A Tale of Two Heroes:Problem Generating Video
Games
2008 Comps Presentation in Mathematics by
Rafael Alejandro Sanchez
Outline
DefinitionsMathematical termsComputer Science terms
ProblemsGeneral explanationsSpecifics
Bridge-CrossingKnights & Knaves
The ProgramIndiana Jones GameKing Arthur GameDemonstrationAnalysis
Possible further work
Math Definitions
ProblemProblem: A class of related questions, not something you can necessarily solve.
Instance of a problemInstance of a problem: specific problem that can be given to someone to solve.
Math Definitions
SolvableSolvable: enough information is given so that the instance of a problem can actually be solved.
TrivialTrivial: the solution to the instance is obvious.
Hard-codedHard-coded: written very specifically, can be more difficult to edit.
Soft-codedSoft-coded: written to be edited more easily, can be longer.
Computer Science Definitions
GUIGUI: Graphical User Interface
AlgorithmAlgorithm: Set of instructions for figuring something out.
NPCNPC: Non-playable character
Computer Science Definitions
Bridge-Crossing Problem
The Problem in General
Group of people need to cross a bridge as fast as possible within certain constraints.
End when everyone is on the other side.
Bridge-Crossing Problem
Details
Two people cross, one comes back.
Each person walks at a different speed.
When two people walk together, they walk at the speed of the slower person.
Knights & Knaves Problem
The Problem in General
Everyone is either a Knight or a Knave.
Knights always tell the truth.
Knaves always lie.
Knights & Knaves Problem
Details
You must figure out who the knights are.
You have 5 questions.
You may ask each question once.
The Program: Overview
Generates instances of these two problems.
Some Programming ChallengesSolvableNon-trivial
The Program: Game 1
Bridge-Crossing ProblemYour role: Indiana Jones and his crew.
Your task: get everyone across the bridge by choosing who crosses at each point.
What you’re given: each character’s speed.
The Program: Game 1
What the program doesRandomly generates the characters’ speeds.
Finds the fastest way across.
Makes sure the instance is non-trivial.
The Program: Game 2
Knights & Knaves ProblemYour role: King Arthur.
You task: find out who the knights are.
What you’re given: five questions. You may ask each once to one character.
The Program: Game 2
What the program doesRandomly generates the characters’ identities as a knight or knave.
Selects five questions.
Creates working characters that you can talk to.
Analysis: Game 1
Your characters cross five times.4 choose 2 = 6 = 4!/(2!2!)2 choose 1 = 23 choose 2 = 33 choose 1 = 32 choose 2 = 1
6 x 2 x 3 x 3 x 1 = 108
Analysis: Game 1
6 x 2 x 3 x 3 x 1 = 108
No choice on the last crossingOn the second-to-last crossing, it’s always best to choose the fastest person.
6 x 2 x 3 x 1 x 1 = 36
Analysis: Game 1
6 x 2 x 3 x 1 x 1 = 36
A <= B <= C <= D
Given first choice, 1 x 2 x 3 x 1 x 1 = 6
AB
AB
AB
AB
AB
AB
AB A
AB A
AB A
AB B
AB B
AB B
AB A AC
AB A AD
AB A CD
AB B
AB B
AB B
AB A AC A
AB A AD A
AB A CD B
AB B
AB B
AB B
AB A AC A AD
AB A AD A AC
AB A CD B AB
AB B
AB B
AB B
AB A AC A AD
AB A AD A AC
AB A CD B AB
AB B BC
AB B BD
AB B CD
AB A AC A AD
AB A AD A AC
AB A CD B AB
AB B BC A
AB B BD A
AB B CD A
AB A AC A AD
AB A AD A AC
AB A CD B AB
AB B BC A AD
AB B BD A AC
AB B CD A AB
AB A AC A AD 2A + B + C + D
AB A AD A AC 2A + B + C + D
AB A CD B AB A + 3B + D
AB B BC A AD A + 2B + C + D
AB B BD A AC A + 2B + C + D
AB B CD A AB A + 3B + D
Analysis: Game 1
2A + B + C + D
A + 3B + D
A + 2B + C + D
Analysis: Game 1
2A + B + C + D
A + 3B + D
Analysis: Game 1
2A + B + C + D – A – B – D A + C
A + 3B + D – A – B – D 2B
(A + C) VS. (2B)
AB A AC A AD 2A + B + C + D
AB A AD A AC 2A + B + C + D
AB A CD B AB A + 3B + D
AB B BC A AD A + 2B + C + D
AB B BD A AC A + 2B + C + D
AB B CD A AB A + 3B + D
A + C
2B
Analysis: Game 2
Forms of the questions givenDoes X claim to be a knight?Is there an odd/even amount of knights/knaves?Are there more/less than three knights/knaves?Is Y a knight?Is Z a knave?
Analysis: Game 2
What can you find out with your questions?
Identity of one character.
Amount of knights
Identities of two particular characters.
Possible Further Work
Expansion of possible instancesMore charactersMore possible questions
Other ModificationsUse different algorithmsImprove GUI
Works Cited
Andreas Söderlund. "Fuzzy logic in your game." BYONDscape: The Journal of New Worlds. 2004. 2 Oct. 2007 <http://www.byondscape.com/ascape.dmb/Gazoot.2004-0315/>.Lewis, John and Joseph Chase. “Java software structures; designing and using data structures.” Scitech Book News. Jun 2004. Vol. 28, Iss. 2.Liskov, Barbara and John Guttang. Program Development in Java. Boston: Addison-Wesley, 2001. Sun Microsystems, Inc. “Java 2 Platform Standard Ed. 5.0.” 2 Oct. 2007 <http://java.sun.com/j2se/1.5.0/docs/api/>.Zeitz, Paul. The Art and Craft of Problem Solving. Hoboken, NJ: John Wiley & Sons, 1999.
Thank You…
Mathematics DepartmentProfessor Ramin NaimiProfessor Rodney Hoffman
Go Class of 2008!Go Class of 2008!
