This documentation is automatically generated by online-judge-tools/verification-helper

:heavy_check_mark: src/graph/scc.cr

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Verified with

Code

require "../graph"

class SCC(Edge, Edge2)
  private def dfs(v : Int32) : Nil
    @visited[v] = true
    @graph[v].each do |edge|
      dfs(edge.to) if !@visited[edge.to]
    end
    @topological_order << v
  end

  private def dfs_reverse(v : Int32) : Nil
    @visited[v] = true
    @ids[v] = @now_id
    @rgraph[v].each do |edge|
      dfs_reverse(edge.to) if !@visited[edge.to]
    end
  end

  getter graph
  @rgraph : Graph(Edge, Edge2)

  delegate size, to: @graph

  def initialize(@graph : Graph(Edge, Edge2))
    @rgraph = @graph.reverse
    @topological_order = [] of Int32
    @visited = Array(Bool).new(size, false)
    @ids = Array(Int32).new(size, -1)
    @now_id = 0

    size.times do |v|
      dfs(v) if !@visited[v]
    end
    @visited.fill(false)
    @topological_order.reverse_each do |v|
      if !@visited[v]
        dfs_reverse(v)
        @now_id += 1
      end
    end
  end

  def count_scc : Int32
    @now_id
  end

  def groups : Array(Set(Int32))
    groups = Array.new(count_scc) { Set(Int32).new }
    size.times do |i|
      groups[@ids[i]] << i
    end
    groups
  end

  def dag : UnweightedDiGraph
    edges = Set({Int32, Int32}).new
    @graph.each do |edge|
      from, to = @ids[edge.from], @ids[edge.to]
      edges << {from, to} if from != to
    end
    UnweightedDiGraph.new count_scc, edges
  end

  def scc : {Int32, Array(Set(Int32)), UnweightedDiGraph}
    {count_scc, groups, dag}
  end
end
# require "../graph"
# require "./graph/edge"
struct WeightedEdge(T)
  include Comparable(WeightedEdge(T))

  property to : Int32, cost : T

  def initialize(@to, @cost : T)
  end

  def <=>(other : WeightedEdge(T))
    {cost, to} <=> {other.cost, other.to}
  end

  def to_s(io) : Nil
    io << '(' << to << ", " << cost << ')'
  end

  def inspect(io) : Nil
    io << "->" << to << '(' << cost << ')'
  end
end

struct WeightedEdge2(T)
  include Comparable(WeightedEdge2(T))

  property from : Int32, to : Int32, cost : T

  def initialize(@from, @to, @cost : T)
  end

  def initialize(@from, edge : WeightedEdge(T))
    @to, @cost = edge.to, edge.cost
  end

  def <=>(other : WeightedEdge2(T))
    {cost, from, to} <=> {other.cost, other.from, other.to}
  end

  def reverse : self
    WeightedEdge2(T).new(to, from, cost)
  end

  def sort : self
    WeightedEdge2(T).new(*{to, from}.minmax, cost)
  end

  def to_s(io) : Nil
    io << '(' << from << ", " << to << ", " << cost << ')'
  end

  def inspect(io) : Nil
    io << from << "->" << to << '(' << cost << ')'
  end
end

struct UnweightedEdge
  property to : Int32

  def initialize(@to)
  end

  def initialize(@to, cost)
  end

  def cost : Int32
    1
  end

  def to_s(io) : Nil
    io << to
  end

  def inspect(io) : Nil
    io << "->" << to
  end
end

struct UnweightedEdge2
  property from : Int32, to : Int32

  def initialize(@from, @to)
  end

  def initialize(@from, @to, cost)
  end

  def initialize(@from, edge : UnweightedEdge)
    @to = edge.to
  end

  def cost : Int32
    1
  end

  def reverse : self
    UnweightedEdge2.new(to, from)
  end

  def sort : self
    UnweightedEdge2.new(*{to, from}.minmax)
  end

  def to_s(io) : Nil
    io << '(' << from << ", " << to << ')'
  end

  def inspect(io) : Nil
    io << from << "->" << to
  end
end

module Graph(Edge, Edge2)
  include Enumerable(Edge2)

  getter graph : Array(Array(Edge))

  def initialize(size : Int)
    @graph = Array(Array(Edge)).new(size) { [] of Edge }
  end

  def initialize(size : Int, edges : Enumerable)
    initialize(size)
    add_edges(edges)
  end

  # Add *edge*.
  abstract def <<(edge : Edge2)

  # :ditto:
  def <<(edge : Tuple) : self
    self << Edge2.new(*edge)
  end

  def add_edges(edges : Enumerable) : self
    edges.each { |edge| self << edge }
    self
  end

  delegate size, :[], to: @graph

  # Yields each edge of the graph, ans returns `nil`.
  def each(&) : Nil
    (0...size).each do |v|
      graph[v].each do |edge|
        yield Edge2.new(v, edge)
      end
    end
  end

  def each_child(vertex : Int, parent, &block) : Nil
    graph[vertex].each do |edge|
      yield edge if edge.to != parent
    end
  end

  def each_child(vertex : Int, parent)
    graph[vertex].each.reject(&.to.== parent)
  end

  def reverse : self
    if self.class.directed?
      each_with_object(self.class.new(size)) do |edge, reversed|
        reversed << edge.reverse
      end
    else
      dup
    end
  end

  def to_undirected : self
    if self.class.directed?
      each_with_object(self.class.new(size)) do |edge, graph|
        graph << edge << edge.reverse
      end
    else
      dup
    end
  end

  def to_s(io : IO) : Nil
    io << '['
    join(", ", io) do |edge, io|
      edge.inspect io
    end
    io << ']'
  end

  def inspect(io : IO) : Nil
    io << "[\n"
    graph.each do |edges|
      io << "  " << edges << ",\n"
    end
    io << ']'
  end
end

class DiGraph(T)
  include Graph(WeightedEdge(T), WeightedEdge2(T))

  def self.weighted?
    true
  end

  def self.directed?
    true
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable(WeightedEdge2(T)))
    super
  end

  def initialize(size : Int, edges : Enumerable({Int32, Int32, T}))
    super
  end

  def <<(edge : WeightedEdge2(T)) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << WeightedEdge.new(edge.to, edge.cost)
    self
  end
end

class UnGraph(T)
  include Graph(WeightedEdge(T), WeightedEdge2(T))

  def self.weighted?
    true
  end

  def self.directed?
    false
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable(WeightedEdge2(T)))
    super
  end

  def initialize(size : Int, edges : Enumerable({Int32, Int32, T}))
    super
  end

  def <<(edge : WeightedEdge2(T)) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << WeightedEdge.new(edge.to, edge.cost)
    @graph[edge.to] << WeightedEdge.new(edge.from, edge.cost)
    self
  end
end

class UnweightedDiGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def self.weighted?
    false
  end

  def self.directed?
    true
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable)
    super
  end

  def <<(edge : UnweightedEdge2) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << UnweightedEdge.new(edge.to)
    self
  end
end

class UnweightedUnGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def self.weighted?
    false
  end

  def self.directed?
    false
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable)
    super
  end

  def <<(edge : UnweightedEdge2) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << UnweightedEdge.new(edge.to)
    @graph[edge.to] << UnweightedEdge.new(edge.from)
    self
  end
end

class SCC(Edge, Edge2)
  private def dfs(v : Int32) : Nil
    @visited[v] = true
    @graph[v].each do |edge|
      dfs(edge.to) if !@visited[edge.to]
    end
    @topological_order << v
  end

  private def dfs_reverse(v : Int32) : Nil
    @visited[v] = true
    @ids[v] = @now_id
    @rgraph[v].each do |edge|
      dfs_reverse(edge.to) if !@visited[edge.to]
    end
  end

  getter graph
  @rgraph : Graph(Edge, Edge2)

  delegate size, to: @graph

  def initialize(@graph : Graph(Edge, Edge2))
    @rgraph = @graph.reverse
    @topological_order = [] of Int32
    @visited = Array(Bool).new(size, false)
    @ids = Array(Int32).new(size, -1)
    @now_id = 0

    size.times do |v|
      dfs(v) if !@visited[v]
    end
    @visited.fill(false)
    @topological_order.reverse_each do |v|
      if !@visited[v]
        dfs_reverse(v)
        @now_id += 1
      end
    end
  end

  def count_scc : Int32
    @now_id
  end

  def groups : Array(Set(Int32))
    groups = Array.new(count_scc) { Set(Int32).new }
    size.times do |i|
      groups[@ids[i]] << i
    end
    groups
  end

  def dag : UnweightedDiGraph
    edges = Set({Int32, Int32}).new
    @graph.each do |edge|
      from, to = @ids[edge.from], @ids[edge.to]
      edges << {from, to} if from != to
    end
    UnweightedDiGraph.new count_scc, edges
  end

  def scc : {Int32, Array(Set(Int32)), UnweightedDiGraph}
    {count_scc, groups, dag}
  end
end
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