# BinaryTournament SΒΆ

- S: OrderedSet

BinaryTournament(S) is the domain of binary trees where elements are ordered down the tree. A binary tournament is either empty or is a node containing a value of type `S`

, and a left and a right which are both BinaryTree(S)

- #: % -> NonNegativeInteger
- from Aggregate
- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- any?: (S -> Boolean, %) -> Boolean
- from HomogeneousAggregate S

- binaryTournament: List S -> %
`binaryTournament(ls)`

creates a binary tournament with the elements of`ls`

as values of the nodes.- child?: (%, %) -> Boolean
- from RecursiveAggregate S
- children: % -> List %
- from RecursiveAggregate S
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- copy: % -> %
- from Aggregate
- count: (S -> Boolean, %) -> NonNegativeInteger
- from HomogeneousAggregate S
- 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)
- every?: (S -> Boolean, %) -> Boolean
- from HomogeneousAggregate S
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory

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

inserts element`x`

as a leave into binary tournament`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
- map: (S -> S, %) -> %
- from HomogeneousAggregate S
- member?: (S, %) -> Boolean
- from HomogeneousAggregate S
- members: % -> List S
- from HomogeneousAggregate S
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- node: (%, S, %) -> %
- from BinaryTreeCategory S
- node?: (%, %) -> Boolean
- from RecursiveAggregate S
- nodes: % -> List %
- from RecursiveAggregate S
- parts: % -> List S
- from HomogeneousAggregate S
- right: % -> %
- from BinaryRecursiveAggregate S
- sample: %
- from Aggregate
- setchildren!: (%, List %) -> %
- from RecursiveAggregate S
- setelt!: (%, left, %) -> %
- from BinaryRecursiveAggregate S
- setelt!: (%, right, %) -> %
- from BinaryRecursiveAggregate S
- setelt!: (%, value, S) -> S
- from RecursiveAggregate S
- setleft!: (%, %) -> %
- from BinaryRecursiveAggregate S
- setright!: (%, %) -> %
- from BinaryRecursiveAggregate S
- setvalue!: (%, S) -> S
- from RecursiveAggregate S
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- value: % -> S
- from RecursiveAggregate S

Evalable S if S has Evalable S

InnerEvalable(S, S) if S has Evalable S