note
	description: "Trees implemented using a two way linked list representation"
	library: "Free implementation of ELKS library"
	legal: "See notice at end of class."
	status: "See notice at end of class."
	names: two_way_tree, tree, two_way_list
	representation: recursive, linked
	access: cursor, membership
	contents: generic
	date: "$Date: 2018-12-15 18:06:16 +0000 (Sat, 15 Dec 2018) $"
	revision: "$Revision: 102608 $"

class interface
	TWO_WAY_TREE [G]

create 
	make (v: like item)
			-- Create single node with item v.

feature -- Access

	at alias "@" (i: INTEGER_32): like child_item assign put_i_th
			-- Item at i-th position
			-- Was declared in CHAIN as synonym of i_th.
			-- (from CHAIN)
		require -- from TABLE
			valid_key: valid_index (i)

	child_cursor: TWO_WAY_TREE_CURSOR [G]
			-- Current cursor position
		require -- from  CURSOR_STRUCTURE
			True
		require -- from  TREE
			True
		ensure -- from CURSOR_STRUCTURE
			cursor_not_void: Result /= Void

	first: like child_item
			-- Item at first position
			-- (from LINKED_LIST)
		require -- from CHAIN
			not_empty: not is_leaf

	first_child: like parent
			-- Leftmost child

	generating_type: TYPE [detachable TWO_WAY_TREE [G]]
			-- Type of current object
			-- (type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generating_type_not_void: Result /= Void

	generator: STRING_8
			-- Name of current object's generating class
			-- (base class of the type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generator_not_void: Result /= Void
			generator_not_empty: not Result.is_empty

	sequential_has (v: like child_item): BOOLEAN
			-- Does structure include an occurrence of v?
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from  CONTAINER
			True
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not is_leaf

	twl_has (v: like child_item): BOOLEAN
			-- Does chain include v?
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from CHAIN)

	i_th alias "[]" (i: INTEGER_32): like child_item assign put_i_th
			-- Item at i-th position
			-- Was declared in CHAIN as synonym of at.
			-- (from CHAIN)
		require -- from TABLE
			valid_key: valid_index (i)
		require -- from READABLE_INDEXABLE
			valid_index: valid_index (i)

	child_index: INTEGER_32
			-- Index of current position
			-- (from LINKED_LIST)
		require -- from  LINEAR
			True
		require -- from  TREE
			True
		ensure -- from TREE
			valid_index: Result >= 0 and Result <= arity + 1

	sequential_index_of (v: like child_item; i: INTEGER_32): INTEGER_32
			-- Index of i-th occurrence of v.
			-- 0 if none.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from LINEAR
			positive_occurrences: i > 0
		ensure -- from LINEAR
			non_negative_result: Result >= 0

	index_of (v: like child_item; i: INTEGER_32): INTEGER_32
			-- Index of i-th occurrence of item identical to v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- 0 if none.
			-- (from CHAIN)

	child_item: G
			-- Current item
			-- (from LINKED_LIST)
		require -- from ACTIVE
			readable: child_readable
		require -- from TRAVERSABLE
			not_off: not child_off
		require -- from TREE
			readable: child_readable

	item: G
			-- Content of cell.
			-- (from CELL)

	item_for_iteration: G
			-- Item at current position
			-- (from LINEAR)
		require -- from LINEAR
			not_off: not child_off

	last: like child_item
			-- Item at last position
			-- (from LINKED_LIST)
		require -- from CHAIN
			not_empty: not is_leaf

	last_child: like parent
			-- Right most child

	left_sibling: detachable TWO_WAY_TREE [G]
			-- Left neighbor
			-- (from BI_LINKABLE)

	twl_new_cursor: TWO_WAY_LIST_ITERATION_CURSOR [G]
			-- (from TWO_WAY_LIST)
		require -- from  ITERABLE
			True
		ensure -- from ITERABLE
			result_attached: Result /= Void

	sequential_occurrences (v: like child_item): INTEGER_32
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from  BAG
			True
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	parent: detachable like new_cell
			-- Parent node

	right_sibling: detachable TWO_WAY_TREE [G]
			-- Right neighbor
			-- (from LINKABLE)

	sublist: detachable TWO_WAY_TREE [G]
			-- Result produced by last split
			-- (from TWO_WAY_LIST)
	
feature -- Measurement

	child_capacity: INTEGER_32
			-- Maximal number of children
			-- (from TREE)

	count: INTEGER_32
			-- Number of items
			-- (from TREE)

	arity: INTEGER_32
			-- Number of items
			-- (from LINKED_LIST)

	Lower: INTEGER_32 = 1
			-- Minimum index.
			-- (from CHAIN)

	occurrences (v: like child_item): INTEGER_32
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from CHAIN)
	
feature -- Comparison

	frozen deep_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void
			-- or attached to isomorphic object structures?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			shallow_implies_deep: standard_equal (a, b) implies Result
			both_or_none_void: (a = Void) implies (Result = (b = Void))
			same_type: (Result and (a /= Void)) implies (b /= Void and then a.same_type (b))
			symmetric: Result implies deep_equal (b, a)

	frozen equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached
			-- to objects considered equal?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.is_equal (b))

	frozen is_deep_equal alias "≡≡≡" (other: TWO_WAY_TREE [G]): BOOLEAN
			-- Are Current and other attached to isomorphic object structures?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			shallow_implies_deep: standard_is_equal (other) implies Result
			same_type: Result implies same_type (other)
			symmetric: Result implies other.is_deep_equal (Current)

	is_equal (other: TWO_WAY_TREE [G]): BOOLEAN
			-- Does other contain the same elements?
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from TREE)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			symmetric: Result implies other ~ Current
			consistent: standard_is_equal (other) implies Result
		ensure then -- from LIST
			indices_unchanged: child_index = old child_index and other.child_index = old other.child_index
			true_implies_same_size: Result implies arity = other.arity

	node_is_equal (other: TWO_WAY_TREE [G]): BOOLEAN
			-- Is other equal to Current?
			-- (from TREE)
		require -- from TREE
			other_not_void: other /= Void

	frozen standard_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached to
			-- field-by-field identical objects of the same type?
			-- Always uses default object comparison criterion.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.standard_is_equal (b))

	frozen standard_is_equal alias "" (other: TWO_WAY_TREE [G]): BOOLEAN
			-- Is other attached to an object of the same type
			-- as current object, and field-by-field identical to it?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			same_type: Result implies same_type (other)
			symmetric: Result implies other.standard_is_equal (Current)
	
feature -- Status report

	child_after: BOOLEAN
			-- Is there no valid cursor position to the right of cursor?
			-- (from LINKED_LIST)

	child_before: BOOLEAN
			-- Is there no valid cursor position to the left of cursor?
			-- (from LINKED_LIST)

	changeable_comparison_criterion: BOOLEAN
			-- May object_comparison be changed?
			-- (Answer: yes by default.)
			-- (from CONTAINER)

	child_isfirst: BOOLEAN
			-- Is cursor under first child?
			-- (from TREE)
		require -- from  CHAIN
			True
		ensure -- from CHAIN
			valid_position: Result implies not is_leaf
		ensure -- from TREE
			not_is_leaf: Result implies not is_leaf

	child_islast: BOOLEAN
			-- Is cursor under last child?
		require -- from  CHAIN
			True
		require -- from  TREE
			True
		ensure -- from CHAIN
			valid_position: Result implies not is_leaf
		ensure -- from TREE
			not_is_leaf: Result implies not is_leaf

	child_readable: BOOLEAN
			-- Is there a current child_item to be read?
			-- (from TREE)
		require -- from  ACTIVE
			True

	child_writable: BOOLEAN
			-- Is there a current child_item that may be modified?
			-- (from TREE)
		require -- from  ACTIVE
			True

	conforms_to (other: ANY): BOOLEAN
			-- Does type of current object conform to type
			-- of other (as per Eiffel: The Language, chapter 13)?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void

	exhausted: BOOLEAN
			-- Has structure been completely explored?
			-- (from LINEAR)
		ensure -- from LINEAR
			exhausted_when_off: child_off implies Result

	Extendible: BOOLEAN = True
			-- May new items be added?
			-- (from DYNAMIC_TREE)

	child_extendible: BOOLEAN
			-- May new items be added? (Answer: yes.)
			-- (from DYNAMIC_CHAIN)
		require -- from  COLLECTION
			True

	Twl_full: BOOLEAN = False
			-- Is structured filled to capacity? (Answer: no.)
			-- (from LINKED_LIST)

	has (v: G): BOOLEAN
			-- Does subtree include v?
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from TREE)
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not is_leaf

	is_empty: BOOLEAN
			-- Is structure empty of items?
			-- (from TREE)

	is_inserted (v: G): BOOLEAN
			-- Has v been inserted at the end by the most recent put or
			-- extend?
			-- (from LINKED_LIST)

	is_leaf: BOOLEAN
			-- Are there no children?
			-- (from TREE)

	is_root: BOOLEAN
			-- Is there no parent?
			-- (from TREE)

	is_sibling (other: attached like parent): BOOLEAN
			-- Are current node and other siblings?
			-- (from TREE)
		require -- from TREE
			other_exists: other /= Void
		ensure -- from TREE
			not_root: Result implies not is_root
			other_not_root: Result implies not other.is_root
			same_parent: Result = not is_root and other.parent = parent

	object_comparison: BOOLEAN
			-- Must search operations use equal rather than =
			-- for comparing references? (Default: no, use =.)
			-- (from CONTAINER)

	child_off: BOOLEAN
			-- Is there no current item?
			-- (from LINKED_LIST)
		require -- from  TRAVERSABLE
			True
		require -- from  TREE
			True

	prunable: BOOLEAN
			-- May items be removed? (Answer: yes.)
			-- (from DYNAMIC_TABLE)
		require -- from  COLLECTION
			True

	Readable: BOOLEAN = True
			-- (from TREE)

	readable_child: BOOLEAN
			-- Is there a current child to be read?
			-- (from TREE)

	replaceable: BOOLEAN
			-- Can current item be replaced?
			-- (from ACTIVE)

	same_type (other: ANY): BOOLEAN
			-- Is type of current object identical to type of other?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			definition: Result = (conforms_to (other) and other.conforms_to (Current))

	valid_cursor (p: CURSOR): BOOLEAN
			-- Can the cursor be moved to position p?
			-- (from LINKED_LIST)

	valid_cursor_index (i: INTEGER_32): BOOLEAN
			-- Is i correctly bounded for cursor movement?
			-- (from TREE)
		require -- from  CHAIN
			True
		ensure -- from CHAIN
			valid_cursor_index_definition: Result = ((i >= 0) and (i <= arity + 1))
		ensure -- from TREE
			valid_cursor_index_definition: Result = (i >= 0) and (i <= child_capacity + 1)

	valid_index (i: INTEGER_32): BOOLEAN
			-- Is i within allowable bounds?
			-- (from CHAIN)
		require -- from  READABLE_INDEXABLE
			True
		require -- from  TABLE
			True
		ensure -- from READABLE_INDEXABLE
			only_if_in_index_set: Result implies (Lower <= i and i <= arity)
		ensure then -- from CHAIN
			valid_index_definition: Result = ((i >= 1) and (i <= arity))

	Writable: BOOLEAN = True
			-- Is there a current item that may be modified?
			-- (from TREE)

	writable_child: BOOLEAN
			-- Is there a current child that may be modified?
			-- (from TREE)
	
feature -- Status setting

	compare_objects
			-- Ensure that future search operations will use equal
			-- rather than = for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion: changeable_comparison_criterion
		ensure -- from CONTAINER
				object_comparison

	compare_references
			-- Ensure that future search operations will use =
			-- rather than equal for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion: changeable_comparison_criterion
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
	
feature -- Cursor movement

	child_back
			-- Move cursor to previous position, if any.
			-- (from TWO_WAY_LIST)
		require -- from BILINEAR
			not_before: not child_before
		require -- from  TREE
			True

	child_finish
			-- Move cursor to last position.
			-- (Go before if empty)
			-- (from TWO_WAY_LIST)
		require -- from  LINEAR
			True
		require -- from  TREE
			True
		ensure then -- from CHAIN
			at_last: not is_leaf implies child_islast
		ensure then -- from LINKED_LIST
			empty_convention: is_leaf implies child_before
		ensure then -- from TWO_WAY_LIST
			not_after: not child_after

	child_forth
			-- Move cursor to next position, if any.
			-- (from TWO_WAY_LIST)
		require -- from LINEAR
			not_after: not child_after
		require -- from  TREE
			True
		ensure then -- from LIST
			moved_forth: child_index = old child_index + 1

	child_go_i_th (i: INTEGER_32)
			-- Move cursor to i-th position.
			-- (from LINKED_LIST)
		require -- from CHAIN
			valid_cursor_index: valid_cursor_index (i)
		require -- from  TREE
			True
		ensure -- from CHAIN
			position_expected: child_index = i
		ensure then -- from TREE
			position: child_index = i

	child_go_to (p: CURSOR)
			-- Move cursor to position p.
			-- (from LINKED_LIST)
		require -- from CURSOR_STRUCTURE
			cursor_position_valid: valid_cursor (p)
		require -- from  TREE
			True

	move (i: INTEGER_32)
			-- Move cursor i positions. The cursor
			-- may end up off if the offset is to big.
			-- (from TWO_WAY_LIST)

	ll_move (i: INTEGER_32)
			-- Move cursor i positions. The cursor
			-- may end up off if the offset is too big.
			-- (from LINKED_LIST)
		require -- from  CHAIN
			True
		ensure -- from CHAIN
			too_far_right: (old child_index + i > arity) implies exhausted
			too_far_left: (old child_index + i < 1) implies exhausted
			expected_index: (not exhausted) implies (child_index = old child_index + i)
		ensure then -- from LINKED_LIST
			moved_if_inbounds: ((old child_index + i) >= 0 and (old child_index + i) <= (arity + 1)) implies child_index = (old child_index + i)
			before_set: (old child_index + i) <= 0 implies child_before
			after_set: (old child_index + i) >= (arity + 1) implies child_after

	search_child (v: like child_item)
			-- Move to first position (at or after current
			-- position) where item and v are equal.
			-- If structure does not include v ensure that
			-- exhausted will be true.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from BILINEAR)
		ensure -- from LINEAR
			object_found: (not exhausted and object_comparison) implies v ~ child_item
			item_found: (not exhausted and not object_comparison) implies v = child_item

	child_start
			-- Move cursor to first position.
			-- (from LINKED_LIST)
		require -- from  TRAVERSABLE
			True
		require -- from  TREE
			True
		ensure then -- from CHAIN
			at_first: not is_leaf implies child_isfirst
		ensure then -- from LINKED_LIST
			empty_convention: is_leaf implies child_after
	
feature -- Element change

	append (s: SEQUENCE [G])
			-- Append a copy of s.
			-- (from CHAIN)
		require -- from SEQUENCE
			argument_not_void: s /= Void
		ensure -- from SEQUENCE
			new_count: arity >= old arity

	extend (v: like item)
			-- Add v as new child.
			-- (from DYNAMIC_TREE)

	child_extend (v: like child_item)
			-- Add v to end.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)
		require -- from COLLECTION
			extendible: child_extendible
		require -- from  DYNAMIC_TREE
			True
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)

	twl_fill (other: CONTAINER [G])
			-- Fill with as many items of other as possible.
			-- The representations of other and current structure
			-- need not be the same.
			-- (from CHAIN)
		require -- from COLLECTION
			other_not_void: other /= Void
			extendible: child_extendible

	force (v: like child_item)
			-- Add v to end.
			-- (from SEQUENCE)
		require -- from SEQUENCE
			extendible: child_extendible
		ensure then -- from SEQUENCE
			new_count: arity = old arity + 1
			item_inserted: has (v)

	twl_merge_left (other: TWO_WAY_TREE [G])
			-- Merge other into current structure before cursor
			-- position. Do not move cursor. Empty other.
			-- (from TWO_WAY_LIST)
		require -- from DYNAMIC_CHAIN
			extendible: child_extendible
			not_before: not child_before
			other_exists: other /= Void
			not_current: other /= Current
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + old other.arity
			new_index: child_index = old child_index + old other.arity
			other_is_empty: other.is_leaf

	twl_merge_right (other: TWO_WAY_TREE [G])
			-- Merge other into current structure after cursor
			-- position. Do not move cursor. Empty other.
			-- (from TWO_WAY_LIST)

	ll_merge_right (other: TWO_WAY_TREE [G])
			-- Merge other into current structure after cursor
			-- position. Do not move cursor. Empty other.
			-- (from LINKED_LIST)
		require -- from DYNAMIC_CHAIN
			extendible: child_extendible
			not_after: not child_after
			other_exists: other /= Void
			not_current: other /= Current
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + old other.arity
			same_index: child_index = old child_index
			other_is_empty: other.is_leaf

	merge_tree_after (other: like new_cell)
			-- Merge children of other into current structure
			-- after cursor position. Do not move cursor.
			-- Make other a leaf.
		require -- from DYNAMIC_TREE
			not_child_off: not child_off
			other_exists: other /= Void
		ensure -- from DYNAMIC_TREE
			other_is_leaf: other.is_leaf

	merge_tree_before (other: like new_cell)
			-- Merge children of other into current structure
			-- before cursor position. Do not move cursor.
			-- Make other a leaf.
		require -- from DYNAMIC_TREE
			not_child_off: not child_off
			other_exists: other /= Void
		ensure -- from DYNAMIC_TREE
			other_is_leaf: other.is_leaf

	prune (n: like new_cell)
			-- Prune n from children.
		require -- from TREE
			is_child: n.parent = Current
		ensure -- from TREE
			n_is_root: n.is_root

	sequence_put (v: like child_item)
			-- Add v to end.
			-- (from SEQUENCE)
		require -- from COLLECTION
			extendible: child_extendible
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)
		ensure then -- from SEQUENCE
			new_count: arity = old arity + 1

	put (v: like item)
			-- Make v the cell's item.
			-- Was declared in CELL as synonym of replace.
			-- (from CELL)
		require -- from TREE
			is_writable: Writable
		ensure -- from TREE
			item_inserted: item = v
		ensure -- from CELL
			item_inserted: item = v

	child_put (v: like child_item)
			-- Replace current item by v.
			-- (Synonym for replace)
			-- (from CHAIN)
		require -- from TREE
			child_writable: child_writable
		require -- from CHAIN
			writeable: child_writable
			replaceable: replaceable
		ensure -- from TREE
			item_inserted: child_item = v
		ensure -- from CHAIN
			same_count: arity = old arity
			is_inserted: is_inserted (v)

	put_child (n: like new_cell)
			-- Add n to the list of children.
			-- Do not move child cursor.
		require -- from TREE
			non_void_argument: n /= Void

	put_child_left (n: like new_cell)
			-- Add n to the left of cursor position.
			-- Do not move cursor.
		require -- from DYNAMIC_TREE
			not_child_before: not child_before
			non_void_argument: n /= Void

	put_child_right (n: like new_cell)
			-- Add n to the right of cursor position.
			-- Do not move cursor.
		require -- from DYNAMIC_TREE
			not_child_after: not child_after
			non_void_argument: n /= Void

	put_front (v: like child_item)
			-- Add v to beginning.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)

	ll_put_front (v: like child_item)
			-- Add v to beginning.
			-- Do not move cursor.
			-- (from LINKED_LIST)
		require -- from DYNAMIC_CHAIN
			extendible: child_extendible
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + 1
			item_inserted: first = v

	put_i_th (v: like child_item; i: INTEGER_32)
			-- Put v at i-th position.
			-- (from CHAIN)
		require -- from TABLE
			valid_key: valid_index (i)
		require -- from TABLE
			valid_key: valid_index (i)
		ensure -- from TABLE
			inserted: i_th (i) = v

	child_put_left (v: like child_item)
			-- Add v to the left of cursor position.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)
		require -- from DYNAMIC_CHAIN
			extendible: child_extendible
			not_before: not child_before
		require -- from DYNAMIC_TREE
			not_child_before: not child_before
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + 1
			new_index: child_index = old child_index + 1
		ensure then -- from LINKED_LIST
			previous_exists: previous /= Void
			item_inserted: attached previous as q and then q.item = v

	ll_put_right (v: like child_item)
			-- Add v to the right of cursor position.
			-- Do not move cursor.
			-- (from LINKED_LIST)
		require -- from DYNAMIC_CHAIN
			extendible: child_extendible
			not_after: not child_after
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + 1
			same_index: child_index = old child_index
		ensure then -- from LINKED_LIST
			next_exists: next /= Void
			item_inserted: not old child_before implies (attached next as n and then n.item = v)
			item_inserted_before: old child_before implies (attached child as c and then c.item = v)

	child_put_right (v: like child_item)
			-- Add v to the right of cursor position.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)
		require -- from DYNAMIC_TREE
			not_child_after: not child_after

	replace (v: like item)
			-- Make v the cell's item.
			-- Was declared in CELL as synonym of put.
			-- (from CELL)
		require -- from TREE
			is_writable: Writable
		ensure -- from TREE
			item_inserted: item = v
		ensure -- from CELL
			item_inserted: item = v

	child_replace (v: like child_item)
			-- Replace current item by v.
			-- (from LINKED_LIST)
		require -- from ACTIVE
			writable: child_writable
			replaceable: replaceable
		require -- from TREE
			child_writable: child_writable
		ensure -- from ACTIVE
			item_replaced: child_item = v
		ensure -- from TREE
			item_inserted: child_item = v

	replace_child (n: like new_cell)
			-- Replace current child by n.
		require -- from TREE
			writable_child: writable_child
		ensure -- from TREE
			child_replaced: child = n

	sprout
			-- Make current node a root.
			-- (from TREE)
	
feature -- Removal

	twl_prune (v: like child_item)
			-- Remove first occurrence of v, if any,
			-- after cursor position.
			-- If found, move cursor to right neighbor;
			-- if not, make structure exhausted.
			-- (from DYNAMIC_CHAIN)
		require -- from COLLECTION
			prunable: prunable

	prune_all (v: like child_item)
			-- Remove all occurrences of v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- Leave structure exhausted.
			-- (from DYNAMIC_CHAIN)
		require -- from COLLECTION
			prunable: prunable
		ensure -- from COLLECTION
			no_more_occurrences: not has (v)
		ensure then -- from DYNAMIC_CHAIN
			is_exhausted: exhausted

	remove_child
			-- Remove current item.
			-- Move cursor to right neighbor
			-- (or after if no right neighbor).
			-- (from TWO_WAY_LIST)
		require -- from ACTIVE
			prunable: prunable
			writable: child_writable
		require -- from DYNAMIC_TREE
			child_not_off: not child_off
		ensure then -- from DYNAMIC_LIST
			after_when_empty: is_leaf implies child_after
		ensure -- from DYNAMIC_TREE
			new_arity: arity = old arity - 1
			new_child_index: child_index = old child_index

	remove_i_th (i: INTEGER_32)
			-- Remove item at index i.
			-- Move cursor to next neighbor (or after if no next neighbor) if it is at i-th position.
			-- Do not change cursor otherwise.
			-- (from DYNAMIC_CHAIN)
		require -- from DYNAMIC_TABLE
			prunable: prunable
			valid_key: valid_index (i)
		ensure then -- from DYNAMIC_CHAIN
			new_count: arity = old arity - 1
			same_index_if_below: child_index <= i implies child_index = old child_index
			new_index_if_above: child_index > i implies child_index = old child_index - 1
			same_leading_items: across
					old twin as c
				all
					c.target_index < i implies c.item = i_th (c.target_index)
				end
			same_trailing_items: across
					old twin as c
				all
					c.target_index > i implies c.item = i_th (c.target_index - 1)
				end

	remove_left_child
			-- Remove item to the left of cursor position.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)
		require -- from DYNAMIC_CHAIN
			left_exists: child_index > 1
		require -- from DYNAMIC_TREE
			is_not_first: not child_isfirst
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity - 1
			new_index: child_index = old child_index - 1
		ensure -- from DYNAMIC_TREE
			new_arity: arity = old arity - 1
			new_child_index: child_index = old child_index - 1

	remove_right_child
			-- Remove item to the right of cursor position.
			-- Do not move cursor.
			-- (from TWO_WAY_LIST)
		require -- from DYNAMIC_CHAIN
			right_exists: child_index < arity
		require -- from DYNAMIC_TREE
			is_not_last: not child_islast
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity - 1
			same_index: child_index = old child_index
		ensure -- from DYNAMIC_TREE
			new_arity: arity = old arity - 1
			new_child_index: child_index = old child_index

	remove_sublist
			-- (from TWO_WAY_LIST)

	split (n: INTEGER_32)
			-- Do nothing.
		require -- from TWO_WAY_LIST
			not_off: not child_off
			valid_sublist: n >= 0

	wipe_out
			-- Remove all items.
			-- (from TWO_WAY_LIST)
		require -- from  TREE
			True
		ensure -- from TREE
			is_leaf: is_leaf

	ll_wipe_out
			-- Remove all items.
			-- (from LINKED_LIST)
		ensure then -- from DYNAMIC_LIST
			is_before: child_before

	chain_wipe_out
			-- Remove all items.
			-- (from DYNAMIC_CHAIN)
		require -- from COLLECTION
			prunable: prunable
		ensure -- from COLLECTION
			wiped_out: is_leaf
	
feature -- Transformation

	swap (i: INTEGER_32)
			-- Exchange item at i-th position with item
			-- at cursor position.
			-- (from CHAIN)
		require -- from CHAIN
			not_off: not child_off
			valid_index: valid_index (i)
		ensure -- from CHAIN
			swapped_to_item: child_item = old i_th (i)
			swapped_from_item: i_th (i) = old child_item
	
feature -- Conversion

	binary_representation: BINARY_TREE [G]
			-- Convert to binary tree representation:
			-- first child becomes left child,
			-- right sibling becomes right child.
			-- (from TREE)
		ensure -- from TREE
			result_is_root: Result.is_root
			result_has_no_right_child: not Result.has_right

	fill_from_binary (b: BINARY_TREE [G])
			-- Fill from a binary tree representation.
			-- Left child becomes first child.
			-- Right child becomes right sibling.
			-- Any right child of b is ignored.
			-- (from DYNAMIC_TREE)

	linear_representation: LINEAR [G]
			-- Representation as a linear structure
			-- (from TREE)
		require -- from  CONTAINER
			True
	
feature -- Duplication

	copy (other: TWO_WAY_TREE [G])
			-- Copy contents from other.
			-- (from TREE)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_equal: Current ~ other

	frozen deep_copy (other: TWO_WAY_TREE [G])
			-- Effect equivalent to that of:
			--		copy (other . deep_twin)
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			deep_equal: deep_equal (Current, other)

	frozen deep_twin: TWO_WAY_TREE [G]
			-- New object structure recursively duplicated from Current.
			-- (from ANY)
		ensure -- from ANY
			deep_twin_not_void: Result /= Void
			deep_equal: deep_equal (Current, Result)

	frozen standard_copy (other: TWO_WAY_TREE [G])
			-- Copy every field of other onto corresponding field
			-- of current object.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_standard_equal: standard_is_equal (other)

	frozen standard_twin: TWO_WAY_TREE [G]
			-- New object field-by-field identical to other.
			-- Always uses default copying semantics.
			-- (from ANY)
		ensure -- from ANY
			standard_twin_not_void: Result /= Void
			equal: standard_equal (Result, Current)

	frozen twin: TWO_WAY_TREE [G]
			-- New object equal to Current
			-- twin calls copy; to change copying/twinning semantics, redefine copy.
			-- (from ANY)
		ensure -- from ANY
			twin_not_void: Result /= Void
			is_equal: Result ~ Current
	
feature -- Basic operations

	frozen default: detachable TWO_WAY_TREE [G]
			-- Default value of object's type
			-- (from ANY)

	frozen default_pointer: POINTER
			-- Default value of type POINTER
			-- (Avoid the need to write p.default for
			-- some p of type POINTER.)
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	default_rescue
			-- Process exception for routines with no Rescue clause.
			-- (Default: do nothing.)
			-- (from ANY)

	frozen do_nothing
			-- Execute a null action.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
	
feature -- Implementation

	child: like first_child
			-- Element at cursor position
			-- (from LINKED_LIST)

	forget_left
			-- Remove links with left neighbor.
			-- (from BI_LINKABLE)
		require -- from  TREE
			True
		ensure -- from BI_LINKABLE
			left_not_chained: left_sibling = Void or else (attached {like left_sibling} old left_sibling as p implies p.right_sibling = Void)

	forget_right
			-- Remove links with right neighbor.
			-- (from BI_LINKABLE)
		require -- from  LINKABLE
			True
		require -- from  TREE
			True
		ensure -- from LINKABLE
			not_chained: right_sibling = Void
		ensure then -- from BI_LINKABLE
			right_not_chained: (attached {like right_sibling} old right_sibling as r) implies r.left_sibling = Void
	
feature -- Iteration

	do_all (action: PROCEDURE [G])
			-- Apply action to every item.
			-- Semantics not guaranteed if action changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			action_exists: action /= Void

	do_if (action: PROCEDURE [G]; test: FUNCTION [G, BOOLEAN])
			-- Apply action to every item that satisfies test.
			-- Semantics not guaranteed if action or test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			action_exists: action /= Void
			test_exists: test /= Void

	for_all (test: FUNCTION [G, BOOLEAN]): BOOLEAN
			-- Is test true for all items?
			-- Semantics not guaranteed if test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exists: test /= Void
		ensure then -- from LINEAR
			empty: is_leaf implies Result

	new_cursor: TWO_WAY_TREE_ITERATION_CURSOR [G]
			-- Fresh cursor associated with current structure

	there_exists (test: FUNCTION [G, BOOLEAN]): BOOLEAN
			-- Is test true for at least one item?
			-- Semantics not guaranteed if test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exists: test /= Void
	
feature -- Output

	Io: STD_FILES
			-- Handle to standard file setup
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			io_not_void: Result /= Void

	out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			out_not_void: Result /= Void

	print (o: detachable ANY)
			-- Write terse external representation of o
			-- on standard output.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	frozen tagged_out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			tagged_out_not_void: Result /= Void
	
feature -- Platform

	Operating_environment: OPERATING_ENVIRONMENT
			-- Objects available from the operating system
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			operating_environment_not_void: Result /= Void
	
invariant
	off_constraint: (child = Void) implies child_off

		-- from DYNAMIC_TREE
	extendible_definition: Extendible
	child_after_definition: child_after = (child_index = arity + 1)

		-- from TREE
	tree_consistency: child_readable implies (attached child as c and then c.parent = Current)
	leaf_definition: is_leaf = (arity = 0)
	child_off_definition: child_off = child_before or child_after
	child_before_definition: child_before = (child_index = 0)
	child_isfirst_definition: child_isfirst = (not is_leaf and child_index = 1)
	child_islast_definition: child_islast = (not is_leaf and child_index = child_capacity)
	child_after_definition: child_after = (child_index >= child_capacity + 1)

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)

		-- from BI_LINKABLE
	right_symmetry: attached right_sibling as r implies (r.left_sibling = Current)
	left_symmetry: attached left_sibling as l implies (l.right_sibling = Current)

		-- from TWO_WAY_LIST
	non_empty_list_has_two_endpoints: not is_leaf implies (first_child /= Void and last_child /= Void)
	empty_list_has_no_endpoints: is_leaf implies last_child = Void
	first_element_constraint: attached first_child as f implies f.left_sibling = Void
	last_element_constraint: attached last_child as l implies l.right_sibling = Void

		-- from LINKED_LIST
	prunable: prunable
	empty_constraint: is_leaf implies ((first_child = Void) and (child = Void))
	not_void_unless_empty: (child = Void) implies is_leaf
	before_constraint: child_before implies (child = first_child)
	after_constraint: child_after implies (child = last_child)

		-- from LIST
	before_definition: child_before = (child_index = 0)
	after_definition: child_after = (child_index = arity + 1)

		-- from CHAIN
	non_negative_index: child_index >= 0
	index_small_enough: child_index <= arity + 1
	off_definition: child_off = ((child_index = 0) or (child_index = arity + 1))
	isfirst_definition: child_isfirst = ((not is_leaf) and (child_index = 1))
	islast_definition: child_islast = ((not is_leaf) and (child_index = arity))
	item_corresponds_to_index: (not child_off) implies (child_item = i_th (child_index))

		-- from ACTIVE
	writable_constraint: child_writable implies child_readable
	empty_constraint: is_leaf implies (not child_readable) and (not child_writable)

		-- from READABLE_INDEXABLE
	consistent_boundaries: Lower <= arity or else Lower = arity + 1

		-- from BILINEAR
	not_both: not (child_after and child_before)
	before_constraint: child_before implies child_off

		-- from LINEAR
	after_constraint: child_after implies child_off

		-- from TRAVERSABLE
	empty_constraint: is_leaf implies child_off

		-- from FINITE
	empty_definition: is_leaf = (arity = 0)

note
	copyright: "Copyright (c) 1984-2018, Eiffel Software and others"
	license: "Eiffel Forum License v2 (see http://www.eiffel.com/licensing/forum.txt)"
	source: "[
		Eiffel Software
		5949 Hollister Ave., Goleta, CA 93117 USA
		Telephone 805-685-1006, Fax 805-685-6869
		Website http://www.eiffel.com
		Customer support http://support.eiffel.com
	]"

end -- class TWO_WAY_TREE

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