2017 ACM ICPC North Central North America Regional Contest

24 Pages·2017·16.24 MB·English

O 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