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Chapter 12
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Chapter 12
Chapter 12: Graphs
2
Algorithms Using Weighted Graphs
&#=
8226; Finding
the shortest path from a vertex to all other vertices
&=
#8226; Solution
formulated by Dijkstra
•
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Chapter 12
Chapter 12: Graphs
Algorithms Using Weighted
Graphs (continued)
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• A minimum
spanning tree is a subset of the edges of a graph such that there is only =
one
edge between each vertex, and all of the vertices are connected
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• The cost =
of a
spanning tree is the sum of the weights of the edges
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• We want t=
o find
the minimum spanning tree or the spanning tree with the smallest cost
=
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• Solution
formulated by R.C. Prim and is very similar to Dijkstra’s algorithm<=
/span>
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Chapter 12
Chapter 12: Graphs
Prim’s Algorithm
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Chapter 12
Chapter 12: Graphs
Chapter Review
<=
nobr>• A graph c=
onsists
of a set of vertices and a set of edges
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• In an und=
irected
graph, if (u,v) is an edge, then there is a path from vertex u to vertex v,
and vice versa
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• In a dire=
cted
graph, if (u,v) is an edge, then (v,u) is not necessarily an edge
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• If there =
is an
edge from one vertex to another, then the second vertex is adjacent to the
first
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• A graph is
considered connected if there is a patch from each vertex to every other
vertex
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Chapter 12
Chapter 12: Graphs
Chapter Review (continued)
<=
nobr>• A tree is=
a
special case of a graph
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• Graphs ma=
y be
represented by an array of adjacency lists
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• Graphs ma=
y be
represented by a two-dimensional square array called an adjacency matrix&#=
13;
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• A breadth=
-first
search of a graph finds all vertices reachable from a given vertex via the
shortest path
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• A depth-f=
irst
search of a graph starts at a given vertex and then follows a path of
unvisited vertices until it reaches a point where there are no unvisited
vertices that are reachable
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Chapter 12
Chapter 12: Graphs
Chapter Review (continued)
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• A topolog=
ical
sort determines an order for starting activities which are dependent on the
completion of other activities
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• Dijkstra&=
#8217;s
algorithm finds the shortest path from a start vertex to all other
vertices
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%'>• Prim̵=
7;s
algorithm finds the minimum spanning tree for a graph
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‹header›
‹date/time› =
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
‹footer›
‹#›
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------=_NextPart_01C58852.0E3705F0
Content-Location: file:///C:/2D6992E8/shortestPath_files/script.js
Content-Transfer-Encoding: quoted-printable
Content-Type: application/javascript; charset="us-ascii"
function LoadSld()
{
var sld=3DGetObj("SlideObj")
if( !g_supportsPPTHTML ) { =09
sld.style.visibility=3D"visible"
return
}
if( MakeNotesVis() ) return
runAnimations =3D _InitAnimations();
=09
if( IsWin("PPTSld") )
parent.SldUpdated(GetSldId())
g_origSz=3DparseInt(SlideObj.style.fontSize)
g_origH=3Dsld.style.posHeight
g_origW=3Dsld.style.posWidth
g_scaleHyperlinks=3D(document.all.tags("AREA").length>0)
if( g_scaleHyperlinks )
InitHLinkArray()
if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) )
document.body.scroll=3D"no"
_RSW()
if( IsWin("PPTSld") && parent.IsFullScrMode() )
FullScrInit();
=09
MakeSldVis();
ChkAutoAdv()
if( runAnimations )
{
if( document.all("NSPlay") )
document.all("NSPlay").autoStart =3D false;
if( sld.filters && sld.filters.revealtrans )
setTimeout( "document.body.start()", sld.filters.revealtrans.duration * =
1000 );
else
document.body.start();
}
}
function MakeSldVis()=20
{
var fTrans=3Dg_showAnimation && SldHasTrans()
if( fTrans )=09
{
if( g_bgSound ) {
idx=3Dg_bgSound.indexOf(",");
pptSound.src=3Dg_bgSound.substr( 0, idx );
pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1)));
}
SlideObj.filters.revealtrans.Apply()=09
}
SlideObj.style.visibility=3D"visible"
if( fTrans )
SlideObj.filters.revealtrans.Play()
}
function MakeNotesVis()=20
{
if( !IsNts() ) return false=20
SlideObj.style.display=3D"none"
nObj =3D document.all.item("NotesObj")
parent.SetHasNts(0)
if( nObj ) {=20
nObj.style.display=3D""
parent.SetHasNts(1)
}
return 1
}
function ChkAutoAdv()
{
if(SldHasTrans())
SlideObj.onfilterchange=3DAutoAdv
else
AutoAdv()
}
function AutoAdv()
{
if(!IsWin("PPTSld") || !gUseSldTimings )return
var sld=3DGetCurSld()
if( (sld.mAdvDelay>0) && !parent.IsFramesMode() )
setTimeout("parent.GoToNextSld()",sld.mAdvDelay)
}
function GetObj(id)
{
if(g_supportsPPTHTML) return document.all(id);
else return document.getElementById(id);
}
function SldHasTrans() { return SlideObj.style.filter !=3D ""; }
function GetSldId() { return sId=3Dlocation.href.substring(location.href.la=
stIndexOf('/')+1) }
function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx=
tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl=
e.display=3D'none'; return true } return false }
function IsWin( name ) { return window.name =3D=3D name }
function IsNts() { return IsWin("PPTNts") }
function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) }
function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"=
&& navigator.appVersion.indexOf("Windows")>0 ) }
function SupportsPPTHTML()
{
var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0
if( msie >=3D 0 )
ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) )
else
ver=3DparseInt(appVer)
return( ver >=3D 4 && msie >=3D 0 )
}
function _RSW()
{
if( !g_supportsPPTHTML || IsNts() ||
( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) )
return
var padding=3D0;
if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6
cltWidth=3Ddocument.body.clientWidth-padding
cltHeight=3Ddocument.body.clientHeight-padding
factor=3D(1.0*cltWidth)/g_origW
if( cltHeight < g_origH*factor )
factor=3D(1.0*cltHeight)/g_origH
newSize =3D g_origSz * factor
if( newSize < 1 ) newSize=3D1
s=3DSlideObj.style
s.fontSize=3DnewSize+"px"
s.posWidth=3Dg_origW*factor
s.posHeight=3Dg_origH*factor
s.posLeft=3D(cltWidth-s.posWidth+padding)/2
s.posTop=3D(cltHeight-s.posHeight+padding)/2
if( g_scaleHyperlinks )
ScaleHyperlinks( factor )
}
function _InitAnimations()
{
animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined';
isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode();
g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc=
reen && parent.IsSldVisited());
if( g_animUseRuntime ) {
collSeq =3D document.all.tags("seq");
if( collSeq !=3D null ) {
for(ii=3D0;ii numSlds )
gSldJumpIdx =3D numSlds;
if ( gSldJumpIdx >=3D 0 ) {
if ( gSldJumpIdx =3D=3D 0 )
gSldJumpIdx =3D 1;
var jumpTo =3D parseInt(gSldJumpIdx);
gSldJump =3D 0; gSldJumpIdx =3D "";
win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )
}
}
}
function _KDH()
{
if( event.keyCode =3D=3D 8 ) {
event.returnValue =3D 0;
parent.GoToPrevSld();
}
}
function DocumentOnClick()
{
if( IsNts() || parent.HideMenu() ) return;
if( ( g_allowAdvOnClick && !parent.IsFramesMode() ) ||
(event && (event.keyCode=3D=3D32) ) )
parent.GoToNextSld();
}
var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""=
, g_bgSound=3D"",
g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser =
=3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1;
var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w=
indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va=
r g_animManager =3D null;
var g_animUseRuntime =3D false;
var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;
var g_animMainSequence =3D null;
var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram=
es", gIsEndShow=3D0, NUM_VIS_SLDS=3D7, SCRIPT_HREF=3D"script.js", FULLSCR_H=
REF=3D"fullscreen.htm";
var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO=
tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true
window.gPPTHTML=3DSupportsPPTHTML()
var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(=
"slide0033.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("=
slide0035.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("s=
lide0004.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1));
/*********************************************
Frameset functions
These functions control slide navigation
and state of the frameset.
**********************************************/
function FullScrInit()
{
g_allowAdvOnClick =3D GetCurSld().mAdvOnClk
document.body.style.backgroundColor=3D"black"
document.oncontextmenu=3Dparent._CM;
document.onkeydown =3D _KDH;
document.ondragstart=3DCancel
document.onselectstart=3DCancel
self.focus()
}
function Redirect( frmId )
{=09
var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId()
if(idx>=3D0) str=3Dstr.substr(1);
if( window.name !=3D frmId && ( sId !=3D str) ) {
obj =3D GetObj("Main-File")
window.location.href=3Dobj.href+"#"+sId
return 1
}
return 0
}
var MHTMLPrefix =3D CalculateMHTMLPrefix();=20
function CalculateMHTMLPrefix()
{
if ( document.location.protocol =3D=3D 'mhtml:') {=20
href=3Dnew String(document.location.href)=20
Start=3Dhref.indexOf('!')+1=20
End=3Dhref.lastIndexOf('/')+1=20
if (End < Start)=20
return href.substring(0, Start)=20
else=20
return href.substring(0, End)=20
}
return '';
}
function GetTags(base,tag)
{
if(g_supportsPPTHTML) return base.all.tags(tag);
else return base.getElementsByTagName(tag);
}
function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP=
refix+GetHrefObj( gCurSld ).mNtsHref ) }
function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }
function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }
function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }
function SetHasNts( fVal )
{
if( gHasNts !=3D fVal ) {
gHasNts=3DfVal
UpdNavPane()
}
}
function ToggleOtlText()
{
gOtlTxtExp=3D!gOtlTxtExp
UpdOtlPane()
}
function ClearMedia()
{
// Clear any sounds playing before launching another browser window. Other=
wise,
// in fullscreen mode, you'll continue to hear the sound in the frames mod=
e.
if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0;
}
function FullScreen()
{=20
if ( PPTSld.g_animUseRuntime )
PPTSld.document.body.pause();
ClearMedia();
var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF =
: FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;
if(PPTNav.event.ctrlKey) {
var w =3D (window.screen.availWidth * 1.0) / 2.0
var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW
win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top=
=3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
else
{
win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
}
function ToggleVNarration()
{
rObj=3DPPTSld.document.all("NSPlay")
if( rObj && !PPTSld.g_animUseRuntime ) {
if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) )
rObj.Play()
else if( rObj.playState =3D=3D 2 )
rObj.Pause()
else
return;
}
else if( PPTSld.g_animUseRuntime )
{
narObj =3D PPTSld.document.all("narrationID")
if( narObj )
narObj.togglePause()
}
}
function GetCurSldNum()
{ =20
obj=3DGetHrefObj(gCurSld)
if( obj.mOrigVis =3D=3D 1 )
return obj.mSldIdx
else =20
return gCurSld
}
function GetNumSlds()
{ =20
if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )
return GetSldList().mNumVisSlds;
else
return GetSldList().mList.length
}
function GetSldNum( href )
{
for(ii=3D0; ii 1 )
PopSldList();
else if( !IsFramesMode() ) {
if( gLoopCont )
GoToFirst()
else
EndShow()
}
}
function GoToPrevSld()
{
ii=3DgCurSld-1
if( ii > 0 ) {
obj=3DGetHrefObj(ii)
while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )
obj=3DGetHrefObj(--ii)
if( ii =3D=3D 0 ) ii=3D1
GoToSldNum(ii)
}
}
function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }
function GoToLast()
{
ii=3DGetSldList().mList.length
if( ii !=3D gCurSld )
GoToSld( GetHrefObj(ii).mSldHref )
}
function GoToSldNum( num )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
obj =3D GetHrefObj( num )
obj.mVis=3D1
gPrevSld=3DgCurSld
gCurSld =3D num;
PPTSld.location.replace(MHTMLPrefix+obj.mSldHref)
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function GoToSld( href )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
GetHrefObj( GetSldNum(href) ).mVis=3D1
PPTSld.location.replace(MHTMLPrefix+href)
}
function SldUpdated( id )
{
if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return
gPrevSld=3DgCurSld
gCurSld=3DGetSldNum(id)
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO=
bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }
function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }
function CloseWindow() {
if( HideMenu() ) return;
=09
var event =3D PPTSld.event;
if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D=
=3D32 || event.type=3D=3D"click" ) )
window.close( self );
CatchNumKeys( self, event );
}
function Unload() { gIsEndShow=3D0; }
function SetupEndShow() {
gIsEndShow=3D1;
PPTSld.document.body.scroll=3D"no";
PPTSld.document.onkeypress=3DCloseWindow;
PPTSld.document.onclick=3DCloseWindow;
PPTSld.document.oncontextmenu=3D_CM;
}
function EndShow()
{
if( IsFramesMode() ) return
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
doc=3DPPTSld.document
var dir =3D doc.body.dir
if( dir !=3D "rtl" ) dir =3D "ltr";
doc.open()
doc.writeln('' + ENDSHOW_MESG + '
0) {
PushSldList(sldList,fEnd);
gCurSld =3D 1;
}
else
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}
function PushSldList(arr,fEnd) {
var ii =3D gSldStack.length;
gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
GoToSld( gSldStack[ii].mList[0].mSldHref );
}
function PopSldList() {
if (gSldStack[gSldStack.length-1].fEndShow)
EndShow()
else {
gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
gSldStack[gSldStack.length-1] =3D null;
gSldStack.length--;
var sldList =3D gSldStack[gSldStack.length-1];
GoToSld( sldList.mList[gCurSld - 1].mSldHref );
}
}
var custShowList=3Dnew Array();
/*********************************************
Navigation button implementation
There are 2 types of buttons: ImgBtn, TxtBtn
implemented as function objects. They share
a similiar interface so the event handlers
can call SetActive, for example, on a button=20
object without needing to know exactly=20
what type of button it is.
**********************************************/
//----------------------------------
function ImgBtn( oId,bId,w,action )
//----------------------------------
{
var t=3Dthis
t.Perform =3D _IBP
t.SetActive =3D _IBSetA
t.SetInactive=3D _IBSetI
t.SetPressed =3D _IBSetP
t.SetDisabled=3D _IBSetD
t.Enabled =3D _IBSetE
t.ChangeIcon =3D null
t.UserAction =3D action
t.ChgState =3D _IBUI
t.mObjId =3D oId
t.mBorderId=3D bId
t.mWidth =3D w
t.mIsOn =3D t.mCurState =3D 0
}
function _IBSetA()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _IBSetI()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0=20
}
}
function _IBSetP()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
obj.style.posLeft+=3D1; obj.style.posTop+=3D1
}
}
function _IBSetD()
{ =20
obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
obj.style.posTop=3D0=20
}
function _IBSetE( state )
{
var t=3Dthis
GetObj( t.mBorderId ).style.visibility=3D"visible"
if( state !=3D t.mIsOn ) {
t.mIsOn=3Dstate
if( state )
t.SetInactive()
else
t.SetDisabled()
}
}
function _IBP()
{
var t=3Dthis
if( t.mIsOn ) {
if( t.UserAction !=3D null )
t.UserAction()
if( t.ChangeIcon ) {
obj=3DGetObj(t.mObjId)
if( t.ChangeIcon() )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
else
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
}
t.SetActive()
} =20
}
function _IBUI( clr1,clr2,nextState )
{
var t=3Dthis
SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
obj=3DGetObj( t.mObjId )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj=
.style.posTop
t.mCurState=3DnextState
return obj
}
//-----------------------------------------
function TxtBtn( oId,oeId,action,chkState )
//-----------------------------------------
{
var t=3Dthis
t.Perform =3D _TBP
t.SetActive =3D _TBSetA
t.SetInactive=3D _TBSetI
t.SetPressed =3D _TBSetP
t.SetDisabled=3D _TBSetD
t.SetEnabled =3D _TBSetE
t.GetState =3D chkState
t.UserAction =3D action
t.ChgState =3D _TBUI
t.mObjId =3D oId
t.m_elementsId=3D oeId
t.mIsOn =3D 1
}
function _TBSetA()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gHiliteClr,gShadowClr,0,0 )
}
function _TBSetI()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
}
function _TBSetP()
{
if( this.mIsOn )
this.ChgState( gShadowClr,gHiliteClr,1,1 )
}
function _TBSetD()
{ =20
this.ChgState( gFaceClr,gFaceClr,0,0 )
this.mIsOn =3D 0
}
function _TBSetE()
{
var t=3Dthis
if( !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
else
t.ChgState( gShadowClr,gHiliteClr,1,1 )
t.mIsOn =3D 1
}
function _TBP()
{
var t=3Dthis
if( t.mIsOn ) {=20
if( t.UserAction !=3D null )
t.UserAction()
if( !t.GetState )
return
if( t.GetState() )
t.SetPressed()
else
t.SetActive()
} =20
}
function _TBUI( clr1,clr2,lOffset,tOffset )
{
SetBorder( GetObj( this.mObjId ),clr1,clr2 )
Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}
function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=
ft }
function SetBorder( obj, upperLeft, lowerRight )
{
s=3Dobj.style;
s.borderStyle =3D "solid"
s.borderWidth =3D 1=20
s.borderLeftColor =3D s.borderTopColor =3D upperLeft
s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}
function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }
function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }
function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }
function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }
function BtnOnUp()
{
b=3DGetBtnObj()
if( b !=3D null )
b.Perform()
else
Upd()
}
function GetNtsState(){ return parent.gNtsOpen }
function GetOtlState(){ return parent.gOtlOpen }
function GetOtlTxtState(){ return parent.gOtlTxtExp }
function NtsBtnSetFlag( fVal )
{
s=3Ddocument.all.item( this.m_flagId ).style
s.display=3D"none"
if( fVal )
s.display=3D""
else
s.display=3D"none"
}
function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etActive() }
function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etInactive() }
function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etPressed() }
function _BSetA_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]=20
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _BSetI_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0
}
}
var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=
THREEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=
e,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=
lPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN=
tsPane )
gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg;
gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg;
gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.=
ToggleNtsPane,GetNtsState )
gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To=
ggleNtsPane,GetNtsState )
gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n=
b_prevBorder",30,parent.GoToPrevSld )
gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n=
b_nextBorder",30,parent.GoToNextSld )
gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=
.FullScreen )
gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=
rent.FullScreen,null )
gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=
.FullScreen,null )
gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice=
","nb_voiceBorder",18,parent.ToggleVNarration )
gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT=
xt","nb_otlTxtBorder",23,parent.ToggleOtlText )
gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts"
gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag
gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState
/*********************************************
Context menu implementation
_CM() is the function that's hooked up to
the oncontextmenu event. Once we're asked to
show the menu, we first build it by creating
DIVs on-the-fly. Then we position it=20
within the screen area so it doesn't get
clipped.
Creating the DIVs using createElement() means
we don't have to write out any extra HTML
into the slide HTML files.
**********************************************/
var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=
row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"
function ShowMenu()
{
BuildMenu();
var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=
=3DPPTSld.event.clientY+doc.scrollTop
m =3D PPTSld.document.all.item("ctxtmenu")
m.style.pixelLeft=3Dx
if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
m.style.pixelLeft=3Dx-m.scrollWidth
m.style.pixelTop=3Dy
if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
m.style.pixelTop=3Dy-m.scrollHeight
m.style.display=3D""
}
function _CM()
{
if( !parent.IsFullScrMode() ) return;
if(!PPTSld.event.ctrlKey) {
ShowMenu()
return false
} else
HideMenu()
}
function BuildMenu()
{
if( PPTSld.document.all.item("ctxtmenu") ) return
var mObj=3DCreateItem( PPTSld.document.body )
mObj.id=3D"ctxtmenu"
mObj.style.visibility=3D"hidden"
var s=3DmObj.style
s.position=3D"absolute"
s.cursor=3D"default"
s.width=3D"120px"
SetCMBorder(mObj,"menu","black")
var iObj=3DCreateItem( mObj )
SetCMBorder( iObj, "threedhighlight","threedshadow" )
iObj.style.padding=3D2
CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
=09
CreateSeparator( iObj )
CreateMenuItem( iObj,sEnd,M_End,M_True )
mObj.style.visibility=3D"visible"
}
function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa=
lue=3Dfalse }
function Highlight() { ChangeClr("activecaption","threedhighlight") }
function Deselect() { ChangeClr("threedface","menutext") }
function Perform()
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() )
e.Action()
else
PPTSld.event.cancelBubble=3Dtrue
}
function ChangeClr( bg,clr )
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() ) {
e.style.backgroundColor=3Dbg
e.style.color=3Dclr
}
}
function M_HasPrevSld() { return( parent.HasPrevSld() ) }
function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }
function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();=
PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() }
function M_True() { return true }
function M_End() { window.close( self ) }
function CreateMenuItem( node,text,action,eval )
{
var e=3DCreateItem( node )
e.type=3D"menuitem"
e.Action=3Daction
e.IsActive=3Deval
e.innerHTML=3Dtext
if( !e.IsActive() )
e.style.color=3D"threedshadow"
e.onclick=3DPerform
e.onmouseover=3DHighlight
e.onmouseout=3DDeselect
s=3De.style;
s.fontFamily=3DsFont
s.fontSize=3D"9pt"
s.paddingLeft=3D2
}
function CreateSeparator( node )
{
var sObj=3DCreateItem( node )
SetCMBorder(sObj,"menu","menu")
var s=3DsObj.style
s.borderTopColor=3D"threedshadow"
s.borderBottomColor=3D"threedhighlight"
s.height=3D1
s.fontSize=3D"0px"
}
function CreateItem( node )
{
var elem=3DPPTSld.document.createElement("DIV")
node.insertBefore( elem )
return elem
}
function SetCMBorder( o,ltClr,rbClr )
{
var s=3Do.style
s.backgroundColor=3D"menu"
s.borderStyle=3D"solid"
s.borderWidth=3D1
s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr
}
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Chapter 12
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No=
tes
1
2
Finding the shortest path from a vertex to all other vertices
Solution formulated by Dijkstra
3
A minimum spanning tree is a subset of the edges of a graph such that
there is only one edge between each vertex, and all of the vertices =
are
connected
The cost of a spanning tree is the sum of the weights of the edges
We want to find the minimum spanning tree or the spanning tree with =
the
smallest cost
Solution formulated by R.C. Prim and is very similar to DijkstraR=
17;s
algorithm
4
5
A graph consists of a set of vertices and a set of edges
In an undirected graph, if (u,v) is an edge, then there is a path fr=
om
vertex u to vertex v, and vice versa
In a directed graph, if (u,v) is an edge, then (v,u) is not necessar=
ily
an edge
If there is an edge from one vertex to another, then the second vert=
ex
is adjacent to the first
A graph is considered connected if there is a patch from each vertex=
to
every other vertex
6
A tree is a special case of a graph
Graphs may be represented by an array of adjacency lists
Graphs may be represented by a two-dimensional square array called an
adjacency matrix
A breadth-first search of a graph finds all vertices reachable from a
given vertex via the shortest path
A depth-first search of a graph starts at a given vertex and then
follows a path of unvisited vertices until it reaches a point where
there are no unvisited vertices that are reachable
7
A topological sort determines an order for starting activities which=
are
dependent on the completion of other activities
Dijkstra’s algorithm finds the shortest path from a start vert=
ex
to all other vertices
Prim’s algorithm finds the minimum spanning tree for a graph
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![](3D"slide0033_image002.jpg")
![](3D"slide0035_image004.jpg")
![](3D"notes_flag.gif")
No=
tes![](3D"buttons.gif")
![](3D"slide0033_image001.png"){kind=link}
![](3D"slide0035_image003.png"){kind=link}