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

:heavy_check_mark: src/graph/tree.cr

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Code

require "../graph"

module Graph(Edge, Edge2)
  private def subtree_size_dfs(v : Int32, p : Int32, a : Array(Int32)) : Int32
    each_child(v, p) do |edge|
      a[v] += subtree_size_dfs(edge.to, v, a)
    end
    a[v] += 1
  end

  def subtree_size(root : Int32) : Array(Int32)
    a = Array.new(size, 0)
    subtree_size_dfs(root, -1, a)
    a
  end

  private def tree_distance_dfs(v : Int32, p : Int32, dist, a) : Nil
    a[v] = dist
    each_child(v, p) do |edge|
      tree_distance_dfs(edge.to, v, dist + edge.cost, a)
    end
  end

  # Returns the distance of each node from *root*.
  def tree_distance(root : Int32)
    a = Array.new(size, typeof(first.cost).zero)
    tree_distance_dfs(root, -1, typeof(first.cost).zero, a)
    a
  end

  # Calculates diameter of the tree and returns `{distance, vertex1, vertex2}`.
  def diameter
    _, v = tree_distance(0).each_with_index.max
    dist, u = tree_distance(v).each_with_index.max
    {dist, v, u}
  end

  private def parent_table_dfs(v : Int32, p : Int32?, a : Array(Int32?)) : Nil
    a[v] = p
    each_child(v, p) do |edge|
      parent_table_dfs(edge.to, v, a)
    end
  end

  def parent_table(root : Int32) : Array(Int32?)
    a = Array(Int32?).new(size, nil)
    parent_table_dfs(root, nil, a)
    a
  end

  def tree_path(start : Int32, goal : Int32, &) : Nil
    parent = parent_table(start)
    yield now = goal
    while now = parent[now]
      yield now
    end
  end

  def tree_path(start : Int32, goal : Int32) : Array(Int32)
    path = [] of Int32
    tree_path { |v| path << v }
    path.reverse
  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

module Graph(Edge, Edge2)
  private def subtree_size_dfs(v : Int32, p : Int32, a : Array(Int32)) : Int32
    each_child(v, p) do |edge|
      a[v] += subtree_size_dfs(edge.to, v, a)
    end
    a[v] += 1
  end

  def subtree_size(root : Int32) : Array(Int32)
    a = Array.new(size, 0)
    subtree_size_dfs(root, -1, a)
    a
  end

  private def tree_distance_dfs(v : Int32, p : Int32, dist, a) : Nil
    a[v] = dist
    each_child(v, p) do |edge|
      tree_distance_dfs(edge.to, v, dist + edge.cost, a)
    end
  end

  # Returns the distance of each node from *root*.
  def tree_distance(root : Int32)
    a = Array.new(size, typeof(first.cost).zero)
    tree_distance_dfs(root, -1, typeof(first.cost).zero, a)
    a
  end

  # Calculates diameter of the tree and returns `{distance, vertex1, vertex2}`.
  def diameter
    _, v = tree_distance(0).each_with_index.max
    dist, u = tree_distance(v).each_with_index.max
    {dist, v, u}
  end

  private def parent_table_dfs(v : Int32, p : Int32?, a : Array(Int32?)) : Nil
    a[v] = p
    each_child(v, p) do |edge|
      parent_table_dfs(edge.to, v, a)
    end
  end

  def parent_table(root : Int32) : Array(Int32?)
    a = Array(Int32?).new(size, nil)
    parent_table_dfs(root, nil, a)
    a
  end

  def tree_path(start : Int32, goal : Int32, &) : Nil
    parent = parent_table(start)
    yield now = goal
    while now = parent[now]
      yield now
    end
  end

  def tree_path(start : Int32, goal : Int32) : Array(Int32)
    path = [] of Int32
    tree_path { |v| path << v }
    path.reverse
  end
end
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