Module

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. Tarjan, “Depth First Search and Linear Graph Algorithms”,

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

Constants
No documentation available
Class Methods

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]

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]

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]]

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

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
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.

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]

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]

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]]

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

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.

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

Should be implemented by a extended class.

tsort_each_child is used to iterate for child nodes of node.

Should be implemented by a extended class.

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