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# 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
#
#     1.  Tarjan, "Depth First Search and Linear Graph Algorithms",
#
#
# *SIAM Journal on Computing*, Vol. 1, No. 2, pp. 146-160, June 1972.
module TSort[Node] : TSort::_Sortable[Node]
  # 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 self.each_strongly_connected_component: [T] (_EachNode[T] each_node, _EachChild[T] each_child) { (Array[T]) -> void } -> void
                                            | [T] (_EachNode[T] each_node, _EachChild[T] each_child) -> Enumerator[Array[T], void]
                                            | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) { (Array[T]) -> void } -> void
                                            | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) -> Enumerator[Array[T], void]

  # 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 self.each_strongly_connected_component_from: [T] (T node, _EachChild[T] each_child, ?untyped id_map, ?untyped stack) { (Array[T]) -> void } -> void
                                                 | [T] (T node, _EachChild[T] each_child, ?untyped id_map, ?untyped stack) -> Enumerator[Array[T], void]
                                                 | [T] (T node, ^(T) { (T) -> void } -> void each_child, ?untyped id_map, ?untyped stack) { (Array[T]) -> void } -> void
                                                 | [T] (T node, ^(T) { (T) -> void } -> void each_child, ?untyped id_map, ?untyped stack) -> Enumerator[Array[T], void]

  # 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 self.strongly_connected_components: [T] (_EachNode[T] each_node, _EachChild[T] each_child) -> Array[Array[T]]
                                        | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) -> Array[Array[T]]

  # 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 self.tsort: [T] (_EachNode[T] each_node, _EachChild[T] each_child) -> Array[T]
                | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) -> Array[T]

  # 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 self.tsort_each: [T] (_EachNode[T] each_node, _EachChild[T] each_child) { (T) -> void } -> void
                     | [T] (_EachNode[T] each_node, _EachChild[T] each_child) -> Enumerator[T, void]
                     | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) { (T) -> void } -> void
                     | [T] (^() { (T) -> void } -> void each_node, ^(T) { (T) -> void } -> void each_child) -> Enumerator[T, void]

  # The iterator version of the #strongly_connected_components method.
  # *`obj*.each_strongly_connected_component` is similar to
  # *`obj*.strongly_connected_components.each`, 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: () { (Array[Node]) -> void } -> void
                                       | () -> Enumerator[Array[Node], void]

  # 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, ?untyped id_map, ?untyped stack) { (Array[Node]) -> void } -> void
                                            | (Node, ?untyped id_map, ?untyped stack) -> Enumerator[Array[Node], void]

  # 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: () -> Array[Array[Node]]

  # 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: () -> Array[Node]

  # The iterator version of the #tsort method. *`obj*.tsort_each` is similar to
  # *`obj*.tsort.each`, 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: () { (Node) -> void } -> void
                | () -> Enumerator[Node, void]
end