# Assignment 5: Question 1
restart;
with(GraphTheory):wtih(SpecialGraphs):
Basketball:=Graph(undirected,{{1,A},{2,A},{1,B},{1,C},{2,C},{3,D},{4,D},{5,D},{2,E},{3,E},{3,G},{4,G},{2,H},{3,H}});
LUkoR1JBUEhMTkc2IjYoSSt1bmRpcmVjdGVkR0YkSSt1bndlaWdodGVkR0YkNy4iIiIiIiMiIiQiIiUiIiZJIkVHRiRJIkdHRiRJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRJIkFHRiRJIkJHRiRJIkNHRiRJIkhHRiQtSSZBcnJheUdGMjYjL0kkJWlkR0YkIikrc2BMSTBHUkFQSExOL3RhYmxlLzRHRiQiIiE=
DrawGraph(Basketball);
6@-%)POLYGONSG607&7$$"$k#!"%$"&k-"!"%7$$"$k#!"%$"%O(*!"%7$$!$k#!"%$"%O(*!"%7$$!$k#!"%$"&k-"!"%7&7$$"%kF!"%$"&k-"!"%7$$"%kF!"%$"%O(*!"%7$$"%OA!"%$"%O(*!"%7$$"%OA!"%$"&k-"!"%7&7$$"%k_!"%$"&k-"!"%7$$"%k_!"%$"%O(*!"%7$$"%OZ!"%$"%O(*!"%7$$"%OZ!"%$"&k-"!"%7&7$$"%kx!"%$"&k-"!"%7$$"%kx!"%$"%O(*!"%7$$"%Os!"%$"%O(*!"%7$$"%Os!"%$"&k-"!"%7&7$$"&k-"!"%$"&k-"!"%7$$"&k-"!"%$"%O(*!"%7$$"%O(*!"%$"%O(*!"%7$$"%O(*!"%$"&k-"!"%7&7$$"+nmmI>!#5$"$k#!"%7$$"+nmmI>!#5$!$k#!"%7$$"+nmm-9!#5$!$k#!"%7$$"+nmm-9!#5$"$k#!"%7&7$$"+LLL(f$!#5$"$k#!"%7$$"+LLL(f$!#5$!$k#!"%7$$"+LLLpI!#5$!$k#!"%7$$"+LLLpI!#5$"$k#!"%7&7$$"%k_!"%$"$k#!"%7$$"%k_!"%$!$k#!"%7$$"%OZ!"%$!$k#!"%7$$"%OZ!"%$"$k#!"%7&7$$"$k#!"%$"$k#!"%7$$"$k#!"%$!$k#!"%7$$!$k#!"%$!$k#!"%7$$!$k#!"%$"$k#!"%7&7$$"&k-"!"%$"$k#!"%7$$"&k-"!"%$!$k#!"%7$$"%O(*!"%$!$k#!"%7$$"%O(*!"%$"$k#!"%7&7$$"+LLL(f)!#5$"$k#!"%7$$"+LLL(f)!#5$!$k#!"%7$$"+LLLp!)!#5$!$k#!"%7$$"+LLLp!)!#5$"$k#!"%7&7$$"+nmmIp!#5$"$k#!"%7$$"+nmmIp!#5$!$k#!"%7$$"+nmm-k!#5$!$k#!"%7$$"+nmm-k!#5$"$k#!"%-%&COLORG6G%$RGBG$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<$"#5!""$"#5!""$"2CK-)H+++?!#<-%&STYLEG6#%,PATCHNOGRIDG-%%TEXTG6%7$$""!!""$"#5!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"16"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontweightGQ%bold6"-%%FONTG6%%*HelveticaG%%BOLDG"#6-%%TEXTG6%7$$"#D!"#$"#5!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"26"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontweightGQ%bold6"-%%FONTG6%%*HelveticaG%%BOLDG"#6-%%TEXTG6%7$$""&!""$"#5!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"36"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontweightGQ%bold6"-%%FONTG6%%*HelveticaG%%BOLDG"#6-%%TEXTG6%7$$"#v!"#$"#5!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"46"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontweightGQ%bold6"-%%FONTG6%%*HelveticaG%%BOLDG"#6-%%TEXTG6%7$$"#5!""$"#5!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"56"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontweightGQ%bold6"-%%FONTG6%%*HelveticaG%%BOLDG"#6-%%TEXTG6%7$$"+nmmm;!#5$""!!""-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q"E6"/%'familyGQ*Helvetica6"/%%sizeGQ#116"/%%boldGQ%true6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ%bold6"/%+fontw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$""!!""$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%&STYLEG6#%%LINEG-%)POLYGONSG6&7$7$$"+LLLL$)!#5$""!!""7$$"#D!"#$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%&STYLEG6#%%LINEG-%)POLYGONSG6&7$7$$"+nmmmm!#5$""!!""7$$"#D!"#$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%&STYLEG6#%%LINEG-%)POLYGONSG6&7$7$$"+nmmmm!#5$""!!""7$$""&!""$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,CONSTRAINEDG-%%ROOTG6'-%)BOUNDS_XG6#$"#]!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%+R!""-%.BOUNDS_HEIGHTG6#$"%+R!""-%)CHILDRENG6"
# where A refers to Alice, and so on
# One feasible starting line up is: Deb-5, Gladys-4, Hermione-3, Ellen-2, Bonnie-1. Note that although there are several feasible starting line ups, Deb must play 5, Gladys must play 4 and Hermione must play 3 (since no one else can play 5, then no one else can play 4, and so on). Therefore there is on feasible line up if Hermione can not play 3.
# Assignment 5: Question 2
restart:
with(GraphTheory):
# Part (a)
G1:=Graph(5,{{1,2},{1,4},{2,5},{4,5},{2,3},{3,5},{1,5}});
LUkoR1JBUEhMTkc2IjYoSSt1bmRpcmVjdGVkR0YkSSt1bndlaWdodGVkR0YkNyciIiIiIiMiIiQiIiUiIiYtSSZBcnJheUclKnByb3RlY3RlZEc2Iy9JJCVpZEdGJCIqTyxRIVFJMEdSQVBITE4vdGFibGUvMUdGJCIiIQ==
DrawGraph(G1);
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
# Part (b)
AdjacencyMatrix(G1);
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
# Part (c)
G2 := Graph(10,{[{1,2},2],[{2,3},2],[{3,4},2],[{1,5},4],[{2,6},7],[{4,6},1],[{5,6},4],[{6,7},2],[{7,8},4],[{5,9},2],[{9,10},6],[{6,10},3],[{8,10},2],[{4,8},8]});
LUkoR1JBUEhMTkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoSSt1bmRpcmVjdGVkR0YnSSl3ZWlnaHRlZEdGJzcsIiIiIiIjIiIkIiIlIiImIiInIiIoIiIpIiIqIiM1LUkmQXJyYXlHRiU2Iy9JJCVpZEdGJyIqc1tLJ1FJMUdSQVBITE4vdGFibGUvMTRHRictSSdNYXRyaXhHRiQ2Iy9GOiIqPzpUIVE=
# Part (d)
DijkstrasAlgorithm(G2,1,8);
NyQ3KSIiIiIiIyIiJCIiJSIiJyIiKCIiKSIjOA==
# with shortest path or weight 13
# Part (e)
T:=MinimalSpanningTree(G2);?MinimalSpanningTree
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DrawGraph(T);
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# with total weight being 20
# Assignment 5: Question 3
with(plots):with(stats):
plot(sqrt(x),x=0.5..1.5);
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
JCIrJD1oZ3kmISM1
MonteCarloProcedure:=proc(n)
COUNTER:=0:
M:=1.5:a:=0.5:b:=1.5:
for i from 1 to n do
xtemp:=evalf((rand()/10^12)*(b-a)+a):
ytemp:=evalf((rand()/10^12)*(M-0)+0):
ftemp:=sqrt(xtemp):
if (ytemp<=ftemp) then
COUNTER:=COUNTER+1:
end if;
end do;
Area:=M*(b-a)*(COUNTER/n):Area;
end proc:
Warning, `COUNTER` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `M` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `a` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `b` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `i` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `xtemp` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `ytemp` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `ftemp` is implicitly declared local to procedure `MonteCarloProcedure`
Warning, `Area` is implicitly declared local to procedure `MonteCarloProcedure`
MonteCarloProcedure(10000);
JCIrKysrdykqISM1
int(sqrt(x),x=0.5..1.5);
JCIrNWhVISopKiEjNQ==
# The total number of random points is 10000. The upper bound on the y coordinates is M=1.5