jrfTypewritten textBinary Tree-Basic terminology

Outline

Binary Tree ADT

Tree ADT

What is a Tree?

In computer science, a tree is an abstract model of a hierarchical structure

A tree consists of nodes with a parent-

child relation

Applications:

Organization

charts

File systems

Computers R Us

Sales R&DManufacturing

Laptops DesktopsUS International

Europe Asia Canada

Tree Terminology

Root: node without a parent (A)

Internal node: node with at least one child (A, B, C, F)

External node (a.k.a. leaf ): node without children (E, I, J, K, G, H, D)

Parent node: node immediately above a given node (parent of C is A)

Child node: node(s) immediately below a given node (children of C are G and H)

Ancestors of a node: parent, grandparent, grand-grandparent, etc. (ancestors of G are C, A)

Depth of a node: number of ancestors (I has depth 3)

Height of a tree: maximum depth of any node (tree with just a root has height 0, this tree has height 3)

Descendant of a node: child, grandchild, grand-grandchild, etc.

Subtree: tree consisting of a node and its descendants

A

B DC

G HE F

I J K

subtree

Tree ADT (Abstract Data Structure)

Tree methods:

int size(): returns the number of nodes

boolean isEmpty(): returns true if the tree is empty

Node root(): returns the root of the tree

Node methods:

Node parent(): returns the parent of the node

Node[ ] children(): returns the children of the node

boolean isInternal(): returns true if the node has children

boolean isExternal(): returns true if the node is a leaf

boolean isRoot(): returns true if the node is the root

Binary Tree

In CS16, well be looking mainly at binary trees

A binary tree is a tree with the following property: Each internal node has at most 2

children: a left child and a right child. Even if there is only one child, the child is still specified as left or right.

Recursive definition: A tree consisting of a single node, or

A tree whose root has at most 2 children, each of which is a binary tree

A

B C

F GD E

H I

Binary Tree ADT

In addition to the methods specified in the Tree ADT, binary

tree Nodes have a few additional methods:

Node left(): returns the left child of the node if there is

one, otherwise null

Node right(): returns the right child of the node if there is

one, otherwise null

boolean hasLeft(): returns true if node has a left child

boolean hasRight(): returns true if node has a right child

Perfection

A binary tree is a perfect binary tree if

every level is completely full

Not perfect Perfect!

Completeness

A binary tree is a left-complete binary tree if:

every level is completely full, possibly excluding the

lowest level

all nodes are as far left as possible

Left-complete! Not left-complete