Module TSort
In: tsort.rb

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:

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

  1. E. Tarjan, "Depth First Search and Linear Graph Algorithms",

SIAM Journal on Computing, Vol. 1, No. 2, pp. 146-160, June 1972.

Methods

Classes and Modules

Class TSort::Cyclic

Public Instance methods

The iterator version of the strongly_connected_components method. obj.each_strongly_connected_component is similar to obj.strongly_connected_components.each, but modification of obj during the iteration may lead to unexpected results.

each_strongly_connected_component returns nil.

[Source]

# File tsort.rb, line 177
  def each_strongly_connected_component # :yields: nodes
    id_map = {}
    stack = []
    tsort_each_node {|node|
      unless id_map.include? node
        each_strongly_connected_component_from(node, 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.

[Source]

# File tsort.rb, line 198
  def each_strongly_connected_component_from(node, id_map={}, stack=[]) # :yields: nodes
    minimum_id = node_id = id_map[node] = id_map.size
    stack_length = stack.length
    stack << node

    tsort_each_child(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 =
          each_strongly_connected_component_from(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

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.

[Source]

# File tsort.rb, line 162
  def strongly_connected_components
    result = []
    each_strongly_connected_component {|component| result << component}
    result
  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.

[Source]

# File tsort.rb, line 133
  def tsort
    result = []
    tsort_each {|element| result << element}
    result
  end

The iterator version of the tsort method. obj.tsort_each is similar to obj.tsort.each, 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.

[Source]

# File tsort.rb, line 147
  def tsort_each # :yields: node
    each_strongly_connected_component {|component|
      if component.size == 1
        yield component.first
      else
        raise Cyclic.new("topological sort failed: #{component.inspect}")
      end
    }
  end

Should be implemented by a extended class.

tsort_each_child is used to iterate for child nodes of node.

[Source]

# File tsort.rb, line 239
  def tsort_each_child(node) # :yields: child
    raise NotImplementedError.new
  end

Should be implemented by a extended class.

tsort_each_node is used to iterate for all nodes over a graph.

[Source]

# File tsort.rb, line 230
  def tsort_each_node # :yields: node
    raise NotImplementedError.new
  end

[Validate]