3. Linear Structuresmouhoubm/=postscript/=c3620/c36203.pdf3. Linear Structures Array Implementation...

3. Linear Structures


• Abstract Data Types (ADTs)

• The List ADT

• The Stack ADT

• The Queue ADT

• Implementation

Malek Mouhoub, CS340 Fall 2004 1


Abstract Data Type (ADT)

• Set of data together with a set of operations.

• Definition of an ADT : [what to do ? ]

– Definition of data and the set of operations (functions).

• Implementation of an ADT : [how to do it ? ]

– How are the objects and operations implemented.

⇒ use the C++ class.



ADT List

Structure List is

Data : A list of elements.

Functions :

for every list ∈ List, item ∈ Element

List createList() ::= return an empty list

List insert(item,i,list) ::= add item at the position i and return the new list

List remove(item,list) ::= remove item and return the new list

Boolean isempty(list) ::= return list == empty

find(item,list) ::= If item ∈ list return position of item

else return ERROR

findKth(i,list) ::= return the item at position i if it exists, ERROR otherwise.



Array Implementation of Lists

• Contiguous allocation of memory to store the elements of the

list.

• Estimation (overestimation) of the maximum size of the list is

required

⇒ waste of memory space.

• O(N) for find , constant time for findKth

• But O(N) is required for insertion and deletion in the worst

case.

⇒ building a list by N successive inserts would require O(N2)in the worst case.



3412521622

n

12345

3412521622

n

12345

find(X): O(n) removeKth: O(n)remove(X):O(n)

3412521612

n

12345

insert(kth,X)O(n)

findKth=List[Kth]O(C)

12521622

n

12345

findKth(3)=52 find(52)=3 remove(34) insert(1,34)

List

Figure 1: Contiguous allocation of memory to store the elements of the list



Linked Lists

• Non contiguous allocation of memory.

• O(N) for find

• O(N) for findKth (but better time in practice if the calls to

findKth are in sorted order by the argument).

• Constant time for insertion and deletion.



3412345 12

52

16

22

678

5

3

7

4

Head Data Link

List = 34 12 52 16 22

34 12 52 16 22

Head

printList():O(n)find(x):O(n)findKth(i):O(i)

\

Figure 2: Non contiguous allocation of memory



A1 A2 A3 A4 A5

(a)

A1 A2 A3 A4 A5

(b)

Figure 3: (a) A double linked list (b) A double circular linked list



header (e) Empty list with header

header

A1 A2 A3 A4 A5

(d) Linked list with a header

34 12 16 22

52

(c) Insertion into a linked list

(b) Deletion from a linked list

34 12 52 16 22

(a) A lilnked list

34 12 52 16 22

remove(52)

insert(3,52)

header

header

header

Figure 4: Linked List Functions



ADT Stack

Structure Stack is


Functions :

for every stack ∈ Stack, item ∈ Element, capacity ∈ Natural

Stack createStack(capacity)::= return an empty stack

Boolean isFull(stack) ::= return (number of items in stack == capacity)

Boolean isEmpty(stack)::= return (stack == createStack(capacity))

Stack push(item,stack)::= If isFull(stack) return stack

else add item at the top of stack and return the new stack

Stack pop(stack) ::= If isEmpty(stack) return stack

else delete the element at the top of the stack and return the new stack

Element topAndPop(stack)::= If isEmpty(stack) return ERROR

else delete and return the element at the top of the stack



string input = "[()]"

push("[")

Top[

Top

push ("(")

[(

top()="("pop()

[

read "[" read "(" read ")"

Top

top()="["pop()

read "]"

Top

empty()

read ""

correct

Figure 5: Application: Balancing Symbols



intput infix = a+b*c+(d*e+f)*g

output:a push ("+")

+

output:ab

+

read "a" read "+" read "b"

push("*")

read "*"

output:abc

read "c"

*+

pop()output:abc*+

push ("(")

+

output:abc*+d

+

read "+" read "(" read "d"

push("*")

read "*"

output:abc*+de

read "e"

(+

pop()output:abc*+de*push("+")

output:abc*+de*f

+

pop()output:abc*+de*f+

pop()

+

read "+" read "f" read ")"

push("*")

read "*"

output:abc*+def+g

read "g"

*+

+

*

+

( (

*

+

(

*

+(

+(

+

*

+

pop()output:abc*+def+g*pop()output:abc*+def+g*+

Figure 6: Application : Infix and Postfix Conversion



ADT Queue

Structure Queue is


Functions :

for every queue∈ Queue, item∈ Element, capacity∈ Natural

Queue createQueue(capacity) ::= return an empty queue

Boolean isFull(queue) ::= return (number of items in stack == capacity)

Boolean isEmpty(queue) ::= return (queue == createQueue(capacity))

Queue enqueue(item,queue) ::= If isFull(queue) return queue

else add item at the end of queue

and return the new queue

Queue dequeue(queue) ::= If isEmpty(queue) return queue

else delete the element at the front of the queue

and return the new queue

Element getFront(stack) ::= If isEmpty(stack) return ERROR

else delete and return the element at the front of queue



2 41

2 41

front^

front^

front^

back^

back^

3

3 2 41 3

2 4

front^

back^

(1)Initial State

2 41

front^

back^

(2)After enqueue(1)

(3)After enqueue(3) (4)After dequeue, which returns 2

2 41

front^

back^

3

(5)After dequeue, which returns 4 (6)After dequeue, which returns 1

back

(7)After dequeue, which return 3 and Makes the Queue Empty

front^

back^

2 41 3

Figure 7: Array Implementation of Queues


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clud

e<

iost

ream

.h>

//F

orN

ULL

tem

plat

e<

clas

sO

bjec

t>

clas

sS

tack

{pu

blic

:

Sta

ck(

);

Sta

ck(

cons

tS

tack

&rh

s);

10˜S

tack

();

bool

isE

mpt

y()

cons

t;is

Em

pty

bool

isF

ull(

)co

nst;

cons

tO

bjec

t&

top(

)co

nst;

void

mak

eEm

pty(

);

void

pop(

);

void

push

(co

nst

Obj

ect

&x

);

Obj

ect

topA

ndP

op(

);

cons

tS

tack

&op

erat

or=

(co

nst

Sta

ck&

rhs

);

priv

ate:

20st

ruct

List

Nod

e

{O

bjec

tel

emen

t;

List

Nod

e*n

ext;

List

Nod

e(co

nst

Obj

ect

&th

eEle

men

t,Li

stN

ode

*n

=N

ULL

)

:el

emen

t(th

eEle

men

t),

next

(n

){}

}; List

Nod

e*t

opO

fSta

ck;

}; #in

clud

e"

Sta

ckLi

.cpp

"30

#en

dif

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0428

3.Li

near

Str

uctu

res

#in

clud

e"

Sta

ckLi

.h"

#in

clud

e<

iost

ream

.h>

tem

plat

e<

clas

sO

bjec

t>

Sta

ck<

Obj

ect>

::Sta

ck(

)::S

tack

{to

pOfS

tack

=N

ULL

;

} tem

plat

e<

clas

sO

bjec

t>

Sta

ck<

Obj

ect>

::Sta

ck(

cons

tS

tack

<O

bjec

t>&

rhs

)::S

tack

{10

topO

fSta

ck=

NU

LL;

*thi

s=

rhs;

} tem

plat

e<

clas

sO

bjec

t>

Sta

ck<

Obj

ect>

::˜S

tack

()

::˜S

tack

{m

akeE

mpt

y();

} tem

plat

e<

clas

sO

bjec

t>20

bool

Sta

ck<

Obj

ect>

::isF

ull(

)co

nst

::isF

ull

{re

turn

fals

e;

} tem

plat

e<

clas

sO

bjec

t>

bool

Sta

ck<

Obj

ect>

::isE

mpt

y()

cons

t::i

sEm

pty

{re

turn

topO

fSta

ck=

=N

ULL

;

}30

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0429

3.Li

near

Str

uctu

res

tem

plat

e<

clas

sO

bjec

t>

void

Sta

ck<

Obj

ect>

::mak

eEm

pty(

)

{w

hile

(!is

Em

pty(

))

pop(

);

} tem

plat

e<

clas

sO

bjec

t>

cons

tO

bjec

t&

Sta

ck<

Obj

ect>

::top

()

cons

t40

::top

{if

(is

Em

pty(

))

thro

wU

nder

flow

();

retu

rnto

pOfS

tack−

>el

emen

t;

} tem

plat

e<

clas

sO

bjec

t>

void

Sta

ck<

Obj

ect>

::pop

()

::pop

{if

(is

Em

pty(

))

50th

row

Und

erflo

w(

);

List

Nod

e*o

ldTo

p=

topO

fSta

ck;

topO

fSta

ck=

topO

fSta

ck−

>ne

xt;

dele

teol

dTop

;

} tem

plat

e<

clas

sO

bjec

t>

Obj

ect

Sta

ck<

Obj

ect>

::top

And

Pop

()

::top

And

Pop

{60

Obj

ect

topI

tem

=to

p();

pop(

);

Mal

ekM

ouho

ub,C

S34

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ll20

0430

3.Li

near

Str

uctu

res

retu

rnto

pIte

m;

} tem

plat

e<

clas

sO

bjec

t>

void

Sta

ck<

Obj

ect>

::pus

h(co

nst

Obj

ect

&x

)::p

ush

{to

pOfS

tack

=ne

wLi

stN

ode(

x,to

pOfS

tack

);

}70

tem

plat

e<

clas

sO

bjec

t>

cons

tS

tack

<O

bjec

t>&

Sta

ck<

Obj

ect>

::

oper

ator

=(

cons

tS

tack

<O

bjec

t>&

rhs

)

{if

(th

is!=

&rh

s)

if{

mak

eEm

pty(

);

if(

rhs.

isE

mpt

y()

)

retu

rn*t

his

;

80Li

stN

ode

*rpt

r=

rhs.

topO

fSta

ck;

List

Nod

e*p

tr=

new

List

Nod

e(rp

tr−

>el

emen

t);

topO

fSta

ck=

ptr;

for(

rptr

=rp

tr−

>ne

xt;

rptr

!=N

ULL

;rp

tr=

rptr−

>ne

xt)

ptr

=pt

r−>

next

=ne

wLi

stN

ode(

rptr−

>el

emen

t);

} retu

rn*t

his

;

}

Mal

ekM

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0431

3.Li

near

Str

uctu

res

#ifn

def

QU

EU

EA

RH

#de

fine

QU

EU

EA

RH

#in

clud

e"

vect

or.h

"

#in

clud

e"

dsex

cept

ions

.h"

tem

plat

e<

clas

sO

bjec

t>

clas

sQ

ueue

{pu

blic

:

expl

icit

Que

ue(

int

capa

city

=10

);

bool

isE

mpt

y()

cons

t;10

bool

isF

ull(

)co

nst;

cons

tO

bjec

t&

getF

ront

()

cons

t;

void

mak

eEm

pty(

);

Obj

ect

dequ

eue(

);

void

enqu

eue(

cons

tO

bjec

t&

x);

priv

ate:

vect

or<

Obj

ect>

theA

rray

;

int

curr

entS

ize;

int

fron

t;

int

back

;20

void

incr

emen

t(in

t&

x);

}; #in

clud

e"

Que

ueA

r.cpp

"

#en

dif

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0432

3.Li

near

Str

uctu

res

#in

clud

e"

Que

ueA

r.h"

tem

plat

e<

clas

sO

bjec

t>

Que

ue<

Obj

ect>

::Que

ue(

int

capa

city

):

theA

rray

(ca

paci

ty)

{m

akeE

mpt

y();

} tem

plat

e<

clas

sO

bjec

t>

bool

Que

ue<

Obj

ect>

::isE

mpt

y()

cons

t

{re

turn

curr

entS

ize

==

0;10

} tem

plat

e<

clas

sO

bjec

t>

bool

Que

ue<

Obj

ect>

::isF

ull(

)co

nst

{re

turn

curr

entS

ize

==

theA

rray

.siz

e();

} tem

plat

e<

clas

sO

bjec

t>

void

Que

ue<

Obj

ect>

::mak

eEm

pty(

)

{cu

rren

tSiz

e=

0;20

fron

t=

0;

back

=−

1;

}

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0433

3.Li

near

Str

uctu

res

tem

plat

e<

clas

sO

bjec

t>

cons

tO

bjec

t&

Que

ue<

Obj

ect>

::get

Fron

t()

cons

t

{if

(is

Em

pty(

))

thro

wU

nder

flow

();

retu

rnth

eArr

ay[

fron

t];

30

} tem

plat

e<

clas

sO

bjec

t>

Obj

ect

Que

ue<

Obj

ect>

::deq

ueue

()

{if

(is

Em

pty(

))

thro

wU

nder

flow

();

curr

entS

ize−−

;

Obj

ect

fron

tItem

=th

eArr

ay[

fron

t];

incr

emen

t(fr

ont

);

retu

rnfr

ontIt

em;

40

} tem

plat

e<

clas

sO

bjec

t>

void

Que

ue<

Obj

ect>

::enq

ueue

(co

nst

Obj

ect

&x

)

{if

(is

Ful

l()

)

thro

wO

verfl

ow(

);

incr

emen

t(ba

ck);

theA

rray

[ba

ck]

=x;

curr

entS

ize+

+;}

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0434

3.Li

near

Str

uctu

res

tem

plat

e<

clas

sO

bjec

t>

void

Que

ue<

Obj

ect>

::inc

rem

ent(

int

&x

)50

{if

(+

+x

==

theA

rray

.siz

e()

)

x=

0;

}

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0435

3.Li

near

Str

uctu

res

#in

clud

e<

iost

ream

.h>

#in

clud

e"

Que

ueA

r.h"

int

mai

n()

mai

n

{Q

ueue

<in

t>q;

for(

int

j=

0;j<

5;j+

+)

{fo

r(in

ti

=0;

i<

5;i+

+)

q.en

queu

e(i

);

10

whi

le(

!q.is

Em

pty(

))

cout

<<

q.de

queu

e()

<<

endl

;

} retu

rn0;

}

Mal

ekM

ouho

ub,C

S34

0Fa

ll20

0436

3. Linear Structuresmouhoubm/=postscript/=c3620/c36203.pdf3. Linear Structures Array Implementation...

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Transcript of 3. Linear Structuresmouhoubm/=postscript/=c3620/c36203.pdf3. Linear Structures Array Implementation...