Problem of the Day

The place where they signed the Declaration of Independence has the same name now as it did then. What is it?

Problem of the Day

The place where they signed the Declaration of Independence has the same name now as it did then. What is it?

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LECTURE 33:TREE TRAVERSALS

CSC 212 – Data Structures

Trees

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

Real-world example: organization chart

Idiot

Kiss-up

Useless

Unknown Lead

?

Blob

Carbon RodLacke

y

Boot-Lick

ThiefDrone

MoronWorker

Hard Worker

Knowledgeable Person

You

Traversing Linear Collections Trees are another Collection of data

Positions required in the Tree ADT methods ADT uses generic type to specify type of

element Want to iterate through tree’s elements

Not required, but order obvious for linear structures

Follow IndexList’s indices from lowest to highest

Iterator for NodeList follows Positions

Traversing Linear Collections Trees are another Collection of data

Positions required in the Tree ADT methods

ADT uses generic type to specify type of element

Want to iterate through tree’s elements Not required, but order obvious for linear

structures Follow IndexList’s indices from lowest to

highest Iterator for NodeList follows Positions

But how do we do this for Trees?

Tree Traversals

Several different, predictable orderings Preorder honors thy elders and treats them

well

Tree Traversals

Several different, predictable orderings Preorder honors thy elders and treats them

well This traversal will start with parent THEN do

kids

Tree Traversals

Several different, predictable orderings Preorder honors thy elders and treats them

well This traversal will start with parent

THEN do kids

Preorder Traversal

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Preorder Traversal

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Preorder Traversal

Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);

Preorder Traversal

Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);

Preorder Traversal

Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);

Preorder Traversal

Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);

Preorder Traversal

Table of Contents

Chapter 1

Appendix A

Chapter 2

Section 2.1

Section 2.2

Section 1.1

Section 1.2

Section 1.2.1

Section 1.2.2

Section 1.2.3

Algorithm preOrder(tree, v)/* Process v */foreach (w : v.children())

preOrder(tree, w);

Preorder Traversal

Visit node first, then visit its children Normal ordering found in every chapter

book Start each section before going into

contents: Table of Contents

§1, §1.1, §1.2, §1.2.1, §1.2.2,

§1.2.3§2, §2.1,

§2.2Appendix A

Tree Traversals

Several different, predictable orderings Preorder honors thy elders and treats them

well Morals also important: postorder places

children first

Tree Traversals

Several different, predictable orderings Morals also important: postorder places

children first Do children THEN do parent using this

traversal

Tree Traversals

Several different, predictable orderings Morals also important: postorder places

children first Do children THEN do parent using this

traversal

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Csc212/

Activities/

Midterm1.tex

Projects/

Project01.tex

Project02.tex

Activity01.tex

Activity02/

Problems.tex

Solution.tex

Solution02.png

Algorithm postOrder(tree, v)foreach (w : v.children())

postOrder(tree, w);/* Process v */

Postorder Traversal

Node visits children before it is processed Needed to compute directory’s disk space First look at size of contents then the main

directory Important whenever leaves contain

actual data Visits external nodes, then works way up

the tree In this traversal, after its descendants node

processed

Binary Trees

Pre- & post-order identical for binary trees Also offer additional type of traversal Traversals used again, so do not let this slip

Equation trees are canonical examples Using them, the different approaches can

be seen Lets (old) Professors reminisce over HP

calculators Kind of stupid, but is actually used in

programs

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Inorder Traversal

Traversal visits equation in proper order:

(1 + (6 * 3)) - (4 / 2) Binary search trees use this again &

again

-

/+

*1

6 3

4 2

Algorithm inOrder(tree, v)if (tree.hasLeft(v))

inOrder(tree, tree.left(v))visit(tree, v)if (tree.hasRight(v)) inOrder(tree, tree.right(v));

Postorder Traversal

Algorithm postOrder(tree, v)if (tree.hasLeft(v))

postOrder(tree, tree.left(v))if (tree.hasRight(v)) postOrder(tree, tree.right(v));visit(tree, v)

-

/+

*1

6 3

4 2

Postorder Traversal

Traversal follows order equation is computed:

1 6 3 * + 4 2 / - Java compiles equations using this

format

Algorithm postOrder(tree, v)if (tree.hasLeft(v))

postOrder(tree, tree.left(v))if (tree.hasRight(v)) postOrder(tree, tree.right(v));visit(tree, v)

-

/+

*1

6 3

4 2

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 to implement

it? What is a template pattern & how do we

use it? I’m lazy; can’t we make this code easy to

write?

Week #12 assignment posted & due Tuesday

Programming Assignment #2 due Saturday