symbolicOutput(0). % set to 1 for DEBUGGING: to see symbolic output only; 0 otherwise. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% A bus company operates services between a set of different cities. %% We want to design the routes of the buses for a given week. %% Every day a bus does exactly one traject (according to the trajects %% given in the input) from one city to another one, and departs from %% there for the next traject the next day. Each traject takes place %% at most once per day, and at least a given minimal amount of days %% per week. No bus can travel more than a total of a given amount of %% kms on two consecutive days. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% begin input example %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% numBuses(8). %% numDays(7). %% maxDistance(1200). % this is the maximal total distance for two consecutive days for a given bus %% % %% traject(mad,bcn,4,630). % the traject mad-bcn has to take place at least 4 days per week, and is 630 km long. %% traject(mad,val,1,360). %% traject(mad,bil,1,400). %% traject(mad,zar,3,320). %% traject(mad,sev,1,450). %% % %% traject(bcn,mad,4,630). %% traject(bcn,val,1,350). %% traject(bcn,bil,2,610). %% traject(bcn,zar,2,320). %% traject(bcn,sev,1,800). %% % %% traject(val,mad,3,360). %% traject(val,bcn,1,350). %% traject(val,bil,1,610). %% traject(val,zar,3,310). %% traject(val,sev,1,700). %% % %% traject(bil,mad,4,400). %% traject(bil,bcn,1,610). %% traject(bil,val,1,610). %% traject(bil,zar,1,300). %% traject(bil,sev,1,900). %% % %% traject(zar,mad,1,320). %% traject(zar,bcn,3,320). %% traject(zar,val,1,310). %% traject(zar,bil,1,300). %% traject(zar,sev,1,800). %%%%%%% end input example %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Some helpful definitions to make the code cleaner: ==================================== day(D) :- numDays(N),between(1,N,D). consecutiveDays(D1,D2) :- day(D1), day(D2), D2 is D1+1. bus(B) :- numBuses(N), between(1,N,B). trip(C1-C2) :- traject(C1,C2,_,_). dist(C1-C2,Dist) :- traject(C1,C2,_,Dist). frequency(C1-C2,F) :- traject(C1,C2,F,_). % WRONG: % tooLongDist(C1-C2-C3) :- trip(C1-C2), trip(C2-C3), C1 \= C3, dist(C1-C2,D1), dist(C2-C3,D2), maxDistance(Max), D1+D2 > Max. % CORRECT: tooLongDist(C1-C2-C3) :- trip(C1-C2), trip(C2-C3), dist(C1-C2,D1), dist(C2-C3,D2), maxDistance(Max), D1+D2 > Max. %%%%%%% End helpful definitions =============================================================== %%%%%%% 1. SAT Variables: ==================================================================== satVariable( bdcc(B,D,C1,C2) ) :- bus(B), day(D), trip(C1-C2). % bus B on day D does C1-C2 % ... more variables may be needed %%%%%%% 2. Clause generation for the SAT solver: ============================================= writeClauses :- exactlyOneTripPerBusAndDay, ... true,!. writeClauses :- told, nl, write('writeClauses failed!'), nl,nl, halt. exactlyOneTripPerBusAndDay :- ... exactlyOneTripPerBusAndDay. ... %%%%%%% 3. DisplaySol: show the solution. Here M contains the literals that are true in the model: % displaySol(M) :- nl, write(M), nl, nl, fail. displaySol(M) :- nl, frequency(C1-C2,F), nl, write('Trip '), write(C1-C2), write(' (min '), write(F), write('/week):'), member(bdcc(B,D,C1,C2),M), write(' Bus'), write(B), write('-Day'), write(D), fail. displaySol(M) :- nl, bus(B), nl, write('Bus '), write(B), write(': '), day(D), member(bdcc(B,D,C1,C2),M), dist(C1-C2,Dist), write(C1-C2), write('('), write(Dist), write(' km) '),fail. displaySol(_). %%%%%%% ======================================================================================= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Everything below is given as a standard library, reusable for solving %% with SAT many different problems. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Cardinality constraints on arbitrary sets of literals Lits: =========================== exactly(K,Lits) :- symbolicOutput(1), write( exactly(K,Lits) ), nl, !. exactly(K,Lits) :- atLeast(K,Lits), atMost(K,Lits),!. atMost(K,Lits) :- symbolicOutput(1), write( atMost(K,Lits) ), nl, !. atMost(K,Lits) :- % l1+...+ln <= k: in all subsets of size k+1, at least one is false: negateAll(Lits,NLits), K1 is K+1, subsetOfSize(K1,NLits,Clause), writeOneClause(Clause),fail. atMost(_,_). atLeast(K,Lits) :- symbolicOutput(1), write( atLeast(K,Lits) ), nl, !. atLeast(K,Lits) :- % l1+...+ln >= k: in all subsets of size n-k+1, at least one is true: length(Lits,N), K1 is N-K+1, subsetOfSize(K1, Lits,Clause), writeOneClause(Clause),fail. atLeast(_,_). negateAll( [], [] ). negateAll( [Lit|Lits], [NLit|NLits] ) :- negate(Lit,NLit), negateAll( Lits, NLits ),!. negate( -Var, Var) :- !. negate( Var, -Var) :- !. subsetOfSize(0,_,[]) :- !. subsetOfSize(N,[X|L],[X|S]) :- N1 is N-1, length(L,Leng), Leng>=N1, subsetOfSize(N1,L,S). subsetOfSize(N,[_|L], S ) :- length(L,Leng), Leng>=N, subsetOfSize( N,L,S). %%%%%%% Express equivalence between a variable and a disjunction or conjunction of literals === % Express that Var is equivalent to the disjunction of Lits: expressOr( Var, Lits ) :- symbolicOutput(1), write( Var ), write(' <--> or('), write(Lits), write(')'), nl, !. expressOr( Var, Lits ) :- member(Lit,Lits), negate(Lit,NLit), writeOneClause([ NLit, Var ]), fail. expressOr( Var, Lits ) :- negate(Var,NVar), writeOneClause([ NVar | Lits ]),!. %% expressOr(a,[x,y]) genera 3 clausulas (como en la Transformación de Tseitin): %% a == x v y %% x -> a -x v a %% y -> a -y v a %% a -> x v y -a v x v y % Express that Var is equivalent to the conjunction of Lits: expressAnd( Var, Lits) :- symbolicOutput(1), write( Var ), write(' <--> and('), write(Lits), write(')'), nl, !. expressAnd( Var, Lits) :- member(Lit,Lits), negate(Var,NVar), writeOneClause([ NVar, Lit ]), fail. expressAnd( Var, Lits) :- findall(NLit, (member(Lit,Lits), negate(Lit,NLit)), NLits), writeOneClause([ Var | NLits]), !. %%%%%%% main: ================================================================================= main:- current_prolog_flag(os_argv, Argv), nth0(1, Argv, InputFile), main(InputFile), !. main:- write('Usage: $ ./ or ?- main().'), nl, halt. main(InputFile):- symbolicOutput(1), !, consult(InputFile), writeClauses, halt. % print the clauses in symbolic form and halt Prolog main(InputFile):- consult(InputFile), initClauseGeneration, tell(clauses), writeClauses, told, % generate the (numeric) SAT clauses and call the solver tell(header), writeHeader, told, numVars(N), numClauses(C), write('Generated '), write(C), write(' clauses over '), write(N), write(' variables. '),nl, shell('cat header clauses > infile.cnf',_), write('Calling solver....'), nl, shell('kissat -v infile.cnf > model', Result), % if sat: Result=10; if unsat: Result=20. treatResult(Result),!. treatResult(20) :- write('Unsatisfiable'), nl, halt. treatResult(10) :- write('Solution found: '), nl, see(model), symbolicModel(M), seen, displaySol(M), nl,nl,halt. treatResult( _) :- write('cnf input error. Wrote anything strange in your cnf?'), nl,nl, halt. initClauseGeneration:- %initialize all info about variables and clauses: retractall(numClauses( _)), retractall(numVars( _)), retractall(varNumber(_,_,_)), assert(numClauses( 0 )), assert(numVars( 0 )), !. writeOneClause([]) :- symbolicOutput(1),!, nl. writeOneClause([]) :- countClause, write(0), nl. writeOneClause([Lit|C]) :- w(Lit), writeOneClause(C),!. w(-Var) :- symbolicOutput(1), satVariable(Var), write(-Var), write(' '),!. w( Var) :- symbolicOutput(1), satVariable(Var), write( Var), write(' '),!. w(-Var) :- satVariable(Var), var2num(Var,N), write(-), write(N), write(' '),!. w( Var) :- satVariable(Var), var2num(Var,N), write(N), write(' '),!. w( Lit) :- told, write('ERROR: generating clause with undeclared variable in literal '), write(Lit), nl,nl, halt. % given the symbolic variable V, find its variable number N in the SAT solver: :- dynamic(varNumber / 3). var2num(V,N) :- hash_term(V,Key), existsOrCreate(V,Key,N),!. existsOrCreate(V,Key,N) :- varNumber(Key,V,N),!. % V already existed with num N existsOrCreate(V,Key,N) :- newVarNumber(N), assert(varNumber(Key,V,N)), !. % otherwise, introduce new N for V writeHeader :- numVars(N),numClauses(C), write('p cnf '),write(N), write(' '),write(C),nl. countClause :- retract( numClauses(N0) ), N is N0+1, assert( numClauses(N) ),!. newVarNumber(N) :- retract( numVars( N0) ), N is N0+1, assert( numVars(N) ),!. % Getting the symbolic model M from the output file: symbolicModel(M) :- get_code(Char), readWord(Char,W), symbolicModel(M1), addIfPositiveInt(W,M1,M),!. symbolicModel([]). addIfPositiveInt(W,L,[Var|L]) :- W = [C|_], between(48,57,C), number_codes(N,W), N>0, varNumber(_,Var,N),!. addIfPositiveInt(_,L,L). readWord( 99,W) :- repeat, get_code(Ch), member(Ch,[-1,10]), !, get_code(Ch1), readWord(Ch1,W),!. % skip line starting w/ c readWord(115,W) :- repeat, get_code(Ch), member(Ch,[-1,10]), !, get_code(Ch1), readWord(Ch1,W),!. % skip line starting w/ s readWord( -1,_) :-!, fail. %end of file readWord(C, []) :- member(C,[10,32]), !. % newline or white space marks end of word readWord(Char,[Char|W]) :- get_code(Char1), readWord(Char1,W), !. %%%%%%% =======================================================================================