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(C) GOYANI MAHESH(C) GOYANI MAHESH 11

DATASTRUCTURE

SMAHESH GOYANI

MAHATMA GANDHI INSTITUE OF TECHNICAL EDUCATION & RESEARCH CENTERmgoyani@rediffmail.com

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(C) GOYANI MAHESH(C) GOYANI MAHESH 33

Stacks in real life: stack of books, stack ofStacks in real life: stack of books, stack of

platesplates

Non Primitive, Linear Data Structure.

Operation can be performed at one end only

Last In Firs Out (LIFO | FILO | FCLS | LCFS)

Most Frequently accessible element is TOP

Insertion -> PUSH : TOP++

Deletion -> POP : TOP--

Stack Full + Push() = Overflow

Stack Empty + Pop() = Underflow

TERMINOLOGY

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(C) GOYANI MAHESH(C) GOYANI MAHESH 44

20

33

20

47

33

20

3320

77

3320

3320 20

Stack EmptyStack Empty

TOP=-1TOP=-1

TOP=0TOP=0

TOP=TOP=

11

TOP=2TOP=2

TOP=1TOP=1

TOP=2TOP=2

TOP=1TOP=1

TOP=TOP=

00

PushPush(20)(20)

PushPush(33)(33)

PushPush(47)(47)

Pop ()Pop () Push (77)Push (77) PopPop()()

Pop ()Pop ()

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(C) GOYANI MAHESH(C) GOYANI MAHESH 55

STACK OPERATION

int pop()

{

return STACK[TOP--];

}

void push(int x){

STACK[++TOP] = x;}

int top(){

return STACK[TOP];}

int IsFull(){

return ( TOP == STACK_SIZE-1);}

int IsEmpty()

{ return ( TOP == -1 );}

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(C) GOYANI MAHESH(C) GOYANI MAHESH 66

STACK implementation can be done in TWO ways;

(I) Static Implementation (Using Array)

(II) Dynamic Implementation (Using Pointers / LinkedList)

IMPLEMENTATION

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(C) GOYANI MAHESH(C) GOYANI MAHESH 77

TOP

2

5

7

1

2 5 7 1

0 1 32 4

TOP = 3

Using ARRAY

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(C) GOYANI MAHESH(C) GOYANI MAHESH 88

PUSH (STACK, TOP,DATA)

1. [Check for Stack Overflow]

If TOP == STACK_SIZE - 1,then

(a). Stack OverFlow

(b). Return.

2. [Increment TOP]

TOP = TOP + 1

3. [Insert Item On to Stack]

STACK[TOP] = DATA

4. Exit

ALGORITHM

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(C) GOYANI MAHESH(C) GOYANI MAHESH 99

POP(STACK, TOP,DATA)

1. [Check for Stack Underflow]If TOP < 0, then

(a). StackUnderflow

(b). Return.

2. [Read The Top Most Element]

DATA = STACK[TOP]

3. [Decrement TOP]TOP = TOP - 1

4. Exit

ALGORITHM

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1010

PEEP(STACK, TOP, I,DATA)

1. [Check for Stack Underflow]

If TOP - I < 0, then

(a). StackUnderflow

(b). Return.

2. [Read Ith Element]

DATA = STACK[I]

3. Exit

ALGORITHM

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1212

TOP

2

5

7

1

1 7 5 2

HEAD

We can avoid the size limitation of a stack implemented withan array by using a linked list to hold the stack elements

No need for the current pointer, head is enough.

Using LINKED LIST

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1313

top

2

5

71 7 5 2

head

pop(1)

OPERATION

top

2

5

7

9

7 5 2

head

push(9)

9

newNode

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1414

Allocating and deallocating memory for list nodes doestake more time than preallocated array.

List uses only as much memory as required by the nodes;array requires allocation ahead of time.

List pointers (head, next) require extra memory.

Array has an upper limit, List is limited by dynamicmemory allocation.

ARRAY v/s LINKED LIST

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1515

START

Initialization

Decision

FinalComputation

PartialComputation

UPDATE

RecursiveCall

Return

STOP

Prologue

Body

Epilogue

Recursion

Infix to Postfix

Tower of Hanoi

APPLICATION

int fact (int no)

{

int f=1;

if(no==1)

return no;

else{

f = no * fact (no - 1);

}

}

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1616

Recursion Iteration It is an process of executing astatement of set of statementsrepeatedly, until some specified

condition is met.

Recursion is a technique todefine anything in terms of it self.

Clear cut four steps. Initialization,Condition, Execution & Updating

There must be exclusive ifstatement for stopping condition

Any recursive problem can besolved iteratively

Not all problem have recursivesolution

More efficient in terms of memoryutilization and execution speed

Worse option to go for simpleproblems, or problems not recursivein nature.

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1818

INFIX TO POSTFIX

1. Push ( on toTEMP_STACK, and add ) to the end ofP.

2. Scan P from left to right and repeat step 3 to 6 for each element

of P untilTEMP_STACKthe stack is empty.

3. If an operand is encountered, add it to OP_STACK

4. If left parenthesis encountered than add it toTEMP_STACK.

5. If an operator is encountered, then:

(a).Repeatedly pop fromTEMP_STACKand add each operator toOP_STACKwhich has same or higher precedence then

(b). AddtoTEMP_STACK

6. If right parenthesis encountered, then:

(a). Repeatedly pop fromTEMP_STACKand add to OP_STACKuntila left parenthesis encountered.

(b). Remove the left parenthesis (Dont add it to OP_STACK)

7. Exit.

E l ti

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(C) GOYANI MAHESH(C) GOYANI MAHESH 1919

CharacterScanned

TEMP_STACK Postfix_STACK

A ( A

+ (+ A

( (+( A

B (+( A B

/ (+( / A B

C (+( / A B C- (+( - A B C /

( (+( - ( A B C /

D (+( - ( A B C / D

P = A +( B / C - ( D * E ^ F ) + G )* H

Evaluation

E l ti

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(C) GOYANI MAHESH(C) GOYANI MAHESH 2020

* (+( - (* A B C / D

E (+( - (* A B C / D E

^ (+( - (* A B C / D E

F (+( - (* A B C / D E F

) (+( - A B C / D E F ^ *

+ (+(+ A B C / D E F * -

G (+(+ A B C / D E F * - G

) (+ A B C / D E F * - G +

* (+ * A B C / D E F * - G +H ( + * A B C / D E F * - G + H

) A B C / D E F * - G + H * +

P = A +( B / C - ( D * E ^ F ) + G )* H

Evaluation

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(C) GOYANI MAHESH(C) GOYANI MAHESH 2121

Tower of Hanoi

A

B

C

D

A

B

C

D

X Y Z

ZX Y

INPUT

OUTPUT