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# 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}[rdoc-ref:Object@What-27s+Here].
# - Includes {module Enumerable}[rdoc-ref:Enumerable@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"