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+#--
+# set.rb - defines the Set class
+#++
+# Copyright (c) 2002-2013 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.
+#
+#   $Id: set.rb 47085 2014-08-06 11:28:21Z knu $
+#
+# == Overview
+#
+# 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.  If you
+# need to keep values sorted in some order, use the SortedSet class.
+#
+# The method +to_set+ is added to Enumerable for convenience.
+#
+# See the Set and SortedSet documentation for examples of usage.
+
+
+#
+# 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.
+# * 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.  However,
+# the <=> operator is intentionally left out because not every pair of
+# sets is comparable. ({x,y} vs. {x,z} for example)
+#
+# == Example
+#
+#   require 'set'
+#   s1 = Set.new [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)
+#
+class Set
+  include Enumerable
+
+  # Creates a new set containing the given objects.
+  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.
+  def initialize(enum = nil, &block) # :yields: o
+    @hash ||= Hash.new
+
+    enum.nil? and return
+
+    if block
+      do_with_enum(enum) { |o| add(block[o]) }
+    else
+      merge(enum)
+    end
+  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
+
+  # Clone internal hash.
+  def initialize_clone(orig)
+    super
+    @hash = orig.instance_variable_get(:@hash).clone
+  end
+
+  def freeze    # :nodoc:
+    @hash.freeze
+    super
+  end
+
+  def taint     # :nodoc:
+    @hash.taint
+    super
+  end
+
+  def untaint   # :nodoc:
+    @hash.untaint
+    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.
+  def clear
+    @hash.clear
+    self
+  end
+
+  # Replaces the contents of the set with the contents of the given
+  # enumerable object and returns self.
+  def replace(enum)
+    if enum.instance_of?(self.class)
+      @hash.replace(enum.instance_variable_get(:@hash))
+      self
+    else
+      do_with_enum(enum)
+      clear
+      merge(enum)
+    end
+  end
+
+  # Converts the set to an array.  The order of elements is uncertain.
+  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!
+    if detect { |e| e.is_a?(Set) }
+      replace(flatten())
+    else
+      nil
+    end
+  end
+
+  # Returns true if the set contains the given object.
+  def include?(o)
+    @hash.include?(o)
+  end
+  alias member? include?
+
+  # Returns true if the set is a superset of the given set.
+  def superset?(set)
+    set.is_a?(Set) or raise ArgumentError, "value must be a set"
+    return false if size < set.size
+    set.all? { |o| include?(o) }
+  end
+  alias >= superset?
+
+  # Returns true if the set is a proper superset of the given set.
+  def proper_superset?(set)
+    set.is_a?(Set) or raise ArgumentError, "value must be a set"
+    return false if size <= set.size
+    set.all? { |o| include?(o) }
+  end
+  alias > proper_superset?
+
+  # Returns true if the set is a subset of the given set.
+  def subset?(set)
+    set.is_a?(Set) or raise ArgumentError, "value must be a set"
+    return false if set.size < size
+    all? { |o| set.include?(o) }
+  end
+  alias <= subset?
+
+  # Returns true if the set is a proper subset of the given set.
+  def proper_subset?(set)
+    set.is_a?(Set) or raise ArgumentError, "value must be a set"
+    return false if set.size <= size
+    all? { |o| set.include?(o) }
+  end
+  alias < proper_subset?
+
+  # Returns true if the set and the given set have at least one
+  # element in common.
+  #
+  # e.g.:
+  #
+  #   require 'set'
+  #   Set[1, 2, 3].intersect? Set[4, 5] # => false
+  #   Set[1, 2, 3].intersect? Set[3, 4] # => true
+  def intersect?(set)
+    set.is_a?(Set) or raise ArgumentError, "value must be a set"
+    if size < set.size
+      any? { |o| set.include?(o) }
+    else
+      set.any? { |o| include?(o) }
+    end
+  end
+
+  # Returns true if the set and the given set have no element in
+  # common.  This method is the opposite of +intersect?+.
+  #
+  # e.g.:
+  #
+  #   require 'set'
+  #   Set[1, 2, 3].disjoint? Set[3, 4] # => false
+  #   Set[1, 2, 3].disjoint? Set[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__)
+    @hash.each_key(&block)
+    self
+  end
+
+  # Adds the given object to the set and returns self.  Use +merge+ to
+  # add many elements at once.
+  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.
+  def add?(o)
+    if include?(o)
+      nil
+    else
+      add(o)
+    end
+  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)
+    if include?(o)
+      delete(o)
+    else
+      nil
+    end
+  end
+
+  # Deletes every element of the set for which block evaluates to
+  # true, and returns self.
+  def delete_if
+    block_given? or return enum_for(__method__)
+    # @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.
+  def keep_if
+    block_given? or return enum_for(__method__)
+    # @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().
+  def collect!
+    block_given? or return enum_for(__method__)
+    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.
+  def reject!(&block)
+    block or return enum_for(__method__)
+    n = size
+    delete_if(&block)
+    size == n ? nil : self
+  end
+
+  # Equivalent to Set#keep_if, but returns nil if no changes were
+  # made.
+  def select!(&block)
+    block or return enum_for(__method__)
+    n = size
+    keep_if(&block)
+    size == n ? nil : self
+  end
+
+  # 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.
+  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.
+  def -(enum)
+    dup.subtract(enum)
+  end
+  alias difference -    ##
+
+  # Returns a new set containing elements common to the set and the
+  # given enumerable object.
+  def &(enum)
+    n = self.class.new
+    do_with_enum(enum) { |o| n.add(o) if include?(o) }
+    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)).
+  def ^(enum)
+    n = Set.new(enum)
+    each { |o| if n.include?(o) then n.delete(o) else n.add(o) end }
+    n
+  end
+
+  # Returns true if two sets are equal.  The equality of each couple
+  # of elements is defined according to Object#eql?.
+  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
+
+  # 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.
+  #
+  # e.g.:
+  #
+  #   require 'set'
+  #   files = Set.new(Dir.glob("*.rb"))
+  #   hash = files.classify { |f| File.mtime(f).year }
+  #   p hash    # => {2000=>#<Set: {"a.rb", "b.rb"}>,
+  #             #     2001=>#<Set: {"c.rb", "d.rb", "e.rb"}>,
+  #             #     2002=>#<Set: {"f.rb"}>}
+  def classify # :yields: o
+    block_given? or return enum_for(__method__)
+
+    h = {}
+
+    each { |i|
+      x = yield(i)
+      (h[x] ||= 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).
+  #
+  # e.g.:
+  #
+  #   require 'set'
+  #   numbers = Set[1, 3, 4, 6, 9, 10, 11]
+  #   set = numbers.divide { |i,j| (i - j).abs == 1 }
+  #   p set     # => #<Set: {#<Set: {1}>,
+  #             #            #<Set: {11, 9, 10}>,
+  #             #            #<Set: {3, 4}>,
+  #             #            #<Set: {6}>}>
+  def divide(&func)
+    func or return enum_for(__method__)
+
+    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
+
+  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
+
+    begin
+      ids << object_id
+      return sprintf('#<%s: {%s}>', self.class, to_a.inspect[1..-2])
+    ensure
+      ids.pop
+    end
+  end
+
+  def pretty_print(pp)  # :nodoc:
+    pp.text sprintf('#<%s: {', self.class.name)
+    pp.nest(1) {
+      pp.seplist(self) { |o|
+        pp.pp o
+      }
+    }
+    pp.text "}>"
+  end
+
+  def pretty_print_cycle(pp)    # :nodoc:
+    pp.text sprintf('#<%s: {%s}>', self.class.name, empty? ? '' : '...')
+  end
+end
+
+#
+# SortedSet implements a Set that guarantees that its elements are
+# yielded in sorted order (according to the return values of their
+# #<=> methods) when iterating over them.
+#
+# All elements that are added to a SortedSet must respond to the <=>
+# method for comparison.
+#
+# Also, all elements must be <em>mutually comparable</em>: <tt>el1 <=>
+# el2</tt> must not return <tt>nil</tt> for any elements <tt>el1</tt>
+# and <tt>el2</tt>, else an ArgumentError will be raised when
+# iterating over the SortedSet.
+#
+# == Example
+#
+#   require "set"
+#
+#   set = SortedSet.new([2, 1, 5, 6, 4, 5, 3, 3, 3])
+#   ary = []
+#
+#   set.each do |obj|
+#     ary << obj
+#   end
+#
+#   p ary # => [1, 2, 3, 4, 5, 6]
+#
+#   set2 = SortedSet.new([1, 2, "3"])
+#   set2.each { |obj| } # => raises ArgumentError: comparison of Fixnum with String failed
+#
+class SortedSet < Set
+  @@setup = false
+
+  class << self
+    def [](*ary)        # :nodoc:
+      new(ary)
+    end
+
+    def setup   # :nodoc:
+      @@setup and return
+
+      module_eval {
+        # a hack to shut up warning
+        alias old_init initialize
+      }
+      begin
+        require 'rbtree'
+
+        module_eval <<-END, __FILE__, __LINE__+1
+          def initialize(*args)
+            @hash = RBTree.new
+            super
+          end
+
+          def add(o)
+            o.respond_to?(:<=>) or raise ArgumentError, "value must respond to <=>"
+            super
+          end
+          alias << add
+        END
+      rescue LoadError
+        module_eval <<-END, __FILE__, __LINE__+1
+          def initialize(*args)
+            @keys = nil
+            super
+          end
+
+          def clear
+            @keys = nil
+            super
+          end
+
+          def replace(enum)
+            @keys = nil
+            super
+          end
+
+          def add(o)
+            o.respond_to?(:<=>) or raise ArgumentError, "value must respond to <=>"
+            @keys = nil
+            super
+          end
+          alias << add
+
+          def delete(o)
+            @keys = nil
+            @hash.delete(o)
+            self
+          end
+
+          def delete_if
+            block_given? or return enum_for(__method__)
+            n = @hash.size
+            super
+            @keys = nil if @hash.size != n
+            self
+          end
+
+          def keep_if
+            block_given? or return enum_for(__method__)
+            n = @hash.size
+            super
+            @keys = nil if @hash.size != n
+            self
+          end
+
+          def merge(enum)
+            @keys = nil
+            super
+          end
+
+          def each(&block)
+            block or return enum_for(__method__)
+            to_a.each(&block)
+            self
+          end
+
+          def to_a
+            (@keys = @hash.keys).sort! unless @keys
+            @keys
+          end
+        END
+      end
+      module_eval {
+        # a hack to shut up warning
+        remove_method :old_init
+      }
+
+      @@setup = true
+    end
+  end
+
+  def initialize(*args, &block) # :nodoc:
+    SortedSet.setup
+    initialize(*args, &block)
+  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
+end
+
+# =begin
+# == RestricedSet class
+# RestricedSet implements a set with restrictions defined by a given
+# block.
+#
+# === Super class
+#     Set
+#
+# === Class Methods
+# --- RestricedSet::new(enum = nil) { |o| ... }
+# --- RestricedSet::new(enum = nil) { |rset, o| ... }
+#     Creates a new restricted set containing the elements of the given
+#     enumerable object.  Restrictions are defined by the given block.
+#
+#     If the block's arity is 2, it is called with the RestrictedSet
+#     itself and an object to see if the object is allowed to be put in
+#     the set.
+#
+#     Otherwise, the block is called with an object to see if the object
+#     is allowed to be put in the set.
+#
+# === Instance Methods
+# --- restriction_proc
+#     Returns the restriction procedure of the set.
+#
+# =end
+#
+# class RestricedSet < Set
+#   def initialize(*args, &block)
+#     @proc = block or raise ArgumentError, "missing a block"
+#
+#     if @proc.arity == 2
+#       instance_eval %{
+#       def add(o)
+#         @hash[o] = true if @proc.call(self, o)
+#         self
+#       end
+#       alias << add
+#
+#       def add?(o)
+#         if include?(o) || !@proc.call(self, o)
+#           nil
+#         else
+#           @hash[o] = true
+#           self
+#         end
+#       end
+#
+#       def replace(enum)
+#         enum.respond_to?(:each) or raise ArgumentError, "value must be enumerable"
+#         clear
+#         enum.each_entry { |o| add(o) }
+#
+#         self
+#       end
+#
+#       def merge(enum)
+#         enum.respond_to?(:each) or raise ArgumentError, "value must be enumerable"
+#         enum.each_entry { |o| add(o) }
+#
+#         self
+#       end
+#       }
+#     else
+#       instance_eval %{
+#       def add(o)
+#         if @proc.call(o)
+#           @hash[o] = true
+#         end
+#         self
+#       end
+#       alias << add
+#
+#       def add?(o)
+#         if include?(o) || !@proc.call(o)
+#           nil
+#         else
+#           @hash[o] = true
+#           self
+#         end
+#       end
+#       }
+#     end
+#
+#     super(*args)
+#   end
+#
+#   def restriction_proc
+#     @proc
+#   end
+# end
+
+# Tests have been moved to test/test_set.rb.