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RD -> RDoc contributed by Lyle Johnson

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git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@4878 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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gsinclair 2003-10-30 22:47:08 +00:00
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lib/tsort.rb
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@ -1,189 +1,150 @@
=begin #!/usr/bin/env ruby
= tsort.rb #--
# tsort.rb - provides a module for topological sorting and strongly connected components.
#++
#
tsort.rb provides a module for topological sorting and #
strongly connected components. # TSort implements topological sorting using Tarjan's algorithm for
# strongly connected components.
== Example #
# TSort is designed to be able to be used with any object which can be interpreted
require 'tsort' # as a directed graph.
# TSort requires two methods to interpret an object as a graph:
class Hash # tsort_each_node and tsort_each_child:
include TSort #
alias tsort_each_node each_key # * tsort_each_node is used to iterate for all nodes over a graph.
def tsort_each_child(node, &block) # * tsort_each_child is used to iterate for child nodes of a given node.
fetch(node).each(&block) #
end # The equality of nodes are defined by eql? and hash since
end # TSort uses Hash internally.
#
{1=>[2, 3], 2=>[3], 3=>[], 4=>[]}.tsort # == A Simple Example
#=> [3, 2, 1, 4] #
# The following example demonstrates how to mix the TSort module into an
{1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}.strongly_connected_components # existing class (in this case, Hash). Here, we're treating each key in
#=> [[4], [2, 3], [1]] # 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
== TSort module # hash, the associated value is an array of the node's child nodes. This
TSort implements topological sorting using Tarjan's algorithm for # choice in turn leads to our implementation of the required #tsort_each_child
strongly connected components. # method, which fetches the array of child nodes and then iterates over that
# array using the user-supplied block.
TSort is designed to be able to use with any object which can be interpreted #
as a directed graph. # require 'tsort'
TSort requires two methods to interpret a object as a graph: #
tsort_each_node and tsort_each_child. # class Hash
# include TSort
* tsort_each_node is used to iterate for all nodes over a graph. # alias tsort_each_node each_key
* tsort_each_child is used to iterate for child nodes of a given node. # def tsort_each_child(node, &block)
# fetch(node).each(&block)
The equality of nodes are defined by eql? and hash since # end
TSort uses Hash internally. # end
#
=== methods # {1=>[2, 3], 2=>[3], 3=>[], 4=>[]}.tsort
--- tsort # #=> [3, 2, 1, 4]
returns a topologically sorted array of nodes. #
The array is sorted from children to parents: # {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}.strongly_connected_components
I.e. the first element has no child and the last node has no parent. # #=> [[4], [2, 3], [1]]
#
If there is a cycle, (({TSort::Cyclic})) is raised. # == A More Realistic Example
#
--- tsort_each {|node| ...} # A very simple `make' like tool can be implemented as follows:
is the iterator version of the (({tsort})) method. #
(({((|obj|)).tsort_each})) is similar to (({((|obj|)).tsort.each})) but # require 'tsort'
modification of ((|obj|)) during the iteration may cause unexpected result. #
# class Make
(({tsort_each})) returns (({nil})). # def initialize
If there is a cycle, (({TSort::Cyclic})) is raised. # @dep = {}
# @dep.default = []
--- strongly_connected_components # end
returns strongly connected components as an array of array of nodes. #
The array is sorted from children to parents. # def rule(outputs, inputs=[], &block)
Each elements of the array represents a strongly connected component. # triple = [outputs, inputs, block]
# outputs.each {|f| @dep[f] = [triple]}
--- each_strongly_connected_component {|nodes| ...} # @dep[triple] = inputs
is the iterator version of the (({strongly_connected_components})) method. # end
(({((|obj|)).each_strongly_connected_component})) is similar to #
(({((|obj|)).strongly_connected_components.each})) but # def build(target)
modification of ((|obj|)) during the iteration may cause unexpected result. # each_strongly_connected_component_from(target) {|ns|
# if ns.length != 1
(({each_strongly_connected_component})) returns (({nil})). # fs = ns.delete_if {|n| Array === n}
# raise TSort::Cyclic.new("cyclic dependencies: #{fs.join ', '}")
--- each_strongly_connected_component_from(node) {|nodes| ...} # end
iterates over strongly connected component in the subgraph reachable from # n = ns.first
((|node|)). # if Array === n
# outputs, inputs, block = n
Return value is unspecified. # inputs_time = inputs.map {|f| File.mtime f}.max
# begin
(({each_strongly_connected_component_from})) doesn't call # outputs_time = outputs.map {|f| File.mtime f}.min
(({tsort_each_node})). # rescue Errno::ENOENT
# outputs_time = nil
--- tsort_each_node {|node| ...} # end
should be implemented by a extended class. # if outputs_time == nil ||
# inputs_time != nil && outputs_time <= inputs_time
(({tsort_each_node})) is used to iterate for all nodes over a graph. # sleep 1 if inputs_time != nil && inputs_time.to_i == Time.now.to_i
# block.call
--- tsort_each_child(node) {|child| ...} # end
should be implemented by a extended class. # end
# }
(({tsort_each_child})) is used to iterate for child nodes of ((|node|)). # end
#
== More Realistic Example # def tsort_each_child(node, &block)
Very simple `make' like tool can be implemented as follows: # @dep[node].each(&block)
# end
require 'tsort' # include TSort
# end
class Make #
def initialize # def command(arg)
@dep = {} # print arg, "\n"
@dep.default = [] # system arg
end # end
#
def rule(outputs, inputs=[], &block) # m = Make.new
triple = [outputs, inputs, block] # m.rule(%w[t1]) { command 'date > t1' }
outputs.each {|f| @dep[f] = [triple]} # m.rule(%w[t2]) { command 'date > t2' }
@dep[triple] = inputs # m.rule(%w[t3]) { command 'date > t3' }
end # m.rule(%w[t4], %w[t1 t3]) { command 'cat t1 t3 > t4' }
# m.rule(%w[t5], %w[t4 t2]) { command 'cat t4 t2 > t5' }
def build(target) # m.build('t5')
each_strongly_connected_component_from(target) {|ns| #
if ns.length != 1 # == Bugs
fs = ns.delete_if {|n| Array === n} #
raise TSort::Cyclic.new("cyclic dependencies: #{fs.join ', '}") # * 'tsort.rb' is wrong name because this library uses
end # Tarjan's algorithm for strongly connected components.
n = ns.first # Although 'strongly_connected_components.rb' is correct but too long.
if Array === n #
outputs, inputs, block = n # == References
inputs_time = inputs.map {|f| File.mtime f}.max #
begin # R. E. Tarjan, "Depth First Search and Linear Graph Algorithms",
outputs_time = outputs.map {|f| File.mtime f}.min # <em>SIAM Journal on Computing</em>, Vol. 1, No. 2, pp. 146-160, June 1972.
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.
#@Article{Tarjan:1972:DFS,
# author = "R. E. Tarjan",
# key = "Tarjan",
# title = "Depth First Search and Linear Graph Algorithms",
# journal = j-SIAM-J-COMPUT,
# volume = "1",
# number = "2",
# pages = "146--160",
# month = jun,
# year = "1972",
# CODEN = "SMJCAT",
# ISSN = "0097-5397 (print), 1095-7111 (electronic)",
# bibdate = "Thu Jan 23 09:56:44 1997",
# bibsource = "Parallel/Multi.bib, Misc/Reverse.eng.bib",
#}
=end
module TSort module TSort
class Cyclic < StandardError class Cyclic < StandardError
end 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.
#
def tsort def tsort
result = [] result = []
tsort_each {|element| result << element} tsort_each {|element| result << element}
result result
end end
def tsort_each #
# The iterator version of the #tsort method.
# <tt><em>obj</em>.tsort_each</tt> is similar to <tt><em>obj</em>.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.
#
def tsort_each # :yields: node
each_strongly_connected_component {|component| each_strongly_connected_component {|component|
if component.size == 1 if component.size == 1
yield component.first yield component.first
@ -193,13 +154,27 @@ module TSort
} }
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.
#
def strongly_connected_components def strongly_connected_components
result = [] result = []
each_strongly_connected_component {|component| result << component} each_strongly_connected_component {|component| result << component}
result result
end end
def each_strongly_connected_component #
# The iterator version of the #strongly_connected_components method.
# <tt><em>obj</em>.each_strongly_connected_component</tt> is similar to
# <tt><em>obj</em>.strongly_connected_components.each</tt>, but
# modification of _obj_ during the iteration may lead to unexpected results.
#
#
# #each_strongly_connected_component returns +nil+.
#
def each_strongly_connected_component # :yields: nodes
id_map = {} id_map = {}
stack = [] stack = []
tsort_each_node {|node| tsort_each_node {|node|
@ -212,7 +187,15 @@ module TSort
nil nil
end end
def each_strongly_connected_component_from(node, id_map={}, stack=[]) #
# 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.
#
def each_strongly_connected_component_from(node, id_map={}, stack=[]) # :yields: nodes
minimum_id = node_id = id_map[node] = id_map.size minimum_id = node_id = id_map[node] = id_map.size
stack_length = stack.length stack_length = stack.length
stack << node stack << node
@ -239,11 +222,21 @@ module TSort
minimum_id minimum_id
end end
def tsort_each_node #
# 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 raise NotImplementedError.new
end end
def tsort_each_child(node) #
# 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 raise NotImplementedError.new
end end
end end
@ -251,7 +244,7 @@ end
if __FILE__ == $0 if __FILE__ == $0
require 'test/unit' require 'test/unit'
class Hash class Hash # :nodoc:
include TSort include TSort
alias tsort_each_node each_key alias tsort_each_node each_key
def tsort_each_child(node, &block) def tsort_each_child(node, &block)
@ -259,7 +252,7 @@ if __FILE__ == $0
end end
end end
class Array class Array # :nodoc:
include TSort include TSort
alias tsort_each_node each_index alias tsort_each_node each_index
def tsort_each_child(node, &block) def tsort_each_child(node, &block)
@ -267,7 +260,7 @@ if __FILE__ == $0
end end
end end
class TSortTest < Test::Unit::TestCase class TSortTest < Test::Unit::TestCase # :nodoc:
def test_dag def test_dag
h = {1=>[2, 3], 2=>[3], 3=>[]} h = {1=>[2, 3], 2=>[3], 3=>[]}
assert_equal([3, 2, 1], h.tsort) assert_equal([3, 2, 1], h.tsort)