Module: Gem::TSort

Included in:
DependencyList, Molinillo::DependencyGraph, RequestSet
Defined in:
lib/rubygems/vendor/tsort/lib/tsort.rb

Overview

Gem::TSort implements topological sorting using Tarjan’s algorithm for strongly connected components.

Gem::TSort is designed to be able to be used with any object which can be interpreted as a directed graph.

Gem::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 Gem::TSort uses Hash internally.

A Simple Example

The following example demonstrates how to mix the Gem::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 'rubygems/vendor/tsort/lib/tsort'

class Hash
  include Gem::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 'rubygems/vendor/tsort/lib/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 Gem::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 Gem::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.

Defined Under Namespace

Classes: Cyclic

Constant Summary collapse

VERSION =
"0.2.0"

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.each_strongly_connected_component(each_node, each_child) ⇒ Object

The iterator version of the Gem::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) }
Gem::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) }
Gem::TSort.each_strongly_connected_component(each_node, each_child) {|scc| p scc }
#=> [4]
#   [2, 3]
#   [1]


345
346
347
348
349
350
351
352
353
354
355
356
357
358
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 345

def self.each_strongly_connected_component(each_node, each_child) # :yields: nodes
  return to_enum(__method__, each_node, each_child) unless block_given?

  id_map = {}
  stack = []
  each_node.call {|node|
    unless id_map.include? node
      each_strongly_connected_component_from(node, each_child, id_map, stack) {|c|
        yield c
      }
    end
  }
  nil
end

.each_strongly_connected_component_from(node, each_child, id_map = {}, stack = []) ⇒ Object

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.

#Gem::TSort.each_strongly_connected_component_from is a class method and it doesn’t need a class to represent a graph which includes Gem::TSort.

graph = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
each_child = lambda {|n, &b| graph[n].each(&b) }
Gem::TSort.each_strongly_connected_component_from(1, each_child) {|scc|
  p scc
}
#=> [4]
#   [2, 3]
#   [1]


411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 411

def self.each_strongly_connected_component_from(node, each_child, id_map={}, stack=[]) # :yields: nodes
  return to_enum(__method__, node, each_child, id_map, stack) unless block_given?

  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 =
        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

.strongly_connected_components(each_node, each_child) ⇒ Object

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 Gem::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 Gem::TSort.strongly_connected_components(each_node, each_child)
#=> [[4], [2, 3], [1]]


283
284
285
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 283

def self.strongly_connected_components(each_node, each_child)
  each_strongly_connected_component(each_node, each_child).to_a
end

.tsort(each_node, each_child) ⇒ Object

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, Gem::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 Gem::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 Gem::TSort.tsort(each_node, each_child) # raises Gem::TSort::Cyclic


178
179
180
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 178

def self.tsort(each_node, each_child)
  tsort_each(each_node, each_child).to_a
end

.tsort_each(each_node, each_child) ⇒ Object

The iterator version of the Gem::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) }
Gem::TSort.tsort_each(each_node, each_child) {|n| p n }
#=> 4
#   2
#   3
#   1


226
227
228
229
230
231
232
233
234
235
236
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 226

def self.tsort_each(each_node, each_child) # :yields: node
  return to_enum(__method__, each_node, each_child) unless block_given?

  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

Instance Method Details

#each_strongly_connected_component(&block) ⇒ Object

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 Gem::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]


316
317
318
319
320
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 316

def each_strongly_connected_component(&block) # :yields: nodes
  each_node = method(:tsort_each_node)
  each_child = method(:tsort_each_child)
  Gem::TSort.each_strongly_connected_component(each_node, each_child, &block)
end

#each_strongly_connected_component_from(node, id_map = {}, stack = [], &block) ⇒ Object

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 Gem::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]


386
387
388
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 386

def each_strongly_connected_component_from(node, id_map={}, stack=[], &block) # :yields: nodes
  Gem::TSort.each_strongly_connected_component_from(node, method(:tsort_each_child), id_map, stack, &block)
end

#strongly_connected_componentsObject

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 Gem::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]]


257
258
259
260
261
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 257

def strongly_connected_components
  each_node = method(:tsort_each_node)
  each_child = method(:tsort_each_child)
  Gem::TSort.strongly_connected_components(each_node, each_child)
end

#tsortObject

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, Gem::TSort::Cyclic is raised.

class G
  include Gem::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 Gem::TSort::Cyclic


152
153
154
155
156
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 152

def tsort
  each_node = method(:tsort_each_node)
  each_child = method(:tsort_each_child)
  Gem::TSort.tsort(each_node, each_child)
end

#tsort_each(&block) ⇒ Object

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, Gem::TSort::Cyclic is raised.

class G
  include Gem::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


205
206
207
208
209
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 205

def tsort_each(&block) # :yields: node
  each_node = method(:tsort_each_node)
  each_child = method(:tsort_each_child)
  Gem::TSort.tsort_each(each_node, each_child, &block)
end

#tsort_each_child(node) ⇒ Object

Should be implemented by a extended class.

#tsort_each_child is used to iterate for child nodes of node.

Raises:

  • (NotImplementedError)


452
453
454
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 452

def tsort_each_child(node) # :yields: child
  raise NotImplementedError.new
end

#tsort_each_nodeObject

Should be implemented by a extended class.

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

Raises:

  • (NotImplementedError)


444
445
446
# File 'lib/rubygems/vendor/tsort/lib/tsort.rb', line 444

def tsort_each_node # :yields: node
  raise NotImplementedError.new
end