Problem of the Day

You drive a bus from Rotterdam to Delft. At the 1st stop, 33 people get in. At the 2nd stop, 7 add people & 11

passengers leave. The 3rd stop, sees 5 people leave and 2 get

in. After one hour, the bus arrives in Delft.

What is the name of the driver?

Problem of the Day

You drive a bus from Rotterdam to Delft. At the 1st stop, 33 people get in. At the 2nd stop, 7 add people & 11

passengers leave. The 3rd stop, sees 5 people leave and 2 get

in. After one hour, the bus arrives in Delft.

What is the name of the driver?It’s your name!

LECTURE 33:TREE AND BINARY TREE ADT

CSC 212 – Data Structures

Trees

Represent hierarchical relationships Parent-child basis of this abstract data type

Real-world example: directories & types

csc213/

homeworks/

ideas.todo

1M

programs/

LLQueue.java

10K

DLNode.java

25K

hard.txt

3K

impossible.txt

2K

Tree.java

20K

Trees

Represent hierarchical relationships Parent-child basis of this abstract data type

Real-world example: organism classificationMamma

l

Cat

Ape

Lion

Human

Chimpanzee

Professors

Yankees Fan

Tree Basics

Yet another Collection Nodes are Positions # of elements is its size

Some things are familiar Using Position

to hold elements Others are very different

Node class has little overlap Cannot discuss next & prev

A

B DC

G HE F

I J K

Tree Terms

Defined by relationships Talk about parents,

siblings, descendant

Nodes have no gender Will often mix in terms

like mother, father, niece, aunt, uncle,cousin, …

A

B DC

G HE F

I J K

Tree Terms

Tree rooted at node A “Top” or “Start” of tree

B, C, D are children of A A is parent of B, C, D B, C, D are siblings E, F, G, H are

grandchildren of A

A

B DC

G HE F

I J K

Tree Relationships

Nodes either leaf or interior Both or neither not options

A, B, C, F are parents At least 1 child for each Also called “interior nodes”

"Leaves" name of others Leaf node has no children

A

B DC

G HE F

I J K

Trees Recursion

Trees are recursive structure Subtree defined by a node

A

B DC

G HE F

I J K

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree

A

B DC

G HE F

I J K

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree D root of this subtree

A

B DC

G HE F

I J K

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree D root of this subtree B root of this subtree

A

B DC

G HE F

I J K

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree D root of this subtree B root of this subtree

Trees are like professors Some are tall & thin

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree D root of this subtree B root of this subtree

Trees are like professors Some are tall & thin Short & boring a possibility

Trees Recursion

Trees are recursive structure Subtree defined by a node C is root of this subtree D root of this subtree B root of this subtree

Trees are like professors Some are tall & thin Short & boring a possibility Others can be empty

Trees vs. Binary Trees

Both represent parent-child relationships Both consist of single "root" node & its

descendants Nodes can have at most one parent

Root nodes are orphans -- do not have a parent

All others, the non-root nodes must have parent

Children not required for any node in the tree No limit to number of children for non-

binary nodes 2 children for node in binary tree is the

maximum

Binary Tree

Extends Tree interface & adds following property 2 or fewer children per node

Typically drawing of tree sets childrens' names “Left child” is name of child to left of the

parent Child towards the right is called “Right

child”

R

B D

HE F

I

Height and Size of a Tree

Level 0 – max. 1 node

Maximum number of nodes doubles each level

Height and Size of a Tree

Level 1 – max. 2 nodes

Level 0 – max. 1 node

Maximum number of nodes doubles each level

Height and Size of a Tree

Level 2 – max. 4 nodes

Level 1 – max. 2 nodes

Level 0 – max. 1 node

Maximum number of nodes doubles each level

Height and Size of a Tree

Level 3 – max. 8 nodes

Level 2 – max. 4 nodes

Level 1 – max. 2 nodes

Level 0 – max. 1 node

Maximum number of nodes doubles each level

For a level i in a binary tree That level can have 2i nodes At most 2(i+1)-1 nodes for tree to that level

Independent of Implementation

A

B

Z F

I Q M

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

Binary Tree, Tree, or Other?

A B C D

Binary Tree, Tree, or Other?

Your Turn

Get into your groups and complete activity

For Next Lecture

Read parts of GT 7.2 & 7.3.6 for Friday Trees are Iterable, but how would it be

done? What are the types of traversals & how do

they differ? When do we do parent first & when do we

do our kid?

Week #12 assignment posted & due Tuesday

Programming Assignment #2 due Friday If you want help do not delay, I’m not

here tomorrow