# BinarySearchTree SΒΆ

- S: OrderedSet

BinarySearchTree(`S`

) is the domain of binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an `S`

, and a left and a right which are both BinarySearchTree(`S`

).

- binarySearchTree: List S -> %
`binarySearchTree(l)`

constructs a binary search tree with elements from list`l`

.- child?: (%, %) -> Boolean
- from RecursiveAggregate S
- children: % -> List %
- from RecursiveAggregate S
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- copy: % -> %
- from Aggregate
- count: (S, %) -> NonNegativeInteger
- from HomogeneousAggregate S
- cyclic?: % -> Boolean
- from RecursiveAggregate S
- distance: (%, %) -> Integer
- from RecursiveAggregate S
- elt: (%, left) -> %
- from BinaryRecursiveAggregate S
- elt: (%, right) -> %
- from BinaryRecursiveAggregate S
- elt: (%, value) -> S
- from RecursiveAggregate S
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- eq?: (%, %) -> Boolean
- from Aggregate
- eval: (%, Equation S) -> % if S has Evalable S
- from Evalable S
- eval: (%, List Equation S) -> % if S has Evalable S
- from Evalable S
- eval: (%, List S, List S) -> % if S has Evalable S
- from InnerEvalable(S, S)
- eval: (%, S, S) -> % if S has Evalable S
- from InnerEvalable(S, S)
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory

- insert!: (S, %) -> %
`insert!(x, b)`

inserts element`x`

as a leave into binary search tree`b`

.

- insertRoot!: (S, %) -> %
`insertRoot!(x, b)`

inserts element`x`

as the root of binary search tree`b`

.- latex: % -> String
- from SetCategory
- leaf?: % -> Boolean
- from RecursiveAggregate S
- leaves: % -> List S
- from RecursiveAggregate S
- left: % -> %
- from BinaryRecursiveAggregate S
- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- map: (S -> S, %) -> %
- from HomogeneousAggregate S
- member?: (S, %) -> Boolean
- from HomogeneousAggregate S
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- node: (%, S, %) -> %
- from BinaryTreeCategory S
- node?: (%, %) -> Boolean
- from RecursiveAggregate S
- nodes: % -> List %
- from RecursiveAggregate S
- right: % -> %
- from BinaryRecursiveAggregate S
- sample: %
- from Aggregate
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate

- split: (S, %) -> Record(less: %, greater: %)
`split(x, b)`

splits binary search tree`b`

into two trees, one with elements less than`x`

, the other with elements greater than or equal to`x`

.- value: % -> S
- from RecursiveAggregate S

Evalable S if S has Evalable S

InnerEvalable(S, S) if S has Evalable S