indexing
	description: "[
		Trees where each node has a fixed number of children
		(The number of children is arbitrary but cannot be
		changed once the node has been created
	]"
	names: fixed_tree, tree, fixed_list
	representation: recursive, array
	access: cursor, membership
	contents: generic
	date: "$Date$"
	revision: "$Revision$"

class interface
	FIXED_TREE [G]

create

	make (n: INTEGER; v: G)
			-- Create node with n void children and item v.
		require
			valid_number_of_children: n >= 0
		ensure
			node_item: item = v
			node_arity: arity = n

feature -- Initialization

	make (n: INTEGER; v: G)
			-- Create node with n void children and item v.
		require
			valid_number_of_children: n >= 0
		ensure
			node_item: item = v
			node_arity: arity = n

feature -- Access

	child_item: like item
			-- Item of active child
		require -- from TREE
			readable: child_readable

	child_cursor: CURSOR
			-- Current cursor position
			-- (from FIXED_LIST)

	first_child: like parent
			-- Leftmost child
		require -- from CHAIN
			not_empty: not is_leaf
		require -- from TREE
			is_not_leaf: not is_leaf

	child_index: INTEGER
			-- Current position in the list
			-- (from FIXED_LIST)

	index_of (v: like child; i: INTEGER): INTEGER
			-- Index of i-th occurrence of item identical to v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- 0 if none.
			-- (from CHAIN)
		require -- from LINEAR
			positive_occurrences: i > 0
		ensure -- from LINEAR
			non_negative_result: Result >= 0

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

	child: FIXED_TREE [G]
			-- Current item
			-- (from FIXED_LIST)
		require -- from TRAVERSABLE
			not_off: not child_off
		require -- from ACTIVE
			readable: fl_readable
		require -- from TREE
			readable: readable_child

	last_child: like first_child
			-- Item at last position
			-- (from FIXED_LIST)
		require -- from CHAIN
			not_empty: not is_leaf
		require -- from TREE
			is_not_leaf: not is_leaf

	left_sibling: like parent
			-- Left neighbor, if any
		require -- from TREE
			is_not_root: not is_root
		ensure -- from TREE
			is_sibling: Result /= void implies is_sibling (Result)
			right_is_current: (Result /= void) implies (Result.right_sibling = Current)

	sequential_occurrences (v: FIXED_TREE [G]): INTEGER
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	parent: FIXED_TREE [G]
			-- Parent of current node

	right_sibling: like parent
			-- Right neighbor, if any
		require -- from TREE
			is_not_root: not is_root
		ensure -- from TREE
			is_sibling: Result /= void implies is_sibling (Result)
			left_is_current: (Result /= void) implies (Result.left_sibling = Current)

	infix "@" (i: INTEGER): FIXED_TREE [G]
			-- Entry at index i, if in index interval
			-- Was declared in ARRAY as synonym of item.
			-- (from ARRAY)
		require -- from TABLE
			valid_key: valid_index (k)

feature  -- Access

	area: SPECIAL [FIXED_TREE [G]]
			-- Special data zone
			-- (from TO_SPECIAL)

feature -- Measurement

	capacity: INTEGER
			-- Number of available indices
			-- Was declared in ARRAY as synonym of count.
			-- (from ARRAY)
		ensure then -- from ARRAY
			consistent_with_bounds: Result = upper - lower + 1

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

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

	arity: INTEGER
			-- (from FIXED_LIST)

	index_set: INTEGER_INTERVAL
			-- Range of acceptable indexes
			-- (from CHAIN)
		ensure -- from INDEXABLE
			not_void: Result /= void
		ensure then -- from CHAIN
			count_definition: Result.count = arity

	occurrences (v: FIXED_TREE [G]): INTEGER
			-- Number of times v appears in structure
			-- (from ARRAY)
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

feature -- Comparison

	is_equal (other: like Current): 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.is_equal (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

feature -- Status report

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

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

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

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

	child_contractable: BOOLEAN
			-- May items be removed?
		ensure
			Result = not child_off

	child_isfirst: BOOLEAN
			-- Is cursor under first child?
			-- (from TREE)
		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?
			-- (from TREE)
		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)

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

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

	Full: BOOLEAN is True
			-- Is tree full?

	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: FIXED_TREE [G]): BOOLEAN
			-- Has v been inserted by the most recent insertion?
			-- (By default, the value returned is equivalent to calling
			-- `has (v)'. However, descendants might be able to provide more
			-- efficient implementations.)
			-- (from COLLECTION)

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

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

	is_sibling (other: 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)

	fl_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 CHAIN)

	prunable: BOOLEAN
			-- May items be removed?
			-- (from FIXED_LIST)

	Readable: BOOLEAN is True
			-- (from TREE)

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

	Resizable: BOOLEAN is False
			-- May capacity be changed? (Answer: no.)
			-- (from FIXED)

	valid_cursor (p: CURSOR): BOOLEAN
			-- Is p a valid cursor?
			-- (from FIXED_LIST)

	valid_cursor_index (i: INTEGER): BOOLEAN
			-- Is i correctly bounded for cursor movement?
			-- (from TREE)
		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): BOOLEAN
			-- Is i within the bounds of the array?
			-- (from ARRAY)
		ensure then -- from INDEXABLE
			only_if_in_index_set: Result implies ((i >= index_set.lower) and (i <= index_set.upper))
		ensure then -- from CHAIN
			valid_index_definition: Result = ((i >= 1) and (i <= arity))

	Writable: BOOLEAN is 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
		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
		ensure -- from CONTAINER
			reference_comparison: not object_comparison

feature -- Cursor movement

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

	child_finish
			-- Move cursor to last position.
			-- (from FIXED_LIST)
		ensure then -- from CHAIN
			at_last: not is_leaf implies child_islast
		ensure then -- from TREE
			is_last_child: not is_leaf implies child_islast

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

	child_go_i_th (i: INTEGER)
			-- Move cursor to i-th position.
			-- (from FIXED_LIST)
		require -- from CHAIN
			valid_cursor_index: valid_cursor_index (i)
		require else -- from TREE
			valid_cursor_index: valid_cursor_index (i)
		ensure -- from CHAIN
			position_expected: child_index = i
		ensure then -- from TREE
			position: child_index = i

	child_go_to (p: CURSOR)
			-- Move cursor to element remembered in p.
			-- (from FIXED_LIST)
		require -- from  TREE
			True
		require -- from CURSOR_STRUCTURE
			cursor_position_valid: valid_cursor (p)

	move (i: INTEGER)
			-- Move cursor i positions.
			-- (from FIXED_LIST)
		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)

	search_child (v: like child)
			-- 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 equal (v, child)
			item_found: (not exhausted and not object_comparison) implies v = child

	child_start
			-- Move cursor to first position.
			-- (from FIXED_LIST)
		ensure then -- from CHAIN
			at_first: not is_leaf implies child_isfirst
		ensure then -- from TREE
			is_first_child: not is_leaf implies child_isfirst

feature -- Element change

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

	child_put (v: like item)
			-- Replace current child item with v
			-- Was declared in FIXED_TREE as synonym of child_replace.
		require -- from TREE
			child_writable: child_writable
		ensure -- from TREE
			item_inserted: child_item = v

	child_replace (v: like item)
			-- Replace current child item with v
			-- Was declared in FIXED_TREE as synonym of child_put.
		require -- from TREE
			child_writable: child_writable
		ensure -- from TREE
			item_inserted: child_item = v

	extend (v: like child)
			-- Add v to end.
			-- Move index to the current item.
			-- (from FIXED_LIST)
		require -- from COLLECTION
			extendible: fl_extendible
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)
		ensure then -- from BAG
			one_more_occurrence: occurrences (v) = old (occurrences (v)) + 1

	fill (other: TREE [G])
			-- Fill with as many items of other as possible.
			-- The representations of other and current node
			-- need not be the same.
			-- (from TREE)

	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

	put_i_th (v: like array_item; i: INTEGER)
			-- Replace i-th entry, if in index interval, by v.
			-- (from ARRAY)
		require -- from TABLE
			valid_key: valid_index (k)
		ensure then -- from INDEXABLE
			insertion_done: array_item (k) = v

	put_child (n: like parent)
			-- Make n the node's child.
			-- Was declared in FIXED_TREE as synonym of replace_child.
		ensure then
			child_replaced: n.parent = Current

	put_left (v: like item)
			-- Add v to the left of current node.
		require
			is_not_root: not is_root
			has_left_sibling: left_sibling /= void
		ensure
			item_put: left_sibling.item = v

	put_left_sibling (other: like parent)
			-- Make other the left sibling of current node.
		require
			is_not_root: not is_root
			has_left_sibling: left_sibling /= void
		ensure
			left_sibling_replaced: left_sibling = other

	put_right (v: like item)
			-- Add v to the right of current node.
		require
			is_not_root: not is_root
			has_right_sibling: right_sibling /= void
		ensure
			item_put: right_sibling.item = v

	put_right_sibling (other: like parent)
			-- Make other the right sibling of current node.
		require
			is_not_root: not is_root
			has_right_sibling: right_sibling /= void
		ensure
			right_sibling_replaced: right_sibling = other

	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

	replace_child (n: like parent)
			-- Make n the node's child.
			-- Was declared in FIXED_TREE as synonym of put_child.
		require -- from TREE
			writable_child: writable_child
			was_root: n.is_root
		ensure -- from TREE
			child_replaced: child = n
		ensure then
			child_replaced: n.parent = Current

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

feature -- Removal

	remove_child
			-- Remove active child.
		ensure then
			child_removed: child = void

feature -- Transformation

	swap (i: INTEGER)
			-- Exchange item at i-th position with item
			-- at cursor position.
			-- (from FIXED_LIST)
		require -- from CHAIN
			not_off: not child_off
			valid_index: valid_index (i)
		ensure -- from CHAIN
			swapped_to_item: child = old array_item (i)
			swapped_from_item: array_item (i) = old child

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

	linear_representation: LINEAR [G]
			-- Representation as a linear structure
			-- (from TREE)

feature -- Duplication

	copy (other: like Current)
			-- Copy contents from other.
		require -- from ANY
			other_not_void: other /= void
			type_identity: same_type (other)
		ensure -- from ANY
			is_equal: is_equal (other)
		ensure then -- from ARRAY
			equal_areas: area.is_equal (other.area)

	duplicate (n: INTEGER): like Current
			-- Copy of sub-tree beginning at cursor position and
			-- having min (n, arity - child_index + 1)
			-- children.
		require -- from CHAIN
			not_off_unless_after: child_off implies child_after
			valid_subchain: n >= 0
		require -- from TREE
			not_child_off: not child_off
			valid_sublist: n >= 0

feature -- Inapplicable

	prune (v: FIXED_TREE [G])
			-- Remove first occurrence of v if any.
			-- (Precondition is False.)
			-- (from ARRAY)
		require -- from COLLECTION
			prunable: prunable
		require -- from TREE
			is_child: n.parent = Current
		ensure -- from TREE
			n_is_root: n.is_root

feature -- Iteration

	do_all (action: PROCEDURE [ANY, TUPLE [FIXED_TREE [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 [ANY, TUPLE [FIXED_TREE [G]]]; test: FUNCTION [ANY, TUPLE [FIXED_TREE [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_exits: test /= void

	for_all (test: FUNCTION [ANY, TUPLE [FIXED_TREE [G]], BOOLEAN]): BOOLEAN
			-- Is test true for all items?
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exits: test /= void

	there_exists (test: FUNCTION [ANY, TUPLE [FIXED_TREE [G]], BOOLEAN]): BOOLEAN
			-- Is test true for at least one item?
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exits: test /= void

invariant

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)
		-- from TREE
	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)
	child_consistency: child_readable implies child.parent = Current
		-- from FIXED_LIST
	empty_means_storage_empty: is_leaf implies all_default
		-- 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 = array_item (child_index))
	index_set_has_same_count: index_set.count = arity
		-- from ACTIVE
	writable_constraint: fl_writable implies fl_readable
	empty_constraint: is_leaf implies (not fl_readable) and (not fl_writable)
		-- from INDEXABLE
	index_set_not_void: index_set /= void
		-- 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)
	non_negative_count: arity >= 0
		-- from ARRAY
	area_exists: area /= void
	consistent_size: capacity = upper - lower + 1
	non_negative_count: arity >= 0
	index_set_has_same_count: valid_index_set
		-- from RESIZABLE
	increase_by_at_least_one: minimal_increase >= 1
		-- from BOUNDED
	valid_count: arity <= capacity
	full_definition: fl_full = (arity = capacity)
		-- from FIXED
	not_resizable: not resizable

indexing
	library: "[
			EiffelBase: Library of reusable components for Eiffel.
	]"
	status: "[
			Copyright 1986-2001 Interactive Software Engineering (ISE).
			For ISE customers the original versions are an ISE product
			covered by the ISE Eiffel license and support agreements.
	]"
	license: "[
			EiffelBase may now be used by anyone as FREE SOFTWARE to
			develop any product, public-domain or commercial, without
			payment to ISE, under the terms of the ISE Free Eiffel Library
			License (IFELL) at http://eiffel.com/products/base/license.html.
	]"
	source: "[
			Interactive Software Engineering Inc.
			ISE Building
			360 Storke Road, Goleta, CA 93117 USA
			Telephone 805-685-1006, Fax 805-685-6869
			Electronic mail <info@eiffel.com>
			Customer support http://support.eiffel.com
	]"
	info: "[
			For latest info see award-winning pages: http://eiffel.com
	]"

end -- class FIXED_TREE