# frozen_string_literal: true #-- # 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. # # class G # include 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 TSort::Cyclic # def tsort each_node = method(:tsort_each_node) each_child = method(:tsort_each_child) 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, 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 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 TSort.tsort(each_node, each_child) # raises TSort::Cyclic # def TSort.tsort(each_node, each_child) 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, TSort::Cyclic is raised. # # class G # include 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) TSort.tsort_each(each_node, each_child, &block) end # The iterator version of the 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) } # 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? 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 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) 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 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 TSort.strongly_connected_components(each_node, each_child) # #=> [[4], [2, 3], [1]] # def TSort.strongly_connected_components(each_node, each_child) 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 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) TSort.each_strongly_connected_component(each_node, each_child, &block) end # The iterator version of the 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) } # 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) } # 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 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 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 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. # # #TSort.each_strongly_connected_component_from is a class method and # it doesn't need a class to represent a graph which includes TSort. # # graph = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]} # each_child = lambda {|n, &b| graph[n].each(&b) } # 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 = 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