pt'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in; height:24.7pt'></td> </tr> <tr style='mso-yfti-irow:7;mso-yfti-lastrow:yes;height:11.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 11.75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=19 valign=top style='width:14.2pt;padding:0in 0in 0in 0in; height:11.75pt'></td> <td width=120 valign=top style='width:1.25in;padding:0in 0in 0in 0in; height:11.75pt'></td> <td width=5 valign=top style='width:.05in;padding:0in 0in 0in 0in;height: 11.75pt'></td> <td width=29 valign=top style='width:21.75pt;padding:0in 0in 0in 0in; height:11.75pt'></td> <td width=6 valign=top style='width:4.45pt;padding:0in 0in 0in 0in; height:11.75pt'></td> <td width=163 valign=top style='width:122.2pt;padding:0in 0in 0in 0in; height:11.75pt'></td> </tr> </table> <div style='margin-top:15.85pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Right left imbalance<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Rotate right child to make a right right<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Then we fix it<o:p></o:p></span></p> </div> <div style='margin-top:30.9pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>c,o,m,p,u,t,e,r<o:p></o:p></span></p> </div> <div style='margin-left:63.65pt;margin-top:.15pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:521.25pt;height:239.25pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image060.png" o:title="image038"/> </v:shape><![endif]--><![if !vml]><img border=0 width=695 height=319 src="cmp251april_files/image061.gif" v:shapes="Picture_x0020_43"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:1.0in;margin-top:16.35pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Book pg 417 rules of the red/black tree<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>&nbsp;<o:p></o:p></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>4/30<o:p></o:p></span></p> </div> <div style='margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Thursday, April 30, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>3:53 PM<o:p></o:p></span></p> </div> <div style='margin-top:14.7pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:561.75pt;height:228pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image062.png" o:title="image039"/> </v:shape><![endif]--><![if !vml]><img border=0 width=749 height=304 src="cmp251april_files/image063.gif" v:shapes="Picture_x0020_44"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:49.4pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Report 4 due 5/7<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Exam 3 on 5/12<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:11.0pt; font-family:"Calibri","sans-serif"'>Proj 5 due 5/14<o:p></o:p></span></p> </div> </div> </div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div style='margin-left:9.7pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>5/5<o:p></o:p></span></p> </div> <div style='margin-left:9.7pt;margin-top:2.75pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>Tuesday, May 05, 2009<o:p></o:p></span></p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:10.0pt; font-family:"Calibri","sans-serif";color:gray'>3:55 PM<o:p></o:p></span></p> </div> <div style='margin-left:9.7pt;margin-top:3.55pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:492pt;height:177pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image064.png" o:title="image040"/> </v:shape><![endif]--><![if !vml]><img border=0 width=656 height=236 src="cmp251april_files/image065.gif" v:shapes="Picture_x0020_45"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:21.75pt'><nobr> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:758.25pt;height:10in;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image066.png" o:title="image041"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1011 height=960 src="cmp251april_files/image067.gif" v:shapes="Picture_x0020_46"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><br> <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:758.25pt;height:177.75pt; visibility:visible;mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image068.png" o:title="image042"/> </v:shape><![endif]--><![if !vml]><img border=0 width=1011 height=237 src="cmp251april_files/image069.gif" v:shapes="Picture_x0020_47"><![endif]></span><br style='mso-special-character:line-break'> <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> <![endif]><o:p></o:p></span></p> </div> </div> </div> </nobr> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <div style='border-width:100%'> <div> <div style='margin-left:26.35pt'> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:17.0pt; font-family:"Calibri","sans-serif"'>5/7 exam review<o:p></o:p></span></p> </div> <div style='margin-left:26.35pt;margin-top:2.75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:601.5pt;height:384.75pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image070.png" o:title="image043"/> </v:shape><![endif]--><![if !vml]><img border=0 width=802 height=513 src="cmp251april_files/image071.gif" v:shapes="Picture_x0020_48"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-top:56.65pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:543.75pt;height:450pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image072.png" o:title="image044"/> </v:shape><![endif]--><![if !vml]><img border=0 width=725 height=600 src="cmp251april_files/image073.gif" v:shapes="Picture_x0020_49"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=714 style='width:535.55pt;margin-left:26.0pt;border-collapse:collapse;mso-yfti-tbllook: 1184;mso-padding-alt:0in 0in 0in 0in' cols=5> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.75pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: .75pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=354 valign=top style='width:265.55pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=3 valign=top style='width:2.25pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=258 valign=top style='width:193.8pt;padding:0in 0in 0in 0in; height:.75pt'></td> <td width=46 valign=top style='width:34.85pt;padding:0in 0in 0in 0in; height:.75pt'></td> </tr> <tr style='mso-yfti-irow:1;height:5.2pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 5.2pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=354 valign=top style='width:265.55pt;padding:0in 0in 0in 0in; height:5.2pt'></td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:5.2pt'></td> <td width=3 valign=top style='width:2.25pt;padding:0in 0in 0in 0in; height:5.2pt'></td> <td width=305 colspan=2 rowspan=2 valign=top style='width:228.65pt; padding:0in 0in 0in 0in;height:5.2pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:228.75pt;height:151.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image074.png" o:title="image045"/> </v:shape><![endif]--><![if !vml]><img border=0 width=305 height=202 src="cmp251april_files/image075.gif" v:shapes="Picture_x0020_50"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:2;height:145.95pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 145.95pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=354 rowspan=3 valign=top style='width:265.55pt;padding:0in 0in 0in 0in; height:145.95pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_51" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:265.5pt;height:288.75pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image076.png" o:title="image046"/> </v:shape><![endif]--><![if !vml]><img border=0 width=354 height=385 src="cmp251april_files/image077.gif" v:shapes="Picture_x0020_51"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:145.95pt'></td> <td width=3 valign=top style='width:2.25pt;padding:0in 0in 0in 0in; height:145.95pt'></td> </tr> <tr style='mso-yfti-irow:3;height:26.5pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 26.5pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:26.5pt'></td> <td width=3 valign=top style='width:2.25pt;padding:0in 0in 0in 0in; height:26.5pt'></td> <td width=258 valign=top style='width:193.8pt;padding:0in 0in 0in 0in; height:26.5pt'></td> <td width=46 valign=top style='width:34.85pt;padding:0in 0in 0in 0in; height:26.5pt'></td> </tr> <tr style='mso-yfti-irow:4;height:115.85pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 115.85pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:115.85pt'></td> <td width=262 colspan=2 rowspan=2 valign=top style='width:196.2pt;padding: 0in 0in 0in 0in;height:115.85pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:196.5pt;height:160.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image078.png" o:title="image047"/> </v:shape><![endif]--><![if !vml]><img border=0 width=262 height=214 src="cmp251april_files/image079.gif" v:shapes="Picture_x0020_52"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=46 valign=top style='width:34.85pt;padding:0in 0in 0in 0in; height:115.85pt'></td> </tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:44.7pt'> <td width=1 valign=top style='width:.75pt;padding:0in 0in 0in 0in;height: 44.7pt'> <p><span style='font-size:1.0pt'>&nbsp;<o:p></o:p></span></p> </td> <td width=354 valign=top style='width:265.55pt;padding:0in 0in 0in 0in; height:44.7pt'></td> <td width=52 valign=top style='width:38.9pt;padding:0in 0in 0in 0in; height:44.7pt'></td> <td width=46 valign=top style='width:34.85pt;padding:0in 0in 0in 0in; height:44.7pt'></td> </tr> </table> <div style='margin-left:20.95pt;margin-top:29.75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:315pt;height:635.25pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image080.png" o:title="image048"/> </v:shape><![endif]--><![if !vml]><img border=0 width=420 height=847 src="cmp251april_files/image081.gif" v:shapes="Picture_x0020_53"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> <div style='margin-left:23.75pt;margin-top:58.25pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:459.75pt;height:454.5pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="cmp251april_files/image082.png" o:title="image049"/> </v:shape><![endif]--><![if !vml]><img border=0 width=613 height=606 src="cmp251april_files/image083.gif" v:shapes="Picture_x0020_54"><![endif]></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </div> </div> </div> <div> <p style='margin:0in;margin-bottom:.0001pt'>&nbsp;</p> <p style='margin:0in;margin-bottom:.0001pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:#969696'>Created with Microsoft Office OneNote 2007<br> One place for all your notes and information<o:p></o:p></span></p> </div> </div> </body> </html>