# traversal.rb
#
# This file defines the basic graph traversal algorithm for DFS and BFS search.
# They are implemented as an RGL::GraphIterator, which is a Stream of vertices
# of a given graph.  The streams are not reversable.
#
# Beside being an iterator in the sense of the Stream mixin, RGL::BFSIterator
# and RGL::DFSIterator follow the BGL
# Visitor[http://www.boost.org/libs/graph/doc/visitor_concepts.html] Concepts
# in a slightly modified fashion (especially for the RGL::DFSIterator).

require 'laser/third_party/rgl/base'
require 'stream'

module RGL

  module GraphWrapper                                   # :nodoc:

    attr_accessor :graph

    # Creates a new GraphWrapper on _graph_.
    def initialize (graph)
      @graph = graph
    end

  end                           # module GraphWrapper

  # A GraphIterator is the abstract superclass of all Iterators on graphs.
  # Each such iterator should implement the protocol defined in module Stream.
  module GraphIterator
    include Stream
    include GraphWrapper
  end

  # Module GraphVisitor defines the BGL
  # BFS[http://www.boost.org/libs/graph/doc/BFSVisitor.html] Visitor Concept).
  #
  # Visitors provide a mechanism for extending an algorithm (i.e., for
  # customizing what is done at each step of the algorithm).  They allow users
  # to insert their own operations at various steps within a graph algorithm.
  #
  # Graph algorithms typically have multiple event points where one may want to
  # insert a call-back.  Therefore, visitors have several methods that
  # correspond to the various event points.  Each algorithm has a different
  # set of event points.  The following are common to both DFS and BFS search.
  #
  #  * examine_vertex
  #  * finish_vertex
  #  * examine_edge
  #  * tree_edge
  #  * back_edge
  #  * forward_edge
  #
  # These methods are all called handle_* and can be set to appropriate blocks,
  # using the methods set_*_event_handler, which are defined for each event
  # mentioned above. 
  #
  # As an alternative, you can also override the handle_* methods in a
  # subclass, to configure the algorithm (as an example, see TarjanSccVisitor).
  #
  # During a graph traversal, vertices are *colored* using the colors :GRAY
  # (when waiting) and :BLACK when finished.  All other vertices are :WHITE.
  # The color_map is also maintained in the visitor.

  module GraphVisitor

    include GraphWrapper

    attr_reader :color_map

    # Create a new GraphVisitor on _graph_.

    def initialize (graph)
      super graph
      reset
    end

    # Mark each vertex unvisited (i.e. :WHITE)

    def reset
      @color_map = Hash.new(:WHITE)
    end

    # Returns true if vertex _v_ is colored :BLACK (i.e. finished).

    def finished_vertex? (v)
      @color_map[v] == :BLACK
    end
 
    # Attach a map to the visitor which records the distance of a visited
    # vertex to the start vertex.
    #
 	# This is similar to BGLs
	# distance_recorder[http://www.boost.org/libs/graph/doc/distance_recorder.html].
    #
    # After the distance_map is attached, the visitor has a new method
    # distance_to_root, which answers the distance to the start vertex.

    def attach_distance_map (map = Hash.new(0))
      @dist_map = map

      class << self

        def handle_tree_edge (u, v)
          super
          @dist_map[v] = @dist_map[u] + 1
        end

        # Answer the distance to the start vertex.

        def distance_to_root (v)
          @dist_map[v]
        end

      end	# class
    end

    # Shall we follow the edge (u,v); i.e. v has color :WHITE

    def follow_edge? (u, v)			# :nodoc:
      @color_map[v] == :WHITE
    end

    # == Visitor Event Points

    def self.def_event_handler (m)
      params = m =~ /edge/ ? "u,v" : "u"
      self.class_eval %{
        def handle_#{m} (#{params})
          @#{m}_event_handler.call(#{params}) if defined? @#{m}_event_handler
        end

        def set_#{m}_event_handler (&b)
          @#{m}_event_handler = b
        end
      }
    end

    %w[examine_vertex finish_vertex examine_edge tree_edge back_edge
       forward_edge].each do |m|
      def_event_handler(m)
    end

  end		# module GraphVisitor

  # A BFSIterator can be used to traverse a graph from a given start vertex in
  # breath first search order.  Since the Iterator also mixins the GraphVisitor,
  # it provides all event points defined there.
  #
  # The vertices which are not yet visited are held in the queue @waiting.
  # During the traversal, vertices are *colored* using the colors :GRAY
  # (when waiting) and :BLACK when finished.  All other vertices are :WHITE.
  #
  # For more doc see the BGL
  # BFS[http://www.boost.org/libs/graph/doc/BFSVisitor.html] Visitor Concept .
  #
  # See the implementation of bfs_search_tree_from for an example usage.

  class BFSIterator

    include GraphIterator
    include GraphVisitor

    attr_accessor :start_vertex

    # Create a new BFSIterator on _graph_, starting at vertex _start_.

    def initialize (graph, start=graph.detect{ |x| true })
      super(graph)
      @start_vertex = start
      set_to_begin
    end

    # Returns true if the @color_map has only one entry (for the start vertex).

    def at_beginning?				# :nodoc:
      @color_map.size == 1
    end
        
    # Returns true if @waiting is empty.

    def at_end?
      @waiting.empty?
    end

    # Reset the iterator to the initial state (i.e. at_beginning? == true).

    def set_to_begin
      color_map[@start_vertex] = :GRAY
      @waiting = [@start_vertex]		# a queue
      handle_tree_edge(nil, @start_vertex)	# discovers start vertex 
    end

    def basic_forward				# :nodoc:
      u = next_vertex
      handle_examine_vertex(u)
      graph.each_adjacent(u) { |v|
        handle_examine_edge(u, v)
        if follow_edge?(u, v)			# (u,v) is a tree edge
          handle_tree_edge(u, v)		# also discovers v
          color_map[v] = :GRAY			# color of v was :WHITE
          @waiting.push(v)
        else					# (u,v) is a non tree edge
          if color_map[v] == :GRAY
            handle_back_edge(u, v)		# (u,v) has gray target
          else
            handle_forward_edge(u, v)		# (u,v) has black target
          end
        end
      }
      color_map[u] = :BLACK
      handle_finish_vertex(u)                       # finish vertex
      u
    end

    protected

    def next_vertex				# :nodoc:
      # waiting is a queue
      @waiting.shift
    end
  end		# class BFSIterator


  module Graph

    # Returns a BFSIterator, starting at vertex _v_.

    def bfs_iterator (v = self.detect { |x| true})
      BFSIterator.new(self, v)
    end

    # Returns a DirectedAdjacencyGraph, which represents a BFS search tree
    # starting at _v_.  This method uses the tree_edge_event of BFSIterator
    # to record all tree edges of the search tree in the result.

    def bfs_search_tree_from (v)
      require 'laser/third_party/rgl/adjacency'
      bfs  = bfs_iterator(v)
      tree = DirectedAdjacencyGraph.new
      bfs.set_tree_edge_event_handler { |from, to|
        tree.add_edge(from, to)
      }
      bfs.set_to_end				# does the search
      tree
    end

  end		# module Graph


  # Iterator for a depth first search, starting at a given vertex.  The only
  # difference from BFSIterator is that @waiting is a stack, instead of a queue.
  #
  # Note that this is different from DFSVisitor, which is used in the recursive
  # version for depth first search (see depth_first_search).

  class DFSIterator < BFSIterator

    def next_vertex
      # waiting is a stack
      @waiting.pop
    end

  end		# class DFSIterator


  # A DFSVisitor is needed by the depth_first_search and depth_first_visit
  # methods of a graph.  Besides the eventpoint of GraphVisitor, it provides
  # an additional eventpoint start_vertex, which is called when a
  # depth_first_search starts a new subtree of the depth first forest that is
  # defined by the search.
  #
  # Note that the discover_vertex event defined in the BGL
  # DFSVisitor[http://www.boost.org/libs/graph/doc/DFSVisitor.html] is not
  # this is also defined in the common mixin GraphVisitor of DFSVisitor,
  # DFSIterator, and BFSIterator.

  class DFSVisitor

    include GraphVisitor

    GraphVisitor.def_event_handler("start_vertex")

  end		# class DFSVisitor


  module Graph

    # Returns a DFSIterator staring at vertex _v_.

    def dfs_iterator (v = self.detect { |x| true })
      DFSIterator.new(self, v)
    end

    # Do a recursive DFS search on the whole graph.  If a block is passed,
    # it is called on each _finish_vertex_ event.  See
    # strongly_connected_components for an example usage.

    def depth_first_search (vis = DFSVisitor.new(self), &b)
      each_vertex do |u|
        unless vis.finished_vertex?(u)
          vis.handle_start_vertex(u)
          depth_first_visit(u, vis, &b)
        end
      end
    end

    # Start a depth first search at vertex _u_.  The block _b_ is called on
    # each finish_vertex event.

    def depth_first_visit (u, vis = DFSVisitor.new(self), &b)
      vis.color_map[u] = :GRAY
      vis.handle_examine_vertex(u)
      each_adjacent(u) { |v|
        vis.handle_examine_edge(u, v)
        if vis.follow_edge?(u, v)            # (u,v) is a tree edge
          vis.handle_tree_edge(u, v)         # also discovers v
          vis.color_map[v] = :GRAY           # color of v was :WHITE
          depth_first_visit(v, vis, &b)
        else                                 # (u,v) is a non tree edge
          if vis.color_map[v] == :GRAY
            vis.handle_back_edge(u, v)       # (u,v) has gray target
          else
            vis.handle_forward_edge(u, v)    # (u,v) is a cross or forward edge 
          end
        end
      }
      vis.color_map[u] = :BLACK
      vis.handle_finish_vertex(u)           # finish vertex
      b.call(u)
    end

  end		# module Graph

=begin
  def acyclic?
    has_cycle = false
    dfs = DFSIterator.new(self)
    dfs.set_back_edge_event {has_cycle = true}
    dfs_each(dfs) do |x|
      puts x,has_cycle,dfs.inspect
      return false if has_cycle
    end
    true
  end
=end

end                             # module RGL
