data structures unit 04 -

Data Structures – Unit 04Bucharest University of Economic Studies

Stacks and Queues

Agenda

•Definition

•Graphical representation

•Internal interpretation

•Characteristics

•Operations

•Implementations

Stack

I t i s a l i n e a r s t r u c t u r e i n w h i c h t h e t w o b a s i c

o p e r a t i o n s , i n s e r t i o n a n d d e l e t i o n a r e m a d e

o n a L I F O b a s e d r u l e . T h e s e o p e r a t i o n s a r e

m a d e i n a s i n g l e p a r t o f t h e s t r u c t u r e c a l l e d

t h e h e a d o f t h e s t a c k , o r t h e t o p .

STACKpop

push

Stack•A logical structure implemented with different type of data structures:

linked lists or arrays;

•A homogenous structure with elements of the same type;

•Basic operations:

•Adding an element, called push operation

•Removing an element, called pop operation

•Looking at the top element, called peek operation

struct Stack{

int info;

Stack * next;

} ;

Stack as an ADT

2

4

1

3

6

top

The implementation rule is

LIFO – Last In First Out

The pop operation from a NULL stack

is considered an error

The push operation into a stack is

considered a limitation

The element from the top of a stack is

the only accessible element

Stack – graphical representation

Stack mechanism

K

C

A

T

S

push pop

Stacks with Linked Lists

2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 NULL

2500 2501

2 NULL

3241 3242

top of the stack

new node


2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 NULL

2500 2501

2 1002

3241 3242

top of the stack


2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 NULL

2500 2501

2 1002

3241 3242

temporary node

top of the stack

Function call simulation

int suma(int x, int y) {

int z = 0, r = 2;

z = x + y;

return z;

}

void main(){

int a = suma(3,8);

}

0x00f11464h


initialization

.…

BP:0x0018FA1Ch

SP:0x0018FA18h

push

b: 8

.…

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h


push a

a: 3

b: 8

.…

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h


push IP

IP: 0x00f11464h

a: 3

b: 8

.…

SP:0x0018FA0Ch


BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

push BP

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

SP:0x0018FA08h


SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

mov SP, BP

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

sub esp,8

r: 2

z: 0

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

SP:0x0018FA00h

mov BP, SP

r: 2

z: 0

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

SP:0x0018FA00h

pop BP

r: 2

z: 0

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

SP:0x0018FA00h

pop BP

return

r: 2

z: 0

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

SP:0x0018FA00h

pop BP

return

r: 2

z: 0

BP: 0x0018FA1Ch

IP: 0x00f11464h

a: 3

b: 8

.…

BP:0x0018FA08h


SP:0x0018FA08h

SP:0x0018FA0Ch

BP:0x0018FA1Ch

SP:0x0018FA18h

SP:0x0018FA14h

SP:0x0018FA10h

SP:0x0018FA00h

pop BP

return

PUSH Pseudocode

1. memory allocation (newNode);

2. newNode initialization;

3. if (stack_full)

stack overflow;

else

newNode >next = empty(head)? NULL: head;

head = newNode;

POP Pseudocode

1. declaring a temporary node (tmpNode);

2. if (stack_empty)

stack underflow;

else

value = head->info;

tmpNode = head;

head = head–>next;

free(tmpNode);

return value;

QUEUESIt is a linear structure in which the two basicoperations, insertion anddeletion

are made on a FIFO based model. The insertion is made on the tail section

andthedeletion ismadeonthefrontsectionofthequeue.

Queue

enqueue

dequeue put

get

Queue•A logical structure implemented with different type of data structures: linked

lists or arrays;

•A homogenous structure with elements of the same type;

•Basic operations:

•Adding an element, called the enqueuer or put operation

•Removing an element, called the dequeuer or get operation

struct Node{

int info;

Node * next;

} ;

struct Queue{

Node* head;

Node* tai l ;

} ;

Implementation model

FIFO – Fifo In First Out

5 2 7 1

backfront

Queue

Queue – Implementation

E U E U Qput get

PUT Pseudocode

1. memory allocation for a new node (newNode);

2. newNode initialization;

3. if (full queue)

queue overflow;

else

if (empty queue)

head = tail = newNode ;

else

tail–>next = newNode;

GET Pseudocode

1. declaring a temporary node (tmpNode);

2. if (empty queue)

queue underflow;

else

value = head–>info;

tmpNode = head;

head = head–>next;

free(tmpNode);

return value;

Queues with Linked Lists

2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 NULL

2500 2501

2 NULL

3241 3242

head of the queue

tail of the queue


2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 3241

2500 2501

2 NULL

3241 3242

head of the queue

tail of the queue


2 1005

1002 1003

5 1328

1005 1006

8 2500

1328 1329

34 3241

2500 2501

2 NULL

3241 3242

temporary node

tail of the queue

head of the queue

Initial state (back < front && empty == true):

back front

Queue – Circular array

Enqueue (2):

2

back

front


Enqueue (4):

2 4

backfront


Enqueue (1):

1 2 4

back front


Queue – Circular arrayEnqueue (3):

1 3 2 4

back front

Queue – Circular arrayDequeue => return 2:

1 3 2 4

back front


1 3 2 4

backfront


1 3 2 4

back

front


1 3 2 4

back front

Palindrome

Able was I ere I saw Elba

Ring buffer

•Evaluating mathematical expressions by using the stack data

structure: reordering the elements so that the expression can be

evaluated easily by one single crossing over the entire expression;

•The Polish notation invented by Jan Lukasiewicz also called the prefix

expression;

•The Reverse Polish notation is called postfix notation.

Infix – Postfix – Prefix notations

Evaluating mathematical expressions:

•Prefix or Polish notation: the operators are written

before the operands

•Postfix or revers Polish notation: the operators are

placed after the operands


The postfix or the reverse Polish notation is easily interpreted than

the infix, normal mathematical expressions:

•the order of operations is straight forward;

•the parentheses are not necessary;

•the evaluation are automatically made by the use of a stack data

structure;


The algorithm for casting an infix expression to a postfix notation is

called Dijkstra Shunting-Yard algorithm:

•using a stack for storing the operators in order to be transferred into

the postfix notation;

•each operator has an adequate hierarchy level as depicted in the

next table;



Operators hierarchy level

4321

( [ { ) ] } + - * /

Mathematical

expression

(the infix notation)

Polish notation

(prefix expression)

Reverse Polish

notation

(postfix expression)

4 + 5 + 4 5 4 5 +

4 + 5 * 5 + 4 * 5 5 4 5 5 * +

4 * 2 + 3 + * 4 2 3 4 2 * 3 +

4 + 2 + 3 + + 4 2 3 4 2 + 3 +

4 * (2 + 3) * 4 + 2 3 4 2 3 + *


•Scan the entire infix expression from left to right for tokens

(operators, operands and parentheses)

•For each token, test whether:

•If token is an operator:

•All operators from the top of the stack that are higher or

equal precedence than the incoming one are popped out

from the stack and appended to the postfix expression;

after this operation the new token is pushed on the stack;

Dijkstra Shunting-Yard algorithm

•If token is an operand, append it to the postfix expression;

•If token is a left parenthesis, push it on the stack;

•If token is a right parenthesis:

•Pop all the operators from the stack and append them to the postfix

expression, till the matching left parenthesis is found, which is

popped out without being added to the result;

•When all tokens of the infix expression have been scanned, pop all the

elements from the stack and append them to the postfix expression;

Dijkstra Shunting-Yard algorithm

Infix to Postfix

2*(4+3)+9/3

Stack:

Output:2

Infix to Postfix

2*(4+3)+9/3

Stack:*

Output:2

Infix to Postfix

2*(4+3)+9/3

Stack:*(

Output:2

Infix to Postfix

2*(4+3)+9/3

Stack:*(

Output:24

Infix to Postfix

2*(4+3)+9/3

Stack:*(+

Output:24

Infix to Postfix

2*(4+3)+9/3

Stack:*(+

Output:243

Infix to Postfix

2*(4+3)+9/3

Stack:*

Output:243+

Infix to Postfix

2*(4+3)+9/3

Stack:+

Output:243+*

Infix to Postfix

2*(4+3)+9/3

Stack:+

Output:243+*9

Infix to Postfix

2*(4+3)+9/3

Stack:+/

Output:243+*9

Infix to Postfix

2*(4+3)+9/3

Stack:+/

Output:243+*93

Infix to Postfix

2*(4+3)+9/3

Stack:

Output:243+*93/+

•Scan the entire postfix expression from left to right for tokens (operands and

operators):

•For each token, test whether:

•If token is an operand is pushed on the stack;

•If token is an operator:

•Pop the left element from the stack into a y variable;

•Pop the right element from the stack into a x variable;

•The operation between x operator y is computed;

•The result is pushed on the stack;

•The last value standing on the stack is the result of the expression.

Postfix evaluation algorithm

Infix->Postifix->Evaluation

E =5*3+2-(3*2+1)

References

•Ion IVAN, Marius POPA, Paul POCATILU, coordonatori – Structuri de date, Editura ASE, Bucuresti,

2008, ISBN 978-606-505-031-0

•Ion SMEUREANU – Programarea in limbajul C/C++, Editura CISON, 2001

•Michael MAIN – Data Structures & Other Objects Using Java, Editura Pearson, 2012, ISBN:

9780132911504

•http://www.acs.ase.ro

•http://www.itcsolutions.eu

data structures unit 04 -

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