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Added tsort.rb from 1.9.2p290.

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1 parent 914caa1 commit d7ae495d4d2762f9dda49181da01b54cb7897b6c @brixen brixen committed Nov 7, 2011
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+#--
+# tsort.rb - provides a module for topological sorting and strongly connected components.
+#++
+#
+
+#
+# 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
+
+ #
+ # 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
+ else
+ raise Cyclic.new("topological sort failed: #{component.inspect}")
+ 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
+ result = []
+ each_strongly_connected_component {|component| result << component}
+ result
+ end
+
+ #
+ # 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|
+ 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.
+ #
+ 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
+
+ #
+ # 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
+
+ #
+ # 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

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