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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 20:34:24 $"
	revision: "$Revision: 1.1.1.1 $"

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