Table Of ContentO fficial Problem Set
DO NOT OPEN UNTIL CONTEST BEGINS
2017 ACM ICPC
North Central North America
R egional Contest
October 28, 2017
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2017ACMICPCNorthCentralNorthAmericaRegionalContest
Problems
A Stoichiometry
B PokemonGoGo
C UrbanDesign
D SmoothArray
E Is-A?Has-A?WhoKnowz-A?
F Atlantis
G Sheba’sAmoebas
H ZebrasandOcelots
I RacingAroundtheAlphabet
J LostMap
NCNA2017 3
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2017ACMICPCNorthCentralNorthAmericaRegionalContest
Problem A
Stoichiometry
You have landed a lucrative contract with Amalga-
mated Chemical Manufacturing (ACM), to help their
chemists with stoichiometry. Stoichiometry is the cal-
culationofreactantsandproductsinchemicalreactions,
based on the law of conservation of mass, which states
thatthetotalmassofthereactantsequalsthetotalmass
oftheproducts. Therelationsamongquantitiesofreac-
tantsandproductstypicallyformaratioofpositiveinte-
gers. Iftheamountsoftheseparatereactantsareknown,
then the amount of the product can be calculated, and
vice-versa. Therelationshipofreactantstoproductscan
bedescribedusingasoichiometricequationsuchas: ImagebyGerdAltmann.
CH +2O →CO +2H O, (1)
4 2 2 2
whichcanbereadas:“OnemoleculeofCH andtwomoleculesofO yieldonemoleculeofCO andtwomolecules
4 2 2
ofH O.” Thetotalnumberofatomsofeachelementonthelefthandsideofthestoichiometricequationmustmatch
2
thenumberofatomsofthatelementonrighthandside. Yourtaskistowriteaprogramthat,givenanequationofthe
form:
_H O+_CO →_O +_C H O , (2)
2 2 2 6 12 6
willfillintheblankstoproduceabalancedequation. Forexample,theaboveequationcouldbebalancedasfollows:
6H O+6CO →6O +1C H O . (3)
2 2 2 6 12 6
Input
AnequationisinputintheformofasequenceofM (1<M ≤20)lines,oneforeachmoleculeintheformula(e.g.,
H OorCO ). Eachlinem(1≤m≤M)hasthefollowingfields:
2 2
sign N element count ... element count
m m m,1 m,1 m,Nm m,Nm
wheresign iseither+1or-1, withasignof+1indicatingthatthismoleculeappearsontheleftoftheequation,
m
and -1 indicating that it appears on the right. N , where 0 < N < 20, is the number of element/count pairs
m m
following on the line. Each element , where 1 ≤ n ≤ N , is an element name consisting of one or two upper
m,n m
orlowercase letters, and eachcount isa positiveinteger, 1 ≤ count ≤ 12. For example, the element/count
m,n m,n
pair“Fe 2”indicatesthatthemoleculecontainstwoatomsoftheelementFe(iron). Therewillbenomorethan10
uniqueelementsinasingleequation.
Notethatanelementmayberepeatedinagivenlineofinput,asin
+1 6 C 1 H 5 C 1 O 1 O 1 H 1
whichspecifiesthatatleastonemoleculeofCH COOHappearsontheleftsideoftheequation.NotethatCH COOH
5 5
canbewrittenasC H O .
2 6 2
Inputendswithalineoftheform
0 0
NCNA2017ProblemA:Stoichiometry 5
2017ACMICPCNorthCentralNorthAmericaRegionalContest
Output
TheprogrammustoutputthenumbersC ,...,C (0 < C ≤ 1000),inorder,tofillintheblanksintheequation.
1 M i
Eachnumber,C | 1 ≤ m ≤ M,mustbetheminimumnumberforwhichtheequationisbalanced(i.e. thereisno
m
commonfactorthatcouldreducealloftheC coefficients). Youmayassumethateveryinputtestcasehasexactly
m
onevalidsolutionmeetingthesecriteria.
SampleInput1 SampleOutput1
+1 2 H 2 O 1 6 6 6 1
+1 2 C 1 O 2
-1 1 O 2
-1 3 C 6 H 12 O 6
0 0
SampleInput2 SampleOutput2
+1 5 Be 2 C 1 O 3 O 2 H 2 2 6 1 5 2
+1 3 Ac 1 O 1 H 1
-1 4 Be 4 O 1 Ac 6 O 6
-1 2 H 2 O 1
-1 2 C 1 O 2
0 0
NCNA2017ProblemA:Stoichiometry 6
2017ACMICPCNorthCentralNorthAmericaRegionalContest
Problem B
Pokemon Go Go
Always Catch your Mon, Inc., (also know as ACM), wants to create a new
product, called Pokémon Go Go. Users can purchase this application to help
themplayPokémongo. Thesoftwareaccessesthepokéstoplocationsnearthe
current location as well as a list of Pokémon that can be found at each stop.
Theapplicationthencomputestheshortestrouteonecanfollowtocatchallthe
uniquePokémon,andreturntothestartingpoint.
The program assumes that the user is in a city where travel is restricted to
moving only in the north–south and east–west directions. The program also
assumesthatallpokéstopsareontheintersectionoftworoads.
For example, consider a case where the application finds five nearby poké
stops. Each stop’s location is indicated by two integers, (r,c), where r is the
numberofblocksnorthofyourstartingpositionandcisthenumberofblocks
westofyourstartingposition.Considerifthelocationsofthefivepokéstopsare
(5,9),(20,20),(1,1),(1,8)and(2,8)whilethenamesofthePokémonfound
atthesestopsareEvevee,Flareon,Flareon,Jolteon,andUmbreon,respectively. ImagebyAnaVerrusio.
It is clear that one does not have to visit both the second and third stops, since the same Pokémon can be caught at
eitherofthem. Thebestrouteistovisitthefirst,fifth,fourth,andthirdstops(inthatorder)foratotaldistanceof28
blocks,since:
• Thedistancefrom(0,0)to(5,9)is14.
• Thedistancefrom(5,9)to(2,8)is4.
• Thedistancefrom(2,8)to(1,8)is1.
• Thedistancefrom(1,8)to(1,1)is7.
• Thedistancefrom(1,1)to(0,0)is2.
Input
Theinputholdsasingletestcase.Thetestcasebeginswithasingleintegern,0<n≤20,whichindicatesthenumber
ofpokéstopstoconsider.EachofthenextnlinesspecifiesthelocationofapokéstopandthenameofaPokémonthat
canbefoundthere. Thelocationisspecifiedbytwointegersrandcseparatedbyasinglespace,−100≤r,c≤100.
The integers r and c indicate that the stop is r blocks north and c blocks east of the starting point. The location is
followedbyasinglespaceandfollowedbythestringpindicatingthenameofthePokémonthatcanbecaughtthere.
Nameshavebetween1and25letters(usingonlya–zandA–Z).ThenumberofuniquePokémonisalwayslessthan
orequalto15. Multiplepokémoncanresideatasinglepokéstopandarelistedonseparatelines.
Output
Givetheshortestdistance,inblocks,requiredtocatchalltheuniquePokémon.
NCNA2017ProblemB:PokemonGoGo 7
2017ACMICPCNorthCentralNorthAmericaRegionalContest
SampleInput1 SampleOutput1
5 28
5 9 Eevee
20 20 Flareon
1 1 Flareon
1 8 Jolteon
2 8 Umbreon
NCNA2017ProblemB:PokemonGoGo 8
2017ACMICPCNorthCentralNorthAmericaRegionalContest
Problem C
Urban Design
A new town is being planned, and the designers have some very
specificideasabouthowthingsshouldbelaidout. First,theylayout
the streets. Each street is perfectly straight and passes completely
fromoneendofthetowntotheother. Thesestreetsdividethetown
intoregions,andeachregionistobedesignatedeither“residential”
or “commercial.” The town planners require that any two regions
directlyacrossthestreetfromoneanothermusthavedifferentdes-
ignations. On this one particular day, all of the streets have been
planned, but none of the regions have been designated. One town
plannerwishestopurchasetwoproperties,anditisimportanttohim
that the properties eventually have different designations. For this
problem,thestreetscanbemodeledbylinesintheplanethatextend
ImagebyDietmarSilber.
foreverinbothdirectionsandhavenowidth,andpropertiesmaybe
modeledbypoints.Giventhelinesandtwopoints,canyoudecidewhetherornottheymustgetdifferentdesignations,
“commercial”or“residential?”
Input
Input begins with an integer S on a single line, giving the number of streets (1 ≤ S ≤ 10000). The next S lines
of input each contain four integers x , y , x , and y , specifying the coordinates of two distinct points (x ,y ) and
1 1 2 2 1 1
(x ,y ). Theuniquelinethroughthesetwopointsgivesoneofthestreets. Eachcoordinateisintherange[0,10000],
2 2
andnotwolineswillbeidentical. Thatis,thetownwillhaveS distinctstreets. ThenextlinecontainsanintegerT,
thenumberofpairsofpropertiestotest(1 ≤ T ≤ 1000). ThisisfollowedbyT linesofinput,eachcontainingfour
integersx ,y ,x ,andy ,representingtwodistinctpoints(x ,y )and(x ,y ),whereeachpointlieswithinoneof
3 3 4 4 3 3 4 4
thetwopropertiestotest. Noneofthesepointswilllieonanyofthestreets,norwillbothpointsliewithinthesame
property. Again,eachcoordinateisintherange[0,10000].
Output
ForeachoftheT pairsofpropertiestobetested,outputeither“same”ifthepropertiesareguaranteedtoreceivethe
samedesignationor“different”iftheyareguaranteedtoreceivedifferentdesignations.
SampleInput1 SampleOutput1
2 different
1 1 2 1 same
1 1 1 2 same
3
2 0 2 2
2 0 0 3
0 0 2 2
NCNA2017ProblemC:UrbanDesign 9
2017ACMICPCNorthCentralNorthAmericaRegionalContest
SampleInput2 SampleOutput2
4 same
1 3 2 4 different
1 3 2 5
1 3 3 4
7 9 8 8
2
14 7 10 13
1 4 2 3
NCNA2017ProblemC:UrbanDesign 10
Description:CH4 + 2O2 → CO2 + 2H2O,. (1) which can be read as: “One molecule of CH4 and two molecules of O2 yield one molecule of CO2 and two molecules .. aphorisms. Assume for simplicity that the player runs at 15 feet per second between stops for pickups and that each pickup takes 1 second. Input.
