Algorithms and Data StructuresExercise I

Banafsheh Azarihttp://www.uni-weimar.de/de/medien/professuren/grafische-

datenverarbeitung/

Bauhaus-University Weimar - CogVis/MMC

November 8, 2016

c©2016 , Algorithms and Data Structures Exercise I Exercise I 1/22

Exercise

• Tuesday ,13:30 , SR013, B11

• Odd weeks

• First Exercise : 08.11.2016

c©2016 , Algorithms and Data Structures Exercise I Exercise I 2/22

Exercise

Conditions

• C/C++ or Java

• Compilable source code (gcc or javac)

• No IDEs

• Readable source code

• Self-contained submission

c©2016 , Algorithms and Data Structures Exercise I Exercise I 3/22

Exercise

Comments

• Sufficient comments (rule of thumb: another Developers canget program logic alone by reading the comments)

• In each! Data: Name, matriculation number, WS2016-2017

c©2016 , Algorithms and Data Structures Exercise I Exercise I 4/22

Exercise

• Tasks: www.uni-weimar.de/de/medien/professuren/grafische-datenverarbeitung/

• Submission: per E-Mail as NameLastname E . . .

c©2016 , Algorithms and Data Structures Exercise I Exercise I 5/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Data Structures

• Array

• Linked Lists

• Stacks• LIFO• Push• pop

• Queues• FIFO• enqueue• dequeue

• Trees

• Graphs

c©2016 , Algorithms and Data Structures Exercise I Exercise I 6/22

Polynomial

Start

p 0 o 1 n 2 m 4

g�x� = mx� + nx + ox + p

coef expo next

c©2016 , Algorithms and Data Structures Exercise I Exercise I 7/22

Polynomial Addition

Start

Start

a 5 b 3 c 1

p 0 o 1 n 2 m 4

f�x� = ax� + bx + cx

g�x� = mx� + nx� + ox + p

h�x� = f�x� + g�x� = ax� +mx� + bx + nx� + �c + o�x + p

c©2016 , Algorithms and Data Structures Exercise I Exercise I 8/22

Infix– and Postfix Expression

• Infix expression(A * (B + (C / D) ) )

• Postfix expression(A (B (C D /) +) *)

• Prefix expression(* A (+ B (/ C D) ) )

c©2016 , Algorithms and Data Structures Exercise I Exercise I 9/22

Converting Example

stack

original expression 5/7+2*4*3

postfix expression 5

push /

5 7

pop / push +

5 7 / 5 7 / 2

push *

5 7 / 2 4

pop * push *

5 7 / 2 4 *

pop *

5 7 / 2 4 * 3 *

pop +

5 7 / 2 4 * 3 * +

+ *

+ *

+

/

+

c©2016 , Algorithms and Data Structures Exercise IExercise I10/22

Calculation Example

stack

original expression

2 4 * 9 5 + -

push 2

push 4

pop 4 pop 2 push 2*4

push 9 push 5

pop 5 pop 9 push 9+5

pop 14 pop 8 push 8-14

-6

8

14

8

9

5

8

2

4

2

c©2016 , Algorithms and Data Structures Exercise IExercise I11/22

Trees

A

S M

E P L

Q T

Terminology

c©2016 , Algorithms and Data Structures Exercise IExercise I12/22

Trees

A

S M

E P L

Q T

Terminology• Node

• External node: leaf• Internal node

• Edge

• Path

• Root

c©2016 , Algorithms and Data Structures Exercise IExercise I13/22

Trees

A

S M

E P L

Q T

N=number of nodesM=number of edgesM=N-1

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Trees

A

F E D

B C

Implementing

c©2016 , Algorithms and Data Structures Exercise IExercise I15/22

Trees

A

S M

E P L

Q T

traversing methods

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Tree

A

S M

E P N L

X K Q T

traversing methods

• Preorder

• Inorder

• Postorder

• Level-Order

c©2016 , Algorithms and Data Structures Exercise IExercise I17/22

Trees

*

A

D

B

C

+

/

c©2016 , Algorithms and Data Structures Exercise IExercise I18/22

Huffman coding

ABACCDA

010100010000000111010 21 bit

Character D C B A

Code 111 000 100 010

00010010101100 14 bit

Character D C B A

Code 11 10 01 00

0110010101110 13 bit

Character D C B A

Code 111 10 110 0

c©2016 , Algorithms and Data Structures Exercise IExercise I19/22

Huffman coding

Character S I N T E

Frequency 4 5 9 10 29

4 5 9 10 29

4 5

4+5

1 0

9 9 10 29

9 9

9+9

1 0

9 9

18

1 0

5

0

4

1

18 29 10

10 18

10+18

1 0

c©2016 , Algorithms and Data Structures Exercise IExercise I20/22

Palindrome & Anagram

”madam”m ———– ma ———– ad ———– da ———– a

m ———– m

c©2016 , Algorithms and Data Structures Exercise IExercise I21/22

Assignment I

Deadline: 21.November 2016 24:00Write a program that use the given table to produce Hoffman codeand read a sentence made of 0 and 1 as input, decode it andreturns the result as output

Character A E S L P O F

Frequency 20 11 6 9 18 5 10

c©2016 , Algorithms and Data Structures Exercise IExercise I22/22