class Sudoku_Topology_Incidence(
    ):
    
    
    def Topology_Incidence_Apply(self,topology):
        musts=self.Topology_Incidence(topology)
        
        texts=[]
        for must in musts:
            r=must[0]
            s=must[1]
            value=must[2]
            descriptor=must[3]

            self.S[r][s]=value
            
            texts.append("S["+str(r)+","+str(s)+"]="+str(value)+" "+descriptor)
            
        if (len(musts)>0):
            print "Setting by Incidence:\n\t"+"\n\t".join(texts)
        else:
            print "No more by Incidence"
            
        topology=self.Topology_Initial()

        return musts
        
    
    def Topology_Incidence(self,topology):
        musts=[]
        musts=musts+self.Topology_Incidence_Rows(topology)
        musts=musts+self.Topology_Incidence_Columns(topology)
        musts=musts+self.Topology_Incidence_Boxes(topology)

        musts_dict={}
        rmusts=[]
        for must in musts:
            key=str(must[0])+"_"+str(must[1])
            
            if (not musts_dict.has_key(key)):
                rmusts.append(must)
                musts_dict[ key ]=True
                
        return rmusts
    
    def Topology_Incidence_Rows(self,topology):
        musts=[]
        for r in range(self.M):
            musts=musts+self.Topology_Incidence_Elements(
                topology,
                self.Sudoku_Row(r),
                "R"+str(r+1)
            )

        return musts
    
    def Topology_Incidence_Columns(self,topology):
        musts=[]
        for s in range(self.M):
            musts=musts+self.Topology_Incidence_Elements(
                topology,
                self.Sudoku_Column(s),
                "C"+str(s+1)
            )

        return musts
    
    def Topology_Incidence_Boxes(self,topology):
        musts=[]
        for rr in range(self.N):
            for ss in range(self.N):
                musts=musts+self.Topology_Incidence_Elements(
                    topology,
                    self.Sudoku_Box(rr,ss),
                    "B"+str(rr+1)+""+str(ss+1)
                )

        return musts
    
    def Topology_Incidence_Elements(self,topology,elements,descriptor):
        values=set()
        for element in elements:
            r=element[0]
            s=element[1]
            
            if (self.S[r][s]==0):
                for value in topology[r][s]:
                    values.add(value)
            
        musts=[]
        for value in values:
            n=0
            rr=ss=-1

            for element in elements:
                r=element[0]
                s=element[1]

                if (self.S[r][s]==0):
                    if (value in topology[r][s]):
                        n+=1
                        rr=r
                        ss=s

            #Unique
            if (n==1):
                musts.append([rr,ss,value,descriptor])
                
               
        return musts