indexing
	description: "Binary tree: each node may have a left child and a right child"
	names: binary_tree, tree, fixed_tree
	representation: recursive, array
	access: cursor, membership
	contents: generic

class interface
	BINARY_TREE [G]

create 

	make (v: like item)
			-- Create a root node with value v
		ensure
			is_root;
			is_leaf

feature -- Initialization

	make (v: like item)
			-- Create a root node with value v
		ensure
			is_root;
			is_leaf
	
feature -- Access

	child: like parent
			-- Child at cursor position
		require -- from TREE
			readable: readable_child

	child_cursor: CURSOR
			-- Current cursor position

	child_index: INTEGER
			-- Index of cursor position

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

	first_child: like parent
			-- Left child
		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 empty

	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)

	last_child: like parent
			-- Right child
		require -- from TREE
			is_not_leaf: not is_leaf

	left_child: like parent
			-- Left child, if any

	left_item: like item
			-- Value of left child
		require
			has_left: left_child /= void

	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)

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

	right_child: like parent
			-- Right child, if any

	right_item: like item
			-- Value of right child
		require
			has_right: right_child /= void

	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)
	
feature -- Measurement

	arity: INTEGER
			-- Number of children
		ensure then
			valid_arity: Result <= 2

	count: INTEGER
			-- Number of items
			-- (from TREE)
	
feature -- Status report

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

	child_after: BOOLEAN
			-- Is there no valid child position to the right of cursor?

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

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

	child_off: BOOLEAN
			-- Is there no current child?
			-- (from TREE)

	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)

	has_both: BOOLEAN
			-- Has current node two children?
		ensure
			Result = (has_left and has_right)

	has_left: BOOLEAN
			-- Has current node a left child?
		ensure
			Result = (left_child /= void)

	has_none: BOOLEAN
			-- Are there no children?
			-- Was declared in BINARY_TREE as synonym of is_leaf and has_none.

	has_right: BOOLEAN
			-- Has current node a right child?
		ensure
			Result = (right_child /= void)

	is_leaf: BOOLEAN
			-- Are there no children?
			-- Was declared in BINARY_TREE as synonym of is_leaf and has_none.

	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)

	Readable: BOOLEAN is true
			-- (from TREE)

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

	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)

	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 child.

	child_finish
			-- Move cursor to last child.
		ensure then -- from TREE
			is_last_child: not is_leaf implies child_islast

	child_forth
			-- Move cursor to next child.

	child_go_i_th (i: INTEGER)
			-- Move cursor to i-th child.
		require else -- from TREE
			valid_cursor_index: valid_cursor_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 child remembered by p.

	child_start
			-- Move to first child.
		ensure then -- from TREE
			is_first_child: not is_leaf implies child_isfirst
	
feature -- Element change

	child_put (v: like item)
			-- Put v at current child position.
			-- Was declared in BINARY_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_replace (v: like item)
			-- Put v at current child position.
			-- Was declared in BINARY_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)

	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)
			-- Put n at current child position.
			-- Was declared in BINARY_TREE as synonym of put_child and replace_child.

	put_left_child (n: like parent)
			-- Set left_child to n.
		require
			no_parent: n = void or else n.is_root

	put_right_child (n: like parent)
			-- Set right_child to n.
		require
			no_parent: n = void or else n.is_root

	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)
			-- Put n at current child position.
			-- Was declared in BINARY_TREE as synonym of put_child and replace_child.
		require -- from TREE
			writable_child: writable_child;
			was_root: n.is_root
		ensure -- from TREE
			child_replaced: child = n

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

	child_remove

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

	remove_left_child
		ensure
			not has_left

	remove_right_child
		ensure
			not has_right
	
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

	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

	duplicate_all: like Current
	
invariant

		-- from GENERAL
	reflexive_equality: standard_is_equal (Current);
	reflexive_conformance: conforms_to (Current);
	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 = arity);
	child_after_definition: child_after = (child_index >= arity + 1);
	child_consistency: child_readable implies child.parent = Current;

end -- class BINARY_TREE