1 / 24

4. Using Structures: Example Programs

4. Using Structures: Example Programs. Contents. Retrieving structured information from a database Doing data abstraction Simulating a non-deterministic automaton Travel planning The eight queens problem. Retrieving Structured Information from a DB.

corbin
Download Presentation

4. Using Structures: Example Programs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 4. Using Structures: Example Programs

  2. Contents • Retrieving structured information from a database • Doing data abstraction • Simulating a non-deterministic automaton • Travel planning • The eight queens problem

  3. Retrieving Structured Information from a DB • This exercise develops the skill of representing and manipulating structured data objects. • It also illustrates Prolog as a natural database query language. • A database can be represented in Prolog as a set of facts.

  4. Retrieving Structured Information from a DB • A database about families: family( person(tom,fox,date(7,may,1950),works(bbc,15200)), person(ann,fox,date(9,may,1951),unemployed), [person(pat,fox,date(5,may,1973),unemployed), person(jim,fox,date(5,may,1973),unemployed)]). • We can refer to all Armstrong families by: family(person(_,armstrong,_,_),_,_) • Refer to all families with three children: family(_,_,[_,_,_])

  5. Retrieving Structured Information from a DB • To find all married women that have at least three children: ?-family(_,person(Name,Surname,_,_), [_,_,_|_]).

  6. Retrieving Structured Information from a DB • Provide a set of procedures that can serve as a utility to make the intersection with the database more comfortable. husband(X):- family(X,_,_). wife(X):- family(_,X,_). child(X):- family(_,_,Children), member(X,Children). exist(X):- husband(X); wife(X); child(X). dateofbirth( person(_,_,Date,_),Date)). salary( person(_,_,_Works(_,S),S)). salary( person(_,_,_,unemployed),0).

  7. Retrieving Structured Information from a DB Find the names of all the people in the DB: ?-exists(person(Name,Surname,_,_)). Find all children born in 1981: ?-child(X),dateofbirth(X,date(_,_,1981)). Find all employed wives: ?-wife(person(Name,Surname,_,works(_,_))). Find the names of unemployed people who were born before 1963: ?-exists(person,N,S,date(_,_,Y),unemployed)), Y<1963. Find people born before 1950 whose salary is less than 8000: ?-exists(P),dateofbirth(P,date(_,_,Year)), Year<1950,salary(P,S),S<8000.

  8. Retrieving Structured Information from a DB • Total income of a family: total([],0). total([Person|List],Sum):- salary(Person,S0, total(List,Rest), Sum is S+Rest.

  9. Simulating an NDA b final(s3). trans(s1,a,a1). trans(s1,a,s2). trans(s1,b,s1). trans(s2,b,s3). trans(s3,b,s4). silent(s2,s4). silent(s3,s1). a s1 s2 null a b null s4 s3 b

  10. Simulating an NDA ?-accepts(s1,[a,a,a,b]). yes ?-accepts(S,[a,b]). S=s1; S=s3. ?-accepts(s1,[X1,X2,X3]). X1=a X2=a X3=b; X1=b X2=a X3=b; no ?-String=[_,_,_], accepts(s1,String). String=[a,a,b]; String=[b,a,b]; no accepts(State,[]):- final(State). accepts(State,[X|Rest]):- trans(State,X,State1), accepts(State1,Rest). accepts(State,String):- silent(State,State1), accepts(State1,String).

  11. Travel Planning • Develop an advisor program that will be able to answer useful questions, such as: • What days of the week is there a direct flight from London to Ljubljana? • How can I get from Ljubljana to Edinburgh on Thursday? • I have to visit Milan, Ljubljana and Zurich, starting from London on Tuesday and returning to London on Friday. In what sequence should I visit these cities so that I have no more than one flight each day of the tour?

  12. Travel Planning • The program will be centered around a DB holding the flight information. timetable(Place1,Place2,List_of_flight) where List_of_flight is of the form: Departure_time/Arrival_time/Flight_number/List_of_days timetable(london,edinburgh, [9:40/10:50/ba4733/alldays, 17:40/20:50/ba4833/[mo,tu,we,th,fr,su]]).

  13. Travel Planning • To find exact routes between two given cities on a given day of the week. route(Place1,Place2,Day,Route) Here Route is a sequence of flight satisfying the following criteria: • the start point of the route is Place1; • the end of the route is Place2; • all the flights are one the same day of the week Day; • all the flight in Route are in the timetable relation; • there is enough time for transfer between flights.

  14. Travel Planning • The route is represented as a list of structured objects of the form: From-to:Flight_Number:departure_time • Some auxiliary predicates: • flight(Place1,Place2,Day,Flight_num,Dep_time,Arr_time) • deptime(Route,Time) • transfer(time1,Time2) There is at least 40 minutes between Time1 and Time2.

  15. Travel Planning • The problem of finding a route is similar to the simulation of the NDA • States of NDA  cities • Transition between two states  a flight between two cities • transition  timetable • Finding a path  finding a route.

  16. Travel Planning • Defining the route relation: • Direct flight route(Place1,Place2,Day,[Place1-Place2:Fnum:Dep]):- flight(Place,Place2,Day,Fnum,Dep,Arr). • Indirect flight route(P1,P2,Day,[P1-P3:Fnum1:Dep1|Route]):- route(P3,P2,Day,Route), flight(P1,P3,Fnum1,Dep1,Arr1), deptime(Route,Dep2), transfer(Arr1,Dep2). See Fig. 4.5, pp 111-112 for the complete program.

  17. Travel Planning • Some example questions: • What days of the week is tehre a direct flight from London to Ljubljana? ?-flight(london,ljubljana,Day,_,_,_). Day=fr; day=su; no • How can I get from Ljubljana to Edinburgh on Thursday? ?-route(ljubljana,edinburgh,th,R). R=[ljubljana-zurich:yu322:11:30, zurich-london:sr806:16:10, london-edinburgh:ba4822:18:40]

  18. The Eight Queens Problem:Program 1 • The problem here is to place eight queens on the empty chessboard in such a way that no queen attacks any other queen. 8 7 6 5 4 3 2 1 1 8 2 3 4 5 6 7

  19. The Eight Queens Problem: Program 1 • The problem is to find such as list [X1/Y1,X2/Y2,X3/Y3,X4/Y4,X5/Y5,X6/Y6,X7/Y7,X8/Y8] • To make the search task easier, we fix the X-coordinates: [1/Y1,2/Y2,3/Y3,4/Y4,5/Y5,6/Y6,7/Y7,8/Y8]

  20. The Eight Queens Problem: Program 1 • Case 1: The list of the queen is empty: the empty list id certainly a solution because there is no attack. Case 2: The list of queen is non-empty: it looks like [X/Y|Others]. Then • There must be no attack between the queens in the list Others; i.e., Others must be a solution. • X and Y must be integers between 1 and 8. • A queen at square X/Y must not attack any of the queens in the list Others.

  21. The Eight Queens Problem: Program 1 solution([]). solution([X/Y|Others]):- solution(Others), member(Y,[1,2,3,4,5,6,7,8]), noattack(X/Y,Others). noattack(_,[]). noattack(X/Y,[X1/Y1|Others]):- Y=\=Y1,Y1-Y=\=X1-X,Y1-Y=\=X-X1, noattack(X/Y,Others). template([1/Y1,2/Y2,3/Y3,4/Y4,5/Y5, 6/Y6,7/Y7,8/Y8]). ?-template(S),solution(S).

  22. The Eight Queens Problem: Program 2 • X-coordinates can be omitted, retaining only Y-coordinates: [Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8]. • To prevent the horizontal attack, no two queens can be in the same row. • Each solution is therefore represented by a permutation of the list: [1,2,3,4,5,6,7,8]. • Such a permutation, S, is a solution if all queens are safe.

  23. The Eight Queens Problem: Program 2 solution(S):- permutation([1,2,3,4,5,6,7,8],S), safe(S). safe([]). safe([Queen|Others]):- sate(Others), noattack(Queen,Others,1). noattack(_,[],_). noattack(Y,[Y1|Ylist],Xdist):- Y1-Y=\=Xdist,Y-Y1=\=Xdist, Dist1 is Xdist+1, noattack(Y,Ylist,Disy1).

  24. The Eight Queens Problem: Program 2 Others Queen Xdist=1 Xdist=3

More Related