symbolicOutput(0). % set to 1 for DEBUGGING: to see symbolic output only; 0 otherwise. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% We want to solve a modified version of the Traveling Salesman Problem: %% given a map with some (possibly one-way) roads between N cities, %% we want find a route starting and finishing in city 1 such that %% each city is visited exactly once. Moreover, we want to find a %% route with cost at most maxCost, considering that: %% -trajects between cities with the same parity have cost 0 euros %% -trajects between cities of different parity have cost 1 euro %% For example, the following solution has cost 10: %% 1 10 4 8 3 20 18 14 12 11 15 2 5 9 17 16 7 13 19 6 1 %% ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ %% Complete the following program to compute one such a route. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% begin input example tsp1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% maxCost(10). %% numCities(20). %% %% adjacency(1,[10]). %% adjacency(2,[7,5,17]). % Three one-way roads Fromm city 2: 2->7, 2->5 and 2->17. %% adjacency(3,[6,20,11]). %% adjacency(4,[14,15,1,8,5]). %% adjacency(5,[16,4,9,10,11]). %% adjacency(6,[1,13,17]). %% adjacency(7,[16,9,13,11]). %% adjacency(8,[7,3,10,6,17]). %% adjacency(9,[6,17,11]). %% adjacency(10,[7,11,5,6,4]). %% adjacency(11,[20,8,15,4,1,16,3]). %% adjacency(12,[15,11,3]). %% adjacency(13,[5,2,19,3,6]). %% adjacency(14,[10,12,9,7]). %% adjacency(15,[20,1,14,18,12,2]). %% adjacency(16,[7,6,4,8,2,10]). %% adjacency(17,[20,5,16,3,8]). %% adjacency(18,[15,16,7,14,3]). %% adjacency(19,[13,6]). %% adjacency(20,[12,6,18,7,16]). %% %%%%%%% end input example tsp1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Some helpful definitions to make the code cleaner: ==================================== position(P) :- numCities(N), between(0,N,P). city(I) :- adjacency(I,_). %%%%%%% End helpful definitions =============================================================== %%%%%%% ======================================================================================= % % Our LI Prolog template for solving problems using a SAT solver. % % It generates the SAT clauses, calls the SAT solver, and shows the solution. Just specify: % 1. SAT Variables % 2. Clause generation % 3. DisplaySol: show the solution. % %%%%%%% ======================================================================================= %%%%%%% 1. SAT Variables: ==================================================================== satVariable( visited(I,P) ) :- city(I), position(P). % visited(I,P) meaning "city I is visited in position P" % Warning: more types of variables might be needed or convenient. %%%%%%% 2. Clause generation for the SAT solver: ============================================= writeClauses :- .... %% Complete this! true, !. writeClauses :- told, nl, write('writeClauses failed!'), nl, nl, halt. %%%%%%% 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) :- position(P), member(visited(City,P),M), write(City), write(' '), fail. displaySol(_) :- nl. %%%%%%% ======================================================================================= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 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), !. %%%%%%% =======================================================================================