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			$antecedent->{_num_successors_in_mem} = $antecedent->{_num_successors_in_mem} - 1;				     
			# update the total number of nodes in the queue.
			$num_states_in_queue--;
			
		    }
		} # end if (num_states_on_queue > max_states)

		# if there is a successor to $best, insert it in the priority queue.
		if($succ){
		    $$priority_queue->insert($succ);
		    $best->{_num_successors_in_mem} = $best->{_num_successors_in_mem} + 1;
		}
		else{
		    croak "Error:  no successor to insert\n";
		}
	    }
	}
	continue {
	    $iteration++;
	}

	print "\n\nreturning unsuccessfully.   iteration: $iteration\n";	
	return;
    }
}    




sub max
{
    my ($n1, $n2) = @_;
    return ($n1 > $n2 ? $n1 : $n2);
}


sub fp_compare {
    my ($a, $b, $dp) = @_;
    my $a_seq = sprintf("%.${dp}g", $a);
    my $b_seq = sprintf("%.${dp}g", $b);
    
    

    if($a_seq eq $b_seq){
	return 0;
    }
    elsif($a_seq lt $b_seq){
	return -1;
    }
    else{ 
	return 1;
    }
}





1;
__END__
# Below is stub documentation for your module. You'd better edit it!

=head1 NAME

AI::Pathfinding::SMAstar - Simplified Memory-bounded A* Search


=head1 SYNOPSIS

 use AI::Pathfinding::SMAstar;
  

=head2 EXAMPLE

 ##################################################################
 #
 # This example uses a hypothetical object called FrontierObj, and
 # shows the functions that the FrontierObj class must feature in 
 # order to perform a path-search in a solution space populated by 
 # FrontierObj objects.
 #
 ##################################################################
 
 my $smastar = AI::Pathfinding::SMAstar->new(
        # evaluates f(n) = g(n) + h(n), returns a number
    	_state_eval_func           => \&FrontierObj::evaluate,

        # when called on a node, returns 1 if it is a goal
	_state_goal_p_func         => \&FrontierObj::goal_test,

        # must return the number of successors of a node
        _state_num_successors_func => \&FrontierObj::get_num_successors,      

        # must return *one* successor at a time
        _state_successors_iterator => \&FrontierObj::get_successors_iterator,   

        # can be any suitable string representation 
        _state_get_data_func       => \&FrontierObj::string_representation,  

        # gets called once per iteration, useful for showing algorithm progress
        _show_prog_func            => \&FrontierObj::progress_callback,      
    );

 # You can start the search from multiple start-states.
 # Add the initial states to the smastar object before starting the search.
 foreach my $frontierObj (@start_states){
    $smastar->add_start_state($frontierObj);
 }

 
 #
 # Start the search.  If successful, $frontierGoalPath will contain the
 # goal path.   The optimal path to the goal node will be encoded in the
 # ancestry of the goal path.   $frontierGoalPath->antecedent() contains
 # the goal path's parent path, and so forth back to the start path, which
 # contains only the start state.
 #
 # $frontierGoalPath->state() contains the goal FrontierObj itself.
 #
 my $frontierGoalPath = $smastar->start_search(
    \&log_function,       # returns a string used for logging progress