indexing
	description: "Trees where the children of each node are kept in an array"
	names: tree
	representation: recursive, array
	access: cursor, membership
	contents: generic

class interface
	ARRAYED_TREE [G]

create 

	make (n: INTEGER; v: G)
			-- Create node with item v.
			-- Allocate space for n children.
		require
			valid_number_of_children: n >= 0
		ensure
			node_item: item = v

feature -- Initialization

	make (n: INTEGER; v: G)
			-- Create node with item v.
			-- Allocate space for n children.
		require
			valid_number_of_children: n >= 0
		ensure
			node_item: item = v

	make_filled (n: INTEGER)
			-- Allocate list with n items.
			-- (n may be zero for empty list.)
			-- This list will be full.
			-- (from ARRAYED_LIST)
		require -- from ARRAYED_LIST
			valid_number_of_items: n >= 0
		ensure -- from ARRAYED_LIST
			correct_position: child_before;

	
feature -- Access

	child_item: like item
			-- Item in current child node
			-- (from TREE)
		require -- from TREE
			readable: child_readable

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

	first_child: ARRAYED_TREE [G]
			-- Item at first position
			-- (from ARRAYED_LIST)
		require -- from CHAIN
			not_empty: not is_leaf
		require -- from TREE
			is_not_leaf: not is_leaf

	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

	child_index: INTEGER
			-- Index of item, if valid.
			-- (from ARRAYED_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

	is_sibling (other: like parent): BOOLEAN
			-- Are current node and other siblings?
			-- (from TREE)
		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

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

	child: like first_child
			-- Current item
			-- (from ARRAYED_LIST)
		require -- from ACTIVE
			readable: readable_child
		require -- from TRAVERSABLE
			not_off: not child_off
		require else -- from ARRAYED_LIST
			index_is_valid: valid_index (child_index)
		require -- from TREE
			readable: readable_child
		require else -- from ARRAYED_LIST
			index_is_valid: valid_index (child_index)

	frozen array_item (i: INTEGER): ARRAYED_TREE [G]
			-- Entry at index i, if in index interval
			-- Was declared in ARRAY as synonym of item, @ and entry.
			-- (from ARRAY)
		require -- from TABLE
			valid_key: valid_index (k)

	last_child: like first_child
			-- Item at last position
			-- (from ARRAYED_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: is_sibling (Result);
			right_is_current: (Result /= void) implies (Result.right_sibling = Current)

	occurrences (v: like child): INTEGER
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from CHAIN)
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	sequential_occurrences (v: ARRAYED_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

	occurrences (v: like child): INTEGER
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from CHAIN)
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	parent: ARRAYED_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: is_sibling (Result);
			left_is_current: (Result /= void) implies (Result.left_sibling = Current)

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

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

	arity: INTEGER
			-- Number of items.
			-- (from ARRAYED_LIST)
	
feature {ANY} -- Measurement

	capacity: INTEGER
			-- Number of available indices
			-- Was declared in ARRAY as synonym of count and capacity.
			-- (from ARRAY)
	
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)

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

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

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

	Extendible: BOOLEAN is true
			-- May new items be added?
			-- (from DYNAMIC_TREE)

	Al_extendible: BOOLEAN is true
			-- May new items be added? (Answer: yes.)
			-- (from DYNAMIC_CHAIN)

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

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

	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? (Answer: yes.)
			-- (from ARRAYED_LIST)

	Readable: BOOLEAN is true
			-- (from TREE)

	readable_child: BOOLEAN
			-- Is there a current item that may be read?
			-- (from SEQUENCE)

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

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

	valid_index (i: INTEGER): BOOLEAN
			-- Is i a valid index?
			-- (from ARRAYED_LIST)
		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 item that may be modified?
			-- (from SEQUENCE)
	
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
		require -- from CONTAINER
			changeable_comparison_criterion
		ensure -- from CONTAINER
			object_comparison
		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
		require -- from CONTAINER
			changeable_comparison_criterion
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
	
feature -- Cursor movement

	child_back
			-- Move cursor one position backward.
			-- (from ARRAYED_LIST)
		require -- from BILINEAR
			not_before: not child_before
		ensure then -- from BILINEAR
			moved_back: child_index = old child_index - 1

	child_finish
			-- Move cursor to last position if any.
			-- (from ARRAYED_LIST)
		ensure then -- from CHAIN
			at_last: not is_leaf implies child_islast
		ensure then -- from ARRAYED_LIST
			before_when_empty: is_leaf implies child_before
		ensure then -- from TREE
			is_last_child: not is_leaf implies child_islast
		ensure then -- from ARRAYED_LIST
			before_when_empty: is_leaf implies child_before

	child_forth
			-- Move cursor one position forward.
			-- (from ARRAYED_LIST)
		require -- LIST
			precursor: 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 ARRAYED_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;
			is_before: (i = 0) implies child_before;
			is_after: (i = arity + 1) implies child_after

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

	move (i: INTEGER)
			-- Move cursor i positions.
			-- (from ARRAYED_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 if any.
			-- (from ARRAYED_LIST)
		ensure then -- from CHAIN
			at_first: not is_leaf implies child_isfirst
		ensure then -- from ARRAYED_LIST
			after_when_empty: is_leaf implies child_after
		ensure then -- from TREE
			is_first_child: not is_leaf implies child_isfirst
		ensure then -- from ARRAYED_LIST
			after_when_empty: is_leaf implies child_after
	
feature -- Element change

	append (s: SEQUENCE [ARRAYED_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_extend (v: like item)
			-- Add v at end.
			-- Do not move child cursor.

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

	child_put_left (v: like item)
			-- Add v to the left of cursor position.
			-- Do not move child cursor.
		require -- from DYNAMIC_TREE
			not_child_before: not child_before

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

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

	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)

	force (v: like child)
			-- Add v to end.
			-- Do not move cursor.
			-- Was declared in ARRAYED_LIST as synonym of force and extend.
			-- (from ARRAYED_LIST)
		require -- from SEQUENCE
			extendible: al_extendible
		ensure then -- from SEQUENCE
			new_count: arity = old arity + 1;
			item_inserted: has (v)

	merge_tree_after (other: like first_child)
			-- 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 first_child)
			-- 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

	frozen put_i_th (v: like array_item; i: INTEGER)
			-- Replace i-th entry, if in index interval, by v.
			-- Was declared in ARRAY as synonym of put and enter.
			-- (from ARRAY)
		require -- from TABLE
			valid_key: valid_index (k)
		ensure then -- from INDEXABLE
			insertion_done: array_item (k) = v

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

	put_child (n: like parent)
			-- Add n to the list of children.
			-- Do not move child cursor.
		require else -- from DYNAMIC_TREE
			non_void_argument: n /= void

	put_child_left (n: like parent)
			-- 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 parent)
			-- Add n to the right of the 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)
			-- Add v to the beginning.
			-- Do not move cursor.
			-- (from ARRAYED_LIST)
		ensure -- from DYNAMIC_CHAIN
			new_count: arity = old arity + 1;
			item_inserted: first_child = v

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

	replace_child (n: like parent)
			-- Make n the node's current 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

	prune (v: like child)
			-- Remove first occurrence of v, if any,
			-- after cursor position.
			-- Move cursor to right neighbor
			-- (or after if no right neighbor or vdoes not occur)
			-- (from ARRAYED_LIST)
		require -- from COLLECTION
			prunable: prunable
		require -- from TREE
			is_child: n.parent = Current
		ensure -- from TREE
			n_is_root: n.is_root

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

	remove_child
			-- Remove child at cursor position.
			-- Move cursor to the next sibling, or after if none.
		require -- from DYNAMIC_TREE
			child_not_off: not child_off
		ensure -- from DYNAMIC_TREE
			new_arity: arity = old arity - 1;
			new_child_index: child_index = old child_index

	remove_left_child
			-- Remove item to the left of cursor position.
			-- Do not move cursor.
		require -- from DYNAMIC_TREE
			is_not_first: not child_isfirst
		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.
		require -- from DYNAMIC_TREE
			is_not_last: not child_islast
		ensure -- from DYNAMIC_TREE
			new_arity: arity = old arity - 1;
			new_child_index: child_index = old child_index

	wipe_out
			-- Remove all items.
			-- (from ARRAYED_LIST)
		require -- from COLLECTION
			prunable
		ensure -- from COLLECTION
			wiped_out: is_leaf
		ensure then -- from DYNAMIC_LIST
			is_before: child_before
	
feature -- Transformation

	swap (i: INTEGER)
			-- Exchange item at i-th position with item
			-- at cursor position.
			-- (from ARRAYED_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

	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)
	
feature -- Duplication

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

		-- from GENERAL
	reflexive_equality: standard_is_equal (Current);
	reflexive_conformance: conforms_to (Current);
		-- from DYNAMIC_TREE
	extendible_definition: extendible;
	child_after_definition: child_after = (child_index = arity + 1);
		-- 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 = arity);
	child_after_definition: child_after = (child_index >= arity + 1);
	child_consistency: child_readable implies child.parent = Current;
		-- from ARRAYED_LIST
	prunable: prunable;
		-- from ARRAY
non_negative_count: arity >= 0;
		-- from BOUNDED
	valid_count: arity <= capacity;
		-- from FINITE
	empty_definition: is_leaf = (arity = 0);
	non_negative_count: arity >= 0;
		-- 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));
		-- from ACTIVE
	writable_constraint: writable_child implies readable_child;
	empty_constraint: is_leaf implies (not readable_child) and (not writable_child);
		-- from BILINEAR
	not_both: not (child_after and child_before);
	empty_property: is_leaf implies (child_after or 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 DYNAMIC_CHAIN
	extendible: al_extendible;

end -- class ARRAYED_TREE