RD -> RDoc contributed by Lyle Johnson

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@ -1,189 +1,150 @@
=begin
= tsort.rb
#!/usr/bin/env ruby
#--
# tsort.rb - provides a module for topological sorting and strongly connected components.
#++
#
tsort.rb provides a module for topological sorting and
strongly connected components.
== Example
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]]
== TSort module
TSort implements topological sorting using Tarjan's algorithm for
strongly connected components.
TSort is designed to be able to use with any object which can be interpreted
as a directed graph.
TSort requires two methods to interpret a 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.
=== methods
--- tsort
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.
--- tsort_each {|node| ...}
is the iterator version of the (({tsort})) method.
(({((|obj|)).tsort_each})) is similar to (({((|obj|)).tsort.each})) but
modification of ((|obj|)) during the iteration may cause unexpected result.
(({tsort_each})) returns (({nil})).
If there is a cycle, (({TSort::Cyclic})) is raised.
--- strongly_connected_components
returns strongly connected components as an array of array of nodes.
The array is sorted from children to parents.
Each elements of the array represents a strongly connected component.
--- each_strongly_connected_component {|nodes| ...}
is 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 cause unexpected result.
(({each_strongly_connected_component})) returns (({nil})).
--- each_strongly_connected_component_from(node) {|nodes| ...}
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})).
--- tsort_each_node {|node| ...}
should be implemented by a extended class.
(({tsort_each_node})) is used to iterate for all nodes over a graph.
--- tsort_each_child(node) {|child| ...}
should be implemented by a extended class.
(({tsort_each_child})) is used to iterate for child nodes of ((|node|)).
== More Realistic Example
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.
#@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
#
# 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",
# <em>SIAM Journal on Computing</em>, 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.
#
def tsort
result = []
tsort_each {|element| result << element}
result
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|
if component.size == 1
yield component.first
@ -193,13 +154,27 @@ module TSort
}
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
result = []
each_strongly_connected_component {|component| result << component}
result
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 = {}
stack = []
tsort_each_node {|node|
@ -212,7 +187,15 @@ module TSort
nil
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
stack_length = stack.length
stack << node
@ -239,11 +222,21 @@ module TSort
minimum_id
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
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
end
end
@ -251,7 +244,7 @@ end
if __FILE__ == $0
require 'test/unit'
class Hash
class Hash # :nodoc:
include TSort
alias tsort_each_node each_key
def tsort_each_child(node, &block)
@ -259,7 +252,7 @@ if __FILE__ == $0
end
end
class Array
class Array # :nodoc:
include TSort
alias tsort_each_node each_index
def tsort_each_child(node, &block)
@ -267,7 +260,7 @@ if __FILE__ == $0
end
end
class TSortTest < Test::Unit::TestCase
class TSortTest < Test::Unit::TestCase # :nodoc:
def test_dag
h = {1=>[2, 3], 2=>[3], 3=>[]}
assert_equal([3, 2, 1], h.tsort)