tsort.rb

# frozen_string_literal: true

#--
# tsort.rb - provides a module for topological sorting and strongly connected components.
#++
#

#
# 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/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/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
#
# 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 Gem
  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, 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
    #
    def tsort
      each_node = method(:tsort_each_node)
      each_child = method(:tsort_each_child)
      Gem::TSort.tsort(each_node, each_child)
    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.
    #
    # 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
    #
    def TSort.tsort(each_node, each_child)
      Gem::TSort.tsort_each(each_node, each_child).to_a
    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, 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
    #
    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

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

      Gem::TSort.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

    # 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]]
    #
    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

    # 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]]
    #
    def TSort.strongly_connected_components(each_node, each_child)
      Gem::TSort.each_strongly_connected_component(each_node, each_child).to_a
    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+.
    #
    #   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]
    #
    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

    # 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]
    #
    def TSort.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
          Gem::TSort.each_strongly_connected_component_from(node, each_child, 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.
    #
    #   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]
    #
    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

    # 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]
    #
    def TSort.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 =
            Gem::TSort.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

    # 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
end