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Project Overview (Fall 2022)
!”#$%&’&%(&#)*+,-$.*/%%$0#+1&.($2,$2,3+*3&%$.+,%(#”.(2,-$/,$45$/-&,($(+$/66#&%%$/$7″‘/,$2,(&**2-&,.&$(&%(8$97&$0#+1&.($2%$6″&$/($(7&$&,6$+:$(7&$%&’&%(&#;$<"($(7&#&$/#& ?+"$+00+#(",2(2&%$(+$%&&$?+"#$.*/%%'/(&%B$/00#+/.7&%$/,6$0+%%2<*?$2,.+#0+#/(&$(7&2#$26&/%$2,(+$?+"#$+>,$0#+1&.(8
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Copyright By PowCoder代写 加微信 powcoder

In a (Large) Nutshell
97&$DEFGHF$.*/%%$0#+1&.($2%$(+$.#&/(&$/,$45$/-&,($(7/($./,$0/%%$/$7″‘/,$2,(&**2-&,.&$(&%(8$I+”B**$6+>,*+/6$/$.+6&$0/.J/-&$(7/($.+,(/2,%$(7&$<+2*&#0*/(&$,&.&%%/#?$(+ #",$/,$/-&,($?+"$6&%2-,$/-/2,%($/$%&($+:$0#+<*&'%$2,%02#&6$&#8
97&#&$/#&$:+”#$%&(%$+:$0#+<*&'%$:+#$?+"#$/-&,($(+$/,%>&#P$Q;$D;$R;$/,6$S8$S/.7$%&($.+,(/2,%$:+”#$(?0&%$+:$0#+<*&'%P$Q/%2.;$9&%(;$D7/**&,-&;$/,6$K/3&,B%8$I+"B**$<&$/<*&$(+ %&&$(7&$Q/%2.$/,6$D7/**&,-&$0#+<*&'%$>72*&$6&%2-,2,-$?+”#$/-&,(;$/,6$?+”#$-#/6&$>2**$<&$&#%$(+$(7&$Q/%2.$/,6$9&%($0#+<*&'%8$97& '2*&%(+,&%$(7#+"-7+"($(7&$%&'&%(&#$>2**$./##?$?+”$(7#+”-7$(/.J*2,-$’+#&$/,6$’+#&$/63/,.&6$0#+<*&'%P$:+#$M2*&%(+,&$T;$?+"B**$1"%($:/'2*2/#2C&$?+"#%&*:$>2(7$(7& %”<'2%%2+,$0#+.&%%$/,6$6/(/$%(#".("#&%8$U+#$M2*&%(+,&$V;$?+"B**$(/#-&($(7&$O#%($%&($+:$0#+<*&'%;$(7&$#&*/(23&*?$&/%?$VWV$0#+<*&'%$:#+'$E&($Q8$U+#$M2*&%(+,&$H;$?+"B** '+3&$+,$(+$(7&$%&.+,6$%&($+:$0#+<*&'%;$(7&$'+#&$.7/**&,-2,-$HWH$0#+<*&'%$:#+'$E&($D8$U+#$M2*&%(+,&$X;$?+"B**$*++J$/($(7&$'+#&$62Y."*($E&($R$/,6$E&($S$0#+<*&'%; <"2*62,-$(+>/#6$(7&$O,/*$6&*23&#/<*&$/$<2($*/(&#8 U+#$/**$0#+<*&'%;$?+"#$/-&,($>2**$<&$-23&,$2'/-&%$(7/($#&0#&%&,($(7&$0#+<*&'$2,$80,-$:+#'/(8$4,$&W/'0*&$+:$/$:"**$0#+<*&'$2%$%7+>,$<&*+>Z$?+”#$/-&,($>+”*6$<&$-23&, %&0/#/(&$O*&%$#&0#&%&,(2,-$(7&$.+,(&,(%$+:$%="/#&%$4;$Q;$D;$T;$V;$H;$X;$[;$/,6$G8 R+,B($>+##?$2:$(7&$/<+3&$6+&%,B($'/J&$%&,%&$="2(&$?&($\$(7&$0#+1&.(%$/#&$/$<2($.+'0*&W$>7&,$?+”B#&$-&((2,-$%(/#(&68$97&$-+/*$+:$(72%$%&.(2+,$2%$1″%($(+$0#+326&$?+”$>2(7 /$72-7)*&3&*$32&>$%+$(7/($(7&$#&%($+:$(72%$6+.”‘&,($’/J&%$/$<2($'+#&$%&,%&8 Background and Goals 972%$%&.(2+,$.+3&#%$(7&$*&/#,2,-$-+/*%$/,6$*&6-&)Q/%&6$4#(2O.2/*$5,(&**2-&,.&$2%$(+$.#&/(&$7″‘/,)*2J&;$7″‘/,)*&3&*$2,(&**2-&,.&;$/,6$(+$”%&$(7/($(+$#&^&.($+,$7+>$7″‘/,%$/.(“/**?$(72,J8$5:$(72%$2% (7&$-+/*$+:$(7&$O&*6;$(7&,$>7/($<&((&#$>/?$(+$&3/*”/(&$2,(&**2-&,.&$+:$/,$/-&,($(7/,$7&#&$(7&$(&%()(/J&#$2%$-23&,$/$’/(#2W$+:$O-“#&%$/,6$/%J&6$(+$%&*&.($(7&$O-“#&$(7/($.+’0*&(&%$(7&$’/(#2W8$4,$&W/’0*&$+:$/$VWV 0#+<*&'$>/%$%7+>,$/<+3&Z$/,$&W/'0*&$+:$/$HWH$0#+<*&'$2%$%7+>,$<&*+>8
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About the Test
97&$:”**$K/3&,B%$L#+-#&%%23&$M/(#2.&%$(&%($.+,%2%(%$+:$G`$32%”/*$/,/*+-?$0#+<*&'%$62326&6$2,(+$O3&$%&(%P$4;$Q;$D;$R;$/,6$S8$E&($4$2%$.+'0#2%&6$+:$TV$%2'0*&$0/((&#,) '/(.72,-$0#+<*&'%$>72.7$>&$>+,B($.+3&#$2,$(7&%&$0#+1&.(%8$E&($Q$2%$.+’0#2%&6$+:$TV$VWV$’/(#2W$0#+<*&'%;$%".7$/%$(7&$O#%($2'/-&$%7+>,$/<+3&8$E&(%$D;$R;$/,6$S$/#& &/.7$.+'0#2%&6$+:$TV$HWH$'/(#2W$0#+<*&'%;$%".7$/%$(7&$%&.+,6$2'/-&$%7+>,$/<+3&8$L#+<*&'%$/#&$,/'&6$>2(7$(7&2#$%&($:+**+>&6$&$./,,+($0#+326&$(7&$#&/*$K/3&,B%$L#+-#&%%23&$M/(#2.&%$(&%($(+$&3&#?+,&8$5,%(&/6;$>&B**$<&$-232,-$?+"$%&(%$+:$0#+<*&'%$\$>72.7$>&$./**$aQ/%2.b 0#+<*&'%$\$2,%02#&6$2**$<&$&3/*"/(&6$$>&**$2($0&#:+#’%$+,$(7&%&$aQ/%2.b$0#+<*&'%;$/%$>&**$/%$/ 0/#/**&*$%&($+:$a9&%(b$0#+<*&'%$(7/($?+"$>2**$,+($%&&$>72*&$6&%2-,2,-$?+”#$/-&,(8$97&%&$9&%($0#+<*&'%$/#&$62#&.(*?$/,/*+-+"%$(+$(7&$Q/%2.$0#+<*&'%Z$#",,2,-$/-/2,%($(7& (>+$%&(%$0#+326&%$/$.7&.J$:+#$-&,&#/*2(?$/,6$+3&#O((2,-8$I+”#$/-&,(%$>2**$/*%+$#”,$/-/2,%($(7&$#&/*$KLM$/%$>&**$/%$/$%&($+:$D7/**&,-&$0#+<*&'%;$<"($,&2(7&#$+:$(7&%&$>2** <&$:/.(+#&6$2,(+$?+"#$-#/6&8 !3&#/**;$2**$/,%>&#$TcV$0#+<*&'%8$M+#&$+,$(7&$%0&.2O.$0#+<*&'%$(7/($?+"#$/-&,($>2**$.+’0*&(&$/#&$2,$(7&$%&.(2+,%$(7/($:+**+>8
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The Problem Sets
4%$’&,(2+,&6$0#&32+”%*?;$2**$#”,$/-/2,%($TcV$0#+<*&'%P$X$E&(%$+:$Xd$0#+<*&'%8$S/.7$+:$(7&$X$E&(%$2%$<#+J&,$6+>,$2,(+$:+”#$%”<%&(%$+: TVP$TV$Q/%2.;$TV$9&%(;$TV$K/3&,B%;$/,6$TV$D7/**&,-&8 I+"$./,$%&&$(7&$Q/%2.$/,6$D7/**&,-&$0#+<*&'%$/,6$(&%($?+"#$/-&,(B%$0&#:+#'/,.&$+,$(7&'$*+./**?8$I+"$./,,+($%&&$(7&$9&%($/,6$K/3&,B%$0#+<*&'%;$/,6$?+"#$/-&,(B% 0&#:+#'/,.&$>2**$+,*?$<&$(&%(&6$>7&,$?+”$%”<'2($(+$e#/6&%.+0&8$I+"#$-#/6&$>2**$<&$$?+”#$/-&,($2%$0&#:+#’2,-$+,$(7&$#&/*$K/3&,B%$(&%(8$97&$D7/**&,-&$0#+<*&'%$/#&$0#2'/#2*?$(7&#&$(+$&W0+%&$?+"# N2(72,$&/.7$%&(;$(7&$Q/%2.;$9&%(;$/,6$K/3&,B%$0#+<*&'%$/#&$.+,%(#".(&6$(+$<&$#+"-7*?$/,/*+-+"%$(+$+,&$/,+(7&#8$97&$Q/%2.$0#+<*&'$2%$.+,%(#".(&6$(+$'2'2.$(7& #&*/(2+,%720%$/,6$(#/,%:+#'/(2+,%$2,$(7&$.+##&%0+,62,-$K/3&,B%$0#+<*&';$/,6$(7&$9&%($0#+<*&'$2%$.+,%(#".(&6$(+$'2'2.$(7&$Q/%2.$0#+<*&'$3&#?;$3&#?$.*+%&*?8$E+;$2:$?+" %&&$(7/($?+"#$/-&,($-&(%$Q/%2.$0#+<*&'$Q)`[$.+##&.($<"($9&%($/,6$K/3&,B%$0#+<*&'%$Q)`[$>#+,-;$?+”$J,+>$(7/($’2-7($<&$/$0*/.&$>7&#&$?+”#$/-&,($2%$&2(7&#$+3&#O((2,- +#$-&((2,-$*”.J?8$972%$/*%+$’&/,%$?+”$./,$/,(2.20/(&$?+”#$/-&,(B%$0&#:+#’/,.&$+,$(7&$9&%($0#+<*&'%$#&*/(23&*?$>&**P$&/.7$9&%($0#+<*&'$"%&%$/$,&/#)26&,(2./*$0#2,.20*& (+$(7&$.+##&%0+,62,-$Q/%2.$0#+<*&'8$5,$(7&$0/%(;$/-&,(%$7/3&$/3&#/-&6$-&((2,-$d[i$/%$'/,?$9&%($0#+<*&'%$#2-7($/%$Q/%2.$0#+<*&'%;$%+$(7&#&B%$/$0#&((?$-++6 .+##&*/(2+,$(7&#&$)*$?+"B#&$"%2,-$/$#+<"%(;$-&,&#/*$'&(7+68 The Problems I+"$/#&$0#+326&6$>2(7$(7&$Q/%2.$/,6$D7/**&,-&$0#+<*&'%$(+$"%&$2,$6&%2-,2,-$?+"#$/-&,(8$97&$9&%($/,6$K/3&,B%$0#+<*&'%$/#&$7266&,$/,6$>2**$+,*?$<&$"%&6$>7&, -#/62,-$?+”#$0#+1&.(8$972%$2%$(+$(&%($?+”#$/-&,(%$:+#$-&,&#/*2(?P$2($2%,B($7/#6$(+$6&%2-,$/,$/-&,($(7/($./,$/,%>&#$=”&%(2+,%$2($7/%$/*#&/6?$%&&,;$1″%($/%$2($>+”*6$,+($<& 7/#6$(+$%.+#&$>&**$+,$/$(&%($?+”$7/3&$/*#&/6?$(/J&,$<&:+#&8$h+>&3&#;$0&#:+#’2,-$>&**$+,$0#+<*&'%$?+"$/,6$?+"#$/-&,($+!,-".&$%&&,$<&:+#&$2%$/$'+#&$#&*2/<*&$(&%($+: 2,(&**2-&,.&8$I+"#$-#/6&$2%$2(72,$(7&$L#+<*&'%$:+*6&#$+:$(7&$6+>,*+/6/<*&8$L#+<*&'%$/#&$62326&6$2,(+$%&(%;$/,6$(7&,$2,(+$2,62326"/*$0#+<*&'%8$S/.7$0#+<*&'B%$:+*6&# 7/%$(7#&&$(72,-%P 97&$0#+<*&'$2(%&*:;$:+#$?+"#$<&,&O(8 4$L#+<*&'R/(/8(W($O*&;$.+,(/2,2,-$2,:+#'/(2+,$/<+"($(7&$0#+<*&';$2,.*"62,-$2(%$.+##&.($/,%>&#$/,6$2(%$(?0&8 o2%”/*$#&0#&%&,(/(2+,%$+:$&/.7$O-“#&;$,/’&6$480,-;$Q8$0,-;$&(.8
I+”$%7+”*6$,+($/((&’0($(+$/..&%%$L#+<*&'R/(/8(W($62#&.(*?Z$2(%$O*&,/'&$>2**$<&$.7/,-&6$>7&,$>&$-#/6&$0#+1&.(%8$e&,&#/**?;$?+”$,&&6$,+($>+##?$/<+"($(72%$62#&.(+#? %(#".("#&Z$/**$0#+<*&'$6/(/$>2**$<&$*+/6&6$2,(+$(7&$K/3&,%L#+<*&'$+<1&.($0/%%&6$(+$?+"#$/-&,(B%$E+*3&$'&(7+6;$/,6$(7&$O*&,/'&%$:+#$(7&$62g&#&,($32%"/* #&0#&%&,(/(2+,%$>2**$<&$2,.*"6&6$2,$(7&2#$.+##&%0+,62,-$K/3&,%U2-"#&%8 Working with the Code 97&$:#/'&>+#J$.+6&$2%$/3/2*/<*&$$",6&#$e&((2,-$E(/#(&6$/<+3&8$I+"$'/?$'+62:?$L#+<*&'E&(k2%(8(W($(+$/*(&#$>7/($0#+<*&'$%&(%$?+"#$.+6&$#",%$/-/2,%($*+./**?Z$(72%$>2** <&$"%&:"*$&/#*?$2,$(7&$(&#'$>7&,$?+”$0#+2**$,+($/g&.($>7/($2($#”,%$/-/2,%($+,$e#/6&%.+0&8
97&$6+>,*+/6/<*&$0/.J/-&$7/%$/$,"'<&#$+:$L?(7+,$O*&%P$K/3&,%L#+1&.(;$L#+<*&'E&(;$K/3&,%L#+<*&';$K/3&,%U2-"#&;$/,6$4-&,(8$!:$(7&%&;$?+"$%7+"*6$+,*?$'+62:?$(7& 4-&,($.*/%%8$I+"$'/?$'/J&$.7/,-&%$(+$(7&$+(7&#$.*/%%&%$(+$(&%($?+"#$/-&,(;$>#2(&$6&<"-$%(/(&'&,(%;$&(.8$h+>&3&#;$>7&,$>&$(&%($?+”#$.+6&;$>&$>2**$”%&$(7&$+#2-2,/* 3&#%2+,%$+:$(7&%&$O*&%$/%$6+>,*+/6&6$7&#&8$R+$,+($#&*?$+,$.7/,-&%$(+$/,?$.*/%%$&W.&0($:+#$4-&,($(+$#”,$?+”#$.+6&8$5,$/662(2+,$(+$4-&,(;$?+”$’/?$/*%+$>#2(&$?+”#$+>, /662(2+,/*$O*&%$/,6$.*/%%&%$:+#$2,.*”%2+,$2,$?+”#$0#+1&.(8
5,$4-&,(;$?+”$>2**$O,6$(>+$’&(7+6%P$/$.+,%(#”.(+#$/,6$/$E+*3&$’&(7+68$97&$.+,%(#”.(+#$>2**$<&$./**&6$/($(7&$<&-2,,2,-$+:$(7&$0#+-#/';$%+$?+"$'/?$"%&$(72%$'&(7+6$(+ 2,2(2/*2C&$/,?$2,:+#'/(2+,$,&.&%%/#?$<&:+#&$?+"#$/-&,($<&-2,%$%+*32,-$0#+<*&'%8$4:(&#$(7/(;$E+*3&$>2**$<&$./**&6$+,$&/.7$0#+<*&'8$I+"$%7+"*6$>#2(&$(7&$E+*3&$’&(7+6$(+ #&(“#,$2(%$/,%>&#$(+$(7&$-23&,$=”&%(2+,P
VWV$=”&%(2+,%$7/3&$%2W$/,%>&#$+0(2+,%;$%+$(+$/,%>&#$(7&$=”&%(2+,;$?+”#$/-&,($%7+”*6$#&(“#,$/,$2,(&-&#$:#+’$T$(+$G8 HWH$=”&%(2+,%$7/3&$&2-7($/,%>&#$+0(2+,%;$%+$?+”#$/-&,($%7+”*6$#&(“#,$/,$2,(&-&#$:#+’$T$(+$d8 5:$?+”#$/-&,($>/,(%$(+$%J20$/$=”&%(2+,;$2($%7+”*6$#&(“#,$/$,&-/(23&$,”‘<&#8$4,?$,&-/(23&$,"'<&#$>2**$<&$(#&/(&6$/%$?+"#$/-&,($%J2002,-$(7&$0#+<*&'8 I+"$'/?$6+$/**$(7&$0#+.&%%2,-$>2(72,$E+*3&;$+#$?+”$’/?$>#2(&$+(7&#$’&(7+6%$/,6$.*/%%&%$(+$7&*0$?+”#$/-&,($%+*3&$(7&$0#+<*&'%8 N7&,$#",,2,-;$(7&$0#+-#/'$>2**$*+/6$=”&%(2+,%$:#+’$(7&$L#+<*&'%$:+*6&#8$5($>2**$(7&,$/%J$?+”#$/-&,($(+$%+*3&$&/.7$0#+<*&'$+,&$#2(&$(7&$#&%”*(%$(+ L#+<*&'K&%"*(%8.%38$I+"$'/?$.7&.J$L#+<*&'K&%"*(%8.%3$(+$%&&$7+>$>&**$?+”#$/-&,($0&#:+#’&68$I+”$’/?$/*%+$.7&.J$E&(K&%”*(%8.%3$(+$32&>$/$%””/#?$+:$?+”#$/-&,(B% 0&#:+#’/,.&$/($(7&$%&($*&3&*8
The Documentation
K/3&,%L#+1&.(P$97&$’/2,$6#23&#$+:$(7&$0#+1&.(8$972%$O*&$>2**$*+/6$(7&$*2%($+:$0#+<*&'$%&(%;$2,2(2/*2C&$?+"#$/-&,(;$(7&,$0/%%$(7&$0#+<*&'%$(+$?+"#$/-&,($+,&$&#%;$(72%$O*&$>2**$.7&.J$(7&$/,%>&#%$/,6$/%%2-,$/$%.+#&8 4-&,(P$97&$.*/%%$2,$>72.7$?+”$>2**$6&O,&$?+”#$/-&,(8$N7&,$?+”$#”,$(7&$0#+1&.(;$?+”#$4-&,($>2**$<&$.+,%(#".(&6;$/,6$(7&,$2(%$E+*3&$'&(7+6$>2**$<&$./**&6$+,$&/.7 L#+<*&'E&(P$4$*2%($+:$K/3&,%L#+<*&'%$>2(72,$/$0/#(2.”*/#$%&(8 K/3&,%L#+<*&'P$4$%2,-*&$0#+<*&';$%".7$/%$(7&$+,&$%7+>,$&/#*2&#$2,$(72%$6+.”‘&,(8$4$K/3&,%L#+<*&'$2,.*"6&%P aQb;$/,6$aDb$/#&$(7&$0#+<*&'$2(%&*:;$/,6$(7+%&$/%%+.2/(&6$>2(7$(7&$J&?%$aTb;$aVb;$aHb;$aXb;$a[b;$/,6$aGb$/#&$(7&$0+(&,(2/*$/,%>&#$.7+2.&%8
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97&$6+.”‘&,(/(2+,$2%$”*(2’/(&*?$%+’&>7/($%(#/2-7(:+#>/#6;$<"($2($./,$<&$.+'0*2./(&6$>7&,$?+”B#&$2,2(2/**?$-&((2,-$”%&6$(+$2(8$97&$’+%($2’0+#(/,($(72,-%$(+$#&’&’<&# /#&P S3&#?$(2'&$E+*3&$2%$./**&6;$?+"#$/-&,($2%$-23&,$/$%2,-*&$0#+<*&'8$Q?$(7&$&,6$+:$E+*3&;$2($%7+"*6$#&("#,$/,$/,%>&#$/%$/,$2,(&-&#8$I+”$6+,B($,&&6$(+$>+##?$/<+"( 7+>$(7&$0#+<*&'%$/#&$*+/6&6$:#+'$(7&$O*&%;$7+>$(7&$0#+<*&'$%&(%$/#&$+#-/,2C&6;$+#$7+>$(7&$#&%”*(%$/#&$0#2,(&68$I+”$,&&6$+,*?$>+##?$/<+"($>#2(2,-$(7&$E+*3& ‘&(7+6;$>72.7$%+*3&%$+,&$=”&%(2+,$/($/$(2’&8 K/3&,%L#+<*&'%$7/3&$/$62.(2+,/#?$+:$K/3&,%U2-"#&%;$>2(7$&/.7$U2-“#&$#&0#&%&,(2,-$+,&$+:$(7&$2’/-&$%=”/#&%$2,$(7&$0#+<*&'$/,6$&/.7$J&?$#&0#&%&,(2,-$2(% #&0#&%&,(/(2+,8 97&$0&#'2((&6$*2<#/#2&%$:+#$(72%$(&#'B%$0#+1&.($/#&P 4662(2+,/**?;$>&$”%&$L?(7+,$H8d8`$:+#$+”#$/”(+-#/6&#8
Submitting Your Code
972%$.*/%%$”%&%$e#/6&%.+0&;$/$%&#3&#)%26&$/”(+-#/6&#;$(+$&3/*”/(&$?+”#$%”<'2%%2+,8$972%$'&/,%$?+"$./,$%&&$7+>$?+”#$.+6&$2%$0&#:+#’2,-$/-/2,%($(7&$9&%($/,6$K/3&,B% 0#+<*&'%$&3&,$>2(7+”($%&&2,-$(7&$0#+<*&'%$(7&'%&*3&%8$I+"$>2**$7/3&$/..&%%$(+$%&0/#/(&$/#&/%$(+$%”<'2($/-/2,%($(7&$M2*&%(+,&$.7&.J%$/,6$(+$%"<'2($:+#$(7&$O,/* 0#+1&.(8 Submitting 9+$-&($%(/#(&6$%"<'2((2,-$?+"#$.+6&;$-+$(+$D/,3/%$/,6$.*2.J$e#/6&%.+0&$+,$(7&$*&:($%26&2**$%&&$O3&$0#+1&.($+0(2+,%P$M2*&%(+,&$T;$M2*&%(+,&$V;$M2*&%(+,&$H;$M2*&%(+,&$X;$U2,/*$L#+1&.(;$/,6$U2,/*$L#+1&.(8
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