linked lists notes

7/23/2019 Linked Lists Notes

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Data St r uct ur es ( 9067)

Linked Lists

Introduction

We have seen repr esent at i on of l i near dat a st r uct ur es by usi ngsequent i al al l ocat i on met hod of st or age, as i n, ar r ays. But t hi s i sunaccept abl e i n cases l i ke:

a.

Unpr edi ct abl e st or age requi r ement s:

The exact amount of dat a st or age r equi r ed by t he program var i eswi t h the amount of data bei ng pr ocessed. Thi s may not be avai l abl e att he t i me we wr i t e pr ogr ams but are t o be determi ned l ater .

For exampl e, l i nked al l ocat i ons ar e ver y benef i ci al i n case ofpol ynomi al s. When we add t wo pol ynomi al s, and none of t hei r degreesmat ch, t he r esul t i ng pol ynomi al has t he si ze equal t o t he sum of t he t wopol ynomi al s t o be added. I n such cases we can generat e nodes ( al l ocat ememory t o t he dat a member ) whenever r equi r ed, i f we use l i nkedr epr esent at i on ( dynami c memor y al l ocat i on) .

b. Extensi ve dat a mani pul at i on t akes pl ace.

Frequent l y many oper at i ons l i ke i nser t i on, del et i on et c, ar e t o beper f or med on t he l i nked l i st .

Poi nt er s are used f or t he dynami c memory al l ocat i on. These poi nt er s areal ways of same l engt h r egar dl ess of whi ch dat a el ement i t i s poi nt i ng t o(i nt , f l oat , st r uct etc, ) . Thi s enabl es t he mani pul at i on of poi nt er s t o beper f ormed i n a uni f orm manner usi ng si mpl e t echni ques. These make us capabl eof r epr esent i ng a much more compl ex rel at i onshi p bet ween t he el ement s of a

dat a st r uct ur e t han a l i near or der met hod.

The use of poi nt er s or l i nks t o r ef er t o el ement s of a data st r uct urei mpl i es t hat el ement s, whi ch ar e l ogi cal l y adj acent , need not be physi cal l yadj acent i n t he memor y. J ust l i ke f ami l y member s di sper sed, but st i l l boundt oget her .

Singly Linked List [or] One way chain

Thi s i s a l i st , whi ch may consi st of an or dered set of el ement s t hat mayvar y i n number . Each el ement i n t hi s l i nked l i st i s cal l ed as node. A node i na si ngl y l i nked l i st consi st s of t wo par t s, a information part where t he

act ual dat a i s st or ed and a link part, whi ch st or es t he addr ess of t hesuccessor ( next ) node i n t he l i st . The or der of t he el ement s i s mai nt ai ned byt hi s expl i ci t l i nk bet ween t hem. The typi cal node i s as shown :

NODE

Li nkI nf o

Fig 1. Structure of a Node

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Consi der an exampl e wher e the marks obt ai ned by t he st udent s ar e st oredi n a l i nked l i st as shown i n t he f i gur e :

| dat a | Next |

- - - > - - - > - - - >70 65 NULL6245

| |

fig 2. Singly Linked List

I n f i gur e 2, t he ar r ows r epr esent t he l i nks. The data par t of each nodeconsi st s of t he marks obt ai ned by a st udent and the next par t i s a poi nt er t ot he next node. The NULL i n t he l ast node i ndi cat es t hat t hi s node i s t he l astnode i n t he l i st and has no successor s at pr esent . I n t he above the exampl et he dat a par t has a si ngl e el ement marks but you can have as many el ement s asyou r equi r e, l i ke hi s name, cl ass et c.

There ar e several oper at i ons t hat we can per f or m on l i nked l i st s. We cansee some of t hem now. To begi n wi t h we must def i ne a st r uct ur e f or t he nodecont ai ni ng a dat a par t and a l i nk par t . We wi l l wr i t e a pr ogr am t o show howt o bui l d a l i nked l i st by addi ng new nodes i n the begi nni ng, at t he end or i nt he mi ddl e of t he l i nked l i st . A f uncti on di spl ay( ) i s used t o di spl ay thecont ent s of t he nodes pr esent i n t he l i nked l i st and a f unct i on del et e( ) ,whi ch can del et e any node i n t he l i nked l i st .

t ypedef st r uct node{ i nt dat a;

st r uct node *l i nk;}NODE;

# i ncl ude < st di o. h ># i ncl ude < al l oc. h > / * r equi r ed f or dynami c memory */

/ * al l ocat i on * /

mai n( ){NODE *p;

P = NULL; / * empt y l i nked l i st */

pr i nt f ( \ n No of el ement s i n t he l i nked l i st = %d,count ( p) ) ;

append( &p, 1) ; / * adds node at t he end of t he l i st */append( &p, 2) ;append( &p, 3) ;append( &p, 4) ;append(&p, 17) ;

cl r s cr ( ) ;di spl ay( p) ;

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add_beg( &p, 999) ; / * adds node at t he begi nni ng of t hel i st * /

add_beg( &p, 888) ;add_beg( &p, 777) ;

di spl ay( p) ;

add_af t er ( p, 7, 0) ; / * adds node af t er speci f i ed node */add_af t er ( p, 2, 1) ;add_af t er ( p, 1, 99) ;

di spl y(p) ;pr i nt f ( \ n No of el ement s i n t he l i nked l i st = %d,

count ( p) ) ;

del et e( &p, 888) ; / * del et es the node speci f i ed */del et e( &p, 1) ;del et e( &p, 10) ;


}

To begi n wi t h t he var i abl ep has been decl ared as poi nt er t o a node.Thi s poi nt er i s a poi nt er t o t he f i r st node i n t he l i st . No mat t er how manynodes get added t o t he l i st , p wi l l al ways be t he f i r st node i n t he l i nkedl i st . When no node exi st s i n t he l i nked l i st , p wi l l be set t o NULL t oi ndi cat e t hat t he l i nked l i st i s empt y. Now we wi l l wr i t e and di scuss each oft hese f unct i ons.

Function to add a node at the end of the linked list

append( NODE **q, i nt num){

NODE *t emp, *r ;

t emp = *q;

i f ( *q == NULL) / *l i st empt y, creat e t he f i r st node */{

t emp = mal l oc( si zeof ( NODE) ) ;t emp- >dat a = num;t emp- >l i nk = NULL;*q = t emp;

}el se{

t emp = *q;

whi l e( t emp- >l i nk ! = NULL ) / * got o t he end of */t emp = t emp- >l i nk; / * l i st */

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r = mal l oc( si zeof ( NODE) ) ;r - >dat a = num; / * add node at t he */r - >l i nk = NULL; / * end of t he l i st */t emp- >l i nk = r ;

}}

The append( ) f unct i on has t o deal wi t h t wo si t uat i ons:

a. The node i s bei ng added t o an empt y l i st .b. The node i s bei ng added t o t he end of t he l i nked l i st .

I n t he f i r st case, t he condi t i on

i f ( *q == NULL )

get s sat i sf i ed. Hence space i s al l ocat ed f or t he node usi ng mal l oc( ) .Dat a and t he l i nk par t of t hi s node ar e set up usi ng t he st at ement s :

t emp- >dat a = num;t emp- >l i nk = NULL;

Last l y p i s made t o poi nt t o t hi s node, si nce t he f i r st node has beenadded t o t he l i nked l i st and p must al ways poi nt t o t he f i r st node. Not e t hat*q i s not hi ng but equal t o p.

I n t he ot her case, when t he l i nked l i st i s not empt y, t he condi t i on :

i f ( *q == NULL)

woul d f ai l , si nce *q ( i . e. p i s non- NULL) . Now t emp i s made t o poi nt t o t hef i r st node i n t he l i nked l i st t hr ough t he st at ement ,

t emp = *q;

Then usi ng t emp we have t r aver sed t hrough t he ent i r e l i nked l i st usi ng t hest at ement s:

whi l e( t emp- >l i nk ! = NULL)t emp=t emp- >l i nk;

The posi t i on of t he poi nt er bef or e and af t er t r aver si ng t he l i nked l i st i sshown bel ow:

p t emp

- - - > - - - > - - - >1 NULL432

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p t emp r

- - - > - - - > - - - >1 NULL432

node

bei ngadded.

Fig 3. Node being added at the end of a SLL

Each t i me t hrough t he l oop t he st at ement t emp= t emp- >l i nk makes t emppoi nt t o the next node i n t he l i st . When t emp r eaches t he l ast node t hecondi t i on t emp- >l i nk ! = NULL woul d f ai l . Once out si de t he l oop we al l ocat et he space f or t he new node t hrough t he st at ement

r = mal l oc( si zeof ( NODE) ) ;

Once the space has been al l ocat ed f or t he new node i t s dat a part i sf i l l ed wi t h num and t he l i nk par t wi t h NULL. Not e that t hi s node i s now goi ngt o be t he l ast node i n t he l i st .

Al l t hat now r emai ns i s connect i ng t he pr evi ous l ast node to t hi s newl ast node. The pr evi ous node i s bei ng poi nt ed t o by t emp and the new l astnode i s by r . t hey ar e connected t hr ough t he st atement

t emp- >l i nk = r ;

There i s of t en a conf usi on amongst t he begi nner s as t o how t he st at ementt emp=t emp- >l i nk makes t emp poi nt t o t he next node i n the l i nked l i st . Let us

under st and t hi s wi t h t he hel p of an exampl e. Suppose i n a l i nked l i stcont ai ni ng 4 nodes t emp i s poi nt i ng t o the f i r st node. Thi s i s shown i n t hef i gur e bel ow:

t emp

150 1 400 2 700 3 910 4 NULL

150 400 700 910

Fig 4. Actual representation of a SLL in memory

I nst ead of showi ng t he l i nks t o t he next node t he above di agr am showst he addresses of t he next node i n t he l i nk par t of each node. When we executet he st at ement t emp = t emp- > l i nk, t he r i ght hand si de yi el ds 400. Thi saddr ess i s now st or ed i n t emp. As a resul t , t emp st ar t s posi t i oni ng nodespr esent at addr ess 400. I n ef f ect t he st at ement has shi f t ed t emp so t hat i thas st ar t ed posi t i oni ng t o t he next node i n t he l i nked l i st .

Function to add a node at the beginning of the linked list

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add_beg( NODE **q, i nt num){

t emp = mal l oc( si zeof ( NODE) ) ;t emp- >dat a = num;t emp- >l i nk = *q;*q = t emp;

}

Suppose t her e ar e al r eady 5 nodes i n the l i st and we wi sh t o add a newnode at t he begi nni ng of t hi s exi st i ng l i nked l i st . Thi s si t uat i on i s showni n t he f i gur e bel ow.

t emp p

1 - - - > 2 - - - > 3 - - - > 4 - - - >17 NULL

Before Addition

t emp p

999 - - - > 1 - - - > 2 - - - > 3 - - - > 4 - - - >17 NULL

After Addition

Fig 5. Addition of a node in the beginning of a SLL

For addi ng a new node at t he begi nni ng, f i r st l y space i s al l ocat ed f or

t hi s node and dat a i s st or ed i n i t t hr ough t he st at ementt emp- >dat a = num;

Now we need t o make t he l i nk par t of t hi s node poi nt t o the exi st i ngf i r st node. Thi s has been achi eved t hr ough t he st atement

t emp- >l i nk = *q;

Last l y t hi s new node must be made t he f i r st node i n t he l i st . Thi s hasbeen at t ai ned t hrough t he st atement

*q = t emp;

Function to add a node after the specified node

add_af t er ( NODE *q, i nt l oc, i nt num){NODE *t emp, *t ;i nt i ;

t emp = q;

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f or ( i =0 ; i l i nk;i f ( t emp == NULL){

pr i nt f ( Ther e ar e l ess t han %d el ement s i nt he l i st , l oc) ;

r et ur n;

}}

r = mal l oc( si zeof ( NODE) ) ;r - >dat a = num;r - >l i nk = t emp- >l i nk;t emp- >l i nk = r ;

}

The add_af t er ( ) f unct i on permi t s us t o add a new node af t er a speci f i ednumber of nodes i n t he l i nked l i st .

To begi n wi t h, t hrough a l oop we ski p t he desi r ed number of nodes af t er

whi ch a new node i s t o be added. Suppose we wi sh t o add a new node cont ai ni ngdat a as 99 af t er t he t hi r d node i n t he l i st . The posi t i on of poi nt er s oncet he cont r ol r eaches out si de t he for l oop i s shown bel ow:

P t emp

1 - - - > 2 - - - > 3 - - - > 4 - - - >17 NULL

r

99

Before Insertion

P t emp

1 - - - > 2 - - - > 3 4 - - - >17 NULL

r

99

After Insertion

Fig 6. Insertion of a node in the specified position

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The space i s al l ocat ed f or t he node t o be i nser t ed and 99 i s st or ed i nt he dat a par t of i t . Al l t hat r emai ns t o be done i s r eadj ust ment of l i nkssuch t hat 99 goes i n between 3 and 4. t hi s i s achi eved t r ough t he st atement s

r - >l i nk = t emp- >l i nk;t emp- >l i nk = r ;

The f i r st st at ement makes l i nk par t of node cont ai ni ng 99 t o poi nt t o

t he node cont ai ng 4. t he second st atement ensures t hat t he l i nk part of t henode cont ai ni ng 3 poi nt s t o t he new node.

Functions for display and count

These f unct i ons ar e ver y si mpl e and st r ai ght f or war d. So no f ur t herexpl anat i on i s r equi r ed f or t hem.

/ * f unct i on t o count t he number of nodes i n t he l i nked l i st */

count ( NODE *q){

i nt c = 0;

whi l e( q ! = NULL) / * tr aver se t he ent i r e l i st */{

q = q- >l i nk;c++;

}

r et ur n ( c) ;}

/ * f uncti on t o di spl ay t he cont ent s of t he l i nked l i st */

di spl ay( NODE *q){

pr i nt f ( \ n ) ;


pr i nt f ( %d, q- >dat a) ;q=q- >l i nk;

}}

Function to delete the specified node from the list

del ete(NODE ** q, i nt num){

NODE *ol d, *t emp;

t emp = *q;

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whi l e( t emp ! = NULL){

i f ( t emp- >dat a == num){

i f ( t emp == q) / * i f i t i s t he f i r st node */{

*q = t emp- >l i nk;f r ee( t emp) ; / * r el ease t he memory */

r et ur n;}

el se{

ol d- >l i nk == t emp- >l i nk;f r ee( t emp) ;r et ur n;

}}

el se{

ol d = t emp;

t emp=t emp- >l i nk;}

}

pr i nt f ( \ n El ement %d not f ound, num) ;}

I n t hi s f unct i on t hr ough t he while l oop , we have t r aversed t hr ought he ent i r e l i nked l i st , checki ng at each node, whet her i t i s t he node t o bedel et ed. I f so, we have checked i f t he node i s t he f i r st node i n t he l i nkedl i st . I f i t i s so, we have s i mpl y shi f t edp t o t he next node and t hen del eted

t he ear l i er node.

I f t he node t o be del et ed i s an i nt er medi at e node, t hen t he posi t i on ofvar i ous poi nt er s and l i nks bef or e and af t er del et i on ar e shown bel ow.

P ol d t emp

1 - - - > 2 - - - > 3 - - - > 4 - - - >17 NULL

node to be del et ed = 4

Before deletion

p ol d

1 - - - > 2 - - - > 3 - - - > 17 NULL

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t emp

Thi s node get s del et ed.4

After deletion

Fig 7. Deletion of a node from SLL

Though t he above l i nked l i st depi ct s a l i st of i nt eger s, a l i nked l i stcan be used f or st or i ng any si mi l ar dat a. For exampl e, we can have a l i nkedl i st of f l oat s, char act er ar r ay, st r uct ure et c.

Doubly Linked Lists [or] Two-way chain

I n a si ngl y l i nked l i st we can t r aver se i n onl y one di r ect i on ( f or war d) ,i . e. each node st or es t he addr ess of t he next node i n t he l i nked l i st . I t has

no knowl edge about wher e t he pr evi ous node l i es i n t he memory. I f we ar e att he 12t h node( say) and i f we want t o reach 11t h node i n t he l i nked l i st , wehave t o t r aver se r i ght f r om t he f i r st node. Thi s i s a cumber some pr ocess.Some appl i cat i ons r equi r e us t o t r averse i n both f or ward and backwar ddi r ect i ons. Here we can st or e i n each node not onl y the addr ess of t he nextnode but al so t he addr ess of t he pr evi ous node i n t he l i nked l i st . Thi sarr angement i s of t en known as a Doubl y l i nked l i st . The node and t hear r angement i s shown bel ow:

PREV NEXT

NODE

Fig 8. Node structure of a DLL

NULL 20 15 70 60 NULL

Fig 9. Doubly Linked List

The l ef t poi nt er of t he l ef t most node and t he r i ght poi nt er of t her i ght most node ar e NULL i ndi cat i ng t he end i n each di r ect i on.

The f ol l owi ng program i mpl ement s t he doubl y l i nked l i st .

/ * pr ogr am t o mai nt ai n a doubl y l i nked l i st */

# i ncl ude < al l oc. h >

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t ypedef st r uct node{ i nt dat a;

st r uct node *pr ev, *next ;}NODE;

mai n( )

{NODE *p;

p = NULL; / * empt y doubl y l i nked l i st */

d_append(&p, 11) ;d_append(&p, 21) ;

cl r s cr ( ) ;di spl ay( p) ;pr i nt f ( \ n No of el ement s i n t he doubl y l i nked l i st =

%d, count ( p) ) ;

d_add_beg( &p, 33) ;d_add_beg( &p, 55) ;

di spl y(p) ;pr i nt f ( \ n No of el ement s i n t he doubl y l i nked l i st =

%d, count ( p) ) ;

d_add_af t er ( p, 1, 4000) ;d_add_af t er ( p, 2, 9000) ;

di spl y(p) ;pr i nt f ( \ n No of el ement s i n t he l i nked l i st = %d,count ( p) ) ;

d_del et e( &p, 51) ;d_del et e( &p, 21) ;


}

/ * adds a new node at t he begi nni ng of t he l i st */

d_add_beg( NODE **s, i nt num){

NODE *q;

/ * cr eat e a new node */q = mal l oc( si zeof ( NODE) ) ;

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/ * assi gn dat a and poi nt er s*/q- >prev = NULL;q- >dat a = num;q- >next = *s ;

/ * make t he new node as head node */( *s) - > pr ev = q;*s = q;

}

/ * adds a new node at t he end of t he doubl y l i nked l i st */

d_append( NODE **s, i nt num){

NODE *r , *q =*s ;

i f ( *s == NULL) / * l i st empt y, creat e t he f i r st node */{

*s = mal l oc( si zeof ( NODE) ) ;( *s ) - >dat a = num;( *s ) - >next =( *s ) - >prev = NULL;

}el se{

whi l e(q- >next ! = NULL ) / * got o the end of */q = q- >next ; / * l i st */

r = mal l oc( si zeof ( NODE) ) ;

r - >dat a = num; / * add node at t he */r - >next = NULL; / * end of t he l i st */r - >prev = q;q- >next = r ;

}}

/ * adds a new node af t er t he speci f i ed number of nodes */

d_add_af t er ( NODE *q, i nt l oc, i nt num){NODE *t emp;i nt i ;

/ * ski p t o t he desi r ed posi t i on*/

f or ( i =0 ; i next ;i f ( q == NULL){

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pr i nt f ( Ther e ar e l ess t han %d el ement s i nt he l i st , l oc) ;

r et ur n;}

}

/ * i nser t a new node */

q = q- >prev;t emp = mal l oc( si zeof ( NODE) ) ;t emp- >dat a = num;t emp- >prev = q;t emp- >next = q- >next ;t emp- >next - >prev = t emp;q- >next = t emp;

}

/ * count s t he number of nodes pr esent i n t he l i nked l i st */

count ( NODE *q)

{i nt c = 0;


q=q- >next ;c++;

}r et ur n ( c) ;

}

/ * Funct i on t o di spl ay t he cont ent s of t he doubl y l i nked l i st *// * i n l ef t t o r i ght order * /

di spl ayLR( NODE *q){

pr i nt f ( \ n ) ;


pr i nt f ( %d, q- >dat a) ;q=q- >next ;

}}

/ * Funct i on t o di spl ay t he cont ent s of t he doubl y l i nked l i st *// * i n r i ght t o l ef t order * /

di spl ayRL( NODE *q){

pr i nt f ( \ n ) ;

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whi l e( q- >next ! = NULL) / * t r aver se t he ent i r e l i st */{

q=q- >next ;}

whi l e( q != NULL){

pr i nt f ( %d, q- >dat a) ;q=q- >prev;

}}

/ * t o del et e t he speci f i ed node f r om t he l i st . * /

d_del ete(NODE ** s, i nt num){

NODE *q= *s;

/ * t r averse t he ent i r e l i nked l i st * /

whi l e( q != NULL){

i f ( q- >dat a == num){

i f (q == *s) / * i f i t i s the f i rs t node * /{

*s = ( *s) - >next ;( *s ) - > prev = NULL;

}el se{

/ * i f t he node i s l ast node */i f ( q- >next == NULL)q- >prev- >next = NULL;

el se/ * node i s i nt er medi at e */

{q- >prev- >next = q- >next ;q- >next - >prev = q- >prev;

}f ree( q) ;

}r et ur n; / * af t er del et i on * /

}q = q- >next ; / * got o next node i f not f ound */

}pr i nt f ( \ n El ement %d not f ound, num) ;

}

As you must have r eal i zed by now any operat i on on l i nked l i st i nvol vesadj ust ment s of l i nks. Si nce we have expl ai ned i n det ai l about al l t he

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f unct i ons f or si ngl y l i nked l i st , i t i s not necessar y t o gi ve step- by- stepworki ng anymore. We can underst and the worki ng of doubl y l i nked l i st s wi t ht he hel p of di agr ams. We have shown al l t he possi bl e oper at i ons i n a doubl yl i nked l i st al ong wi t h t he f unct i ons used i n di agr ams bel ow:

Addition of new node to an empty linked list

Case 1: Addi t i on t o an empt y l i st

Rel at ed f unct i on : d_append( )

p = *s = NULL

Before Addition

P

NULL 1 NULL

New node

After Addition

Case 2: Addi t i on t o an exi st i ng l i nked l i stRel at ed f unct i on : d_append( )

P q

2 3

4 NN 1

r

99 N

Before Appending

P q

2 3

4N 1

99 Nr

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After Appending

Addition of new node at the beginning.

Rel at ed Funct i on : d_add_beg( )

p

2 3 4 NN 1

q

2 3 4 N

33N

Before Addition

q p

33N

1

After Addition

Fig 10. Addition of nodes at various positions in the DLL

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Insertion of a new node after a specified node

Rel at ed f unct i on : d_add_af t er ( )

p

q

2 3 4 NN 1

t emp

66N

New Node

Before Insertion

P q t emp

42 3 66 N 1

N

After Insertion

Fig 11. Insertion of node in the DLL

Deletion Of a Node

Case 1: Del et i on of f i r st nodeRel at ed f unct i on : d_del et e( )

p q

1 2 3 NN 55

Node to be del et ed : 55

Before Deletion

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p q

2 3 N 1

After Deletion

Case 2: Del et i on of t he l ast nodeRel at ed f unct i on : d_del et e( )

p q

2 3 N88 N 1


Before Deletion

p q

2 3 N 1

After Deletion

Case 3: Del et i on of t he i nt er medi at e nodeRel at ed f unct i on : d_del et e( )

p q

2 N4 N 1 377


Before Deletion

p

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2 3 4 NNN 1

After Deletion

Fig 11.Deletion of nodes from various positions in the DLL

Applications of the linked lists

I n comput er sci ence l i nked l i st s are extensi vel y used i n Dat a BaseManagement Syst ems Pr ocess Management , Oper at i ng Syst ems, Edi t ors et c.Ear l i er we saw t hat how si ngl y l i nked l i st and doubl y l i nked l i st can bei mpl ement ed usi ng t he poi nt ers. We al so saw t hat whi l e usi ng arr ays var yof t en t he l i st of i t ems t o be st or ed i n an ar r ay i s ei t her t oo shor t or t oobi g as compared t o t he decl ar ed si ze of t he ar r ay. Mor eover , dur i ng pr ogr amexecut i on the l i st cannot gr ow beyond the si ze of t he decl ar ed ar r ay. Al so,oper at i ons l i ke i nser t i ons and del et i ons at a speci f i ed l ocat i on i n a l i st

r equi r e a l ot of movement of dat a, t her eby l eadi ng t o an i nef f i ci ent andt i me- consumi ng al gor i t hm.

The pr i mar y advant age of l i nked l i st over an ar r ay i s t hat t he l i nkedl i st can gr ow or shr i nk i n si ze dur i ng i t s l i f et i me. I n par t i cul ar , t hel i nked l i st s maxi mum si ze need not be known i n advance. I n pr act i calappl i cat i ons t hi s of t en makes i t possi bl e t o have sever al dat a st r uct ur esshar e t he same space, wi t hout payi ng par t i cul ar at t ent i on t o t hei r r el at i vesi ze at any t i me.

The second advant age of provi di ng f l exi bi l i t y i n al l owi ng t he i t ems t obe r ear r anged ef f i ci ent l y i s gai ned at t he expense of qui ck access t o any

ar bi t r ar y i t em i n t he l i st . I n ar r ays we can access any i t em at t he same t i meas no t r aver si ng i s r equi r ed.

We are not suggest i ng t hat you shoul d not use ar r ays at al l . Ther e ar esever al appl i cat i ons wher e usi ng ar r ays i s mor e benef i ci al t han usi ng l i nkedl i st s. We must sel ect a par t i cul ar dat a st r uct ur e dependi ng on t her equi r ement s.

Let us now see some mor e appl i cat i ons of t he l i nked l i st s, l i ke mer gi ngt wo l i st s and how t he l i nked l i st s can be used f or pol ynomi alr epr esent at i ons.

Function to Merge the two lists.

Mer ge( NODE *p, NODE *q, NODE **s){NODE *z;

/ * I f bot h l i st s ar e empt y */i f ( p==NULL && q == NULL){

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r et ur n;}

/ * t r aver se bot h l i nked l i st s t i l l t he end. I f end of any one l i nkedl i st i s encount er ed t hen t he l oop i s t er mi nat ed */

whi l e( p ! = NULL && q ! = NULL){

/ * i f node bei ng added i n t he f i r st l i st * /

i f ( *s == NULL){

*s = mal l oc( si zeof ( NODE) ) ;z = *s;

}el se{

z- >l i nk = mal l oc( si zeof ( NODE) ) ;z = z- >l i nk;

}

i f ( p- >data < q- >data){

z- >dat a = p- >dat a;p = p- >l i nk;

}el se{

i f ( p- >dat a > q- >data){

z- >dat a = q- >dat a;q = q- >l i nk;

}el se{i f ( p- >dat a == q- >dat a){

z- >dat a = q- >dat a;q = q- >l i nk;p = p- >l i nk;

}}

}}

/ * i f end of f i r st l i st has not been r eached */

whi l e( p ! = NULL){

z- >l i nk = mal l oc( si zeof ( NODE) ) ;z = z- >l i nk;z- >dat a = p- >dat a;p = p- >l i nk;

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}

/ * i f end of second l i st has not been r eached */

whi l e( q ! = NULL){

z- >l i nk = mal l oc( si zeof ( NODE) ) ;z = z- >l i nk;

z- >dat a = q- >dat a;q = q- >l i nk;

}

z- >l i nk = NULL;}

I n t hi s progr am, assume t hat st r uct ur e NODE wi t h data and l i nk i savai l abl e. Al so usi ng add( ) used f or si ngl y l i nked l i st ear l i er we have t wol i nked l i st s. Thr ee poi nt er s poi nt t o t hr ee l i nked l i st s. The mer ge f uncti oncan be cal l ed t o mer ge t he t wo l i nked l i st s. Thi s mer ged l i st i s poi nt ed t oby t he poi nt er t hi r d. Whi l e mer gi ng t wo l i st s i t i s assumed t hat t he l i st s

t hemsel ves are i n ascendi ng order.

Linked lists and Polynomials.

Pol ynomi al s can be mai nt ai ned usi ng a l i nked l i st . To have a pol ynomi all i ke 5x4 _ 2x3 + 7x2 + 10x 8 , each node shoul d consi st of t hree el ement s,namel y coef f i ci ent , exponent and a l i nk t o t he next i t em. Whi l e mai nt ai ni ngt he pol ynomi al i t i s assumed t hat t he exponent of each successi ve t er m i sl ess t han t hat of t he pr evi ous t er m. I f t hi s i s not t he case you can al so usea f unct i on t o bui l d a l i st , whi ch mai nt ai ns t hi s or der . Once we bui l d al i nked l i st t o r epr esent t he pol ynomi al we can per f or m oper at i ons l i keaddi t i on and mul t i pl i cat i on. Consi der t he pr ogr am gi ven bel ow.

/ * progr am t o add t wo pol ynomi al s */

t ypedef st r uct node{

f l oat coef f ;i nt exp;st r uct node *l i nk;

}PNODE;

voi d p_append( PNODE **, f l oat , i nt ) ;voi d p_addi t i on( PNODE *, PNODE *, PNODE **) ;

mai n( ){PNODE ( f i r st , *second, *t ot al ;i nt i = 0;

f i r st = second = t ot al = NULL; / * empt y l i nked l i st s */

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p_append( &f i r st , 1, 4, 5) ;p_append( &f i r st , 1, 5, 4) ;p_append( &f i r st , 1, 7, 2) ;p_append( &f i r st , 1, 8, 1) ;p_append( &f i r st , 1, 9, 0) ;

cl r s cr ( ) ;di spl ay_p( f i r s t ) ;

p_append( &second, 1, 5, 6) ;p_append( &second, 2, 5, 5) ;p_append( &second, - 3, 5, 4) ;p_append( &second, 4, 5, 3) ;p_append( &second, 6, 5, 1) ;

di spl ay_p( second) ;

p_addi t i on( f i r st , second, &t ot al )

di spl ay_p( t ot al ) ;

};

The f unct i on t o append t he pol ynomi al p_append( ) and di spl ay_p( ) ar esi mi l ar t o our f unct i ons f or si ngl y l i nked l i st . So t hey ar e expect ed t o bewr i t t en by t he user. The f unct i on t o add t wo pol ynomi al s i s gi ven bel ow.

voi d p_addi t i on( PNODE *x, PNODE *y, PNODE **s){PNODE *z;

/ * i f bot h l i st s ar e empt y */

i f ( x == NULL && y == NULL )r et ur n;

/ * t r aver se t i l l one node ends */

whi l e( x ! = NULL && y ! = NULL ){i f ( *s == NULL)

{*s = mal l oc( si zeof ( PNODE) ) ;z = *s;

}el se{

z- >l i nk = mal l oc( si zeof ( PNODE) ) ;z = z- >l i nk;

}

/ * st or e a t er m of l ar ger degr ee i f pol ynomi al */i f ( x- >exp < y- >exp)

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{z- >coef f = y- >coef f ;z- >exp = y- >exp;y = y- >l i nk; / * got o t he next node */

}el se{

i f ( x- >exp > y- >exp)

{z- >coef f = x- >coef f ;x- >exp = x- >exp;x = x- >l i nk; / * got o t he next node */

}el se{

i f ( x- >exp == y- >exp){

z- >coef f = x- >coef f + y- >coef f ;x- >exp = x- >exp;x = x- >l i nk; / * got o t he next node */

y = y- >l i nk; / * got o t he next node */}

}}

}

/ *assi gn r emai ni ng el ement s of t he f i r st pol ynomi al t o t heresul t * /

whi l e( x ! = NULL){

i f ( *s == NULL)

{ *s = mal l oc( si zeof ( PNODE) ) ;z = *s;

}el se{


}z- >coef = x- >coef ;z- >exp = x- >exp;x = x- >l i nk;

}

/ *assi gn r emai ni ng el ement s of t he second pol ynomi al t o theresul t * /

whi l e( y ! = NULL){

i f ( *s == NULL){

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*s = mal l oc( si zeof ( PNODE) ) ;z = *s;

}el se{


}

z- >coef = y- >coef ;z- >exp = y- >exp;y = y- >l i nk;

}

z- >l i nk = NULL; / * at t he end of l i st append NULL*/

}

I n t hi s pr ogr am t wo pol ynomi al s ar e bui l t and poi nt ed by the poi nt er sf i r st and second. Next t he f unct i on p_addi t i on( ) i s cal l ed t o car r y out t headdi t i on of t hese t wo pol ynomi al s. I n t hi s f uncti on t he l i nked l i st s

r epr esent i ng t he t wo pol ynomi al s ar e t r aver sed t i l l t he end of one of t hem i sr eached. Whi l e doi ng t hi s t r aver sal t he pol ynomi al s are compared on t er m- by-t erm basi s. I f t he exponent s of t he t wo t er ms bei ng compared ar e equal t hent hei r coef f i ci ent s r e added and t he r esul t i s st or ed i n t he t hi r d pol ynomi al .I f t he exponent s are not equal t hen t he bi gger exponent i s added to the thi r dpol ynomi al . Dur i ng t he tr aver sal i f t he end of one l i st i s r eached t hecont r ol br eaks out of t he whi l e l oop. Now t he remai ni ng t er ms of t hatpol ynomi al ar e si mpl y appended t o t he resul t i ng pol ynomi al . Last l y t he resul ti s di spl ayed.

Exercises:

1.

WAP f or addi ng and del et i ng nodes f r om an ascendi ng or der l i nked l i st .2.

WAP t o r ever se a si ngl y l i nked l i st by adj ust i ng t he l i nks.3. Wr i t e pr ogr ams f or r ever si ng a doubl y l i nked l i st ( t hough i t does not

ser ve any pur pose i t wi l l gi ve pr act i ce t o mani pul at e t he poi nt er s.4. WAP to del et e a node af t er t he speci f i ed node and bef ore a speci f i ed

node usi ng bot h si ngl y and doubl y l i nked l i st s.5. WAP to br eak a l i nked l i st i nt o t wo l i nked l i st s usi ng bot h SLL and

DLL.6. Wr i t e a pr ogr am t o add t wo pol ynomi al s usi ng a DLL.7. WAP to mul t i pl y t wo pol ynomi al s f or bot h SLL and DLL.8. WAP t o add two l ong i nt egers. Each i nt eger may cont ai n 15 to 20 di gi t s,

whi ch can be st ored i n nodes, a di gi t each or more dependi ng on t heuser s choi ce. Add t hese l ong i nt eger s (f r om l east si gni f i cant di gi tbackwar ds) and di spl ay the r esul t ant l i st .

linked lists notes

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