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Code Editor : tsort.rb

#--
# tsort.rb - provides a module for topological sorting and strongly connected components.
#++
#

#
# TSort implements topological sorting using Tarjan's algorithm for
# strongly connected components.
#
# TSort is designed to be able to be used with any object which can be
# interpreted as a directed graph.
#
# TSort requires two methods to interpret an object as a graph,
# tsort_each_node and tsort_each_child.
#
# * tsort_each_node is used to iterate for all nodes over a graph.
# * tsort_each_child is used to iterate for child nodes of a given node.
#
# The equality of nodes are defined by eql? and hash since
# TSort uses Hash internally.
#
# == A Simple Example
#
# The following example demonstrates how to mix the TSort module into an
# existing class (in this case, Hash). Here, we're treating each key in
# the hash as a node in the graph, and so we simply alias the required
# #tsort_each_node method to Hash's #each_key method. For each key in the
# hash, the associated value is an array of the node's child nodes. This
# choice in turn leads to our implementation of the required #tsort_each_child
# method, which fetches the array of child nodes and then iterates over that
# array using the user-supplied block.
#
# require 'tsort'
#
# class Hash
# include TSort
# alias tsort_each_node each_key
# def tsort_each_child(node, &block)
# fetch(node).each(&block)
# end
# end
#
# {1=>[2, 3], 2=>[3], 3=>[], 4=>[]}.tsort
# #=> [3, 2, 1, 4]
#
# {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}.strongly_connected_components
# #=> [[4], [2, 3], [1]]
#
# == A More Realistic Example
#
# A very simple `make' like tool can be implemented as follows:
#
# require 'tsort'
#
# class Make
# def initialize
# @dep = {}
# @dep.default = []
# end
#
# def rule(outputs, inputs=[], &block)
# triple = [outputs, inputs, block]
# outputs.each {|f| @dep[f] = [triple]}
# @dep[triple] = inputs
# end
#
# def build(target)
# each_strongly_connected_component_from(target) {|ns|
# if ns.length != 1
# fs = ns.delete_if {|n| Array === n}
# raise TSort::Cyclic.new("cyclic dependencies: #{fs.join ', '}")
# end
# n = ns.first
# if Array === n
# outputs, inputs, block = n
# inputs_time = inputs.map {|f| File.mtime f}.max
# begin
# outputs_time = outputs.map {|f| File.mtime f}.min
# rescue Errno::ENOENT
# outputs_time = nil
# end
# if outputs_time == nil ||
# inputs_time != nil && outputs_time <= inputs_time
# sleep 1 if inputs_time != nil && inputs_time.to_i == Time.now.to_i
# block.call
# end
# end
# }
# end
#
# def tsort_each_child(node, &block)
# @dep[node].each(&block)
# end
# include TSort
# end
#
# def command(arg)
# print arg, "\n"
# system arg
# end
#
# m = Make.new
# m.rule(%w[t1]) { command 'date > t1' }
# m.rule(%w[t2]) { command 'date > t2' }
# m.rule(%w[t3]) { command 'date > t3' }
# m.rule(%w[t4], %w[t1 t3]) { command 'cat t1 t3 > t4' }
# m.rule(%w[t5], %w[t4 t2]) { command 'cat t4 t2 > t5' }
# m.build('t5')
#
# == Bugs
#
# * 'tsort.rb' is wrong name because this library uses
# Tarjan's algorithm for strongly connected components.
# Although 'strongly_connected_components.rb' is correct but too long.
#
# == References
#
# R. E. Tarjan, "Depth First Search and Linear Graph Algorithms",
# SIAM Journal on Computing, Vol. 1, No. 2, pp. 146-160, June 1972.
#

module TSort
 class Cyclic < StandardError
 end

# Returns a topologically sorted array of nodes.
  # The array is sorted from children to parents, i.e.
  # the first element has no child and the last node has no parent.
  #
  # If there is a cycle, TSort::Cyclic is raised.
  #
  #   class G
  #     include TSort
  #     def initialize(g)
  #       @g = g
  #     end
  #     def tsort_each_child(n, &b) @g[n].each(&b) end
  #     def tsort_each_node(&b) @g.each_key(&b) end
  #   end
  #
  #   graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
  #   p graph.tsort #=> [4, 2, 3, 1]
  #
  #   graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
  #   p graph.tsort # raises TSort::Cyclic
  #
  def tsort
    each_node = method(:tsort_each_node)
    each_child = method(:tsort_each_child)
    TSort.tsort(each_node, each_child)
  end

# Returns a topologically sorted array of nodes.
 # The array is sorted from children to parents, i.e.
 # the first element has no child and the last node has no parent.
 #
 # The graph is represented by _each_node_ and _each_child_.
 # _each_node_ should have +call+ method which yields for each node in the graph.
 # _each_child_ should have +call+ method which takes a node argument and yields for each child node.
 #
 # If there is a cycle, TSort::Cyclic is raised.
 #
 # g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
 # each_node = lambda {|&b| g.each_key(&b) }
 # each_child = lambda {|n, &b| g[n].each(&b) }
 # p TSort.tsort(each_node, each_child) #=> [4, 2, 3, 1]
 #
 # g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
 # each_node = lambda {|&b| g.each_key(&b) }
 # each_child = lambda {|n, &b| g[n].each(&b) }
 # p TSort.tsort(each_node, each_child) # raises TSort::Cyclic
 #
 def TSort.tsort(each_node, each_child)
 result = []
 TSort.tsort_each(each_node, each_child) {|element| result << element}
 result
 end

# The iterator version of the #tsort method.
 # <tt>obj.tsort_each</tt> is similar to <tt>obj.tsort.each</tt>, but
 # modification of _obj_ during the iteration may lead to unexpected results.
 #
 # #tsort_each returns +nil+.
 # If there is a cycle, TSort::Cyclic is raised.
 #
 # class G
 # include TSort
 # def initialize(g)
 # @g = g
 # end
 # def tsort_each_child(n, &b) @g[n].each(&b) end
 # def tsort_each_node(&b) @g.each_key(&b) end
 # end
 #
 # graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
 # graph.tsort_each {|n| p n }
 # #=> 4
 # # 2
 # # 3
 # # 1
 #
 def tsort_each(&block) # :yields: node
 each_node = method(:tsort_each_node)
 each_child = method(:tsort_each_child)
 TSort.tsort_each(each_node, each_child, &block)
 end

# The iterator version of the TSort.tsort method.
  #
  # The graph is represented by _each_node_ and _each_child_.
  # _each_node_ should have +call+ method which yields for each node in the graph.
  # _each_child_ should have +call+ method which takes a node argument and yields for each child node.
  #
  #   g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
  #   each_node = lambda {|&b| g.each_key(&b) }
  #   each_child = lambda {|n, &b| g[n].each(&b) }
  #   TSort.tsort_each(each_node, each_child) {|n| p n }
  #   #=> 4
  #   #   2
  #   #   3
  #   #   1
  #
  def TSort.tsort_each(each_node, each_child) # :yields: node
    TSort.each_strongly_connected_component(each_node, each_child) {|component|
      if component.size == 1
        yield component.first
      else
        raise Cyclic.new("topological sort failed: #{component.inspect}")
      end
    }
  end

# Returns strongly connected components as an array of arrays of nodes.
  # The array is sorted from children to parents.
  # Each elements of the array represents a strongly connected component.
  #
  #   class G
  #     include TSort
  #     def initialize(g)
  #       @g = g
  #     end
  #     def tsort_each_child(n, &b) @g[n].each(&b) end
  #     def tsort_each_node(&b) @g.each_key(&b) end
  #   end
  #
  #   graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
  #   p graph.strongly_connected_components #=> [[4], [2], [3], [1]]
  #
  #   graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
  #   p graph.strongly_connected_components #=> [[4], [2, 3], [1]]
  #
  def strongly_connected_components
    each_node = method(:tsort_each_node)
    each_child = method(:tsort_each_child)
    TSort.strongly_connected_components(each_node, each_child)
  end

# Returns strongly connected components as an array of arrays of nodes.
 # The array is sorted from children to parents.
 # Each elements of the array represents a strongly connected component.
 #
 # The graph is represented by _each_node_ and _each_child_.
 # _each_node_ should have +call+ method which yields for each node in the graph.
 # _each_child_ should have +call+ method which takes a node argument and yields for each child node.
 #
 # g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
 # each_node = lambda {|&b| g.each_key(&b) }
 # each_child = lambda {|n, &b| g[n].each(&b) }
 # p TSort.strongly_connected_components(each_node, each_child)
 # #=> [[4], [2], [3], [1]]
 #
 # g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
 # each_node = lambda {|&b| g.each_key(&b) }
 # each_child = lambda {|n, &b| g[n].each(&b) }
 # p TSort.strongly_connected_components(each_node, each_child)
 # #=> [[4], [2, 3], [1]]
 #
 def TSort.strongly_connected_components(each_node, each_child)
 result = []
 TSort.each_strongly_connected_component(each_node, each_child) {|component| result << component}
 result
 end

# The iterator version of the #strongly_connected_components method.
 # <tt>obj.each_strongly_connected_component</tt> is similar to
 # <tt>obj.strongly_connected_components.each</tt>, but
 # modification of _obj_ during the iteration may lead to unexpected results.
 #
 # #each_strongly_connected_component returns +nil+.
 #
 # class G
 # include TSort
 # def initialize(g)
 # @g = g
 # end
 # def tsort_each_child(n, &b) @g[n].each(&b) end
 # def tsort_each_node(&b) @g.each_key(&b) end
 # end
 #
 # graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
 # graph.each_strongly_connected_component {|scc| p scc }
 # #=> [4]
 # # [2]
 # # [3]
 # # [1]
 #
 # graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
 # graph.each_strongly_connected_component {|scc| p scc }
 # #=> [4]
 # # [2, 3]
 # # [1]
 #
 def each_strongly_connected_component(&block) # :yields: nodes
 each_node = method(:tsort_each_node)
 each_child = method(:tsort_each_child)
 TSort.each_strongly_connected_component(each_node, each_child, &block)
 end

# The iterator version of the TSort.strongly_connected_components method.
  #
  # The graph is represented by _each_node_ and _each_child_.
  # _each_node_ should have +call+ method which yields for each node in the graph.
  # _each_child_ should have +call+ method which takes a node argument and yields for each child node.
  #
  #   g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
  #   each_node = lambda {|&b| g.each_key(&b) }
  #   each_child = lambda {|n, &b| g[n].each(&b) }
  #   TSort.each_strongly_connected_component(each_node, each_child) {|scc| p scc }
  #   #=> [4]
  #   #   [2]
  #   #   [3]
  #   #   [1]
  #
  #   g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
  #   each_node = lambda {|&b| g.each_key(&b) }
  #   each_child = lambda {|n, &b| g[n].each(&b) }
  #   TSort.each_strongly_connected_component(each_node, each_child) {|scc| p scc }
  #   #=> [4]
  #   #   [2, 3]
  #   #   [1]
  #
  def TSort.each_strongly_connected_component(each_node, each_child) # :yields: nodes
    id_map = {}
    stack = []
    each_node.call {|node|
      unless id_map.include? node
        TSort.each_strongly_connected_component_from(node, each_child, id_map, stack) {|c|
          yield c
        }
      end
    }
    nil
  end

# Iterates over strongly connected component in the subgraph reachable from
  # _node_.
  #
  # Return value is unspecified.
  #
  # #each_strongly_connected_component_from doesn't call #tsort_each_node.
  #
  #   class G
  #     include TSort
  #     def initialize(g)
  #       @g = g
  #     end
  #     def tsort_each_child(n, &b) @g[n].each(&b) end
  #     def tsort_each_node(&b) @g.each_key(&b) end
  #   end
  #
  #   graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
  #   graph.each_strongly_connected_component_from(2) {|scc| p scc }
  #   #=> [4]
  #   #   [2]
  #
  #   graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
  #   graph.each_strongly_connected_component_from(2) {|scc| p scc }
  #   #=> [4]
  #   #   [2, 3]
  #
  def each_strongly_connected_component_from(node, id_map={}, stack=[], &block) # :yields: nodes
    TSort.each_strongly_connected_component_from(node, method(:tsort_each_child), id_map, stack, &block)
  end

# Iterates over strongly connected components in a graph.
 # The graph is represented by _node_ and _each_child_.
 #
 # _node_ is the first node.
 # _each_child_ should have +call+ method which takes a node argument
 # and yields for each child node.
 #
 # Return value is unspecified.
 #
 # #TSort.each_strongly_connected_component_from is a class method and
 # it doesn't need a class to represent a graph which includes TSort.
 #
 # graph = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
 # each_child = lambda {|n, &b| graph[n].each(&b) }
 # TSort.each_strongly_connected_component_from(1, each_child) {|scc|
 # p scc
 # }
 # #=> [4]
 # # [2, 3]
 # # [1]
 #
 def TSort.each_strongly_connected_component_from(node, each_child, id_map={}, stack=[]) # :yields: nodes
 minimum_id = node_id = id_map[node] = id_map.size
 stack_length = stack.length
 stack << node

each_child.call(node) {|child|
 if id_map.include? child
 child_id = id_map[child]
 minimum_id = child_id if child_id && child_id < minimum_id
 else
 sub_minimum_id =
 TSort.each_strongly_connected_component_from(child, each_child, id_map, stack) {|c|
 yield c
 }
 minimum_id = sub_minimum_id if sub_minimum_id < minimum_id
 end
 }

if node_id == minimum_id
      component = stack.slice!(stack_length .. -1)
      component.each {|n| id_map[n] = nil}
      yield component
    end

minimum_id
  end

# Should be implemented by a extended class.
  #
  # #tsort_each_node is used to iterate for all nodes over a graph.
  #
  def tsort_each_node # :yields: node
    raise NotImplementedError.new
  end

# Should be implemented by a extended class.
  #
  # #tsort_each_child is used to iterate for child nodes of _node_.
  #
  def tsort_each_child(node) # :yields: child
    raise NotImplementedError.new
  end
end

${this.title}

Code Editor : tsort.rb