453 lines
14 KiB
Ruby
453 lines
14 KiB
Ruby
# frozen_string_literal: true
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#--
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# tsort.rb - provides a module for topological sorting and strongly connected components.
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#++
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#
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#
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# TSort implements topological sorting using Tarjan's algorithm for
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# strongly connected components.
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#
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# TSort is designed to be able to be used with any object which can be
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# interpreted as a directed graph.
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#
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# TSort requires two methods to interpret an object as a graph,
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# tsort_each_node and tsort_each_child.
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#
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# * tsort_each_node is used to iterate for all nodes over a graph.
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# * tsort_each_child is used to iterate for child nodes of a given node.
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#
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# The equality of nodes are defined by eql? and hash since
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# TSort uses Hash internally.
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#
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# == A Simple Example
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#
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# The following example demonstrates how to mix the TSort module into an
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# existing class (in this case, Hash). Here, we're treating each key in
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# the hash as a node in the graph, and so we simply alias the required
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# #tsort_each_node method to Hash's #each_key method. For each key in the
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# hash, the associated value is an array of the node's child nodes. This
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# choice in turn leads to our implementation of the required #tsort_each_child
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# method, which fetches the array of child nodes and then iterates over that
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# array using the user-supplied block.
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#
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# require 'tsort'
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#
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# class Hash
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# include TSort
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# alias tsort_each_node each_key
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# def tsort_each_child(node, &block)
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# fetch(node).each(&block)
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# end
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# end
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#
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# {1=>[2, 3], 2=>[3], 3=>[], 4=>[]}.tsort
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# #=> [3, 2, 1, 4]
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#
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# {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}.strongly_connected_components
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# #=> [[4], [2, 3], [1]]
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#
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# == A More Realistic Example
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#
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# A very simple `make' like tool can be implemented as follows:
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#
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# require 'tsort'
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#
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# class Make
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# def initialize
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# @dep = {}
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# @dep.default = []
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# end
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#
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# def rule(outputs, inputs=[], &block)
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# triple = [outputs, inputs, block]
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# outputs.each {|f| @dep[f] = [triple]}
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# @dep[triple] = inputs
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# end
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#
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# def build(target)
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# each_strongly_connected_component_from(target) {|ns|
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# if ns.length != 1
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# fs = ns.delete_if {|n| Array === n}
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# raise TSort::Cyclic.new("cyclic dependencies: #{fs.join ', '}")
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# end
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# n = ns.first
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# if Array === n
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# outputs, inputs, block = n
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# inputs_time = inputs.map {|f| File.mtime f}.max
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# begin
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# outputs_time = outputs.map {|f| File.mtime f}.min
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# rescue Errno::ENOENT
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# outputs_time = nil
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# end
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# if outputs_time == nil ||
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# inputs_time != nil && outputs_time <= inputs_time
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# sleep 1 if inputs_time != nil && inputs_time.to_i == Time.now.to_i
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# block.call
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# end
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# end
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# }
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# end
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#
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# def tsort_each_child(node, &block)
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# @dep[node].each(&block)
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# end
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# include TSort
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# end
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#
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# def command(arg)
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# print arg, "\n"
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# system arg
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# end
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#
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# m = Make.new
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# m.rule(%w[t1]) { command 'date > t1' }
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# m.rule(%w[t2]) { command 'date > t2' }
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# m.rule(%w[t3]) { command 'date > t3' }
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# m.rule(%w[t4], %w[t1 t3]) { command 'cat t1 t3 > t4' }
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# m.rule(%w[t5], %w[t4 t2]) { command 'cat t4 t2 > t5' }
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# m.build('t5')
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#
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# == Bugs
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#
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# * 'tsort.rb' is wrong name because this library uses
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# Tarjan's algorithm for strongly connected components.
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# Although 'strongly_connected_components.rb' is correct but too long.
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#
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# == References
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#
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# R. E. Tarjan, "Depth First Search and Linear Graph Algorithms",
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# <em>SIAM Journal on Computing</em>, Vol. 1, No. 2, pp. 146-160, June 1972.
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#
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module TSort
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class Cyclic < StandardError
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end
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# Returns a topologically sorted array of nodes.
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# The array is sorted from children to parents, i.e.
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# the first element has no child and the last node has no parent.
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#
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# If there is a cycle, TSort::Cyclic is raised.
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#
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# class G
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# include TSort
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# def initialize(g)
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# @g = g
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# end
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# def tsort_each_child(n, &b) @g[n].each(&b) end
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# def tsort_each_node(&b) @g.each_key(&b) end
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# end
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#
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# graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
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# p graph.tsort #=> [4, 2, 3, 1]
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#
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# graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
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# p graph.tsort # raises TSort::Cyclic
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#
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def tsort
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each_node = method(:tsort_each_node)
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each_child = method(:tsort_each_child)
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TSort.tsort(each_node, each_child)
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end
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# Returns a topologically sorted array of nodes.
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# The array is sorted from children to parents, i.e.
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# the first element has no child and the last node has no parent.
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#
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# The graph is represented by _each_node_ and _each_child_.
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# _each_node_ should have +call+ method which yields for each node in the graph.
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# _each_child_ should have +call+ method which takes a node argument and yields for each child node.
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#
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# If there is a cycle, TSort::Cyclic is raised.
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#
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# g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# p TSort.tsort(each_node, each_child) #=> [4, 2, 3, 1]
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#
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# g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# p TSort.tsort(each_node, each_child) # raises TSort::Cyclic
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#
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def self.tsort(each_node, each_child)
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tsort_each(each_node, each_child).to_a
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end
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# The iterator version of the #tsort method.
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# <tt><em>obj</em>.tsort_each</tt> is similar to <tt><em>obj</em>.tsort.each</tt>, but
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# modification of _obj_ during the iteration may lead to unexpected results.
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#
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# #tsort_each returns +nil+.
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# If there is a cycle, TSort::Cyclic is raised.
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#
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# class G
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# include TSort
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# def initialize(g)
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# @g = g
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# end
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# def tsort_each_child(n, &b) @g[n].each(&b) end
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# def tsort_each_node(&b) @g.each_key(&b) end
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# end
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#
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# graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
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# graph.tsort_each {|n| p n }
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# #=> 4
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# # 2
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# # 3
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# # 1
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#
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def tsort_each(&block) # :yields: node
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each_node = method(:tsort_each_node)
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each_child = method(:tsort_each_child)
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TSort.tsort_each(each_node, each_child, &block)
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end
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# The iterator version of the TSort.tsort method.
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#
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# The graph is represented by _each_node_ and _each_child_.
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# _each_node_ should have +call+ method which yields for each node in the graph.
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# _each_child_ should have +call+ method which takes a node argument and yields for each child node.
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#
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# g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# TSort.tsort_each(each_node, each_child) {|n| p n }
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# #=> 4
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# # 2
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# # 3
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# # 1
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#
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def self.tsort_each(each_node, each_child) # :yields: node
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return to_enum(__method__, each_node, each_child) unless block_given?
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each_strongly_connected_component(each_node, each_child) {|component|
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if component.size == 1
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yield component.first
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else
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raise Cyclic.new("topological sort failed: #{component.inspect}")
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end
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}
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end
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# Returns strongly connected components as an array of arrays of nodes.
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# The array is sorted from children to parents.
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# Each elements of the array represents a strongly connected component.
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#
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# class G
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# include TSort
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# def initialize(g)
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# @g = g
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# end
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# def tsort_each_child(n, &b) @g[n].each(&b) end
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# def tsort_each_node(&b) @g.each_key(&b) end
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# end
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#
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# graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
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# p graph.strongly_connected_components #=> [[4], [2], [3], [1]]
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#
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# graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
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# p graph.strongly_connected_components #=> [[4], [2, 3], [1]]
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#
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def strongly_connected_components
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each_node = method(:tsort_each_node)
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each_child = method(:tsort_each_child)
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TSort.strongly_connected_components(each_node, each_child)
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end
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# Returns strongly connected components as an array of arrays of nodes.
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# The array is sorted from children to parents.
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# Each elements of the array represents a strongly connected component.
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#
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# The graph is represented by _each_node_ and _each_child_.
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# _each_node_ should have +call+ method which yields for each node in the graph.
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# _each_child_ should have +call+ method which takes a node argument and yields for each child node.
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#
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# g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# p TSort.strongly_connected_components(each_node, each_child)
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# #=> [[4], [2], [3], [1]]
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#
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# g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# p TSort.strongly_connected_components(each_node, each_child)
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# #=> [[4], [2, 3], [1]]
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#
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def self.strongly_connected_components(each_node, each_child)
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each_strongly_connected_component(each_node, each_child).to_a
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end
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# The iterator version of the #strongly_connected_components method.
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# <tt><em>obj</em>.each_strongly_connected_component</tt> is similar to
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# <tt><em>obj</em>.strongly_connected_components.each</tt>, but
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# modification of _obj_ during the iteration may lead to unexpected results.
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#
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# #each_strongly_connected_component returns +nil+.
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#
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# class G
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# include TSort
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# def initialize(g)
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# @g = g
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# end
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# def tsort_each_child(n, &b) @g[n].each(&b) end
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# def tsort_each_node(&b) @g.each_key(&b) end
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# end
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#
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# graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
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# graph.each_strongly_connected_component {|scc| p scc }
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# #=> [4]
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# # [2]
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# # [3]
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# # [1]
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#
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# graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
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# graph.each_strongly_connected_component {|scc| p scc }
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# #=> [4]
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# # [2, 3]
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# # [1]
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#
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def each_strongly_connected_component(&block) # :yields: nodes
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each_node = method(:tsort_each_node)
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each_child = method(:tsort_each_child)
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TSort.each_strongly_connected_component(each_node, each_child, &block)
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end
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# The iterator version of the TSort.strongly_connected_components method.
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#
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# The graph is represented by _each_node_ and _each_child_.
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# _each_node_ should have +call+ method which yields for each node in the graph.
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# _each_child_ should have +call+ method which takes a node argument and yields for each child node.
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#
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# g = {1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# TSort.each_strongly_connected_component(each_node, each_child) {|scc| p scc }
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# #=> [4]
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# # [2]
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# # [3]
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# # [1]
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#
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# g = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
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# each_node = lambda {|&b| g.each_key(&b) }
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# each_child = lambda {|n, &b| g[n].each(&b) }
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# TSort.each_strongly_connected_component(each_node, each_child) {|scc| p scc }
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# #=> [4]
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# # [2, 3]
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# # [1]
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#
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def self.each_strongly_connected_component(each_node, each_child) # :yields: nodes
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return to_enum(__method__, each_node, each_child) unless block_given?
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id_map = {}
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stack = []
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each_node.call {|node|
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unless id_map.include? node
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each_strongly_connected_component_from(node, each_child, id_map, stack) {|c|
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yield c
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}
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end
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}
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nil
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end
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# Iterates over strongly connected component in the subgraph reachable from
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# _node_.
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#
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# Return value is unspecified.
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#
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# #each_strongly_connected_component_from doesn't call #tsort_each_node.
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#
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# class G
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# include TSort
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# def initialize(g)
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# @g = g
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# end
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# def tsort_each_child(n, &b) @g[n].each(&b) end
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# def tsort_each_node(&b) @g.each_key(&b) end
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# end
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#
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# graph = G.new({1=>[2, 3], 2=>[4], 3=>[2, 4], 4=>[]})
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# graph.each_strongly_connected_component_from(2) {|scc| p scc }
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# #=> [4]
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# # [2]
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#
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# graph = G.new({1=>[2], 2=>[3, 4], 3=>[2], 4=>[]})
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# graph.each_strongly_connected_component_from(2) {|scc| p scc }
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# #=> [4]
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# # [2, 3]
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#
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def each_strongly_connected_component_from(node, id_map={}, stack=[], &block) # :yields: nodes
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TSort.each_strongly_connected_component_from(node, method(:tsort_each_child), id_map, stack, &block)
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end
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# Iterates over strongly connected components in a graph.
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# The graph is represented by _node_ and _each_child_.
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#
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# _node_ is the first node.
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# _each_child_ should have +call+ method which takes a node argument
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# and yields for each child node.
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#
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# Return value is unspecified.
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#
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# #TSort.each_strongly_connected_component_from is a class method and
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# it doesn't need a class to represent a graph which includes TSort.
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#
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# graph = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
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# each_child = lambda {|n, &b| graph[n].each(&b) }
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# TSort.each_strongly_connected_component_from(1, each_child) {|scc|
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# p scc
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# }
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# #=> [4]
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# # [2, 3]
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# # [1]
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#
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def self.each_strongly_connected_component_from(node, each_child, id_map={}, stack=[]) # :yields: nodes
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return to_enum(__method__, node, each_child, id_map, stack) unless block_given?
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minimum_id = node_id = id_map[node] = id_map.size
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stack_length = stack.length
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stack << node
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each_child.call(node) {|child|
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if id_map.include? child
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child_id = id_map[child]
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minimum_id = child_id if child_id && child_id < minimum_id
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else
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sub_minimum_id =
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each_strongly_connected_component_from(child, each_child, id_map, stack) {|c|
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yield c
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}
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minimum_id = sub_minimum_id if sub_minimum_id < minimum_id
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end
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}
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if node_id == minimum_id
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component = stack.slice!(stack_length .. -1)
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component.each {|n| id_map[n] = nil}
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yield component
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end
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minimum_id
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end
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# Should be implemented by a extended class.
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#
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# #tsort_each_node is used to iterate for all nodes over a graph.
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#
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def tsort_each_node # :yields: node
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raise NotImplementedError.new
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end
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# Should be implemented by a extended class.
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#
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# #tsort_each_child is used to iterate for child nodes of _node_.
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#
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def tsort_each_child(node) # :yields: child
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raise NotImplementedError.new
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end
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end
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