Exercise$2.(50$points$)$Monopoly

Inthisexercise,wewill implementasimplifiedMonopolygame.Wewill seewhetherandwhenpure luck

cancreateextremeinequalityinwealth.

OurMonopolygamehastwomajorcomponents: anarrayofplayersandanarrayofproperties.Thenumber

ofplayersismandthenumberofpropertiesisn.

Thenpropertiesarearrangedinacircular fashion. The indexof thepropertiesstarts from$0$andgoesto

n$1$inaclockwisedirection.Thentheindexgoesbackto$0,$ thestartingpoint.

Atthebeginningof thegame,all theplayershavendollarsastheir initialbalance.All theplayerstartat

property$0,$andplayerstaketurnsaccordingtotheincreasingorderof their id$.$Whenit isaplayer$$sturn$,$

theplayertossestwodicetodeterminethenumberofstepstheyneedtomoveinaclockwisedirection.The

facevalueofthetwo$6-$sideddicearesummedtofindthenumberofsteps.Theplayermovesthisnumberof

stepsandlandsonthecorrespondingproperty. Ifthispropertyisownedbysomeoneotherthanthisplayer,

thisplayerneedstopayrenttotheowner.Otherwise, ifthispropertyhasnoowneryet, itwillbeownedby

thisplayer.Rent increaselinearlyfrom$1$tonbetweenthefirstandfinalproperties.

Wheneveraplayergoesbacktoorpassesoverproperty$0,$ndollarswillbeawardedtotheplayer.

Thegameendswhenaplayer is requiredtopaymoremoneythantheyown. Whenthishappens, that

playerpaysallof theirmoneytotheplayerwhoownsthepropertytheyjust landedon.Attheendof the

game,wewillestimatethe$$inequality$$oftheplayersasthehighestwealthdividedbytheaveragewealth$.$

Todescribeaplayer,weneedtousethestructure

typedefstructPlayer

$\{$

intid;

intloc;

longbalance;

$\}$TPlayer;

Here, id is inthe range$0...$m$1,$ loc is inthe range$0...$n$1,$ andbalancerepresents thewealth

accumulatedbytheuser.

Similarly, todescribeaproperty,weusethefollowingstructure

$3$

typedef struct Property

$\{$

int id;

int owner$\_$id;

int rent;

$\}$ TProperty;

Here, id is in the range $0...$n$1,$ owner

id is in the range $0...$m$1,$ and rent is the rent of the property.

Below is the main$()$ function of the program; note how we use the command line arguments. Here m is

the number of players, n is the number of properties, and rounds is the maximum rounds of game in case

the game does not end.

int main$($int argc, char $*$argv$[])$

$\{$

if$($argc $!=4)$

$\{$

printf$("$Usage: $\%$s m n rounds

$",$ argv$[0])$;

return$-1$;

$\}$

int m $=$ atoi$($argv$[1])$;

int n $=$ atoi$($argv$[2])$;

int rounds $=$ atoi$($argv$[3])$;

TPlayer p$[$m$]$;

TProperty prop$[$n$]$;

for$($int i $=0$; i $<$ n; i$++)$

$\{$

prop$[$i$].$id $=$ i;

prop$[$i$].$owner$\_$id $=-1$;

prop$[$i$].$rent $=$ i $+1$;

$\}$

for$($int j $=0$; j $<$ m; j$++)$

$\{$

p$[$j$].$id $=$ j;

p$[$j$].$loc $=0$;

p$[$j$].$balance $=$ n;

$\}$

monopoly$($m$,$ n$,$ p$,$ prop, rounds$)$;

return $0$;

$\}$

Note how we initialize the player array p$[$m$]$ and the property array prop$[$n$].$ The owner id for each property

is set to $1$ since, at the beginning, it is not owned by any player. We use $1$ instead of $0$ because id $0$ is

the id for the first player.

We need to implement the following function.

$//$Implement the following function

void monopoly$($int m$,$ int n$,$ TPlayer p$[],$ TProperty prop$[],$ int max$\_$rounds$)$

$\{$

$4$

srand$(12345)$;

introunds$=1$;

$//$The followinglineofcodeisneededforcorrectoutput

print$\_$result$($m$,$p$)$;

printf$("$after$\%$drounds

$",$rounds$)$;

$\}$

Belowareoutputsfromafewsampleruns.Wecanusetheseoutputstocheckourcode.

$$./$monopoly$15100100000$

id balance

$067$

$195$

$2204$

$3244$

$4102$

$5228$

$60$

$772$

$833$

$90$

$1054$

$1127$

$1276$

$1318$

$14280$

average:$100\mathrm{.}000000$max:$280,$max$/$average$=2\mathrm{.}800000$

after$5$rounds

$$./$monopoly$20100100000$

id balance

$0340$

$1200$

$2203$

$3260$

$474$

$5137$

$6199$

$768$

$840$

$90$

$1039$

$1146$

$1216$

$13137$

$1447$

$1556$

$1628$

$5$

$1715$

$1857$

$1938$

average:$100\mathrm{.}000000$max:$340,$max$/$average$=3\mathrm{.}400000$

after$5$rounds