BinaryTree 1 October 2020 OSU CSE 1 BinaryTree The BinaryTree - - PowerPoint PPT Presentation

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BinaryTree 1 October 2020 OSU CSE 1 BinaryTree The BinaryTree component family allows you to manipulate values modeled as mathematical binary trees with any label type T (i.e., binary tree of T ) Another generic type like Sequence and

SLIDE 1

BinaryTree

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SLIDE 2

BinaryTree

The BinaryTree component family

allows you to manipulate values modeled as mathematical binary trees with any label type T (i.e., binary tree of T)

– Another generic type like Sequence and Set

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SLIDE 3

Interfaces and Classes

BinaryTree- Kernel extends Standard extends

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BinaryTree implements BinaryTree1 Iterable extends

SLIDE 4

Interfaces and Classes

BinaryTree- Kernel extends Standard extends

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BinaryTree implements BinaryTree1 Iterable extends BinaryTreeKernel has contracts for three methods: assemble disassemble size

SLIDE 5

Interfaces and Classes

BinaryTree- Kernel extends Standard extends

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BinaryTree implements BinaryTree1 Iterable extends BinaryTree has contracts for four methods (the last of which we will skip): root replaceRoot height inOrderAssemble

SLIDE 6

Interfaces and Classes

BinaryTree- Kernel extends Standard extends

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BinaryTree implements BinaryTree1 Iterable extends There is really an abstract class as usual in the chain here, but it is not shown because these slides describe the client view, and a client needs only interface BinaryTree and class BinaryTree1.

SLIDE 7

Mathematical Model

type BinaryTreeKernel is modeled by binary tree of T

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SLIDE 8

No-argument Constructor

Ensures:

this = empty_tree

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SLIDE 9

Example

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Code State

BinaryTree<NaturalNumber> bn = new BinaryTree1<>();

SLIDE 10

Example

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Code State

BinaryTree<NaturalNumber> bn = new BinaryTree1<>();

bn =

SLIDE 11

assemble

void assemble(T root, BinaryTree<T> left, BinaryTree<T> right)

Assembles in this a binary tree with root label root

and subtrees left and right; the declaration notwithstanding, the dynamic type of left and right must be the same as the dynamic type of this.

Aliases: reference root
Replaces: this
Clears: left, right
Ensures:

this = compose(root, #left, #right)

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SLIDE 12

Example

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Code State

x = 70 bn = ? lt = rt = bn.assemble(x, lt, rt);

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Example

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Code State

x = 70 bn = ? lt = rt = bn.assemble(x, lt, rt); x = 70 bn = lt = rt = 70

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Example

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Code State

x = 70 bn = ? lt = rt = bn.assemble(x, lt, rt); x = 70 bn = lt = rt = 70

Note the alias created here, which you cannot see in the tracing table.

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disassemble

T disassemble(BinaryTree<T> left, BinaryTree<T> right)

Disassembles this into its root label, which is returned as

the value of the function, and subtrees left and right; the declaration notwithstanding, the dynamic type of left and right must be the same as the dynamic type of this.

Replaces: left, right
Clears: this
Requires:

this /= empty_tree

Ensures:

#this = compose(disassemble, left, right)

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SLIDE 16

Example

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Code State

lt = ? bn = rt = ? NaturalNumber root = bn.disassemble(lt, rt); 13

SLIDE 17

Example

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Code State

lt = ? bn = rt = ? NaturalNumber root = bn.disassemble(lt, rt); root = 13 bn = lt = rt = 13

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size

int size()

Reports the size of this.
Ensures:

size = |this|

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SLIDE 19

iterator

Iterator<T> iterator()

Returns an iterator over a set of elements
f type T.
Ensures:

~this.seen * ~this.unseen = IN_ORDER(this)

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SLIDE 20

Traversal Orders

There are three named traversal orders

for the nodes of a binary tree, named according to when the root is “visited” relative to the (recursive) traversals of the left and right subtrees

– Pre-order: root is visited before left and right – In-order: root is visited between left and right – Post-order: root is visited after left and right

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SLIDE 21

Traversal Orders

There are three named traversal orders

for the nodes of a binary tree, named according to when the root is “visited” relative to the (recursive) traversals of the left and right subtrees

– Pre-order: root is visited before left and right – In-order: root is visited between left and right – Post-order: root is visited after left and right

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The iterator method returns an Iterator<T> that visits the node labels in this order.

SLIDE 22

Pre-order traversal: <4, 2, 1, 3, 5>
In-order traversal: <1, 2, 3, 4, 5>
Post-order traversal: <1, 3, 2, 5, 4>

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1 3 2 4 5

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root

T root()

Reports the root of this.
Aliases: reference returned by root
Requires:

this /= empty_tree

Ensures:

there exists lt, rt: binary tree of T (this = compose(root, lt, rt))

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SLIDE 24

Example

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Code State

bn =

NaturalNumber k = bn.root();

SLIDE 25

Example

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Code State

bn =

NaturalNumber k = bn.root();

k = 13 bn = 13 13

SLIDE 26

Example

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Code State

bn =

NaturalNumber k = bn.root();

k = 13 bn = 13 13

Note the alias created here, which you cannot see in the tracing table.

SLIDE 27

replaceRoot

T replaceRoot(T x)

Replaces the root of this with x, and returns the
ld root.
Aliases: reference x
Requires:

this /= empty_tree

Ensures:

there exists lt, rt: binary tree of T (#this = compose(replaceRoot, lt, rt) and this = compose(x, lt, rt))

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SLIDE 28

Example

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Code State

n = 4 bn =

NaturalNumber k = bn.replaceRoot(n);

SLIDE 29

Example

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Code State

n = 4 bn =

NaturalNumber k = bn.replaceRoot(n);

n = 4 bn = k = 13 13 4

SLIDE 30

Example

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Code State

n = 4 bn =

NaturalNumber k = bn.replaceRoot(n);

n = 4 bn = k = 13 13 4

Note the alias created here, which you cannot see in the tracing table.

SLIDE 31

Another Example

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Code State

n = 4 bn =

n = bn.replaceRoot(n);

SLIDE 32

Another Example

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Code State

n = 4 bn =

n = bn.replaceRoot(n);

n = 13 bn = 13 4

SLIDE 33

Another Example

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Code State

n = 4 bn =

n = bn.replaceRoot(n);

n = 13 bn = 13 4

This use of the method avoids creating an alias: it swaps n with the old root.

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height

int height()

Reports the height of this.
Ensures:

height = ht(this)

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SLIDE 35

Resources

OSU CSE Components API: BinaryTree

– http://cse.osu.edu/software/common/doc/

Big Java (4th ed), Sections 16.6

– https://library.ohio-state.edu/record=b8540788~S7

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