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indexing
	description: "[
		Binary search trees; left child item is less than current item,
		right child item is greater
	]"
	status: "See notice at end of class"
	names: binary_search_tree, tree
	representation: recursive, array
	access: cursor, membership
	contents: generic
	date: "$Date: 2001-11-16 20:32:23 +0000 (Fri, 16 Nov 2001) $"
	revision: "$Revision: 51435 $"

class 
	BINARY_SEARCH_TREE [G -> COMPARABLE]

create 
	make

feature -- Initialization

	make (v: like item) is
			-- Create single node with item v.
		require
			item_exists: v /= void
		do
			bt_make (v)
		ensure
			node_item: item = v
			no_child: (left_child = void) and (right_child = void)
		end

	bt_make (v: like item) is
			-- Create a root node with value v.
			-- (from BINARY_TREE)
		do
			item := v
		ensure -- from BINARY_TREE
			is_root: is_root
			is_leaf: is_leaf
		end
	
feature -- Access

	child: like parent is
			-- Child at cursor position
			-- (from BINARY_TREE)
		require -- from TREE
			readable: readable_child
		do
			inspect child_index
			when 1 then 
				Result := left_child
			when 2 then 
				Result := right_child
			end
		end

	child_cursor: CURSOR is
			-- Current cursor position
			-- (from BINARY_TREE)
		do
			create {ARRAYED_LIST_CURSOR} Result.make (child_index)
		end

	child_index: INTEGER
			-- Index of cursor position
			-- (from BINARY_TREE)

	child_item: like item is
			-- Item in current child node
			-- (from TREE)
		require -- from TREE
			readable: child_readable
		do
			Result := child.item
		end

	first_child: like parent is
			-- Left child
			-- (from BINARY_TREE)
		require -- from TREE
			is_not_leaf: not is_leaf
		do
			Result := left_child
		end

	has (v: like item): BOOLEAN is
			-- Does tree contain a node whose item
			-- is equal to v (object comparison)?
		require -- from  CONTAINER
			True
		require else
			argument_not_void: v /= void
		do
			if items_equal (item, v) then
				Result := True
			elseif v < item then
				if left_child /= void then
					set_comparison_mode (left_child);
					Result := left_child.has (v)
				end
			else
				if right_child /= void then
					set_comparison_mode (right_child)
					Result := right_child.has (v)
				end
			end
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not is_empty
		end

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

	last_child: like parent is
			-- Right child
			-- (from BINARY_TREE)
		require -- from TREE
			is_not_leaf: not is_leaf
		do
			Result := right_child
		end

	left_child: like parent
			-- Left child, if any
			-- (from BINARY_TREE)

	left_item: like item is
			-- Value of left child
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			has_left: left_child /= void
		do
			Result := left_child.item
		end

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

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

	right_child: like parent
			-- Right child, if any
			-- (from BINARY_TREE)

	right_item: like item is
			-- Value of right child
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			has_right: right_child /= void
		do
			Result := right_child.item
		end

	right_sibling: like parent is
			-- Right neighbor, if any
			-- (from BINARY_TREE)
		require -- from TREE
			is_not_root: not is_root
		do
			if parent.left_child = Current then
				Result := parent.right_child
			end
		ensure -- from TREE
			is_sibling: Result /= void implies is_sibling (Result)
			left_is_current: (Result /= void) implies (Result.left_sibling = Current)
		end
	
feature -- Measurement

	arity: INTEGER is
			-- Number of children
			-- (from BINARY_TREE)
		do
			if has_left then
				Result := Result + 1
			end
			if has_right then
				Result := Result + 1
			end
		ensure then -- from BINARY_TREE
			valid_arity: Result <= 2
		end

	count: INTEGER is
			-- Number of items
			-- (from TREE)
		do
			Result := subtree_count + 1
		end

	max: like item is
			-- Maximum item in tree
		do
			if has_right then
				Result := right_child.max
			else
				Result := item
			end
		ensure
			maximum_present: has (Result)
		end

	min: like item is
			-- Minimum item in tree
		do
			if has_left then
				Result := left_child.min
			else
				Result := item
			end
		ensure
			minimum_present: has (Result)
		end
	
feature -- Comparison

	is_equal (other: like Current): BOOLEAN is
			-- Does other contain the same elements?
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from TREE)
		require -- from ANY
			other_not_void: other /= void
		do
			if Current = other then
				Result := True
			else
				Result := (is_empty = other.is_empty) and (object_comparison = other.object_comparison) and (child_capacity = other.child_capacity)
				if Result and not is_empty then
					Result := tree_is_equal (Current, other)
				end
			end
		ensure -- from ANY
			symmetric: Result implies other.is_equal (Current)
			consistent: standard_is_equal (other) implies Result
		end
	
feature -- Status report

	changeable_comparison_criterion: BOOLEAN is
			-- May object_comparison be changed?
			-- (Answer: yes by default.)
			-- (from CONTAINER)
		do
			Result := True
		end

	child_after: BOOLEAN is
			-- Is there no valid child position to the right of cursor?
			-- (from BINARY_TREE)
		do
			Result := child_index >= child_capacity + 1
		end

	child_before: BOOLEAN is
			-- Is there no valid child position to the left of cursor?
			-- (from TREE)
		do
			Result := child_index = 0
		end

	child_isfirst: BOOLEAN is
			-- Is cursor under first child?
			-- (from TREE)
		do
			Result := not is_leaf and child_index = 1
		ensure -- from TREE
			not_is_leaf: Result implies not is_leaf
		end

	child_islast: BOOLEAN is
			-- Is cursor under last child?
			-- (from TREE)
		do
			Result := not is_leaf and child_index = child_capacity
		ensure -- from TREE
			not_is_leaf: Result implies not is_leaf
		end

	child_off: BOOLEAN is
			-- Is there no current child?
			-- (from TREE)
		do
			Result := child_before or child_after
		end

	child_readable: BOOLEAN is
			-- Is there a current child_item to be read?
			-- (from TREE)
		do
			Result := not child_off and then (child /= void)
		end

	child_writable: BOOLEAN is
			-- Is there a current child_item that may be modified?
			-- (from TREE)
		do
			Result := not child_off and then (child /= void)
		end

	empty: BOOLEAN is
		obsolete "ELKS 2000: Use `is_empty' instead"
			-- Is there no element?
			-- (from CONTAINER)
		do
			Result := is_empty
		end

	has_both: BOOLEAN is
			-- Has current node two children?
			-- (from BINARY_TREE)
		do
			Result := left_child /= void and right_child /= void
		ensure -- from BINARY_TREE
			Result = (has_left and has_right)
		end

	has_left: BOOLEAN is
			-- Has current node a left child?
			-- (from BINARY_TREE)
		do
			Result := left_child /= void
		ensure -- from BINARY_TREE
			Result = (left_child /= void)
		end

	has_none: BOOLEAN is
			-- Are there no children?
			-- Was declared in BINARY_TREE as synonym of is_leaf.
			-- (from BINARY_TREE)
		do
			Result := left_child = void and right_child = void
		end

	has_right: BOOLEAN is
			-- Has current node a right child?
			-- (from BINARY_TREE)
		do
			Result := right_child /= void
		ensure -- from BINARY_TREE
			Result = (right_child /= void)
		end

	is_empty: BOOLEAN is
			-- Is structure empty of items?
			-- (from TREE)
		do
			Result := False
		end

	is_leaf: BOOLEAN is
			-- Are there no children?
			-- Was declared in BINARY_TREE as synonym of has_none.
			-- (from BINARY_TREE)
		do
			Result := left_child = void and right_child = void
		end

	is_root: BOOLEAN is
			-- Is there no parent?
			-- (from TREE)
		do
			Result := parent = void
		end

	is_sibling (other: like parent): BOOLEAN is
			-- Are current node and other siblings?
			-- (from TREE)
		require -- from TREE
			other_exists: other /= void
		do
			Result := not is_root and other.parent = parent
		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
		end

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

	Readable: BOOLEAN is True
			-- (from TREE)

	readable_child: BOOLEAN is
			-- Is there a current child to be read?
			-- (from TREE)
		do
			Result := not child_off
		end

	sorted: BOOLEAN is
			-- Is tree sorted?
		do
			Result := True
			if (has_left and then left_item > item) or (has_right and then right_item < item) then
				Result := False
			else
				if has_left then
					Result := left_child.sorted_and_less (item)
				end
				if has_right and Result then
					Result := right_child.sorted
				end
			end
		end

	sorted_and_less (i: like item): BOOLEAN is
			-- Is tree sorted and all its elements less then i
		do
			Result := True
			if (has_left and then left_item > item) or (has_right and then right_item < item) then
				Result := False
			else
				if has_left then
					Result := left_child.sorted_and_less (item)
				end
				if has_right and Result then
					Result := right_child.sorted_and_less (i)
				end
			end
		end

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

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

	writable_child: BOOLEAN is
			-- Is there a current child that may be modified?
			-- (from TREE)
		do
			Result := not child_off
		end
	
feature -- Status setting

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

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

	child_back is
			-- Move cursor to previous child.
			-- (from BINARY_TREE)
		do
			child_index := child_index - 1
		end

	child_finish is
			-- Move cursor to last child.
			-- (from BINARY_TREE)
		do
			child_index := 2
		ensure then -- from TREE
			is_last_child: not is_leaf implies child_islast
		end

	child_forth is
			-- Move cursor to next child.
			-- (from BINARY_TREE)
		do
			child_index := child_index + 1
		end

	child_go_i_th (i: INTEGER) is
			-- Move cursor to i-th child.
			-- (from BINARY_TREE)
		require else -- from TREE
			valid_cursor_index: valid_cursor_index (i)
		do
			child_index := i
		ensure then -- from TREE
			position: child_index = i
		end

	child_go_to (p: ARRAYED_LIST_CURSOR) is
			-- Move cursor to child remembered by p.
			-- (from BINARY_TREE)
		do
			child_index := p.index
		end

	child_start is
			-- Move to first child.
			-- (from BINARY_TREE)
		do
			child_index := 1
		ensure then -- from TREE
			is_first_child: not is_leaf implies child_isfirst
		end

	i_infix is
			-- Apply node_action to every node's item
			-- in tree, using infix order.
		do
			if left_child /= void then
				left_child.i_infix
			end
			node_action (item)
			if right_child /= void then
				right_child.i_infix
			end
		end

	node_action (v: like item) is
			-- Operation on node item,
			-- to be defined by descendant classes.
			-- Here it is defined as an empty operation.
			-- Redefine this procedure in descendant classes if useful
			-- operations are to be performed during traversals.
		do
		end

	postorder is
			-- Apply node_action to every node's item
			-- in tree, using post-order.
		do
			if left_child /= void then
				left_child.postorder
			end
			if right_child /= void then
				right_child.postorder
			end
			node_action (item)
		end

	preorder is
			-- Apply node_action to every node's item
			-- in tree, using pre-order.
		do
			node_action (item)
			if left_child /= void then
				left_child.preorder
			end
			if right_child /= void then
				right_child.preorder
			end
		end
	
feature -- Element change

	child_put (v: like item) is
			-- Put v at current child position.
			-- Was declared in BINARY_TREE as synonym of child_replace.
			-- (from BINARY_TREE)
		require -- from TREE
			child_writable: child_writable
		local
			node: like Current
		do
			if child /= void then
				if object_comparison then
					child.compare_objects
				else
					child.compare_references
				end
				child.bt_put (v)
			else
				create node.bt_make (v)
				if object_comparison then
					node.compare_objects
				end
				put_child (node)
			end
		ensure -- from TREE
			item_inserted: child_item = v
		end

	child_replace (v: like item) is
			-- Put v at current child position.
			-- Was declared in BINARY_TREE as synonym of child_put.
			-- (from BINARY_TREE)
		require -- from TREE
			child_writable: child_writable
		local
			node: like Current
		do
			if child /= void then
				if object_comparison then
					child.compare_objects
				else
					child.compare_references
				end
				child.bt_put (v)
			else
				create node.bt_make (v)
				if object_comparison then
					node.compare_objects
				end
				put_child (node)
			end
		ensure -- from TREE
			item_inserted: child_item = v
		end

	extend (v: like item) is
			-- Put v at proper position in tree
			-- (unless v exists already).
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- Was declared in BINARY_SEARCH_TREE as synonym of put.
		require
			new_item_exists: v /= void
		do
			if not items_equal (v, item) then
				if v < item then
					if left_child = void then
						put_left_child (new_tree)
						left_child.replace (v)
					else
						left_child.put (v)
					end
				else
					if right_child = void then
						put_right_child (new_tree)
						right_child.replace (v)
					else
						right_child.put (v)
					end
				end
			end
		ensure
			item_inserted: has (v)
		end

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

	put (v: like item) is
			-- Put v at proper position in tree
			-- (unless v exists already).
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- Was declared in BINARY_SEARCH_TREE as synonym of extend.
		require
			new_item_exists: v /= void
		do
			if not items_equal (v, item) then
				if v < item then
					if left_child = void then
						put_left_child (new_tree)
						left_child.replace (v)
					else
						left_child.put (v)
					end
				else
					if right_child = void then
						put_right_child (new_tree)
						right_child.replace (v)
					else
						right_child.put (v)
					end
				end
			end
		ensure
			item_inserted: has (v)
		end

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

	put_child (n: like parent) is
			-- Put n at current child position.
			-- Was declared in BINARY_TREE as synonym of replace_child.
			-- (from BINARY_TREE)
		do
			if object_comparison then
				n.compare_objects
			else
				n.compare_references
			end
			n.attach_to_parent (Current)
			inspect child_index
			when 1 then 
				left_child := n
			when 2 then 
				right_child := n
			end
		end

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

	replace_child (n: like parent) is
			-- Put n at current child position.
			-- Was declared in BINARY_TREE as synonym of put_child.
			-- (from BINARY_TREE)
		require -- from TREE
			writable_child: writable_child
			was_root: n.is_root
		do
			if object_comparison then
				n.compare_objects
			else
				n.compare_references
			end
			n.attach_to_parent (Current)
			inspect child_index
			when 1 then 
				left_child := n
			when 2 then 
				right_child := n
			end
		ensure -- from TREE
			child_replaced: child = n
		end

	sprout is
			-- Make current node a root.
			-- (from TREE)
		do
			if parent /= void then
				parent.prune (Current)
			end
		end
	
feature {BINARY_SEARCH_TREE} -- Element change

	put_left_child (n: like parent) is
			-- Set left_child to n.
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			no_parent: n = void or else n.is_root
		do
			if n /= void then
				if object_comparison then
					n.compare_objects
				else
					n.compare_references
				end
			end
			if left_child /= void then
				left_child.attach_to_parent (void)
			end
			if n /= void then
				n.attach_to_parent (Current)
			end
			left_child := n
		end

	put_right_child (n: like parent) is
			-- Set right_child to n.
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			no_parent: n = void or else n.is_root
		do
			if n /= void then
				if object_comparison then
					n.compare_objects
				else
					n.compare_references
				end
			end
			if right_child /= void then
				right_child.attach_to_parent (void)
			end
			if n /= void then
				n.attach_to_parent (Current)
			end
			right_child := n
		end
	
feature {BINARY_SEARCH_TREE} -- Removal

	remove_left_child is
			-- Remove left child.
			-- (from BINARY_TREE)
		do
			if left_child /= void then
				left_child.attach_to_parent (void)
			end
			left_child := void
		ensure -- from BINARY_TREE
			not has_left
		end

	remove_right_child is
			-- Remove right child.
			-- (from BINARY_TREE)
		do
			if right_child /= void then
				right_child.attach_to_parent (void)
			end
			right_child := void
		ensure -- from BINARY_TREE
			not has_right
		end
	
feature -- Removal

	child_remove is
			-- Remove current child.
			-- (from BINARY_TREE)
		do
			inspect child_index
			when 1 then 
				left_child.attach_to_parent (void);
				left_child := void
			when 2 then 
				right_child.attach_to_parent (void);
				right_child := void
			end
		end

	prune (n: like parent) is
			-- Prune n from child nodes.
			-- (from BINARY_TREE)
		require -- from TREE
			is_child: n.parent = Current
		do
			if left_child = n then
				remove_left_child
			elseif right_child = n then
				remove_right_child
			end
		ensure -- from TREE
			n_is_root: n.is_root
		end
	
feature -- Transformation

	sort is
			-- Sort tree.
		local
			seq: LINEAR [G]
			temp: ARRAY [G]
			heap: HEAP_PRIORITY_QUEUE [G]
			i: INTEGER
		do
			seq := linear_representation
			i := count
			remove_left_child
			remove_right_child
			from
				seq.start
				create heap.make (i)
			until
				seq.off
			loop
				heap.put (seq.item)
				seq.forth
			end
			from
				create temp.make (1, heap.count)
				i := 1
			until
				heap.is_empty
			loop
				temp.put (heap.item, i)
				heap.remove
				i := i + 1
			end
			replace (temp.item ((temp.count) // 2 + 1))
			fill_from_sorted_special (temp.area, 0, temp.count - 1)
		ensure
			is_sorted: sorted
		end
	
feature -- Conversion

	binary_representation: BINARY_TREE [G] is
			-- Convert to binary tree representation:
			-- first child becomes left child,
			-- right sibling becomes right child.
			-- (from TREE)
		local
			current_sibling: BINARY_TREE [G]
		do
			create Result.make (item)
			if not is_leaf then
				Result.put_left_child (first_child.binary_representation)
				from
					child_start
					child_forth
					current_sibling := Result.left_child
				until
					child_after
				loop
					current_sibling.put_right_child (child.binary_representation)
					current_sibling := current_sibling.right_child
					child_forth
				end
			end
		ensure -- from TREE
			result_is_root: Result.is_root
			result_has_no_right_child: not Result.has_right
		end

	linear_representation: LINEAR [G] is
			-- Representation as a linear structure
			-- (from TREE)
		local
			al: ARRAYED_LIST [G]
		do
			create al.make (count)
			al.start
			al.extend (item)
			fill_list (al)
			Result := al
		end
	
feature -- Duplication

	copy (other: like Current) is
			-- Copy contents from other.
			-- (from BINARY_TREE)
		require -- from ANY
			other_not_void: other /= void
			type_identity: same_type (other)
		local
			tmp_tree: like Current
		do
			create tmp_tree.bt_make (other.item)
			if not other.is_leaf then
				tree_copy (other, tmp_tree)
			end
		ensure -- from ANY
			is_equal: is_equal (other)
		end

	duplicate (n: INTEGER): like Current is
			-- Copy of sub-tree beginning at cursor position and
			-- having min (n, arity - child_index + 1)
			-- children.
			-- (from BINARY_TREE)
		require -- from TREE
			not_child_off: not child_off
			valid_sublist: n >= 0
		do
			Result := new_tree
			if child_index <= 1 and child_index + n >= 1 and has_left then
				Result.put_left_child (left_child.duplicate_all)
			end
			if child_index <= 2 and child_index + n >= 2 and has_right then
				Result.put_right_child (right_child.duplicate_all)
			end
		end

	duplicate_all: like Current is
			-- (from BINARY_TREE)
		do
			Result := new_tree
			if has_left then
				Result.put_left_child (left_child.duplicate_all)
			end
			if has_right then
				Result.put_right_child (right_child.duplicate_all)
			end
		end
	
feature {BINARY_SEARCH_TREE, BINARY_SEARCH_TREE_SET} -- Implementation

	intersect (other: BINARY_SEARCH_TREE [G]) is
			-- Remove all items not in other.
		do
			if right_child /= void then
				right_child.intersect (other)
			end
			if left_child /= void then
				left_child.intersect (other)
			end
			if not other.has (item) then
				remove_node
			end
		end

	is_subset (other: like Current): BOOLEAN is
			-- Is Current a subset of other
		do
			Result := other.has (item)
			if Result and left_child /= void then
				Result := left_child.is_subset (other)
			end
			if Result and right_child /= void then
				Result := right_child.is_subset (other)
			end
		end

	max_node: like Current is
			-- Node containing max
		do
			if has_right then
				Result := right_child.min_node
			else
				Result := Current
			end
		end

	merge (other: like Current) is
			-- Add all items of other.
		do
			if other.right_child /= void then
				merge (other.right_child)
			end
			if other.left_child /= void then
				merge (other.left_child)
			end
			extend (other.item)
		end

	min_node: like Current is
			-- Node containing min
		do
			if has_left then
				Result := left_child.min_node
			else
				Result := Current
			end
		end

	pruned (v: like item; par: like Current): like Current is
			-- Prune v.
			-- (par is the parent node of the current node, needed to update
			-- parent correctly.)
		local
			m: like Current
		do
			if items_equal (item, v) then
				if has_none then
				elseif not has_right then
					left_child.attach_to_parent (par);
					Result := left_child
				elseif not has_left then
					right_child.attach_to_parent (par);
					Result := right_child
				else
					m := right_child.min_node
					m.remove_node
					item := m.item
					Result := Current
				end
			else
				Result := Current
				if v < item then
					if left_child /= void then
						left_child := left_child.pruned (v, Current)
					end
				else
					if right_child /= void then
						right_child := right_child.pruned (v, Current)
					end
				end
			end
		end

	remove_node is
			-- Remove current node from the tree.
		require
			is_not_root: not is_root
		local
			is_left_child: BOOLEAN
			m: like Current
		do
			is_left_child := Current = parent.left_child
			if not has_right then
				if left_child /= void then
					left_child.attach_to_parent (void)
				end
				if is_left_child then
					parent.put_left_child (left_child)
				else
					parent.put_right_child (left_child)
				end
				parent := void
			elseif not has_left then
				if right_child /= void then
					right_child.attach_to_parent (void)
				end;
				if is_left_child then
					parent.put_left_child (right_child)
				else
					parent.put_right_child (right_child)
				end;
				parent := void
			else
				m := right_child.min_node
				m.remove_node
				item := m.item
			end
		end

	subtract (other: BINARY_SEARCH_TREE [G]) is
			-- Remove all items also in other.
		require
			set_exists: other /= void
		do
			if right_child /= void then
				right_child.subtract (other)
			end
			if left_child /= void then
				left_child.subtract (other)
			end
			if other.has (item) then
				remove_node
			end
		end
	
feature {NONE} -- Implementation

	Child_capacity: INTEGER is 2
			-- (from BINARY_TREE)

	fill_from_sorted_special (t: SPECIAL [G]; s, e: INTEGER) is
			-- Put values from t into tree in such an order that
			-- the tree will be balanced if t is sorted.
		local
			m: INTEGER
		do
			m := (s + e) // 2
			put (t.item (m))
			if m - 1 >= s then
				fill_from_sorted_special (t, s, m - 1)
			end
			if m + 1 <= e then
				fill_from_sorted_special (t, m + 1, e)
			end
		end

	fill_subtree (other: BINARY_TREE [G]) is
			-- Copy other to subtee.
			-- (from BINARY_TREE)
		do
			if not other.is_leaf then
				put_left_child (other.left_child.duplicate_all)
			end
			if other.arity >= 2 then
				put_right_child (other.right_child.duplicate_all)
			end
		end

	items_equal (src, dest: like item): BOOLEAN is
			-- Are src and dest equal?
			-- (depending on object_comparison)
		do
			if object_comparison then
				Result := src /= void and then src.is_equal (dest)
			else
				Result := (src = dest)
			end
		end

	new_tree: like Current is
			-- New tree node
			-- (from BINARY_TREE)
		do
			create Result.bt_make (item)
			if object_comparison then
				Result.compare_objects
			end
		end

	remove is
			-- Remove current item
			-- (from TREE)
		do
		end

	set_comparison_mode (t: like Current) is
			-- Set comparison mode of t to the same mode as Current.
		require
			not_void: t /= void
		do
			if object_comparison then
				t.compare_objects
			else
				t.compare_references
			end
		ensure
			mode_set: object_comparison = t.object_comparison
		end

	subtree_count: INTEGER is
			-- Number of items in subtree
			-- (from BINARY_TREE)
		do
			if left_child /= void then
				Result := left_child.count
			end
			if right_child /= void then
				Result := Result + right_child.count
			end
		end

	subtree_has (v: G): BOOLEAN is
			-- Does subtree contain v?
			-- (from BINARY_TREE)
		do
			if left_child /= void then
				Result := left_child.has (v)
			end
			if right_child /= void and not Result then
				Result := right_child.has (v)
			end
		end

	tree_copy (other, tmp_tree: like Current) is
			-- Generic implementation of copy. other is copied onto
			-- Current. tmp_tree is used as temporary storage during
			-- copying. Since it cannot be created locally because of the
			-- generic implementation, it has to be passed in.
			-- (from TREE)
		require -- from TREE
			other_not_empty: other /= void and then not other.is_empty
			other_not_leaf: not other.is_leaf
			tmp_tree_exists: tmp_tree /= void
			same_rule: object_comparison = other.object_comparison
		local
			i: INTEGER
			p1, p2: like Current
			other_stack, tmp_stack: LINKED_STACK [like Current]
			idx_stack, orgidx_stack: LINKED_STACK [INTEGER]
		do
			create other_stack.make
			create tmp_stack.make
			create idx_stack.make
			create orgidx_stack.make
			if other.object_comparison then
				tmp_tree.compare_objects
			end
			orgidx_stack.put (other.child_index)
			from
				i := 1
				p1 := other
				p2 := tmp_tree
			invariant
				same_count: other_stack.count = tmp_stack.count and tmp_stack.count = idx_stack.count
			until
				i > p1.child_capacity and other_stack.is_empty
			loop
				p1.child_go_i_th (i)
				p2.child_go_i_th (i)
				if p1.child_readable then
					check
						source_tree_not_void: p1 /= void
						target_tree_not_void: p2 /= void
						source_child_not_void: p1.child /= void
						target_child_void: p2.child = void
					end
					p2.replace_child (clone (p1.child))
					if other_stack.is_empty then
						p2.child.attach_to_parent (Current)
					end
					check
						comparison_mode_ok: p2.child.object_comparison = p1.child.object_comparison
						p1_consistent: p1.child.parent = p1
						p2_consistent: p2.child.parent = p2
					end
					if not p1.child.is_leaf then
						other_stack.put (p1)
						tmp_stack.put (p2)
						idx_stack.put (i + 1)
						p1 := p1.child
						p2 := p2.child
						orgidx_stack.put (p1.child_index)
						i := 0
					end
				end
				if i <= p1.child_capacity then
					i := i + 1
				else
					from
					invariant
						same_count: other_stack.count = tmp_stack.count and tmp_stack.count = idx_stack.count
					until
						other_stack.is_empty or else i <= p1.child_capacity
					loop
						p1.child_go_i_th (orgidx_stack.item)
						p1 := other_stack.item
						p2 := tmp_stack.item
						check
							p1_not_void: p1 /= void
							p2_not_void: p2 /= void
						end
						i := idx_stack.item
						other_stack.remove
						tmp_stack.remove
						idx_stack.remove
						orgidx_stack.remove
					end
				end
			end
			check
				tree_stacks_empty: other_stack.is_empty and tmp_stack.is_empty
				at_root: p1 = other and p2 = tmp_tree
			end
			standard_copy (tmp_tree)
			child_go_i_th (orgidx_stack.item)
			orgidx_stack.remove
			check
				index_stack_empty: orgidx_stack.is_empty
			end
		end

	tree_is_equal (t1, t2: like Current): BOOLEAN is
			-- Are t1 and t2 recursively equal?
			-- (from TREE)
		require -- from TREE
			trees_exist: t1 /= void and t2 /= void
			trees_not_empty: not t1.is_empty and not t2.is_empty
			same_rule: t1.object_comparison = t2.object_comparison
		local
			i: INTEGER
			p1, p2: like Current
			t1_stack, t2_stack: LINKED_STACK [like Current]
			idx_stack, orgidx1_stack, orgidx2_stack: LINKED_STACK [INTEGER]
		do
			if t1.is_leaf and t2.is_leaf then
				if t1.object_comparison then
					Result := equal (t1.item, t2.item)
				else
					Result := (t1.item = t2.item)
				end
			elseif t1.is_leaf xor t2.is_leaf then
				Result := False
			else
				create t1_stack.make
				create t2_stack.make
				create idx_stack.make
				create orgidx1_stack.make
				create orgidx2_stack.make
				orgidx1_stack.put (t1.child_index)
				orgidx2_stack.put (t2.child_index)
				from
					Result := True
					i := 1
					p1 := t1
					p2 := t2
				invariant
					same_count: t1_stack.count = t2_stack.count and t2_stack.count = idx_stack.count
				until
					not Result or else (i > p1.child_capacity and t1_stack.is_empty)
				loop
					check
						p1_not_void: p1 /= void
						p2_not_void: p2 /= void
					end
					p1.child_go_i_th (i)
					p2.child_go_i_th (i)
					if p1.child_readable and p2.child_readable and p1.child_capacity = p2.child_capacity then
						check
							p1_consistent: p1.child.parent = p1
							p2_consistent: p2.child.parent = p2
						end
						if t1.object_comparison then
							Result := equal (p1.item, p2.item)
						else
							Result := (p1.item = p2.item)
						end
						if not (p1.child.is_leaf or p2.child.is_leaf) then
							t1_stack.put (p1)
							t2_stack.put (p2)
							idx_stack.put (i + 1)
							p1 := p1.child
							p2 := p2.child
							orgidx1_stack.put (p1.child_index)
							orgidx2_stack.put (p2.child_index)
							i := 0
						elseif p1.child.is_leaf xor p2.child.is_leaf then
							Result := False
						end
					elseif p1.child_capacity /= p2.child_capacity or else (p1.child_readable xor p2.child_readable) then
						Result := False
					end
					if i <= p1.child_capacity then
						i := i + 1
					else
						from
						invariant
							same_count: t1_stack.count = t2_stack.count and t2_stack.count = idx_stack.count
						until
							t1_stack.is_empty or else i <= p1.child_capacity
						loop
							p1.child_go_i_th (orgidx1_stack.item)
							p2.child_go_i_th (orgidx2_stack.item)
							p1 := t1_stack.item
							p2 := t2_stack.item
							i := idx_stack.item
							t1_stack.remove
							t2_stack.remove
							idx_stack.remove
							orgidx1_stack.remove
							orgidx2_stack.remove
						end
					end
				end
				if not Result then
					from
					invariant
						same_count: t1_stack.count = t2_stack.count and orgidx1_stack.count = orgidx2_stack.count
					until
						orgidx1_stack.count = 1
					loop
						p1.child_go_i_th (orgidx1_stack.item)
						p2.child_go_i_th (orgidx2_stack.item)
						p1 := t1_stack.item
						p2 := t2_stack.item
						check
							p1_not_void: p1 /= void
							p2_not_void: p2 /= void
						end
						t1_stack.remove
						t2_stack.remove
						orgidx1_stack.remove
						orgidx2_stack.remove
					end
					check
						tree_stacks_empty: t1_stack.is_empty and t2_stack.is_empty
						at_root: p1 = t1 and p2 = t2
						p1_not_void: p1 /= void
						p2_not_void: p2 /= void
					end
					p1.child_go_i_th (orgidx1_stack.item)
					p2.child_go_i_th (orgidx2_stack.item)
					orgidx1_stack.remove
					orgidx2_stack.remove
					check
						index_stacks_empty: orgidx1_stack.is_empty and orgidx2_stack.is_empty
					end
				end
			end
		end
	
feature {BINARY_TREE} -- Implementation

	fill_list (al: ARRAYED_LIST [G]) is
			-- Fill al with all the children's items.
			-- (from BINARY_TREE)
		do
			if left_child /= void then
				al.extend (left_child.item)
				left_child.fill_list (al)
			end
			if right_child /= void then
				al.extend (right_child.item)
				right_child.fill_list (al)
			end
		end
	
feature {TREE} -- Implementation

	attach_to_parent (n: like parent) is
			-- Make n parent of current node.
			-- (from TREE)
		do
			parent := n
		ensure -- from TREE
			new_parent: parent = n
		end
	
invariant

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)
		-- from BINARY_TREE
	tree_is_binary: child_capacity = 2
		-- 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

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 BINARY_SEARCH_TREE


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