Skip to content
This repository
Fetching contributors…

Octocat-spinner-32-eaf2f5

Cannot retrieve contributors at this time

file 243 lines (230 sloc) 6.958 kb
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242
#--
# 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
Something went wrong with that request. Please try again.