indexing
	description: "Sorted sets implemented as binary search trees"
	names: binary_search_tree_set, set, binary_search_tree
	representation: recursive, array
	access: membership, min, max
	contents: generic

class interface
	BINARY_SEARCH_TREE_SET [G -> COMPARABLE]

create 

	make

feature -- Initialization

	make
	
feature -- Access

	has (v: like item): BOOLEAN
			-- Is there a node with item v in tree?
			-- (Reference or object equality,
			-- based on object_comparison.)
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not empty
	
feature -- Measurement

	count: INTEGER
			-- Number of items in tree

	item: G
		require -- from TRAVERSABLE
			not_off: not off

	max: like item
			-- Maximum item in tree
		require -- from COMPARABLE_SET
			not_empty: not empty

	min: like item
			-- Minimum item in tree
		require -- from COMPARABLE_SET
			not_empty: not empty
	
feature -- Comparison

	disjoint (other: like Current): BOOLEAN
			-- Do current set and other have no
			-- items in common?
			-- (from SUBSET)
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison

	is_subset (other: like Current): BOOLEAN
			-- Is current structure a subset of other?
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison

	is_superset (other: like Current): BOOLEAN
			-- Is current set a superset of other?
			-- (from SUBSET)
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison
	
feature -- Status report

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

	before: BOOLEAN
			-- Is there no valid cursor position to the left of cursor?

	empty: BOOLEAN

	Extendible: BOOLEAN is true
			-- Can new items be added? (Answer: yes.)

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

	Prunable: BOOLEAN is true
			-- Can items be removed? (Answer: yes.)
	
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

	back
		require -- from BILINEAR
			not_before: not before

	finish

	forth
		require -- from LINEAR
			not_after: not after

	start
	
feature -- Element change

	extend (v: like item)
			-- Put v at proper position in set
			-- (unless one already exists).
			-- Was declared in BINARY_SEARCH_TREE_SET as synonym of put and extend.
		require -- from COLLECTION
			extendible: extendible
		require else
			item_exists: v /= void
		ensure -- from COLLECTION
			item_inserted: has (v)
		ensure then -- from SET
			in_set_already: old has (v) implies (count = old count);
			added_to_set: not old has (v) implies (count = old count + 1)

	fill (other: CONTAINER [G])
			-- Fill with as many items of other as possible.
			-- The representations of other and current structure
			-- need not be the same.
			-- (from COLLECTION)
		require -- from COLLECTION
			other_not_void: other /= void;
			extendible

	put (v: like item)
			-- Put v at proper position in set
			-- (unless one already exists).
			-- Was declared in BINARY_SEARCH_TREE_SET as synonym of put and extend.
		require -- from COLLECTION
			extendible: extendible
		require else
			item_exists: v /= void
		ensure -- from COLLECTION
			item_inserted: has (v)
		ensure then -- from SET
			in_set_already: old has (v) implies (count = old count);
			added_to_set: not old has (v) implies (count = old count + 1)
	
feature -- Removal

	changeable_comparison_criterion: BOOLEAN
			-- May object_comparison be changed?
			-- (Answer: only if set empty; otherwise insertions might
			-- introduce duplicates, destroying the set property.)
			-- (from SET)
		ensure then -- from SET
			only_on_empty: Result = empty
		ensure then -- from SET
			only_on_empty: Result = empty

	prune (v: like item)
		require -- from COLLECTION
			prunable: prunable
		ensure then -- from SET
			removed_count_change: old has (v) implies (count = old count - 1);
			not_removed_no_count_change: not old has (v) implies (count = old count);
			item_deleted: not has (v)

	prune_all (v: G)
			-- Remove all occurrences of v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from COLLECTION)
		require -- from COLLECTION
			prunable
		ensure -- from COLLECTION
			no_more_occurrences: not has (v)

	wipe_out
			-- Remove all items.
		require -- from COLLECTION
			prunable
		ensure -- from COLLECTION
			wiped_out: empty
	
feature -- Conversion

	linear_representation: LINEAR [G]
			-- Representation as a linear structure
			-- (from LINEAR)
	
feature -- Duplication

	duplicate (n: INTEGER): BINARY_SEARCH_TREE_SET [G]
			-- New structure containing min (n, count)
			-- items from current structure
		require -- from SUBSET
			non_negative: n >= 0
		ensure -- from SUBSET
			correct_count_1: n <= count implies Result.count = n;
			correct_count_2: n >= count implies Result.count = count
	
feature -- Basic operations

	intersect (other: like Current)
			-- Remove all items not in other.
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison
		require else
			set_exists: other /= void
		ensure -- from SUBSET
			is_subset_other: is_subset (other)

	merge (other: like Current)
			-- Add all items of other.
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison
		ensure -- from SUBSET
			is_superset: is_superset (other)

	subtract (other: like Current)
			-- Remove all items also in other.
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison
		require else
			set_exists: other /= void
		ensure -- from SUBSET
			is_disjoint: disjoint (other)

	symdif (other: like Current)
			-- Remove all items also in other, and add all
			-- items of other not already present.
			-- (from SUBSET)
		require -- from SUBSET
			set_exists: other /= void;
			same_rule: object_comparison = other.object_comparison
	
invariant

		-- from GENERAL
	reflexive_equality: standard_is_equal (Current);
	reflexive_conformance: conforms_to (Current);
		-- from BILINEAR
	not_both: not (after and before);
	empty_property: empty implies (after or before);

end -- class BINARY_SEARCH_TREE_SET