# cspConsistency.py - Arc Consistency and Domain splitting for solving a CSP # AIFCA Python3 code Version 0.9.1 Documentation at http://aipython.org # Artificial Intelligence: Foundations of Computational Agents # http://artint.info # Copyright David L Poole and Alan K Mackworth 2017-2020. # This work is licensed under a Creative Commons # Attribution-NonCommercial-ShareAlike 4.0 International License. # See: http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en from display import Displayable class Con_solver(Displayable): """Solves a CSP with arc consistency and domain splitting """ def __init__(self, csp, **kwargs): """a CSP solver that uses arc consistency * csp is the CSP to be solved * kwargs is the keyword arguments for Displayable superclass """ self.csp = csp super().__init__(**kwargs) # Or Displayable.__init__(self,**kwargs) def make_arc_consistent(self, orig_domains=None, to_do=None): """Makes this CSP arc-consistent using generalized arc consistency orig_domains is the original domains to_do is a set of (variable,constraint) pairs returns the reduced domains (an arc-consistent variable:domain dictionary) """ if orig_domains is None: orig_domains = {var:var.domain for var in self.csp.variables} if to_do is None: to_do = {(var, const) for const in self.csp.constraints for var in const.scope} else: to_do = to_do.copy() # use a copy of to_do domains = orig_domains.copy() self.display(2,"Performing AC with domains", domains) while to_do: var, const = self.select_arc(to_do) self.display(3, "Processing arc (", var, ",", const, ")") other_vars = [ov for ov in const.scope if ov != var] new_domain = {val for val in domains[var] if self.any_holds(domains, const, {var: val}, other_vars)} if new_domain != domains[var]: self.display(4, "Arc: (", var, ",", const, ") is inconsistent") self.display(3, "Domain pruned", "dom(", var, ") =", new_domain, " due to ", const) domains[var] = new_domain add_to_do = self.new_to_do(var, const) - to_do to_do |= add_to_do # set union self.display(3, " adding", add_to_do if add_to_do else "nothing", "to to_do.") self.display(4, "Arc: (", var, ",", const, ") now consistent") self.display(2, "AC done. Reduced domains", domains) return domains def new_to_do(self, var, const): """returns new elements to be added to to_do after assigning variable var in constraint const. """ return {(nvar, nconst) for nconst in self.csp.var_to_const[var] if nconst != const for nvar in nconst.scope if nvar != var} def select_arc(self, to_do): """Selects the arc to be taken from to_do . * to_do is a set of arcs, where an arc is a (variable,constraint) pair the element selected must be removed from to_do. """ return to_do.pop() def any_holds(self, domains, const, env, other_vars, ind=0): """returns True if Constraint const holds for an assignment that extends env with the variables in other_vars[ind:] env is a dictionary Warning: this has side effects and changes the elements of env """ if ind == len(other_vars): return const.holds(env) else: var = other_vars[ind] for val in domains[var]: # env = dict_union(env,{var:val}) # no side effects! env[var] = val if self.any_holds(domains, const, env, other_vars, ind + 1): return True return False def solve_one(self, domains=None, to_do=None): """return a solution to the current CSP or False if there are no solutions to_do is the list of arcs to check """ new_domains = self.make_arc_consistent(domains, to_do) if any(len(new_domains[var]) == 0 for var in new_domains): return False elif all(len(new_domains[var]) == 1 for var in new_domains): self.display(2, "solution:", {var: select( new_domains[var]) for var in new_domains}) return {var: select(new_domains[var]) for var in new_domains} else: var = self.select_var(x for x in self.csp.variables if len(new_domains[x]) > 1) if var: dom1, dom2 = partition_domain(new_domains[var]) self.display(3, "...splitting", var, "into", dom1, "and", dom2) new_doms1 = copy_with_assign(new_domains, var, dom1) new_doms2 = copy_with_assign(new_domains, var, dom2) to_do = self.new_to_do(var, None) self.display(3, " adding", to_do if to_do else "nothing", "to to_do.") return self.solve_one(new_doms1, to_do) or self.solve_one(new_doms2, to_do) def select_var(self, iter_vars): """return the next variable to split""" return select(iter_vars) def partition_domain(dom): """partitions domain dom into two. """ split = len(dom) // 2 dom1 = set(list(dom)[:split]) dom2 = dom - dom1 return dom1, dom2 def copy_with_assign(domains, var=None, new_domain={True, False}): """create a copy of the domains with an assignment var=new_domain if var==None then it is just a copy. """ newdoms = domains.copy() if var is not None: newdoms[var] = new_domain return newdoms def select(iterable): """select an element of iterable. Returns None if there is no such element. This implementation just picks the first element. For many of the uses, which element is selected does not affect correctness, but may affect efficiency. """ for e in iterable: return e # returns first element found from cspExamples import test_csp def ac_solver(csp): "arc consistency (solve_one)" return Con_solver(csp).solve_one() if __name__ == "__main__": test_csp(ac_solver) from searchProblem import Arc, Search_problem class Search_with_AC_from_CSP(Search_problem,Displayable): """A search problem with arc consistency and domain splitting A node is a CSP """ def __init__(self, csp): self.cons = Con_solver(csp) #copy of the CSP self.domains = self.cons.make_arc_consistent() def is_goal(self, node): """node is a goal if all domains have 1 element""" return all(len(node[var])==1 for var in node) def start_node(self): return self.domains def neighbors(self,node): """returns the neighboring nodes of node. """ neighs = [] var = select(x for x in node if len(node[x])>1) if var: dom1, dom2 = partition_domain(node[var]) self.display(2,"Splitting", var, "into", dom1, "and", dom2) to_do = self.cons.new_to_do(var,None) for dom in [dom1,dom2]: newdoms = copy_with_assign(node,var,dom) cons_doms = self.cons.make_arc_consistent(newdoms,to_do) if all(len(cons_doms[v])>0 for v in cons_doms): # all domains are non-empty neighs.append(Arc(node,cons_doms)) else: self.display(2,"...",var,"in",dom,"has no solution") return neighs from cspExamples import test_csp from searchGeneric import Searcher def ac_search_solver(csp): """arc consistency (search interface)""" sol = Searcher(Search_with_AC_from_CSP(csp)).search() if sol: return {v:select(d) for (v,d) in sol.end().items()} if __name__ == "__main__": test_csp(ac_search_solver) from cspExamples import csp1, csp2, csp3, csp4, crossword1, crossword1d ## Test Solving CSPs with Arc consistency and domain splitting: #Con_solver.max_display_level = 4 # display details of AC (0 turns off) #Con_solver(csp1).solve_one() #searcher1d = Searcher(Search_with_AC_from_CSP(csp1)) #print(searcher1d.search()) #Searcher.max_display_level = 2 # display search trace (0 turns off) #searcher2c = Searcher(Search_with_AC_from_CSP(csp2)) #print(searcher2c.search()) #searcher3c = Searcher(Search_with_AC_from_CSP(crossword1)) #print(searcher3c.search()) #searcher4c = Searcher(Search_with_AC_from_CSP(crossword1d)) #print(searcher4c.search())