ruby--ruby/lib/set.rb

# frozen_string_literal: true
# :markup: markdown
#
# set.rb - defines the Set class
#
# Copyright (c) 2002-2020 Akinori MUSHA <knu@iDaemons.org>
#
# Documentation by Akinori MUSHA and Gavin Sinclair.
#
# All rights reserved.  You can redistribute and/or modify it under the same
# terms as Ruby.


##
# This library provides the Set class, which deals with a collection
# of unordered values with no duplicates.  It is a hybrid of Array's
# intuitive inter-operation facilities and Hash's fast lookup.
#
# The method `to_set` is added to Enumerable for convenience.
#
# Set implements a collection of unordered values with no duplicates.
# This is a hybrid of Array's intuitive inter-operation facilities and
# Hash's fast lookup.
#
# Set is easy to use with Enumerable objects (implementing `each`).
# Most of the initializer methods and binary operators accept generic
# Enumerable objects besides sets and arrays.  An Enumerable object
# can be converted to Set using the `to_set` method.
#
# Set uses Hash as storage, so you must note the following points:
#
# * Equality of elements is determined according to Object#eql? and
#   Object#hash.  Use Set#compare_by_identity to make a set compare
#   its elements by their identity.
# * Set assumes that the identity of each element does not change
#   while it is stored.  Modifying an element of a set will render the
#   set to an unreliable state.
# * When a string is to be stored, a frozen copy of the string is
#   stored instead unless the original string is already frozen.
#
# ## Comparison
#
# The comparison operators `<`, `>`, `<=`, and `>=` are implemented as
# shorthand for the {proper_,}{subset?,superset?} methods.  The `<=>`
# operator reflects this order, or return `nil` for sets that both
# have distinct elements (`{x, y}` vs. `{x, z}` for example).
#
# ## Example
#
# ```ruby
# require 'set'
# s1 = Set[1, 2]                        #=> #<Set: {1, 2}>
# s2 = [1, 2].to_set                    #=> #<Set: {1, 2}>
# s1 == s2                              #=> true
# s1.add("foo")                         #=> #<Set: {1, 2, "foo"}>
# s1.merge([2, 6])                      #=> #<Set: {1, 2, "foo", 6}>
# s1.subset?(s2)                        #=> false
# s2.subset?(s1)                        #=> true
# ```
#
# ## Contact
#
# - Akinori MUSHA <<knu@iDaemons.org>> (current maintainer)
#
# ## What's Here
#
#  First, what's elsewhere. \Class \Set:
#
# - Inherits from {class Object}[https://docs.ruby-lang.org/en/master/Object.html#class-Object-label-What-27s+Here].
# - Includes {module Enumerable}[https://docs.ruby-lang.org/en/master/Enumerable.html#module-Enumerable-label-What-27s+Here],
#   which provides dozens of additional methods.
#
# In particular, class \Set does not have many methods of its own
# for fetching or for iterating.
# Instead, it relies on those in \Enumerable.
#
# Here, class \Set provides methods that are useful for:
#
# - [Creating a Set](#class-Set-label-Methods+for+Creating+a+Set)
# - [Set Operations](#class-Set-label-Methods+for+Set+Operations)
# - [Comparing](#class-Set-label-Methods+for+Comparing)
# - [Querying](#class-Set-label-Methods+for+Querying)
# - [Assigning](#class-Set-label-Methods+for+Assigning)
# - [Deleting](#class-Set-label-Methods+for+Deleting)
# - [Converting](#class-Set-label-Methods+for+Converting)
# - [Iterating](#class-Set-label-Methods+for+Iterating)
# - [And more....](#class-Set-label-Other+Methods)
#
# ### Methods for Creating a \Set
#
# - ::[]:
#   Returns a new set containing the given objects.
# - ::new:
#   Returns a new set containing either the given objects
#   (if no block given) or the return values from the called block
#   (if a block given).
#
# ### Methods for \Set Operations
#
# - [|](#method-i-7C) (aliased as #union and #+):
#   Returns a new set containing all elements from +self+
#   and all elements from a given enumerable (no duplicates).
# - [&](#method-i-26) (aliased as #intersection):
#   Returns a new set containing all elements common to +self+
#   and a given enumerable.
# - [-](#method-i-2D) (aliased as #difference):
#   Returns a copy of +self+ with all elements
#   in a given enumerable removed.
# - [\^](#method-i-5E):
#   Returns a new set containing all elements from +self+
#   and a given enumerable except those common to both.
#
# ### Methods for Comparing
#
# - [<=>](#method-i-3C-3D-3E):
#   Returns -1, 0, or 1 as +self+ is less than, equal to,
#   or greater than a given object.
# - [==](#method-i-3D-3D):
#   Returns whether +self+ and a given enumerable are equal,
#   as determined by Object#eql?.
# - \#compare_by_identity?:
#   Returns whether the set considers only identity
#   when comparing elements.
#
# ### Methods for Querying
#
# - \#length (aliased as #size):
#   Returns the count of elements.
# - \#empty?:
#   Returns whether the set has no elements.
# - \#include? (aliased as #member? and #===):
#   Returns whether a given object is an element in the set.
# - \#subset? (aliased as [<=](#method-i-3C-3D)):
#   Returns whether a given object is a subset of the set.
# - \#proper_subset? (aliased as [<](#method-i-3C)):
#   Returns whether a given enumerable is a proper subset of the set.
# - \#superset? (aliased as [<=](#method-i-3E-3D])):
#   Returns whether a given enumerable is a superset of the set.
# - \#proper_superset? (aliased as [>](#method-i-3E)):
#   Returns whether a given enumerable is a proper superset of the set.
# - \#disjoint?:
#   Returns +true+ if the set and a given enumerable
#   have no common elements, +false+ otherwise.
# - \#intersect?:
#   Returns +true+ if the set and a given enumerable:
#   have any common elements, +false+ otherwise.
# - \#compare_by_identity?:
#   Returns whether the set considers only identity
#   when comparing elements.
#
# ### Methods for Assigning
#
# - \#add (aliased as #<<):
#   Adds a given object to the set; returns +self+.
# - \#add?:
#   If the given object is not an element in the set,
#   adds it and returns +self+; otherwise, returns +nil+.
# - \#merge:
#   Adds each given object to the set; returns +self+.
# - \#replace:
#   Replaces the contents of the set with the contents
#   of a given enumerable.
#
# ### Methods for Deleting
#
# - \#clear:
#   Removes all elements in the set; returns +self+.
# - \#delete:
#   Removes a given object from the set; returns +self+.
# - \#delete?:
#   If the given object is an element in the set,
#   removes it and returns +self+; otherwise, returns +nil+.
# - \#subtract:
#   Removes each given object from the set; returns +self+.
# - \#delete_if - Removes elements specified by a given block.
# - \#select! (aliased as #filter!):
#   Removes elements not specified by a given block.
# - \#keep_if:
#   Removes elements not specified by a given block.
# - \#reject!
#   Removes elements specified by a given block.
#
# ### Methods for Converting
#
# - \#classify:
#   Returns a hash that classifies the elements,
#   as determined by the given block.
# - \#collect! (aliased as #map!):
#   Replaces each element with a block return-value.
# - \#divide:
#   Returns a hash that classifies the elements,
#   as determined by the given block;
#   differs from #classify in that the block may accept
#   either one or two arguments.
# - \#flatten:
#   Returns a new set that is a recursive flattening of +self+.
#  \#flatten!:
#   Replaces each nested set in +self+ with the elements from that set.
# - \#inspect (aliased as #to_s):
#   Returns a string displaying the elements.
# - \#join:
#   Returns a string containing all elements, converted to strings
#   as needed, and joined by the given record separator.
# - \#to_a:
#   Returns an array containing all set elements.
# - \#to_set:
#   Returns +self+ if given no arguments and no block;
#   with a block given, returns a new set consisting of block
#   return values.
#
# ### Methods for Iterating
#
# - \#each:
#   Calls the block with each successive element; returns +self+.
#
# ### Other Methods
#
# - \#reset:
#   Resets the internal state; useful if an object
#   has been modified while an element in the set.
#
class Set
  include Enumerable

  # Creates a new set containing the given objects.
  #
  #     Set[1, 2]                   # => #<Set: {1, 2}>
  #     Set[1, 2, 1]                # => #<Set: {1, 2}>
  #     Set[1, 'c', :s]             # => #<Set: {1, "c", :s}>
  def self.[](*ary)
    new(ary)
  end

  # Creates a new set containing the elements of the given enumerable
  # object.
  #
  # If a block is given, the elements of enum are preprocessed by the
  # given block.
  #
  #     Set.new([1, 2])                       #=> #<Set: {1, 2}>
  #     Set.new([1, 2, 1])                    #=> #<Set: {1, 2}>
  #     Set.new([1, 'c', :s])                 #=> #<Set: {1, "c", :s}>
  #     Set.new(1..5)                         #=> #<Set: {1, 2, 3, 4, 5}>
  #     Set.new([1, 2, 3]) { |x| x * x }      #=> #<Set: {1, 4, 9}>
  def initialize(enum = nil, &block) # :yields: o
    @hash ||= Hash.new(false)

    enum.nil? and return

    if block
      do_with_enum(enum) { |o| add(block[o]) }
    else
      merge(enum)
    end
  end

  # Makes the set compare its elements by their identity and returns
  # self.  This method may not be supported by all subclasses of Set.
  def compare_by_identity
    if @hash.respond_to?(:compare_by_identity)
      @hash.compare_by_identity
      self
    else
      raise NotImplementedError, "#{self.class.name}\##{__method__} is not implemented"
    end
  end

  # Returns true if the set will compare its elements by their
  # identity.  Also see Set#compare_by_identity.
  def compare_by_identity?
    @hash.respond_to?(:compare_by_identity?) && @hash.compare_by_identity?
  end

  def do_with_enum(enum, &block) # :nodoc:
    if enum.respond_to?(:each_entry)
      enum.each_entry(&block) if block
    elsif enum.respond_to?(:each)
      enum.each(&block) if block
    else
      raise ArgumentError, "value must be enumerable"
    end
  end
  private :do_with_enum

  # Dup internal hash.
  def initialize_dup(orig)
    super
    @hash = orig.instance_variable_get(:@hash).dup
  end

  if Kernel.instance_method(:initialize_clone).arity != 1
    # Clone internal hash.
    def initialize_clone(orig, **options)
      super
      @hash = orig.instance_variable_get(:@hash).clone(**options)
    end
  else
    # Clone internal hash.
    def initialize_clone(orig)
      super
      @hash = orig.instance_variable_get(:@hash).clone
    end
  end

  def freeze    # :nodoc:
    @hash.freeze
    super
  end

  # Returns the number of elements.
  def size
    @hash.size
  end
  alias length size

  # Returns true if the set contains no elements.
  def empty?
    @hash.empty?
  end

  # Removes all elements and returns self.
  #
  #     set = Set[1, 'c', :s]             #=> #<Set: {1, "c", :s}>
  #     set.clear                         #=> #<Set: {}>
  #     set                               #=> #<Set: {}>
  def clear
    @hash.clear
    self
  end

  # Replaces the contents of the set with the contents of the given
  # enumerable object and returns self.
  #
  #     set = Set[1, 'c', :s]             #=> #<Set: {1, "c", :s}>
  #     set.replace([1, 2])               #=> #<Set: {1, 2}>
  #     set                               #=> #<Set: {1, 2}>
  def replace(enum)
    if enum.instance_of?(self.class)
      @hash.replace(enum.instance_variable_get(:@hash))
      self
    else
      do_with_enum(enum)  # make sure enum is enumerable before calling clear
      clear
      merge(enum)
    end
  end

  # Converts the set to an array.  The order of elements is uncertain.
  #
  #     Set[1, 2].to_a                    #=> [1, 2]
  #     Set[1, 'c', :s].to_a              #=> [1, "c", :s]
  def to_a
    @hash.keys
  end

  # Returns self if no arguments are given.  Otherwise, converts the
  # set to another with `klass.new(self, *args, &block)`.
  #
  # In subclasses, returns `klass.new(self, *args, &block)` unless
  # overridden.
  def to_set(klass = Set, *args, &block)
    return self if instance_of?(Set) && klass == Set && block.nil? && args.empty?
    klass.new(self, *args, &block)
  end

  def flatten_merge(set, seen = Set.new) # :nodoc:
    set.each { |e|
      if e.is_a?(Set)
        if seen.include?(e_id = e.object_id)
          raise ArgumentError, "tried to flatten recursive Set"
        end

        seen.add(e_id)
        flatten_merge(e, seen)
        seen.delete(e_id)
      else
        add(e)
      end
    }

    self
  end
  protected :flatten_merge

  # Returns a new set that is a copy of the set, flattening each
  # containing set recursively.
  def flatten
    self.class.new.flatten_merge(self)
  end

  # Equivalent to Set#flatten, but replaces the receiver with the
  # result in place.  Returns nil if no modifications were made.
  def flatten!
    replace(flatten()) if any? { |e| e.is_a?(Set) }
  end

  # Returns true if the set contains the given object.
  #
  # Note that <code>include?</code> and <code>member?</code> do not test member
  # equality using <code>==</code> as do other Enumerables.
  #
  # See also Enumerable#include?
  def include?(o)
    @hash[o]
  end
  alias member? include?

  # Returns true if the set is a superset of the given set.
  def superset?(set)
    case
    when set.instance_of?(self.class) && @hash.respond_to?(:>=)
      @hash >= set.instance_variable_get(:@hash)
    when set.is_a?(Set)
      size >= set.size && set.all? { |o| include?(o) }
    else
      raise ArgumentError, "value must be a set"
    end
  end
  alias >= superset?

  # Returns true if the set is a proper superset of the given set.
  def proper_superset?(set)
    case
    when set.instance_of?(self.class) && @hash.respond_to?(:>)
      @hash > set.instance_variable_get(:@hash)
    when set.is_a?(Set)
      size > set.size && set.all? { |o| include?(o) }
    else
      raise ArgumentError, "value must be a set"
    end
  end
  alias > proper_superset?

  # Returns true if the set is a subset of the given set.
  def subset?(set)
    case
    when set.instance_of?(self.class) && @hash.respond_to?(:<=)
      @hash <= set.instance_variable_get(:@hash)
    when set.is_a?(Set)
      size <= set.size && all? { |o| set.include?(o) }
    else
      raise ArgumentError, "value must be a set"
    end
  end
  alias <= subset?

  # Returns true if the set is a proper subset of the given set.
  def proper_subset?(set)
    case
    when set.instance_of?(self.class) && @hash.respond_to?(:<)
      @hash < set.instance_variable_get(:@hash)
    when set.is_a?(Set)
      size < set.size && all? { |o| set.include?(o) }
    else
      raise ArgumentError, "value must be a set"
    end
  end
  alias < proper_subset?

  # Returns 0 if the set are equal,
  # -1 / +1 if the set is a proper subset / superset of the given set,
  # or nil if they both have unique elements.
  def <=>(set)
    return unless set.is_a?(Set)

    case size <=> set.size
    when -1 then -1 if proper_subset?(set)
    when +1 then +1 if proper_superset?(set)
    else 0 if self.==(set)
    end
  end

  # Returns true if the set and the given enumerable have at least one
  # element in common.
  #
  #     Set[1, 2, 3].intersect? Set[4, 5]   #=> false
  #     Set[1, 2, 3].intersect? Set[3, 4]   #=> true
  #     Set[1, 2, 3].intersect? 4..5        #=> false
  #     Set[1, 2, 3].intersect? [3, 4]      #=> true
  def intersect?(set)
    case set
    when Set
      if size < set.size
        any? { |o| set.include?(o) }
      else
        set.any? { |o| include?(o) }
      end
    when Enumerable
      set.any? { |o| include?(o) }
    else
      raise ArgumentError, "value must be enumerable"
    end
  end

  # Returns true if the set and the given enumerable have
  # no element in common.  This method is the opposite of `intersect?`.
  #
  #     Set[1, 2, 3].disjoint? Set[3, 4]   #=> false
  #     Set[1, 2, 3].disjoint? Set[4, 5]   #=> true
  #     Set[1, 2, 3].disjoint? [3, 4]      #=> false
  #     Set[1, 2, 3].disjoint? 4..5        #=> true
  def disjoint?(set)
    !intersect?(set)
  end

  # Calls the given block once for each element in the set, passing
  # the element as parameter.  Returns an enumerator if no block is
  # given.
  def each(&block)
    block or return enum_for(__method__) { size }
    @hash.each_key(&block)
    self
  end

  # Adds the given object to the set and returns self.  Use `merge` to
  # add many elements at once.
  #
  #     Set[1, 2].add(3)                    #=> #<Set: {1, 2, 3}>
  #     Set[1, 2].add([3, 4])               #=> #<Set: {1, 2, [3, 4]}>
  #     Set[1, 2].add(2)                    #=> #<Set: {1, 2}>
  def add(o)
    @hash[o] = true
    self
  end
  alias << add

  # Adds the given object to the set and returns self.  If the
  # object is already in the set, returns nil.
  #
  #     Set[1, 2].add?(3)                    #=> #<Set: {1, 2, 3}>
  #     Set[1, 2].add?([3, 4])               #=> #<Set: {1, 2, [3, 4]}>
  #     Set[1, 2].add?(2)                    #=> nil
  def add?(o)
    add(o) unless include?(o)
  end

  # Deletes the given object from the set and returns self.  Use
  # `subtract` to delete many items at once.
  def delete(o)
    @hash.delete(o)
    self
  end

  # Deletes the given object from the set and returns self.  If the
  # object is not in the set, returns nil.
  def delete?(o)
    delete(o) if include?(o)
  end

  # Deletes every element of the set for which block evaluates to
  # true, and returns self. Returns an enumerator if no block is
  # given.
  def delete_if
    block_given? or return enum_for(__method__) { size }
    # @hash.delete_if should be faster, but using it breaks the order
    # of enumeration in subclasses.
    select { |o| yield o }.each { |o| @hash.delete(o) }
    self
  end

  # Deletes every element of the set for which block evaluates to
  # false, and returns self. Returns an enumerator if no block is
  # given.
  def keep_if
    block_given? or return enum_for(__method__) { size }
    # @hash.keep_if should be faster, but using it breaks the order of
    # enumeration in subclasses.
    reject { |o| yield o }.each { |o| @hash.delete(o) }
    self
  end

  # Replaces the elements with ones returned by `collect()`.
  # Returns an enumerator if no block is given.
  def collect!
    block_given? or return enum_for(__method__) { size }
    set = self.class.new
    each { |o| set << yield(o) }
    replace(set)
  end
  alias map! collect!

  # Equivalent to Set#delete_if, but returns nil if no changes were
  # made. Returns an enumerator if no block is given.
  def reject!(&block)
    block or return enum_for(__method__) { size }
    n = size
    delete_if(&block)
    self if size != n
  end

  # Equivalent to Set#keep_if, but returns nil if no changes were
  # made. Returns an enumerator if no block is given.
  def select!(&block)
    block or return enum_for(__method__) { size }
    n = size
    keep_if(&block)
    self if size != n
  end

  # Equivalent to Set#select!
  alias filter! select!

  # Merges the elements of the given enumerable object to the set and
  # returns self.
  def merge(enum)
    if enum.instance_of?(self.class)
      @hash.update(enum.instance_variable_get(:@hash))
    else
      do_with_enum(enum) { |o| add(o) }
    end

    self
  end

  # Deletes every element that appears in the given enumerable object
  # and returns self.
  def subtract(enum)
    do_with_enum(enum) { |o| delete(o) }
    self
  end

  # Returns a new set built by merging the set and the elements of the
  # given enumerable object.
  #
  #     Set[1, 2, 3] | Set[2, 4, 5]         #=> #<Set: {1, 2, 3, 4, 5}>
  #     Set[1, 5, 'z'] | (1..6)             #=> #<Set: {1, 5, "z", 2, 3, 4, 6}>
  def |(enum)
    dup.merge(enum)
  end
  alias + |
  alias union |

  # Returns a new set built by duplicating the set, removing every
  # element that appears in the given enumerable object.
  #
  #     Set[1, 3, 5] - Set[1, 5]                #=> #<Set: {3}>
  #     Set['a', 'b', 'z'] - ['a', 'c']         #=> #<Set: {"b", "z"}>
  def -(enum)
    dup.subtract(enum)
  end
  alias difference -

  # Returns a new set containing elements common to the set and the
  # given enumerable object.
  #
  #     Set[1, 3, 5] & Set[3, 2, 1]             #=> #<Set: {3, 1}>
  #     Set['a', 'b', 'z'] & ['a', 'b', 'c']    #=> #<Set: {"a", "b"}>
  def &(enum)
    n = self.class.new
    if enum.is_a?(Set)
      if enum.size > size
        each { |o| n.add(o) if enum.include?(o) }
      else
        enum.each { |o| n.add(o) if include?(o) }
      end
    else
      do_with_enum(enum) { |o| n.add(o) if include?(o) }
    end
    n
  end
  alias intersection &

  # Returns a new set containing elements exclusive between the set
  # and the given enumerable object.  `(set ^ enum)` is equivalent to
  # `((set | enum) - (set & enum))`.
  #
  #     Set[1, 2] ^ Set[2, 3]                   #=> #<Set: {3, 1}>
  #     Set[1, 'b', 'c'] ^ ['b', 'd']           #=> #<Set: {"d", 1, "c"}>
  def ^(enum)
    n = Set.new(enum)
    each { |o| n.add(o) unless n.delete?(o) }
    n
  end

  # Returns true if two sets are equal.  The equality of each couple
  # of elements is defined according to Object#eql?.
  #
  #     Set[1, 2] == Set[2, 1]                       #=> true
  #     Set[1, 3, 5] == Set[1, 5]                    #=> false
  #     Set['a', 'b', 'c'] == Set['a', 'c', 'b']     #=> true
  #     Set['a', 'b', 'c'] == ['a', 'c', 'b']        #=> false
  def ==(other)
    if self.equal?(other)
      true
    elsif other.instance_of?(self.class)
      @hash == other.instance_variable_get(:@hash)
    elsif other.is_a?(Set) && self.size == other.size
      other.all? { |o| @hash.include?(o) }
    else
      false
    end
  end

  def hash      # :nodoc:
    @hash.hash
  end

  def eql?(o)   # :nodoc:
    return false unless o.is_a?(Set)
    @hash.eql?(o.instance_variable_get(:@hash))
  end

  # Resets the internal state after modification to existing elements
  # and returns self.
  #
  # Elements will be reindexed and deduplicated.
  def reset
    if @hash.respond_to?(:rehash)
      @hash.rehash # This should perform frozenness check.
    else
      raise FrozenError, "can't modify frozen #{self.class.name}" if frozen?
    end
    self
  end

  # Returns true if the given object is a member of the set,
  # and false otherwise.
  #
  # Used in case statements:
  #
  #     require 'set'
  #
  #     case :apple
  #     when Set[:potato, :carrot]
  #       "vegetable"
  #     when Set[:apple, :banana]
  #       "fruit"
  #     end
  #     # => "fruit"
  #
  # Or by itself:
  #
  #     Set[1, 2, 3] === 2   #=> true
  #     Set[1, 2, 3] === 4   #=> false
  #
  alias === include?

  # Classifies the set by the return value of the given block and
  # returns a hash of {value => set of elements} pairs.  The block is
  # called once for each element of the set, passing the element as
  # parameter.
  #
  #     require 'set'
  #     files = Set.new(Dir.glob("*.rb"))
  #     hash = files.classify { |f| File.mtime(f).year }
  #     hash       #=> {2000=>#<Set: {"a.rb", "b.rb"}>,
  #                #    2001=>#<Set: {"c.rb", "d.rb", "e.rb"}>,
  #                #    2002=>#<Set: {"f.rb"}>}
  #
  # Returns an enumerator if no block is given.
  def classify # :yields: o
    block_given? or return enum_for(__method__) { size }

    h = {}

    each { |i|
      (h[yield(i)] ||= self.class.new).add(i)
    }

    h
  end

  # Divides the set into a set of subsets according to the commonality
  # defined by the given block.
  #
  # If the arity of the block is 2, elements o1 and o2 are in common
  # if block.call(o1, o2) is true.  Otherwise, elements o1 and o2 are
  # in common if block.call(o1) == block.call(o2).
  #
  #     require 'set'
  #     numbers = Set[1, 3, 4, 6, 9, 10, 11]
  #     set = numbers.divide { |i,j| (i - j).abs == 1 }
  #     set        #=> #<Set: {#<Set: {1}>,
  #                #           #<Set: {11, 9, 10}>,
  #                #           #<Set: {3, 4}>,
  #                #           #<Set: {6}>}>
  #
  # Returns an enumerator if no block is given.
  def divide(&func)
    func or return enum_for(__method__) { size }

    if func.arity == 2
      require 'tsort'

      class << dig = {}         # :nodoc:
        include TSort

        alias tsort_each_node each_key
        def tsort_each_child(node, &block)
          fetch(node).each(&block)
        end
      end

      each { |u|
        dig[u] = a = []
        each{ |v| func.call(u, v) and a << v }
      }

      set = Set.new()
      dig.each_strongly_connected_component { |css|
        set.add(self.class.new(css))
      }
      set
    else
      Set.new(classify(&func).values)
    end
  end

  # Returns a string created by converting each element of the set to a string
  # See also: Array#join
  def join(separator=nil)
    to_a.join(separator)
  end

  InspectKey = :__inspect_key__         # :nodoc:

  # Returns a string containing a human-readable representation of the
  # set ("#<Set: {element1, element2, ...}>").
  def inspect
    ids = (Thread.current[InspectKey] ||= [])

    if ids.include?(object_id)
      return sprintf('#<%s: {...}>', self.class.name)
    end

    ids << object_id
    begin
      return sprintf('#<%s: {%s}>', self.class, to_a.inspect[1..-2])
    ensure
      ids.pop
    end
  end

  alias to_s inspect

  def pretty_print(pp)  # :nodoc:
    pp.group(1, sprintf('#<%s:', self.class.name), '>') {
      pp.breakable
      pp.group(1, '{', '}') {
        pp.seplist(self) { |o|
          pp.pp o
        }
      }
    }
  end

  def pretty_print_cycle(pp)    # :nodoc:
    pp.text sprintf('#<%s: {%s}>', self.class.name, empty? ? '' : '...')
  end
end

module Enumerable
  # Makes a set from the enumerable object with given arguments.
  # Needs to `require "set"` to use this method.
  def to_set(klass = Set, *args, &block)
    klass.new(self, *args, &block)
  end unless method_defined?(:to_set)
end

autoload :SortedSet, "#{__dir__}/set/sorted_set"