note
	description: "[
		Binary search trees; left child item is less than current item,
		right child item is greater
	]"
	library: "Free implementation of ELKS library"
	legal: "See notice at end of class."
	status: "See notice at end of class."
	names: binary_search_tree, tree
	representation: recursive, array
	access: cursor, membership
	contents: generic
	date: "$Date: 2018-11-14 15:15:17 +0000 (Wed, 14 Nov 2018) $"
	revision: "$Revision: 102463 $"

class interface
	BINARY_SEARCH_TREE [G -> COMPARABLE]

create 
	make (v: like item)
			-- Create single node with item v.
		require
			v_not_void: v /= Void
		ensure
			item_set: item = v
			is_root: is_root
			is_leaf: is_leaf


create {BINARY_SEARCH_TREE}
	bt_make (v: like item)
			-- Create a root node with value v.
			-- (from BINARY_TREE)
		ensure -- from BINARY_TREE
			node_item: item = v
			is_root: is_root
			is_leaf: is_leaf

feature -- Access

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

	child_cursor: ARRAYED_LIST_CURSOR
			-- Current cursor position
			-- (from BINARY_TREE)

	child_index: INTEGER_32
			-- Index of cursor position
			-- (from BINARY_TREE)

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

	first_child: like parent
			-- Left child
			-- (from BINARY_TREE)
		require -- from TREE
			is_not_leaf: not is_leaf

	generating_type: TYPE [detachable BINARY_SEARCH_TREE [G]]
			-- Type of current object
			-- (type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generating_type_not_void: Result /= Void

	generator: STRING_8
			-- Name of current object's generating class
			-- (base class of the type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generator_not_void: Result /= Void
			generator_not_empty: not Result.is_empty

	has (v: like item): BOOLEAN
			-- Does tree contain a node whose item
			-- is equal to v (object comparison)?
		require -- from  CONTAINER
			True
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not is_empty

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

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

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

	left_item: like item
			-- Value of left child
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			has_left: left_child /= Void

	left_sibling: like parent
			-- Left neighbor, if any
			-- (from BINARY_TREE)
		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)

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

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

	right_item: like item
			-- Value of right child
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			has_right: right_child /= Void

	right_sibling: like parent
			-- Right neighbor, if any
			-- (from BINARY_TREE)
		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)

	tree_item (v: like item): detachable like Current
			-- Node whose item is equal to v (object_comparison)
			-- otherwise default value.
		require
			v_not_void: v /= Void
	
feature -- Measurement

	arity: INTEGER_32
			-- Number of children
			-- (from BINARY_TREE)
		require -- from  TREE
			True
		ensure then -- from BINARY_TREE
			valid_arity: Result <= Child_capacity

	Child_capacity: INTEGER_32 = 2
			-- Maximum number of children
			-- (from BINARY_TREE)

	count: INTEGER_32
			-- Number of items
			-- (from TREE)

	max: like item
			-- Maximum item in tree
		ensure
			maximum_present: has (Result)

	min: like item
			-- Minimum item in tree
		ensure
			minimum_present: has (Result)
	
feature -- Comparison

	frozen deep_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void
			-- or attached to isomorphic object structures?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			shallow_implies_deep: standard_equal (a, b) implies Result
			both_or_none_void: (a = Void) implies (Result = (b = Void))
			same_type: (Result and (a /= Void)) implies (b /= Void and then a.same_type (b))
			symmetric: Result implies deep_equal (b, a)

	frozen equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached
			-- to objects considered equal?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.is_equal (b))

	frozen is_deep_equal alias "≡≡≡" (other: BINARY_SEARCH_TREE [G]): BOOLEAN
			-- Are Current and other attached to isomorphic object structures?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			shallow_implies_deep: standard_is_equal (other) implies Result
			same_type: Result implies same_type (other)
			symmetric: Result implies other.is_deep_equal (Current)

	is_equal (other: BINARY_SEARCH_TREE [G]): 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 ~ Current
			consistent: standard_is_equal (other) implies Result

	node_is_equal (other: BINARY_SEARCH_TREE [G]): BOOLEAN
			-- Is other equal to Current?
			-- (from TREE)
		require -- from TREE
			other_not_void: other /= Void

	frozen standard_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached to
			-- field-by-field identical objects of the same type?
			-- Always uses default object comparison criterion.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.standard_is_equal (b))

	frozen standard_is_equal alias "≜" (other: BINARY_SEARCH_TREE [G]): BOOLEAN
			-- Is other attached to an object of the same type
			-- as current object, and field-by-field identical to it?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			same_type: Result implies same_type (other)
			symmetric: Result implies other.standard_is_equal (Current)
	
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?
			-- (from BINARY_TREE)

	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)

	conforms_to (other: ANY): BOOLEAN
			-- Does type of current object conform to type
			-- of other (as per Eiffel: The Language, chapter 13)?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void

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

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

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

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

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

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

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

	is_sibling (other: attached 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)

	Readable: BOOLEAN = True
			-- (from TREE)

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

	same_type (other: ANY): BOOLEAN
			-- Is type of current object identical to type of other?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			definition: Result = (conforms_to (other) and other.conforms_to (Current))

	sorted: BOOLEAN
			-- Is tree sorted?

	sorted_and_less (i: like item): BOOLEAN
			-- Is tree sorted and all its elements less then i

	valid_cursor_index (i: INTEGER_32): BOOLEAN
			-- Is i correctly bounded for cursor movement?
			-- (from TREE)
		ensure -- from TREE
			valid_cursor_index_definition: Result = (i >= 0) and (i <= Child_capacity + 1)

	Writable: BOOLEAN = 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: 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: changeable_comparison_criterion
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
	
feature -- Cursor movement

	child_back
			-- Move cursor to previous child.
			-- (from BINARY_TREE)

	child_finish
			-- Move cursor to last child.
			-- (from BINARY_TREE)

	child_forth
			-- Move cursor to next child.
			-- (from BINARY_TREE)

	child_go_i_th (i: INTEGER_32)
			-- Move cursor to i-th child.
			-- (from BINARY_TREE)
		ensure then -- from TREE
			position: child_index = i

	child_go_to (p: ARRAYED_LIST_CURSOR)
			-- Move cursor to child remembered by p.
			-- (from BINARY_TREE)

	child_start
			-- Move to first child.
			-- (from BINARY_TREE)

	i_infix
			-- Apply node_action to every node's item
			-- in tree, using infix order.

	node_action (v: like item)
			-- 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.

	postorder
			-- Apply node_action to every node's item
			-- in tree, using post-order.

	preorder
			-- Apply node_action to every node's item
			-- in tree, using pre-order.
	
feature -- Element change

	child_put (v: like item)
			-- 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
		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.
			-- (from BINARY_TREE)
		require -- from TREE
			child_writable: child_writable
		ensure -- from TREE
			item_inserted: child_item = v

	extend (v: like item)
			-- 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
		ensure
			item_inserted: has (v)

	put (v: like item)
			-- 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
		ensure
			item_inserted: has (v)

	bt_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_child (n: like new_tree)
			-- Put n at current child position.
			-- Was declared in BINARY_TREE as synonym of replace_child.
			-- (from BINARY_TREE)
		require -- from TREE
			non_void_argument: n /= Void

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

	put_right_child (n: like parent)
			-- Set right_child to n.
			-- (from BINARY_TREE)
		require -- from BINARY_TREE
			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.
			-- (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 new_tree)
			-- 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
		ensure -- from TREE
			child_replaced: child = n

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

	child_remove
			-- Remove current child.
			-- (from BINARY_TREE)

	forget_left
			-- Forget left sibling.
			-- (from BINARY_TREE)

	forget_right
			-- Forget right sibling.
			-- (from BINARY_TREE)

	prune (n: like new_tree)
			-- Prune n from child nodes.
			-- (from BINARY_TREE)
		require -- from TREE
			is_child: n.parent = Current
		ensure -- from TREE
			n_is_root: n.is_root

	remove_left_child
			-- Remove left child.
			-- (from BINARY_TREE)
		ensure -- from BINARY_TREE
				not has_left

	remove_right_child
			-- Remove right child.
			-- (from BINARY_TREE)
		ensure -- from BINARY_TREE
				not has_right

	wipe_out
			-- Remove all children.
			-- (from BINARY_TREE)
		ensure -- from TREE
			is_leaf: is_leaf
	
feature -- Transformation

	sort
			-- Sort tree.
		ensure
			is_sorted: sorted
	
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: BINARY_SEARCH_TREE [G])
			-- Copy contents from other.
			-- (from TREE)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_equal: Current ~ other

	frozen deep_copy (other: BINARY_SEARCH_TREE [G])
			-- Effect equivalent to that of:
			--		copy (other . deep_twin)
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			deep_equal: deep_equal (Current, other)

	frozen deep_twin: BINARY_SEARCH_TREE [G]
			-- New object structure recursively duplicated from Current.
			-- (from ANY)
		ensure -- from ANY
			deep_twin_not_void: Result /= Void
			deep_equal: deep_equal (Current, Result)

	frozen standard_copy (other: BINARY_SEARCH_TREE [G])
			-- Copy every field of other onto corresponding field
			-- of current object.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_standard_equal: standard_is_equal (other)

	frozen standard_twin: BINARY_SEARCH_TREE [G]
			-- New object field-by-field identical to other.
			-- Always uses default copying semantics.
			-- (from ANY)
		ensure -- from ANY
			standard_twin_not_void: Result /= Void
			equal: standard_equal (Result, Current)

	frozen twin: BINARY_SEARCH_TREE [G]
			-- New object equal to Current
			-- twin calls copy; to change copying/twinning semantics, redefine copy.
			-- (from ANY)
		ensure -- from ANY
			twin_not_void: Result /= Void
			is_equal: Result ~ Current
	
feature -- Basic operations

	frozen default: detachable BINARY_SEARCH_TREE [G]
			-- Default value of object's type
			-- (from ANY)

	frozen default_pointer: POINTER
			-- Default value of type POINTER
			-- (Avoid the need to write p.default for
			-- some p of type POINTER.)
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	default_rescue
			-- Process exception for routines with no Rescue clause.
			-- (Default: do nothing.)
			-- (from ANY)

	frozen do_nothing
			-- Execute a null action.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
	
feature -- Iteration

	new_cursor: TREE_ITERATION_CURSOR [G]
			-- Fresh cursor associated with current structure
			-- (from TREE)
		ensure -- from ITERABLE
			result_attached: Result /= Void
	
feature -- Output

	Io: STD_FILES
			-- Handle to standard file setup
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			io_not_void: Result /= Void

	out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			out_not_void: Result /= Void

	print (o: detachable ANY)
			-- Write terse external representation of o
			-- on standard output.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	frozen tagged_out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			tagged_out_not_void: Result /= Void
	
feature -- Platform

	Operating_environment: OPERATING_ENVIRONMENT
			-- Objects available from the operating system
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			operating_environment_not_void: Result /= Void
	
invariant
		-- from BINARY_TREE
	tree_is_binary: Child_capacity = 2

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)

		-- from TREE
	tree_consistency: child_readable implies (attached child as c and then c.parent = Current)
	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)

note
	copyright: "Copyright (c) 1984-2018, Eiffel Software and others"
	license: "Eiffel Forum License v2 (see http://www.eiffel.com/licensing/forum.txt)"
	source: "[
		Eiffel Software
		5949 Hollister Ave., Goleta, CA 93117 USA
		Telephone 805-685-1006, Fax 805-685-6869
		Website http://www.eiffel.com
		Customer support http://support.eiffel.com
	]"

end -- class BINARY_SEARCH_TREE

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