Fundamentals of Data Structure in C_S. Sahni , S. Anderson-Freed and E. Horowitz (1)

8/12/2019 Fundamentals of Data Structure in C_S. Sahni , S. Anderson-Freed and E. Horowitz (1)

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Scilab Textbook Companion for

Fundamentals Of Data Structure In C

by S. Sahni , S. Anderson-freed And E.

Horowitz1

Created byAakash Yadav

B-TECHComputer Engineering

Swami Keshvanand Institute of Technology

College TeacherRicha Rawal

Cross-Checked byLavitha Pereira

August 17, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the Textbook Companion Projectsection at the website http://scilab.in


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Book Description

Title: Fundamentals Of Data Structure In C

Author: S. Sahni , S. Anderson-freed And E. Horowitz

Publisher: University Press (India) Pvt. Ltd., New Delhi

Edition: 2

Year: 2008

ISBN: 9788173716058

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 4

1 Basic concepts 6

2 Arrays and Structures 16

3 Stacks and Queues 19

4 Linked lists 31

5 Trees 44

6 Graphs 58

7 Sorting 68

8 Hashing 76

9 Priority Queues 78

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List of Scilab Codes

Exa 1.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 6Exa 1.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 7Exa 1.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 7Exa 1.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 8Exa 1.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 8Exa 1.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exa 1.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exa 1.8 example . . . . . . . . . . . . . . . . . . . . . . . . . . 10Exa 1.9 example . . . . . . . . . . . . . . . . . . . . . . . . . . 10Exa 1.10 example . . . . . . . . . . . . . . . . . . . . . . . . . . 11Exa 1.11 example . . . . . . . . . . . . . . . . . . . . . . . . . . 12Exa 1.12 example . . . . . . . . . . . . . . . . . . . . . . . . . . 13Exa 1.13 example . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Exa 1.14 example . . . . . . . . . . . . . . . . . . . . . . . . . . 14Exa 1.15 example . . . . . . . . . . . . . . . . . . . . . . . . . . 14Exa 2.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 16Exa 2.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 16Exa 2.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 17Exa 1.1.b example . . . . . . . . . . . . . . . . . . . . . . . . . . 19Exa 3.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 21Exa 3.1.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 21Exa 1.2.b example . . . . . . . . . . . . . . . . . . . . . . . . . . 22Exa 3.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 24Exa 1.3.a example . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Exa 3.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 27Exa 4.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 31Exa 4.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 31Exa 4.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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Exa 4.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Exa 5.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 44Exa 5.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 47Exa 5.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 51Exa 5.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 55Exa 6.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 58Exa 6.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 59Exa 6.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 61Exa 6.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 62Exa 6.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 63Exa 6.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 64Exa 6.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Exa 7.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 68Exa 7.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 69Exa 7.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 69Exa 7.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 70Exa 7.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 71Exa 7.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 72Exa 7.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 73Exa 7.8 example . . . . . . . . . . . . . . . . . . . . . . . . . . 74Exa 8.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 76Exa 8.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Exa 9.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 78

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Chapter 1

Basic concepts

Scilab code Exa 1.1 example

1 // t o do s o r t i n g o f no s . c on t ai n ed i n a l i s t2 function [ ] = s o r t i n g ( a )

3 i = 1 ;

4 [ j , k ] = size ( a ) ;

5 j = i ;

6 for i = 1 : k - 1

7 for j = i : k8 if a ( i ) > a ( j ) then

9 z = a ( i ) ;

10 a ( i ) = a ( j ) ;

11 a ( j ) = z ;

12 end

13 end

14 end

15 for i = 1 : k

16 disp ( a ( i ) ) ;

17 end18

19 funcprot ( 0 ) ;

20 e n d f u n c t i o n

21 // c a l l i n r o u t i n e

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22 a =[5 7 45 23 78]

23 sort = s o r t i n g ( a )


1 // t o do b i na r y s e a r ch . .2 function [ ] = s e a r c h ( a )

3 i = 1 ;

4 [ j , k ] = size ( a ) ;

5 for i = 1 : k6 if z = = a ( i ) then

7 printf ( \nFOUND and i nd e x no . i s=%d\ t , i ) ;

8 end

9 end

10 funcprot ( 0 ) ;


12 // c a l l i n r o u t i ne13 a = [5 7 45 28 99]

14 z = 4 5

15 b i n a r y = s e a r c h ( a )


1 // t o do b i na r y s e a r ch . .2 function [ ] = s e a r c h ( a )

3 i = 1 ;

4 [ j , k ] = size ( a ) ;

5 for i = 1 : k6 if x = = a ( i ) then

7 printf ( \nFOUND and i nd e x no . i s=%d\ t , i ) ;

8 end

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9 end

10 funcprot ( 0 ) ;11 e n d f u n c t i o n

12 // c a l l i n r o u t i ne13 a = [5 7 45 28 99]

14 x = 4 5

15 b i n a r y = s e a r c h ( a )


1 / / e xa mp le 1 . 42 // p er mu ta ti on o f a s t r i n g o r c h a r ac t e r a r r ay . . .3 c l e ar a ll ;

4 clc ;

5 x =[ a b c d ]6 printf ( \n p o s s i b l e p er m ut at io n o f g i v en s t r i n g a re \n

) ;7 y = p e r m s ( x ) ;

8 disp ( y ) ;


1 // ex ampl e 1 . 52 / / ADT( A b st r ac t Data t yp e ) d e f i n a t i o n o f n a t u r a l

number .3 function [ ] = A D T ( x )

4 printf ( ADT n a t u r a l no . i s ) ;5 printf ( \nOBJECTS : a n o r d e r e d s u b r a n g e o f t h e

i n t e g e r s s t a r t i n g a t z er o a nd ) ;6 printf ( e n d i n g a t t h e maximun i n t e g e r ( INT MAX )

on t h e c om pu te r ) ;7 I N T _ M A X = 3 2 7 6 7 ;

8 if x = = 0 // N at ur al N umbe r Z e r o ( )

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9 printf ( \n ,0);

10 end11 if x = = I N T _ M A X then //N a t u r a l N u m b e r S u c c e s s o r ( x )

12 printf ( \nans . i s=%d , x ) ;13 else

14 printf ( \nans . i s=%d , x + 1 ) ;15 end


17 // c a l l i n r o u t i n e18 x = 5 6

19 y = A D T ( x ) ;


1 / / f u n c ti o n abc a c c e p t in g o nl y t h r e e s i mp l e v a r i a b l e sg i v e n t he f u n c t i o n ha s

2 / / o n l y f i x e d s a c e r e q u ir e m e nt . .3 function [ ] = a b c ( a , b , c )

4 x = a + b + c * c +( a + b - c ) / ( a + b) + 4 . 0 0;

5 disp ( x ) ;6 funcprot ( 0 ) ;


8 .... // c a l l i n g r o u t i n e9 a = [ 1 ] , b = [ 2 ] , c = [ 3 ]

10 a b c ( a , b , c )


1 // To add a l i s t o f no . u s i ng a r ra y .2 function [ ] = a d d ( a )

3 r e s u l t = sum ( a ) ;

4

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5 printf ( a d d i t i o n o f no . on t h e l i s t i s =%d ,

r e s u l t ) ;6 funcprot ( 0 ) ;


8 // c a l l i n g r o u t i n e9 a =[5 2 7 8 9 4 6]

10 r = a d d ( a )


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 1 . 8 ) ;4 a = [ 2 ; 5 ; 4 ; 6 4 ; 7 8 ]

5 i = 1 ;

6 x = 1 ; . . . . . . . . . . . . // i n i t i a l i s i n g sum e q ua l s t o one .7 c = 1 ; . . . . . . . . . . . . . . / / i n i t i a l i s i n g c o u n t e q u a l s t o

one .8 while i


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4 a = [1 2 3;4 5 6];

5 b = [7 8 9 ;10 11 12 ];6 x =matri x ( a , 3 , 2 ) ; . . . . . . . . // no . o f r ow s =3 , no . o f c o l .=2.

7 y =matri x ( b , 3 , 2 ) ; . . . . . . . . // no , o f r ow s =3 , no . o f c o l. = 2 .

8 printf ( m a t r i x x= ) ;9 disp ( x ) ;

10 printf ( m a t r i x y= ) ;11 disp ( y ) ;

12 [ p , q ] = size ( x ) ;

13 i = 1 ;

14 j = 1 ;15 c = 1 ;

16 for i = 1 : p

17 for j = 1 : q

18 z ( i , j ) = x ( i , j ) + y ( i , j ) ; . . . . . . . . . . //summing twom a t r i c e s

19 c = c + 1 ; . . . . . . . . . . . / / s t e p c o un t20 end

21 end

22 printf ( \n R e s ul t an t m at ri x a f t e r a d d i ti o n = ) ;23 disp ( z ) ; . . . . . . . . . . . . .

// d i s p l a y i n sum o f two m a t r i ce s.24 printf ( \n s t e p c o un t i s =%d , ( c - 1 ) ) ;


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 1 . 1 0 ) ;4 / / f u n c t i o n t o sum a l i s t o f n umb ers .5 function [ ] = a d d ( )

6 printf ( \n no . i n t he l i s t a r e ) ;7 disp ( a ) ;

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8 x = sum ( a ) ;

9 printf ( \n Re su lt=%d , x ) ;10 funcprot ( 0 ) ;11 e n d f u n c t i o n

12 // c a l l i n g r o u t i n e .13 a =[2 5 6 7 9 1 6 3 7 45]

14 a d d ( )


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 1 . 1 1 ) ;4 / / M at ri x a d d i t i o n .5 a = [1 2 3;4 5 6];

6 b = [7 8 9 ;10 11 12 ];

7 x =matri x ( a , 3 , 2 ) ; . . . . . . . . // no . o f r ow s =3 , no . o f c o l .=2.

8 y =matri x ( b , 3 , 2 ) ; . . . . . . . . // no , o f r ow s =3 , no . o f c o l. = 2 .

9 printf ( m a t r i x x= ) ;10 disp ( x ) ;

11 printf ( m a t r i x y= ) ;12 disp ( y ) ;

13 [ p , q ] = size ( x ) ;

14 i = 1 ;

15 j = 1 ;

16 for i = 1 : p

17 for j = 1 : q

18 z ( i , j ) = x ( i , j ) + y ( i , j ) ; . . . . . . . . . . //summing two

m a t r i c e s19 end20 end

21 printf ( \n R e s ul t an t m at ri x a f t e r a d d i ti o n = ) ;22 disp ( z ) ; . . . . . . . . . . . . . // d i s p l a y i n sum o f two m a t r i ce s

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.


1 c l e ar a ll ;

2 clc ;

3 printf ( E xa mp le 1 . 1 2 ) ;4 / / [ BIG o h ] f ( n )=O( g ( n ) ) . ( b i g o h n o t a t i o n ) .5 printf ( \n \n 3n+2=O(n ) as 3n+2=2. ) ;

6 printf ( \n \n 3n+3=O(n ) as 3n+3

=3. ); . . . . . . . . . . . . // O( n) i s c a l l e d l i n e a r .7 printf ( \n \n 3n+2=O(n ) as 100n+6=10. ) ;8 printf ( \n \n 10n2+4n+2=O(n 2 ) as 10n2+4n+2=5. ) ; . . . . . . . . . . //O( n 2 ) i s c a l l e dq u a d r a t i c .

9 printf ( \n \n 1 0 0 0 n 2+ 10 0 n6=O( n 2) as 1000n2+ 100n6=100.) ;

10 printf ( \n \n 62n+n2=4) ;11 printf ( \n \n 3n+3=O(n 2 ) as 3n+3=2) ;

12 printf ( \n \n 10n2+4n+2=O(n 4 ) as 10n2+4n+2=2. ) ;

13 printf ( \n \n 3 n+2 i s no t O( 1 ) a s 3n+2 i s l e s s t hano r e q ua l t o c f o r any c on st an t c and a l l n , n>=n0 . ) ; . . . . . . . . . . . . // O( 1 ) means c om pu ti ng t im e i sc o n s t a n t .

14 printf ( \n \n 1 0n 2+4 n+2 i s n o t O( n ) ) ;


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 1 . 1 3 ) ;

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4 printf ( \n \n [ Omega ] f ( n )=ome ga ( g ( n ) ) ) ;

5 printf ( \n \n 3n+2=omega( n) as 3n+2>

=3n f o r n>

=1) ;6 printf ( \n \n 3n+3=omega( n) as 3n+3>=3n f o r n>=1) ;7 printf ( \n \n 100n+6=ome ga ( n ) as 100n+6>=100n f o r n

>=1) ;8 printf ( \n \n 10n2+4n+2=omega (n 2 ) as 10n2+4n+2>=n

2 f o r n>=1) ;9 printf ( \n \n 62n+n2= omega( n) as 62n+n2>=2n

f o r n>=1) ;10 printf ( \n \n 3n+3=omega ( 1 ) ) ;11 printf ( \n \n \ t [ Omega] f ( n )=omega ( 1 ) ) ;


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 1 . 1 4 ) ;4 printf ( \n \n [ T h et a ] f ( n )= t h e t a ( g ( n ) ) ) ;5 printf ( \n \n 3 n+2= t h e t a ( n ) a s 3 n+2>=3n f o r a l n>=2

) ;

6 printf ( \n \n 3n+3= t h e t a ( n ) ) ;7 printf ( \n \n 10n2+4n+2=th et a (n 2 ) ) ;8 printf ( \n \n 62n+n2= t he t a ( 2 n) ) ;9 printf ( \n \n 3n+2 i s no t t h et a ( 1 ) ) ;

10 printf ( \n \n 3 n+3 i s n ot t h e ta ( n 2) \n ) ;11 printf ( \n \n The Theta n o t at i on i s more p r e c i s e

t ha n b ot h b i g oh and omega n o t a i o n ) ;


1 c l e ar a ll ;

2 clc ;

3 printf ( \n \ t E xa mp le 1 . 1 5 ) ;

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4 / / how v a r i o u s f u n c t i o n s grow w it h n , p l o t t i n g o f

v a r i o u s f u n c t i o n s i s b ei ng shown .5 / / l i k e f u n c t i o n 2 n g ro ws v er y r a p i d l y w i th n . andu t i l i t y o f p ro g ra ms w i th e x p o n e n t i a l c o m p l e x i t yi s l i m i t e d t o s m a l l n ( t y p i c a l l y n , f > ) ;12 printf ( \n \n X a x i s i s r e p r e s e n t e d by v al u e s o f

n a n d Ya x i s i f r e p re s e n te d by f ) ;

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Chapter 2

Arrays and Structures


1 c l e ar a ll ;

2 clc ;

3 printf ( \n e xa mp le 2 . 1 ) ;4 / / p r i n t i n g o ut v a l ue s o f t h e a rr ay .5 a = [3 1 40 57 46 97 8 4] ;

6 printf ( \ n va l u es a re : \ n ) ;

7 disp ( a ) ;


1 c l e ar a ll ;

2 clc ;

3 printf ( \n E xa mp le 2 . 2 \ n ) ;4 // S t r i n g i n s e r t i o n .5 s = a u t o ; . . . . . . . . . . . . . . . // 1 s t s t r i n g o r c h ar a c t e r

a r r a y .6 x = m o b i l e ; . . . . . . . . . . . . . . . // 2nd s t r i n g o r c h a r ac t e r

a r r a y .

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7 z = s + x ; . . . . . . . . . . // c o nc a t e n at i on o f 2 s t r i n g s .

8 printf ( \t s t r i n g s= ) ;9 disp ( s ) ;10 printf ( \t s t r i n g x= ) ;11 disp ( x ) ;

12 printf ( \ t c o nc a t en a t e d s t r i n g z= ) ;13 disp ( z ) ; . . . . . . . . // d i s p a l y i n g c o nc a te n at e d s t r i n g .


1 c l e ar a ll ;

2 clc ;

3 printf ( \n Ex am pl e 2 . 3\ n ) ;4 // c om pa r i si on o f 2 s t r i n g s .5 a = hak unah ; . . . . . . . . . . // s t r i n g 1 .6 b = m a t a t a ; . . . . . . . . . . . . . // s t r i n g 2 .7 disp ( a & b r e s p e c t i v e l y a re = ) ;8 disp ( a ) ;

9 disp ( b ) ;

10 disp ( c o mp ar in g s t r i n g s ) ;

11 z = s t r c m p ( a , b ) ; . . . . . . . . . // c om pa r i s io n o f 2 s t r i n g s .12 if ( z = = 0 )

13 printf ( \nMATCHED\n ) ; . . . . . . . // i f s t r i n g sm atch ed s tr cm p r e t u r n s 0 .

14 else

15 printf ( \nNOT MATCHED\n ) ; . . . . . . . . . // i f s t r i n gd oe sn t m at ch ed s t rc mp r e t u r n s 1.

16 end

17 q = a k a s h ;18 w = a k a s h ;

19 disp ( q & w r e s p e c t i v e l y a re= ) ;20 disp ( q ) ;21 disp ( w ) ;

22 disp ( c o mp ar in g s t r i n g s ) ;23 x = s t r c m p ( q , w ) ;

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24 if ( x = = 0 )

25 printf ( \nMATCHED\n ) ; . . . . . . . // i f s t r i n g sm atch ed s tr cm p r e t u r n s 0 .26 else

27 printf ( \nNOT MATCHED\n ) ; . . . . . . . . . // i f s t r i n gd oe sn t m at ch ed s t rc mp r e t u r n s 1.

28 end

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Chapter 3

Stacks and Queues

Scilab code Exa 1.1.b example

1 // E x e r c i s e q u e s t i o n 2 :2 / / I m p l e m e n ti n g P ush And Pop F u n c t i o n s :3 function [ y , s t a 1 ] = e m p t y ( s t a )

4 y = 0 ;

5 s t a 1 = 0 ;

6 if ( s t a . t o p = = 0 )

7 y = 0 ;8 else

9 y = 1 ;

10 end

11 s t a 1 = s t a


13

14 function [ s t a ] = p u s h ( s t a c , e l e )

15 sta=0;

16 if ( e m p t y ( s t a c ) = = 0 )

17 s t a c . a = e l e ;18 s t a c . t o p = s t a c . t o p + 1 ;

19 else

20 s t ac . a = [ s t a c . a ( : , :) e le ]

21 s t a c . t o p = s t a c . t o p + 1 ;

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22 end

23 disp ( s t a c ) ;24 s t a = s t a c ;

25 funcprot (0)


27

28 function [ e l e , s t a ] = p o p ( s t a c k )

29 e l e =1 ;30 if ( e m p t y ( s t a c k ) = = 0 )

31 disp ( S t a c k U n de r fl o w ) ;32 break ;

33 else

34 e l e = s t a c k . a ( s t a c k . t o p ) ;35 s t a c k . t o p = s t a c k . t o p - 1 ;

36 if ( s t a c k . t o p ~ = 0 )

37 b = s t a c k . a ( 1 ) ;

38 for i 2 = 2 : s t a c k . t o p

39 b = [ b ( : , :) s t ac k . a ( i 2 ) ] ;

40 end

41 s t a c k . a = b ;

42 else

43 s t a c k . a = 0 ;44 end

45 end

46 disp ( s t a c k ) ;

47 s t a = s t a c k ;


49 global stack

50 / / C a l l i n g R o ut i n e :51 s t a c k = s t r u c t ( a ,0 , top ,0);52 stack= push( stack ,4);

53 stack= push( stack ,55);

54 stack= push( stack ,199);

55 stack= push( stack ,363);56 [ e l e , s t a c k ] = p o p ( s t a c k ) ;

57 disp ( s t a c k , A f t er t he abov e o p e r a ti o n s s t ac k i s : ) ;

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1 c l e ar a ll ;

2 clc ;

3 printf ( \n ex a mp l e 3 . 1 \ n ) ;4 // s t a c k s f o l l o w LIFO i . e l a s t i n f i r s t o ut . s o

p r i n t i n g ou t a rr ay from l a s t t o f i r s t w i l l besame a s s t a c k .

5 a = [ 1 2 ; 3 5 ; 1 6 ; 4 8 ; 2 9 ; 1 7 ; 1 3 ]

6 i = 7 ;

7 printf ( \t s t a c k = ) ;8 while i >0

9 printf ( \n\t%d , a ( i ) ) ;10 i = i - 1 ;

11 end

Scilab code Exa 3.1.2 example

1 / / U n ol ve d E xa mp le 2 :2 c l e ar a ll ;

3 clc ;

4 disp ( U n s o lv e d e xa mp le 2 ) ;5 / / I m p le m en t i ng S t a ck u s i n g u n io n :6 function [ s t a c k ] = s t a _ u n i o n ( e t y p e , a )

7 s t a c k e l e m e n t = s t r u c t ( e t y pe , e t y p e ) ;8 [ k , l ] = size ( a ) ;

9 select s t a c k e l e m e n t . e t y p e ,

10 case i n t then11 a = int32 ( a ) ;

12 s t a c k = s t r u c t ( top ,l , i t e ms , a ) ; ,13 case f l o a t then14 a = double ( a ) ;

21


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15 s t a c k = s t r u c t ( top ,l , i t e ms , a ) ; ,

16 case cha r then17 a = string ( a ) ;18 s t a c k = s t r u c t ( top ,l , i t e ms , a ) ; ,19 end

20 disp ( s t a c k , S t a ck i s : ) ;21 e n d f u n c t i o n

22 a = [ 32 1 2. 34 2 32 3 2. 3 22 ]

23 s t a c k = s t a _ u n i o n ( f l o a t ,a )24 s t a c k = s t a _ u n i o n ( i n t ,a )25 s t a c k = s t a _ u n i o n ( cha r ,a )

Scilab code Exa 1.2.b example

1 / / U n s o l v e d E xa mp le 12 c l e ar a ll ;

3 clc ;

4 disp ( e x a m pl e 3 . 7 ) ;5 //To d et er mi ne t h e s y n t a c t i c a l y v a l i d s t r i n g6 function [ l ] = s t r l e n ( x )

7 i = 1 ;8 l = 0 ;

9 [ j , k ] = size ( x )

10 for i = 1 : k

11 l = l + length ( x ( i ) ) ;

12 end


14 function [ ] = s t r i n g v a l i d ( s t r )

15 s t r = string ( s t r ) ;

16 s t a c k = s t r u c t ( a , 0 , top ,0);

17 l 1 = s t r l e n ( s t r ) ;18 v a l i d = 1 ;

19 l = 1 ;

20 while ( l < = l 1 )

21 if ( s t r ( l ) = = ( | s t r ( l ) = = [ | s t r ( l ) = = { )

22


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22 if ( s t a c k . t o p = = 0 )

23 s t a c k . a = s t r ( l ) ;24 s t a c k . t o p = s t a c k . t o p + 1 ;

25 else

26 s t ac k . a = [ s t ac k . a ( : , : ) s tr ( l ) ] ;

27 s t a c k . t o p = s t a c k . t o p + 1 ;

28 end

29 disp ( s t a c k ) ;

30 end

31 if ( s t r ( l ) = = ) | s t r ( l ) = = ] | s t r ( l ) = = } )32 if ( s t a c k . t o p = = 0 )

33 v a l i d = 0 ;

34 break ;35 else

36 i = s t a c k . a ( s t a c k . t o p ) ;

37 b = s t a c k . a ( 1 ) ;

38 for i 1 = 2 : s t a c k . t o p - 1

39 b = [ b ( : , :) s t ac k . a ( i 1 ) ]

40 end

41 s t a c k . a = b ;

42 s t a c k . t o p = s t a c k . t o p - 1 ;

43 s y m b = s t r ( l ) ;

44 disp ( s t a c k ) ;

45 if ( ( ( s y m b = = ) ) & ( i = = ( ) ) | ( ( s y m b = = ] ) & ( i = = [ ) ) | ( ( s y m b = = } ) & ( i = = { ) ) )

46 else

47 v a l i d = 0 ;

48 break ;

49 end

50 end

51 end

52 l = l + 1 ;

53 end

54 if ( s t a c k . t o p ~ = 0 )55 v a l i d = 0 ;

56 end

57 if ( v a l i d = = 0 )

58 disp ( I n v a l i d S t r i n g ) ;

23


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59 else

60 disp ( V a l id S t r i n g ) ;61 end62 e n d f u n c t i o n

63 / / C a l l i n g R o ut i ne :64 s t r i n g v a l i d ( [ ( A + B } ) ])65 s t r i n g v a l i d ( [ { [ A + B ] [ (

C D ) ] ])66 s t r i n g v a l i d ( [ ( A + B ) { C +

D } [ F + G ] ])67 s t r i n g v a l i d ( [ ( ( H ) { ( [ J

+ K ] ) } ) ])

68 s t r i n g v a l i d ( [ ( ( ( A ) ) ) ])


1 / / e xa mp le 3 . 22 / / Queue O p e r a t i o n s3 c l e ar a ll ;

4 clc ;

5 function [ q 2 ] = p u s h ( e l e , q 1 )6 if ( q 1 . r e a r = = q 1 . f r o n t )

7 q 1 . a = e l e ;

8 q 1 . r e a r = q 1 . r e a r + 1 ;

9 else

10 q 1 . a =[ q 1 . a ( : , :) e l e ];

11 q 1 . r e a r = q 1 . r e a r + 1 ;

12 end

13 q 2 = q 1 ;


15 funcprot ( 0 ) ;16 function [ e l e , q 2 ] = p o p ( q 1 )

17 e l e = - 1 ;

18 q 2 = 0 ;

19 if ( q 1 . r e a r = = q 1 . f r o n t )

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20 disp ( Q ueu e U n d e r f l o w ) ;

21 return ;22 else

23 e l e = q 1 . a ( q 1 . r e a r - q 1 . f r o n t ) ;

24 q 1 . f r o n t = q 1 . f r o n t + 1 ;

25 i = 1 ;

26 a = q 1 . a ( 1 ) ;

27 for i = 2 : ( q 1 . r e a r - q 1 . f r o n t )

28 a = [ a ( : , :) q 1 . a ( i ) ];

29 end

30 q 1 . a = a ;

31 end

32 q 2 = q 1 ;33 e n d f u n c t i o n

34 funcprot ( 0 ) ;

35 / / C a l l i n g R o ut i n e :36 q 1 = s t r u c t ( a ,0 , r e a r ,0 , f r o n t ,0)37 q 1 = p u s h ( 3 , q 1 )

38 q 1 = p u s h ( 2 2 , q 1 ) ;

39 q 1 = p u s h ( 2 1 , q 1 ) ;

40 disp ( q 1 , Queue a f t e r i n s e r t i o n ) ;41 [ e l e , q 1 ] = p o p ( q 1 )

42 disp ( e l e , p op ed e l e m en t

) ;

43 disp ( q 1 , Queue a f t e r p o pi n g ) ;44 [ e l e , q 1 ] = p o p ( q 1 ) ;

45 [ e l e , q 1 ] = p o p ( q 1 ) ;

46 [ e l e , q 1 ] = p o p ( q 1 ) ; / / U n d er f lo w C o n d i t i o n

Scilab code Exa 1.3.a example

1 c l e ar a ll ;2 clc ;

3 disp ( U n s o lv e d e xa mp le 3 ) ;4 function [ l ] = s t r l e n ( x )

5 i = 1 ;

25


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6 l = 0 ;

7 [ j , k ] = size ( x )8 for i = 1 : k

9 l = l + length ( x ( i ) ) ;

10 end


12 function [ ] = s t r ( s t )

13 s t a c k = s t r u c t ( a ,0 , top ,0);14 st = string ( s t ) ;

15 l = 1 ;

16 l 1 = s t r l e n ( s t ) ;

17 s y m b = s t ( l ) ;

18 v a l i d = 1 ;19 while ( l < l 1 )

20 while ( s y m b ~ = C )21 if ( s t a c k . t o p = = 0 )

22 s t a c k . a = s t ( l ) ;


24 else

25 s t ac k . a = [ s t ac k . a ( : , : ) s t ( l ) ];


27 end

28 l = l + 1 ;

29 s y m b = s t ( l ) ;

30 end

31 i = s t ( l + 1 ) ;

32 if ( s t a c k . t o p = = 0 )

33 v a l i d = 0 ;

34 break ;

35 else

36 s y m b 1 = s t a c k . a ( s t a c k . t o p ) ;


38 if ( i ~ = s y m b 1 )

39 v a l i d = 0 ;40 break ;

41 end

42 end

43 l = l + 1 ;

26


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44 end

45 if ( s t a c k . t o p ~ = 0 )46 v a l i d = 0 ;

47 end

48 if ( v a l i d = = 0 )

49 disp ( Not o f t he g i ve n f or ma t ) ;50 else

51 disp ( S t r i n g Of t h e G iv en Fo rma t ) ;52 end


54 / / C a l l i n g R o ut i n e :55 s t = [A A B A C A B A A ]

56 s t r ( s t )57 s t = [A A B A C A B A ]58 s t r ( s t )


1 / / S o l v e d E xamp le 3 . 3 :2 / / Co nv e r i n g an i n f i x e x p r e s s i o n t o a P o s t f i x

E x p r e s s i o n :3 function [ s t a ] = p u s h ( s t a c , e l e )

4 sta=0;

5 if ( s t a c . t o p = = 0 )

6 s t a c . a = e l e ;

7 s t a c . t o p = s t a c . t o p + 1 ;

8 else

9 s t ac . a = [ s t a c . a ( : , :) e le ]

10 s t a c . t o p = s t a c . t o p + 1 ;

11 end

12 disp ( s t a c ) ;13 s t a = s t a c ;


15

16 function [ e l e , s t a ] = p o p ( s t a c k )

27


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17 e l e =1 ;

18 if ( s t a c k . t o p = = 0 )19 disp ( S t a c k U n de r fl o w ) ;20 break ;

21 else

22 e l e = s t a c k . a ( s t a c k . t o p ) ;


24 if ( s t a c k . t o p ~ = 0 )

25 b = s t a c k . a ( 1 ) ;

26 for i 2 = 2 : s t a c k . t o p

27 b = [ b ( : , :) s t ac k . a ( i 2 ) ] ;

28 end

29 s t a c k . a = b ;30 else

31 s t a c k . a = 0 ;32 end

33 end

34 s t a = s t a c k ;


36 function [ l ] = s t r l e n ( x )

37 i = 1 ;

38 l = 0 ;

39 [ j , k ] = size ( x )

40 for i = 1 : k

41 l = l + length ( x ( i ) ) ;

42 end


44 function [ p ] = p r e ( s 1 , s 2 )

45 i 1 = 0 ;

46 select s1 ,

47 case + then i 1 = 5 ;48 case then i 1 = 5 ;49 case then i 1 = 9 ;

50 case / then i 1 = 9 ;51 end

52 i 2 = 0 ;

53 select s2 ,

54 case + then i 2 = 5 ;

28


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55 case then i 2 = 5 ;

56 case then i 2 = 9 ;57 case / then i 2 = 9 ;58 end

59 p = 0 ;

60 p = i 1 - i 2 ;

61 if ( s 1 = = ( )62 p = - 1 ;

63 end

64 if ( s 2 = = ( & s 1 ~ = ) )65 p = - 1 ;

66 end

67 if ( s 1 ~ = ( & s 2 = = ) )68 p = 1 ;

69 end

70


72 function [ a 2 ] = i n t o p o ( a 1 , n )

73 s t a c k = s t r u c t ( a ,0 , top ,0);74 l 1 = 1 ;

75 l 2 = s t r l e n ( a 1 ( 1 ) )

76 for i = 2 : n

77 l 2 = l 2 + s t r l e n ( a 1 ( i ) )

78 end

79 a2 = list () ;

80 while ( l 1 < = l 2 )

81 s y m b = a 1 ( l 1 ) ;

82 if ( i s a l p h a n u m ( string ( a 1 ( l 1 ) ) ) )

83 a2 = list ( a 2 , s y m b ) ;

84 else

85 while ( s t a c k . t o p ~ = 0 & ( p r e ( s t a c k . a ( s t a c k . t o p ) ,

s y m b ) > = 0 ) )

86 [ t o p s y mb , s t a c k ] = p o p ( s t a c k ) ;

87 if ( t o p s y m b = = ) | t o p s y m b = = ( )88 a 2 = a 2 ;

89 else

90 a2 = list ( a 2 , t o p s y m b ) ;

91 end

29


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92 end

93 if ( s t a c k . t o p = = 0 | s y m b ~ = ) )94 s t a c k = p u s h ( s t a c k , s y m b ) ;95 else

96 [ e l e , s t a c k ] = p o p ( s t a c k ) ;

97 end

98 end

99 l 1 = l 1 + 1 ;

100 end

101 while ( s t a c k . t o p ~ = 0 )

102 [ t o p s ym b , s t a c k ] = p o p ( s t a c k ) ;

103 if ( t o p s y m b = = ) | t o p s y m b = = ( )

104 a 2 = a 2 ;105 else

106 a2 = list ( a 2 , t o p s y m b ) ;

107 end

108 end

109 disp ( a 2 ) ;


111 / / C a l l i n g R o ut i n e :112 a 1 = [ ( 2 + 3 ) ( 5 4 ) ]113 a 2 = i n t o p o ( a 1 , 1 1 )

30


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Chapter 4

Linked lists


1 // L i s t o f word s i n a l i n k e d l i s t .2 c l e ar a ll ;

3 clc ;

4 printf ( \n E xa pm le 4 . 1 \ n ) ;5 x = list ( s c i , l a b , t e x t , c o m p a n i o n s h i p , p r o j e c t )

;

6 disp ( x= ) ;7 disp ( x ) ;


1 //CIRCULAR LINKED LIST2 c l e ar a ll ;

3 clc ;

4 funcprot ( 0 ) ;

5 disp ( E xa mp le 4 . 2 ) ;6 function [ l i n k 2 ] = a p p e n d ( e l e , l i n k 1 )

7 l i n k 2 = list

31


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( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , , 0

;8 if ( l i n k 1 ( 1 ) ( 1 ) . a d d = = 0 )

9 l i n k 1 ( 1 ) ( 1 ) . d a t a = e l e ;

10 l i n k 1 ( 1 ) ( 1 ) . a d d = 1 ;

11 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = 1 ;

12 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

13 else

14 if ( l i n k 1 ( 1 ) ( 1 ) . n e x a d d = = l i n k 1 ( 1 ) ( 1 ) . a d d )

15 l i n 2 = l i n k 1 ( 1 ) ( 1 ) ;

16 l i n 2 . d a t a = e l e ;

17 l i n 2 . a d d = l i n k 1 ( 1 ) ( 1 ) . a d d + 1 ;

18 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = l i n 2 . a d d ;19 l i n 2 . n e x a d d = l i n k 1 ( 1 ) ( 1 ) . a d d ;

20 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

21 l i n k 2 ( 2 ) = l i n 2 ;

22 else

23 l i n 2 = l i n k 1 ( 1 ) ( 1 ) ;

24 i = 1 ;

25 while ( l i n k 1 ( i ) ( 1 ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

26 i = i + 1 ;

27 end

28 j = i ;

29 l i n 2 . d a t a = e l e ;

30 l i n 2 . a d d = l i n k 1 ( i ) . a d d + 1 ;

31 l i n 2 . n e x a d d = l i n k 1 ( 1 ) ( 1 ) . a d d ;

32 l i n k 1 ( i ) . n e x a d d = l i n 2 . a d d ;

33 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

34 i = 2 ;

35 while ( l i n k 1 ( i ) . n e x a d d ~ = l i n 2 . a d d )

36 l i n k 2 ( i ) = ( l i n k 1 ( i ) ) ;

37 i = i + 1 ;

38 end

39 l i n k 2 ( i ) = l i n k 1 ( i ) ;40 l i n k 2 ( i + 1 ) = l i n 2 ;

41 end

42 end


32


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44 function [ l i n k 2 ] = a d d ( e l e , p o s , l i n k 1 ) ;

45 l i n k 2 = list( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,

;

46 i = 1 ;

47 while ( i < = p o s )

48 if ( l i n k 1 ( i ) . n e x a d d = = l i n k 1 ( 1 ) ( 1 ) . a d d )

49 break ;

50 else

51 i = i + 1 ;

52 end

53 end

54 if ( l i n k 1 ( i ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )55 i = i - 1 ;

56 l i n 2 . d a t a = e l e ;

57 l i n 2 . a d d = i ;

58 j = i ;

59 while ( l i n k 1 ( j ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

60 l i n k 1 ( j ) . a d d = l i n k 1 ( j ) . a d d + 1 ;

61 l i n k 1 ( j ) . n e x a d d = l i n k 1 ( j ) . n e x a d d + 1 ;

62 j = j + 1 ;

63 end


65 l i n 2 . n e x a d d = l i n k 1 ( i ) . a d d ;

66 l i n k 1 ( i - 1 ) . n e x a d d = l i n 2 . a d d ;

67 k = 1 ;

68 while ( k < i )

69 l i n k 2 ( k ) = l i n k 1 ( k ) ;

70 k = k + 1 ;

71 end

72 l i n k 2 ( k ) = l i n 2 ;

73 k = k + 1 ;

74 l i n k 2 ( k ) = l i n k 1 ( k - 1 ) ;

75 k = k + 176 l = k - 1 ;

77 while ( k ~ = j )

78 l i n k 2 ( k ) = l i n k 1 ( l ) ;

79 k = k + 1 ;

33


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80 l = l + 1 ;

81 end82 l i n k 2 ( j ) = l i n k 1 ( j - 1 ) ; ;

83 l i n k 2 ( j + 1 ) = l i n k 1 ( j ) ;

84 else

85 if ( i = = p o s )

86 k = 1 ;

87 l i n 2 . d a t a = e l e ;

88 l i n 2 . a d d = l i n k 1 ( i - 1 ) . a d d + 1 ;

89 l i n k 1 ( i ) . a d d = l i n k 1 ( i ) . a d d + 1 ;


91 l i n k 1 ( i ) . n e x a d d = l i n k 1 ( 1 ) ( 1 ) . a d d ;

92 k = 1 ;93 while ( k < p o s )

94 l i n k 2 ( k ) = l i n k 1 ( k ) ;

95 k = k + 1 ;

96 end

97 l i n k 2 ( k ) = l i n 2 ;

98 l i n k 2 ( k + 1 ) = l i n k 1 ( k )

99 end

100 end

101


103 function [ l i n k 2 ] = d e l e t e 1 ( p o s , l i n k 1 )

104 l i n k 2 = list

( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , , 0

;

105 i = 1 ;

106 j = 1 ;

107 while ( i < p o s )

108 if ( ( l i n k 1 ( j ) . n e x a d d = = l i n k 1 ( 1 ) ( 1 ) . a d d ) )

109 j = 1 ;

110 i = i + 1 ;

111 else112 i = i + 1 ;

113 j = j + 1 ;

114 end

115 end

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116 if ( l i n k 1 ( j ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

117 k = 1 ;118 if ( j = = 1 )

119 k = 2 ;

120 while ( l i n k 1 ( k ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

121 l i n k 2 ( k - 1 ) = l i n k 1 ( k ) ;

122 k = k + 1 ;

123 end

124 l i n k 2 ( k - 1 ) = l i n k 1 ( k ) ;

125 l i n k 2 ( k - 1 ) . n e x a d d = l i n k 2 ( 1 ) . a d d ;

126 else

127 l i n 2 = l i n k 1 ( j ) ;

128 l i n k 1 ( j - 1 ) . n e x a d d = l i n k 1 ( j + 1 ) . a d d ;129 k = 1 ;

130 while ( l i n k 1 ( k ) . n e x a d d ~ = l i n k 1 ( j + 1 ) . a d d )

131 l i n k 2 ( k ) = l i n k 1 ( k ) ;

132 k = k + 1 ;

133 end

134 l i n k 2 ( k ) = l i n k 1 ( k ) ;

135 k = k + 2 ;

136 while ( l i n k 1 ( k ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

137 l i n k 2 ( k - 1 ) = l i n k 1 ( k ) ;

138 k = k + 1 ;

139 end

140 l i n k 2 ( k - 1 ) = l i n k 1 ( k ) ;

141 end

142 else

143 l i n k 1 ( j - 1 ) . n e x a d d = l i n k 1 ( 1 ) ( 1 ) . a d d ;

144 l = 1 ;

145 while ( l i n k 1 ( l ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

146 l i n k 2 ( l ) = l i n k 1 ( l ) ;

147 l = l + 1 ;

148 end

149 l i n k 2 ( l ) = l i n k 1 ( l ) ;150 end


152 / / C a l l i n g R o ut i n e :153 l i n k 1 = s t r u c t ( da ta ,0 , add ,0 , ne x add ,0);

35


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154 l i n k 1 = a p p e n d ( 4 , l i n k 1 ) ; // T hi s w i l l a c t u a l y c r e a t e a

l i s t and 4 a s s t a r t155 l i n k 1 = a p p e n d ( 6 , l i n k 1 ) ;156 l i n k 1 = a d d ( 1 0 , 2 , l i n k 1 ) ;

157 l i n k 1 = d e l e t e 1 ( 4 , l i n k 1 ) ; // As t h e l i s t i s c i r c u l a r t h e4 th e le me nt r e f e r s t o a c t u a l y t he 1 s t one

158 disp ( l i n k 1 , A f t e r t he a bo ve m an up la ti on s t he l i s t i s ) ;


1 // L i s t I n s e r t i o n .2 clc ;

3 c l e ar a ll ;

4 disp ( E xa mp le 4 . 3 ) ;5 funcprot (0)

6 function [ l i n k 2 ] = i n s e r t _ p r i ( e l e , l i n k 1 )

7 l i n k 2 = list

( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , , 0

;

8 if ( l i n k 1 ( 1 ) ( 1 ) . a d d = = 0 )9 l i n k 1 ( 1 ) ( 1 ) . d a t a = e l e ;

10 l i n k 1 ( 1 ) ( 1 ) . a d d = 1 ;

11 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = 1 ;

12 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

13 else

14 if ( l i n k 1 ( 1 ) ( 1 ) . n e x a d d = = l i n k 1 ( 1 ) ( 1 ) . a d d )

15 if ( e l e > = l i n k 1 ( 1 ) ( 1 ) . d a t a )

16 t = e l e ;

17 p = l i n k 1 ( 1 ) ( 1 ) . d a t a ;

18 else19 t = l i n k 1 ( 1 ) ( 1 ) . d a t a ;

20 p = e l e ;

21 end

22 l i n k 1 ( 1 ) ( 1 ) . d a t a = t ;

36


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23 l i n 2 = l i n k 1 ( 1 ) ( 1 ) ;

24 l i n 2 . d a t a = p ;25 l i n 2 . a d d = 2 ;


27 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = l i n 2 . a d d ;

28 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

29 l i n k 2 ( 2 ) = l i n 2 ;

30 else

31 i = 1 ;

32 a = [ ] ;

33 while ( l i n k 1 ( i ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

34 a = [ a ( : , :) l i nk 1 ( i ) . d a ta ] ;

35 i = i + 1 ;36 end

37 a = [ a ( : , :) l i nk 1 ( i ) . d a ta ] ;

38 a = gsort ( a ) ;

39 j = 1 ;

40 while ( j < = i )

41 l i n k 1 ( j ) . d a t a = a ( j ) ;

42 j = j + 1 ;

43 end

44 k = 1 ;

45 while ( l i n k 1 ( k ) . d a t a > = e l e )

46 if ( l i n k 1 ( k ) . n e x a d d = = l i n k 1 ( 1 ) ( 1 ) . a d d )

47 break ;

48 else

49 l i n k 2 ( k ) = l i n k 1 ( k ) ;

50 k = k + 1 ;

51 end

52 end

53 if ( l i n k 1 ( k ) . n e x a d d ~ = l i n k 1 ( 1 ) ( 1 ) . a d d )

54 l i n 2 = l i n k 1 ( k ) ;

55 l i n 2 . d a t a = e l e ;

56 l i n 2 . a d d = l i n k 1 ( k ) . a d d ;57 j = k ;

58 y = l i n k 1 ( 1 ) ( 1 ) . a d d ;

59 while ( l i n k 1 ( k ) . n e x a d d ~ = y )

60 l i n k 1 ( k ) . a d d = l i n k 1 ( k ) . a d d + 1 ;

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61 l i n k 1 ( k ) . n e x a d d = l i n k 1 ( k ) . n e x a d d + 1 ;

62 k = k + 1 ;63 end

64 l i n k 1 ( k ) . a d d = l i n k 1 ( k ) . a d d + 1 ;

65 l i n 2 . n e x a d d = l i n k 1 ( j ) . a d d ;

66 l i n k 2 ( j ) = l i n 2 ;

67 j = j + 1 ;

68 while ( j < = k + 1 )

69 l i n k 2 ( j ) = l i n k 1 ( j - 1 ) ;

70 j = j + 1 ;

71 end

72 else

73 l i n 2 = l i n k 1 ( k ) ;74 l i n 2 . d a t a = e l e ;


76 l i n 2 . a d d = l i n k 1 ( k ) . a d d + 1 ;

77 l i n k 1 ( k ) . n e x a d d = l i n 2 . a d d ;

78 j = 1 ;

79 while ( j < = k )

80 l i n k 2 ( j ) = l i n k 1 ( j ) ;

81 j = j + 1 ;

82 end

83 l i n k 2 ( j ) = l i n 2 ;

84 end

85 end

86 end


88 / / C a l l i n g R o u ti n e :89 l i n k 1 = s t r u c t ( dat a ,0 , add ,0 , ne x add ,0);90 l i n k 1 = i n s e r t _ p r i ( 3 , l i n k 1 ) ;

91 l i n k 1 = i n s e r t _ p r i ( 4 , l i n k 1 ) ;

92 l i n k 1 = i n s e r t _ p r i ( 2 2 , l i n k 1 ) ;

93 l i n k 1 = i n s e r t _ p r i ( 2 1 , l i n k 1 ) ;

94 l i n k 1 = i n s e r t _ p r i ( 1 1 , l i n k 1 ) ;95 disp ( l i n k 1 , L i s t A f t e r I n s e r t i o n s ) ;

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1 / / D e l e t i o n f ro m t h e l i s t :2 function [ l i n k 2 ] = a p p e n d ( e l e , l i n k 1 )

3 l i n k 2 = list

( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , , 0

;

4 if ( l i n k 1 ( 1 ) ( 1 ) . a d d = = 0 )

5 l i n k 1 ( 1 ) ( 1 ) . d a t a = e l e ;

6 l i n k 1 ( 1 ) ( 1 ) . a d d = 1 ;

7 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = 0 ;

8 l i n k 1 ( 1 ) ( 1 ) . p r e v a d d = 0 ;

9 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

10 else

11 if ( l i n k 1 ( 1 ) ( 1 ) . n e x a d d = = 0 )

12 l i n 2 = l i n k 1 ( 1 ) ( 1 ) ;

13 l i n 2 . d a t a = e l e ;

14 l i n 2 . a d d = l i n k 1 ( 1 ) ( 1 ) . a d d + 1 ;

15 l i n k 1 ( 1 ) ( 1 ) . n e x a d d = l i n 2 . a d d ;

16 l i n 2 . n e x a d d = 0 ;17 l i n 2 . p r e v a d d = l i n k 1 ( 1 ) ( 1 ) . a d d ;

18 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;

19 l i n k 2 ( 2 ) = l i n 2 ;

20 else

21 l i n 2 = l i n k 1 ( 1 ) ( 1 ) ;

22 i = 1 ;

23 while ( l i n k 1 ( i ) ( 1 ) . n e x a d d ~ = 0 )

24 i = i + 1 ;

25 end

26 j = i ;

27 l i n 2 . d a t a = e l e ;

28 l i n 2 . a d d = l i n k 1 ( i ) . a d d + 1 ;

29 l i n 2 . n e x a d d = 0 ;

30 l i n k 1 ( i ) . n e x a d d = l i n 2 . a d d ;

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31 l i n 2 . p r e v a d d = l i n k 1 ( i ) . a d d ;

32 l i n k 2 ( 1 ) = l i n k 1 ( 1 ) ( 1 ) ;33 i = 2 ;

34 while ( l i n k 1 ( i ) . n e x a d d ~ = l i n 2 . a d d )

35 l i n k 2 ( i ) = ( l i n k 1 ( i ) ) ;

36 i = i + 1 ;

37 end

38 l i n k 2 ( i ) = l i n k 1 ( i ) ;

39 l i n k 2 ( i + 1 ) = l i n 2 ;

40 end

41 end


43 function [ l i n k 2 ] = a d d ( e l e , p o s , l i n k 1 ) ;44 l i n k 2 = list

( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,

;

45 i = 1 ;

46 while ( i < = p o s )

47 if ( l i n k 1 ( i ) . n e x a d d = = 0 )

48 break ;

49 else

50 i = i + 1 ;

51 end

52 end

53 if ( l i n k 1 ( i ) . n e x a d d ~ = 0 )

54 i = i - 1 ;

55 l i n 2 . d a t a = e l e ;

56 l i n 2 . a d d = i ;

57 j = i ;

58 while ( l i n k 1 ( j ) . n e x a d d ~ = 0 )

59 l i n k 1 ( j ) . p r e v a d d = l i n k 1 ( j ) . p r e v a d d + 1 ;


61 l i n k 1 ( j ) . n e x a d d = l i n k 1 ( j ) . n e x a d d + 1 ;

62 j = j + 1 ;63 end

64 l i n k 1 ( j ) . p r e v a d d = l i n k 1 ( j ) . p r e v a d d + 1 ;



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67 l i n k 1 ( i ) . p r e v a d d = l i n 2 . a d d ;

68 l i n 2 . p r e v a d d = l i n k 1 ( i - 1 ) . a d d ;69 l i n k 1 ( i - 1 ) . n e x a d d = l i n 2 . a d d ;

70 k = 1 ;

71 while ( k < i )

72 l i n k 2 ( k ) = l i n k 1 ( k ) ;

73 k = k + 1 ;

74 end

75 l i n k 2 ( k ) = l i n 2 ;

76 k = k + 1 ;

77 l i n k 2 ( k ) = l i n k 1 ( k - 1 ) ;

78 k = k + 1

79 l = k - 1 ;80 while ( k ~ = j )

81 l i n k 2 ( k ) = l i n k 1 ( l ) ;

82 k = k + 1 ;

83 l = l + 1 ;

84 end

85 l i n k 2 ( j ) = l i n k 1 ( j - 1 ) ; ;

86 l i n k 2 ( j + 1 ) = l i n k 1 ( j ) ;

87 else

88 if ( i = = p o s )

89 k = 1 ;

90 l i n 2 . d a t a = e l e ;

91 l i n 2 . a d d = l i n k 1 ( i - 1 ) . a d d + 1 ;

92 l i n k 1 ( i ) . a d d = l i n k 1 ( i ) . a d d + 1 ;


94 l i n k 1 ( i ) . p r e v a d d = l i n 2 . a d d ;

95 l i n 2 . p r e v a d d = l i n k 1 ( i - 1 ) . a d d ;

96 k = 1 ;

97 while ( k < p o s )

98 l i n k 2 ( k ) = l i n k 1 ( k ) ;

99 k = k + 1 ;

100 end101 l i n k 2 ( k ) = l i n 2 ;

102 l i n k 2 ( k + 1 ) = l i n k 1 ( k )

103 end

104 end

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105

106 e n d f u n c t i o n107 function [ l i n k 2 ] = d e l e t e 1 ( p o s , l i n k 1 )

108 l i n k 2 = list

( 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , , 0

;

109 i = 1 ;

110 while ( i < = p o s )

111 if ( ( l i n k 1 ( i ) . n e x a d d = = 0 ) )

112 break ;

113 else

114 i = i + 1 ;

115 end116 end

117 if ( l i n k 1 ( i ) . n e x a d d ~ = 0 )

118 i = i - 1 ;

119 j = 1 ;

120 if ( i = = 1 )

121 j = 1 ;

122 while ( l i n k 1 ( j ) . n e x a d d ~ = 0 )

123 l i n k 2 ( j ) = l i n k 1 ( j ) ;

124 j = j + 1 ;

125 end

126 l i n k 2 ( j ) = l i n k 1 ( j ) ;

127 else

128 l i n k 1 ( i - 1 ) . n e x a d d = l i n k 1 ( i + 1 ) . a d d ;

129 l i n k 1 ( i + 1 ) . p r e v a d d = l i n k 1 ( i - 1 ) . a d d ;

130 while ( l i n k 1 ( j ) . n e x a d d ~ = l i n k 1 ( i + 1 ) . a d d )

131 l i n k 2 ( j ) = l i n k 1 ( j ) ;

132 j = j + 1 ;

133 end

134 if ( j ~ = i - 1 )

135 l i n k 2 ( j ) = l i n k 1 ( j ) ;

136 l i n k 2 ( j + 1 ) = l i n k 1 ( j + 1 ) ;137 k = i + 1 ;

138 l = 2 ;

139 else

140 l i n k 2 ( j ) = l i n k 1 ( j ) ;

42


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Chapter 5

Trees


1

2 funcprot ( 0 ) ;

3 function [ t r e e ] = m a k e t r e e ( x )

4 t r e e = zeros ( 3 0 , 1 ) ;

5 for i = 1 : 3 0

6 t r e e ( i ) = - 1 ;

7 end8 t r e e ( 1 ) = x ;

9 t r e e ( 2 ) = - 2 ;


11 function [ t r e e 1 ] = s e t l e f t ( t r e e , t r e , x )

12 t r e e 1 = [ ] ;

13 i = 1 ;

14 while ( t r e e ( i ) ~ = - 2 )

15 if ( t r e e ( i ) = = t r e )

16 j = i ;

17 end18 i = i + 1 ;

19 end

20 if ( i > 2 * j )

21 t r e e ( 2 * j ) = x ;

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22 else

23 t r e e ( 2 * j ) = x ;24 t r e e ( 2 * j + 1 ) = - 2 ;

25 for l = i : 2 * j - 1

26 t r e e ( i ) = - 1 ;

27 end

28 end

29 t r e e 1 = t r e e ;


31 function [ t r e e 1 ] = s e t r i g h t ( t r e e , t r e , x )

32 t r e e 1 = [ ] ;

33 i = 1 ;

34 while ( t r e e ( i ) ~ = - 2 )35 if ( t r e e ( i ) = = t r e )

36 j = i ;

37 end

38 i = i + 1 ;

39 end

40 if ( i > 2 * j + 1 )

41 t r e e ( 2 * j + 1 ) = x ;

42 else

43 t r e e ( 2 * j + 1 ) = x ;

44 t r e e ( 2 * j + 2 ) = - 2 ;

45 for l = i : 2 * j

46 t r e e ( i ) = - 1 ;

47 end

48 end

49 t r e e 1 = t r e e ;


51 function [ x ] = i s l e f t ( t r e e , t r e )

52 i = 1 ;

53 x = 0 ;

54 while ( t r e e ( i ) ~ = - 2 )

55 if ( t r e e ( i ) = = t r e )56 j = i ;

57 end

58 i = i + 1 ;

59 end

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60 if ( i > = 2 * j )

61 if ( ( t r e e ( 2 * j ) ~ = - 1 ) | ( t r e e ( 2 * j ) ~ = - 2 ) )62 x = 1 ;

63 return 1;

64 else

65 return 0;

66 end

67 else

68 x = 0 ;

69 return x ;

70 end


72 function [ x ] = i s r i g h t ( t r e e , t r e )73 i = 1 ;

74 x = 0 ;

75 while ( t r e e ( i ) ~ = - 2 )

76 if ( t r e e ( i ) = = t r e )

77 j = i ;

78 end

79 i = i + 1 ;

80 end

81 if ( i > = 2 * j + 1 )

82 if ( ( t r e e ( 2 * j + 1 ) ~ = - 1 ) | ( t r e e ( 2 * j + 1 ) ~ = - 2 ) )

83 x = 1 ;

84 return 1;

85 else

86 return 0;

87 end

88 else

89 x = 0 ;

90 return x ;

91 end


93 / / C a l l i n g R o ut i n e :94 t r e e = m a k e t r e e ( 3 ) ;

95 disp ( t r e e , T r e e made ) ;96 tree= setleft (tree ,3,1);

97 disp ( t r e e , A f te r s e t t i n g 1 t o l e f t o f 3 ) ;

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98 t r e e = s e t r i g h t ( t r e e , 3 , 2 ) ;

99 disp ( t r e e , A ft e r s e t t i n g 2 t o r i g h t o f 3 ) ;100 t r e e = s e t r i g h t ( t r e e , 2 , 4 ) ;101 tree= setleft (tree ,2,5);



104 disp ( t r e e , A f t e r a bo ve o p e r a t i o n s : ) ;105 x= isright (tree ,3);

106 disp (x , Ch e c k i n g f o r t h e r i g h t s o n o f 3 y e s i f 1e l s e no ) ;

107 x= isleft( tree ,2);

108 disp (x , Check f o r l e f t s on o f 2 ) ;


1 funcprot ( 0 ) ;


3 t r e e = zeros ( 3 0 , 1 ) ;

4 for i = 1 : 3 0

5 t r e e ( i ) = - 1 ;

6 end7 t r e e ( 1 ) = x ;

8 t r e e ( 2 ) = - 2 ;



11 t r e e 1 = [ ] ;

12 i = 1 ;

13 while ( t r e e ( i ) ~ = - 2 )

14 if ( t r e e ( i ) = = t r e )

15 j = i ;

16 end17 i = i + 1 ;

18 end

19 if ( i > 2 * j )

20 t r e e ( 2 * j ) = x ;

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21 else

22 t r e e ( 2 * j ) = x ;23 t r e e ( 2 * j + 1 ) = - 2 ;

24 for l = i : 2 * j - 1

25 t r e e ( i ) = - 1 ;

26 end

27 end

28 t r e e 1 = t r e e ;



31 t r e e 1 = [ ] ;

32 i = 1 ;

33 while ( t r e e ( i ) ~ = - 2 )34 if ( t r e e ( i ) = = t r e )

35 j = i ;

36 end

37 i = i + 1 ;

38 end

39 if ( i > 2 * j + 1 )

40 t r e e ( 2 * j + 1 ) = x ;

41 else

42 t r e e ( 2 * j + 1 ) = x ;

43 t r e e ( 2 * j + 2 ) = - 2 ;

44 for l = i : 2 * j

45 t r e e ( i ) = - 1 ;

46 end

47 end

48 t r e e 1 = t r e e ;



51 i = 1 ;

52 x = 0 ;

53 while ( t r e e ( i ) ~ = - 2 )

54 if ( t r e e ( i ) = = t r e )55 j = i ;

56 end

57 i = i + 1 ;

58 end

48


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59 if ( i > = 2 * j )

60 if ( ( t r e e ( 2 * j ) ~ = - 1 ) | ( t r e e ( 2 * j ) ~ = - 2 ) )61 x = 1 ;

62 return 1;

63 else

64 return 0;

65 end

66 else

67 x = 0 ;

68 return x ;

69 end


71 function [ x ] = i s r i g h t ( t r e e , t r e )72 i = 1 ;

73 x = 0 ;

74 while ( t r e e ( i ) ~ = - 2 )

75 if ( t r e e ( i ) = = t r e )

76 j = i ;

77 end

78 i = i + 1 ;

79 end

80 if ( i > = 2 * j + 1 )

81 if ( ( t r e e ( 2 * j + 1 ) ~ = - 1 ) | ( t r e e ( 2 * j + 1 ) ~ = - 2 ) )

82 x = 1 ;

83 return 1;

84 else

85 return 0;

86 end

87 else

88 x = 0 ;

89 return x ;

90 end


92 funcprot ( 0 ) ;93 function [ ] = i n o r d e r ( t r e e , p )

94 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

95 return ;

96 else

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97 inorder (tree ,2*p);

98 printf ( %d\ t , t r e e ( p ) ) ;99 inorder (tree ,2*p+1) ;100 end


102 function [ ] = p r e o r d e r ( t r e e , p )

103 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

104 return ;

105 else

106 printf ( %d\ t , t r e e ( p ) ) ;107 preorder (tree ,2*p);

108 preorder (tree ,2*p +1);

109 end110 e n d f u n c t i o n

111 function [ ] = p o s t o r d e r ( t r e e , p )

112 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

113 return ;

114 else

115 postorder (tree ,2*p);

116 postorder (tree ,2*p +1);

117 printf ( %d\ t , t r e e ( p ) ) ;118 end



122 tree= setleft (tree ,3,1);


124 tree= setleft (tree ,2,4);


126 disp ( I n o r d er t r a v e r s a l ) ;127 inorder (tree ,1);

128 disp ( P r e o rd e r t r a v e r s a l ) ;129 preorder (tree ,1);

130 disp ( P o s to r de r t r a v e r s a l ) ;131 postorder (tree ,1);

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1 funcprot ( 0 ) ;


3 t r e e = zeros ( 1 , 3 0 ) ;

4 for i = 1 : 3 0

5 t r e e ( i ) = - 1 ;

6 end

7 t r e e ( 1 ) = x ;

8 t r e e ( 2 ) = - 2 ;



11 t r e e 1 = [ ] ;

12 i = 1 ;

13 while ( t r e e ( i ) ~ = - 2 )

14 if ( t r e e ( i ) = = t r e )

15 j = i ;

16 end

17 i = i + 1 ;

18 end19 if ( i > 2 * j )

20 t r e e ( 2 * j ) = x ;

21 else

22 t r e e ( 2 * j ) = x ;

23 t r e e ( 2 * j + 1 ) = - 2 ;

24 for l = i : 2 * j - 1

25 t r e e ( i ) = - 1 ;

26 end

27 end

28 t r e e 1 = t r e e ;



31 t r e e 1 = [ ] ;

32 i = 1 ;

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33 while ( t r e e ( i ) ~ = - 2 )

34 if ( t r e e ( i ) = = t r e )35 j = i ;

36 end

37 i = i + 1 ;

38 end

39 if ( i > 2 * j + 1 )

40 t r e e ( 2 * j + 1 ) = x ;

41 else

42 t r e e ( 2 * j + 1 ) = x ;

43 t r e e ( 2 * j + 2 ) = - 2 ;

44 for l = i : 2 * j

45 t r e e ( i ) = - 1 ;46 end

47 end

48 t r e e 1 = t r e e ;



51 i = 1 ;

52 x = 0 ;

53 while ( t r e e ( i ) ~ = - 2 )

54 if ( t r e e ( i ) = = t r e )

55 j = i ;

56 end

57 i = i + 1 ;

58 end

59 if ( i > = 2 * j )

60 if ( ( t r e e ( 2 * j ) ~ = - 1 ) | ( t r e e ( 2 * j ) ~ = - 2 ) )

61 x = 1 ;

62 return 1;

63 else

64 return 0;

65 end

66 else67 x = 0 ;

68 return x ;

69 end


52


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71 function [ x ] = i s r i g h t ( t r e e , t r e )

72 i = 1 ;73 x = 0 ;

74 while ( t r e e ( i ) ~ = - 2 )

75 if ( t r e e ( i ) = = t r e )

76 j = i ;

77 end

78 i = i + 1 ;

79 end

80 if ( i > = 2 * j + 1 )

81 if ( ( t r e e ( 2 * j + 1 ) ~ = - 1 ) | ( t r e e ( 2 * j + 1 ) ~ = - 2 ) )

82 x = 1 ;

83 return 1;84 else

85 return 0;

86 end

87 else

88 x = 0 ;

89 return x ;

90 end


92 funcprot ( 0 ) ;

93 function [ ] = i n o r d e r ( t r e e , p )

94 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

95 return ;

96 else

97 inorder (tree ,2*p);

98 disp ( t r e e ( p ) , ) ;99 inorder (tree ,2*p+1) ;

100 end


102 function [ ] = p r e o r d e r ( t r e e , p )

103 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

104 return ;105 else

106 disp ( t r e e ( p ) , ) ;107 preorder (tree ,2*p);

108 preorder (tree ,2*p +1);

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109 end

110 e n d f u n c t i o n111 function [ ] = p o s t o r d e r ( t r e e , p )

112 if ( t r e e ( p ) = = - 1 | t r e e ( p ) = = - 2 )

113 return ;

114 else

115 postorder (tree ,2*p);

116 postorder (tree ,2*p +1);

117 disp ( t r e e ( p ) , ) ;118 end


120 function [ t r e e 1 ] = b i n a r y ( t r e e , x )

121 p = 1 ;122 while ( t r e e ( p ) ~ = - 1 & t r e e ( p ) ~ = - 2 )

123 q = p ;

124 if ( t r e e ( p ) > x )

125 p = 2 * p ;

126 else

127 p = 2 * p + 1 ;

128 end

129 end

130 i = 1 ;

131 while ( t r e e ( i ) ~ = - 2 )

132 i = i + 1 ;

133 end

134 if ( t r e e ( q ) > x )

135 if ( i = = 2 * q )

136 t r e e ( 2 * q ) = x ;

137 t r e e ( 2 * q + 1 ) = - 2

138 else

139 if ( i < 2 * q )

140 t r e e ( i ) = - 1 ;

141 t r e e ( 2 * q + 1 ) = - 2 ;

142 t r e e ( 2 * q ) = x ;143 end

144 end

145

146 else

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147 if ( i = = 2 * q + 1 )

148 t r e e ( 2 * q + 1 ) = x ;149 t r e e ( 2 * q + 2 ) = - 2 ;

150 else

151 if ( i < 2 * q + 1 )

152 t r e e ( i ) = - 1 ;

153 t r e e ( 2 * q + 1 ) = x ;

154 t r e e ( 2 * q + 2 ) = - 2 ;

155 end

156 end

157

158 end

159 t r e e 1 = t r e e ;160 e n d f u n c t i o n


163 tree= binary( tree ,1);




167 disp ( t r e e , B i n ar y t r e e t hu s o bt a i ne by i n s e r t i n g1 , 2 , 4 and5 i n t r e e r o o te d 3 i s : ) ;


1 function [ t r e e 1 ] = b i n a r y ( t r e e , x )

2 p = 1 ;

3 while ( t r e e ( p ) ~ = - 1 & t r e e ( p ) ~ = - 2 )

4 q = p ;

5 if ( t r e e ( p ) > x )

6 p = 2 * p ;7 else

8 p = 2 * p + 1 ;

9 end

10 end

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11 if ( t r e e ( q ) > x )

12 if ( t r e e ( 2 * q ) = = - 2 )13 t r e e ( 2 * q ) = x ;

14 t r e e ( 2 * q + 1 ) = - 2 ;

15 else

16 t r e e ( 2 * q ) = x ;

17 end

18 else

19 if ( t r e e ( 2 * q + 1 ) = = - 2 )

20 t r e e ( 2 * q + 1 ) = x ;

21 t r e e ( 2 * q + 2 ) = - 2 ;

22 else

23 t r e e ( 2 * q + 1 ) = x ;24 end

25 end

26 t r e e 1 = t r e e ;


28 funcprot ( 0 ) ;


30 t r e e = zeros ( 4 0 , 1 ) ;

31 for i = 1 : 4 0

32 t r e e ( i ) = - 1 ;

33 end

34 t r e e ( 1 ) = x ;

35 t r e e ( 2 ) = - 2 ;


37 function [ ] = d u p l i c a t e 1 ( a , n )

38 t r e e = m a k e t r e e ( a ( 1 ) ) ;

39 q = 1 ;

40 p = 1 ;

41 i = 2 ;

42 x = a ( i )

43 while ( i < n )

44 while ( t r e e ( p ) ~ = x & t r e e ( q ) ~ = - 1 & t r e e ( q ) ~ = - 2 )45 p = q ;

46 if ( t r e e ( p ) < x )

47 q = 2 * p ;

48 else

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49 q = 2 * p + 1 ;

50 end51 end

52 if ( t r e e ( p ) = = x )

53 disp (x , Du p li ca te ) ;54 else

55 t r e e = b i n a r y ( t r e e , x ) ;

56 end

57 i = i + 1 ;

58 x = a ( i ) ;

59 end

60 while ( t r e e ( p ) ~ = x & t r e e ( q ) ~ = - 1 & t r e e ( q ) ~ = - 2 )

61 p = q ;62 if ( t r e e ( p ) < x )

63 q = 2 * p ;

64 else

65 q = 2 * p + 1 ;

66 end

67 end

68 if ( t r e e ( p ) = = x )

69 disp (x , Du p li ca te ) ;70 else

71 t r e e = b i n a r y ( t r e e , x ) ;

72 end


74 / / C a l l i n g A d r es s :75 a = [2 2 11 33 22 21 1 3 34]

76 d u p l i c a t e 1 ( a , 6 )

77 a = [2 1 11 33 22 22 33 4]

78 d u p l i c a t e 1 ( a , 6 )

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Chapter 6

Graphs


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 6 . 1 ) ;4 / / Depth F i r s t S ea rc h T r a v er s a l5 funcprot (0)

6 function [ ] = D f s ( a d j , n ) ;

7 i = 1 , j = 1 ;8 c o l o u r = [ ] ;

9 for i = 1 : n

10 for j = 1 : n

11 c o lo u r = [ c o l ou r ( : , : ) 0 ];

12 end

13 end

14 disp ( The DFS t r a v e r s a l i s ) ;15 dfs(adj ,colour ,1,n) ;


17 function [ ] = d f s ( a d j , c o l o u r , r , n )18 c o l o u r ( r ) = 1 ;

19 disp (r , ) ;20 for i = 1 : n

21 if ( a d j ( ( r - 1 ) * n + i ) & ( c o l o u r ( i ) = = 0 ) )

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22 d f s ( a d j , c o l o u r , i , n ) ;

23 end24 end

25 c o l o u r ( r ) = 2 ;


27 / / C a l l i n g R o ut i n e :28 n = 4 ;

29 adj =[0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0]

30 D f s ( a d j , n )


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 6 . 2 ) ;4 / / / / BFS T r a v e r s a l5 funcprot (0)

6 function [ q 2 ] = p u s h ( e l e , q 1 )

7 if ( q 1 . r e a r = = q 1 . f r o n t )

8 q 1 . a = e l e ;

9 q 1 . r e a r = q 1 . r e a r + 1 ;10 else

11 q 1 . a =[ q 1 . a ( : , :) e l e ];

12 q 1 . r e a r = q 1 . r e a r + 1 ;

13 end

14 q 2 = q 1 ;


16 function [ e l e , q 2 ] = p o p ( q 1 )

17 e l e = - 1 ;

18 q 2 = 0 ;

19 if ( q 1 . r e a r = = q 1 . f r o n t )20 return ;

21 else

22 e l e = q 1 . a ( q 1 . r e a r - q 1 . f r o n t ) ;

23 q 1 . f r o n t = q 1 . f r o n t + 1 ;

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24 i = 1 ;

25 a = q 1 . a ( 1 ) ;26 for i = 2 : ( q 1 . r e a r - q 1 . f r o n t )

27 a = [ a ( : , :) q 1 . a ( i ) ];

28 end

29 q 1 . a = a ;

30 end

31 q 2 = q 1 ;


33

34 function [ ] = B f s ( a d j , n ) ;

35 i = 1 , j = 1 ;

36 c o l o u r = [ ] ;37 for i = 1 : n

38 for j = 1 : n

39 c o lo u r = [ c o l ou r ( : , : ) 0 ];

40 end

41 end

42 disp ( The BFS T r a v e r s a l i s ) ;43 bfs(adj ,colour ,1,n) ;


45 function [ ] = b f s ( a d j , c o l o u r , s , n )

46 c o l o u r ( s ) = 1 ;

47 q = s t r u c t ( r e a r ,0 , f r o n t ,0 , a ,0);48 q = p u s h ( s , q ) ;

49 while ( ( q . r e a r ) - ( q . f r o n t ) > 0 )

50 [ u , q ] = p o p ( q ) ;

51 disp (u , ) ;52 for i = 1 : n

53 if ( a d j ( ( u - 1 ) * n + i ) & ( c o l o u r ( i ) = = 0 ) )

54 c o l o u r ( i ) = 1 ;

55 q = p u s h ( i , q ) ;

56 end

57 end58 c o l o u r ( u ) = 2 ;

59 end


61 / / C a l l i n g R o ut i n e :

60


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62 n = 4 ;

63 adj =[0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0]64 B f s ( a d j , n )


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 6 . 3 ) ;

4 / / W a r s h al l s A l g o r i t hm5 clc ;

6 c l e ar a ll ;

7 funcprot (0)

8 function [ p a t h ] = t r a n s c l o s e ( a d j , n )

9 for i = 1 : n

10 for j = 1 : n

11 p a t h ( ( i - 1 ) * n + j ) = a d j ( ( i - 1 ) * n + j ) ;

12 end

13 end

14 for k = 1 : n

15 for i = 1 : n16 if ( p a t h ( ( i - 1 ) * n + k ) = = 1 )

17 for j = 1 : n

18 p a t h ( ( i - 1 ) * n + j ) = p a t h ( ( i - 1 ) * n + j ) | p a t h ( ( k - 1 )

* n + j ) ;

19 end

20 end

21 end

22 end

23 printf ( T r a n s i t i v e c l o s u r e f o r t h e g iv en g r aph i s

:\ n ) ;24 for i = 1 : n25 printf ( F or v e r t e x %d \n , i ) ;26 for j = 1 : n

27 printf ( %d %d i s %d\n , i , j , p a t h ( ( i - 1 ) * n + j ) ) ;

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28 end

29 end30 e n d f u n c t i o n


33 adj =[0 1 0 0 0 1 0 0 0]

34 p a t h = t r a n s c l o s e ( a d j , n )


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 6 . 4 ) ;4 / / F in nd in g T r a n s i t i v e C l os u r e5 funcprot ( 0 ) ;

6 function [ p a t h ] = T r a n c l o s e ( a d j , n ) ;

7 i = 1 , j = 1 ;

8 p a t h = zeros ( n * n , 1 ) ;

9 p a t h = t r a n c l o s e ( a d j , n ) ;

10 printf ( T r a n s i t i v e C l o s u re Of G iv en Graph i s :\ n ) ;

11 for i = 1 : n12 printf ( F o r V e r t ex %d\n , i ) ;13 for j = 1 : n

14 printf ( %d %d i s %d\n , i , j , p a t h ( ( i - 1 ) * n + j ) ) ;15 end

16 end

17


19 function [ p a t h ] = t r a n c l o s e ( a d j , n )

20 a d j p r o d = zeros ( n * n , 1 ) ;

21 k = 1 ;22 n e w p r o d = zeros ( n * n , 1 ) ;

23 for i = 1 : n

24 for j = 1 : n

25 p a t h ( ( i - 1 ) * n + j ) = a d j ( ( i - 1 ) * n + j ) ;

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26 a d j pr o d ( ( i - 1) * n + j ) = p a th ( ( i - 1 ) * n + j ) ;

27 end28 end

29 for i = 1 : n

30 n e w p r o d = p r o d 1 ( a d j p r o d , a d j , n ) ;

31 for j = 1 : n

32 for k = 1 : n

33 p a t h ( ( j - 1 ) * n + k ) = p a t h ( ( j - 1 ) * n + k ) | n e w p r o d ( ( j

- 1 ) * n + k ) ;

34 end

35 end

36 for j = 1 : n

37 for k = 1 : n38 a d j p r o d ( ( j - 1 ) * n + k ) = n e w p r o d ( ( j - 1 ) * n + k ) ;

39 end

40 end

41 end


43 function [ c ] = p r o d 1 ( a , b , n )

44 for i = 1 : n

45 for j = 1 : n

46 val=0

47 for k = 1 : n

48 v a l = v a l | ( a ( ( i - 1 ) * n + k ) & b ( ( k - 1 ) * n + j ) ) ;

49 end

50 c ( ( i - 1 ) * n + j ) = v a l ;

51 end

52 end



56 adj =[0 1 0 0 0 1 0 0 0]

57 p a t h = T r a n c l o s e ( a d j , n )


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1 c l e ar a ll ;

2 clc ;3 disp ( E xa mp le 6 . 5 ) ;4 / / F i n d i n g The Number Of S i m p l e P a th s From One P o i n t

To A n ot h er I n A G iv en Graph5 funcprot (0)

6 function [ ] = s i m _ p a t h ( n , a d j , i , j ) ;

7 l = 0 ;

8 m = 1 ;

9 for m = 1 : n

10 l = l + p a t h ( m , n , a d j , i , j ) ;

11 end

12 printf ( Ther e a r e %d s i m pl e p at hs from %d t o %di n t he g i ve n gr a ph \n , l , i , j ) ;


14 function [ b ] = p a t h ( k , n , a d j , i , j )

15 b = 0 ;

16 if ( k = = 1 )

17 b = a d j ( ( i - 1 ) * n + j ) ;

18 else

19 for c = 1 : n

20 if ( a d j ( ( i - 1 ) * n + c ) = = 1 )

21 b = b + p a t h ( k - 1 , n , a d j , c , j ) ;

22 end

23 end

24 end

25 return b ;


27 n = 3 ;

28 adj =[0 1 1 0 0 1 0 0 0];

29 b = s i m _ p a t h ( n , a d j , 1 , 3 )


1 c l e ar a ll ;

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2 clc ;

3 disp ( E xa mp le 6 . 6 ) ;4 / / D i j k s t r a s A lg o ri th m5 funcprot (0)

6 function [ l ] = s h o r t ( a d j , w , i 1 , j 1 , n )

7 for i = 1 : n

8 for j = 1 : n

9 if ( w ( ( i - 1 ) * n + j ) = = 0 )

10 w ( ( i - 1 ) * n + j ) = 9 9 9 9 ;

11 end

12 end

13 end

1415 d i s t a n c e = [ ] ;

16 p e r m = [ ] ;

17 for i = 1 : n

18 d i s ta n c e = [ d i s ta n c e ( : , :) 9 9 99 9 ] ;

19 p e rm = [ p e r m ( : , :) 0 ] ;

20 end

21 p e r m ( i 1 ) = 1 ;

22 d i s t a n c e ( i 1 ) = 0 ;

23 c u r r e n t = i 1 ;

24 while ( c u r r e n t ~ = j 1 )

25 s m a l l d i s t = 9 9 9 9 ;

26 d c = d i s t a n c e ( c u r r e n t ) ;

27 for i = 1 : n

28 if ( p e r m ( i ) = = 0 )

29 n e w d i s t = d c + w ( ( c u r r e n t - 1 ) * n + i ) ;

30 if ( n e w d i st < d i s t a n c e ( i ) )

31 d i s t a n c e ( i ) = n e w d i s t ;

32 end

33 if ( d i s t a n c e ( i ) < s m a l l d i s t )

34 s m a l l d i s t = d i s t a n c e ( i ) ;

35 k = i ;36 end

37 end

38 end

39 c u r r e n t = k ;

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40 p e r m ( c u r r e n t ) = 1 ;

41 end42 l = d i s t a n c e ( j 1 ) ;

43 printf ( The s h o r t e s t p at h b et we en %d and %d i s %d , i 1 , j 1 , l ) ;



47 adj =[0 1 1 0 0 1 0 0 0] // A dj a ce nc y L i s t48 w =[0 12 22 0 0 9 0 0 0] / / w ei g ht l i s t f i l l 0 f o r no

e d g e49 s h o r t ( a d j , w , 1 , 3 , n ) ;


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 6 . 7 ) ;4 / / F i n d i n g The Number Of P a t h s From One V e r t e x To

A n ot h er Of A G iv en L e ng t h

56 function [ b ] = p a t h ( k , n , a d j , i , j )

7 b = 0 ;

8 if ( k = = 1 )

9 b = a d j ( ( i - 1 ) * n + j ) ;

10 else

11 for c = 1 : n

12 if ( a d j ( ( i - 1 ) * n + c ) = = 1 )

13 b = b + p a t h ( k - 1 , n , a d j , c , j ) ;

14 end

15 end16 end

17 printf ( Number o f p a t h s f ro m v e r t e x %d t o %d o f l e n g t h %d a r e %d , i , j , k , b ) ;

18 return b ;

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20 / / C a l l i n g R o ut i n e :21 n = 3 ;22 adj =[0 1 1 0 0 1 0 0 0]

23 b = p a t h ( 1 , n , a d j , 1 , 3 )

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Chapter 7

Sorting


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 7 . 1 ) ;4 funcprot ( 0 ) ;

5 function [ a 1 ] = i n s e r t i o n ( a , n )

6 for k = 1 : n

7 y = a ( k ) ;8 i = k ;

9 while ( i > = 1 )

10 if ( y < a ( i ) )

11 a ( i + 1 ) = a ( i ) ;

12 a ( i ) = y ;

13 end

14 i = i - 1 ;

15 end

16 end

17 a 1 = a ;18 disp ( a 1 , S o r te d a r ra y i s : ) ;19 e n d f u n c t i o n

20 / / C a l l i n g R o ut i n e :21 a =[5 4 3 2 1] / / w or stc a se b eh av io ur o f

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i n s e r t i o n s o r t .

22 disp (a , G i ve n A rr a y ) ;23 a 1 = i n s e r t i o n ( a , 5 )


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 7 . 2 ) ;

4 funcprot ( 0 ) ;5 function [ a 1 ] = i n s e r t i o n ( a , n )

6 for k = 1 : n

7 y = a ( k ) ;

8 i = k ;

9 while ( i > = 1 )

10 if ( y < a ( i ) )

11 a ( i + 1 ) = a ( i ) ;

12 a ( i ) = y ;

13 end

14 i = i - 1 ;

15 end16 end

17 a 1 = a ;

18 disp ( a 1 , S o r te d a r ra y i s : ) ;19 e n d f u n c t i o n

20 / / C a l l i n g R o ut i n e :21 a =[2 3 4 5 1]



1 c l e ar a ll ;

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2 clc ;

3 disp ( E xa mp le 7 . 3 ) ;4 funcprot ( 0 ) ;5 function [ a 1 ] = q u i c k ( a ) ;

6 a = gsort ( a ) ; // IN BUILT QUICK SORT FUNCTION7 n = length ( a ) ;

8 a 1 = [ ] ;

9 for i = 1 : n

10 a 1 = [ a1 ( : , : ) a ( n + 1 - i ) ];

11 end


14 / / C a l l i n g R o ut i n e :15 a =[26 5 37 1 61 11 59 15 48 19]

16 disp (a , G i ve n A rr a y ) ;17 a 1 = q u i c k ( a )


1 c l e ar a ll ;

2 clc ;3 disp ( E xa mp le 7 . 4 ) ;4 function [ a 1 ] = i n s e r t i o n ( a , n )

5 for k = 1 : n

6 y = a ( k ) ;

7 i = k ;

8 while ( i > = 1 )

9 if ( y < a ( i ) )

10 a ( i + 1 ) = a ( i ) ;

11 a ( i ) = y ;

12 end13 i = i - 1 ;

14 end

15 end

16 a 1 = a ;

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17 disp ( a 1 , S o r te d a r ra y i s : ) ;

18 e n d f u n c t i o n19 / / C a l l i n g R o ut i n e :20 a = [3 1 2]



1 c l e ar a ll ;2 clc ;

3 disp ( E xa mp le 7 . 5 ) ;4 funcprot ( 0 ) ;

5 function [ a 1 ] = m e r g e s o r t ( a , p , r )

6 if ( p < r )

7 q = int ( ( p + r ) / 2 ) ;

8 a = m e r g e s o r t ( a , p , q ) ;

9 a = m e r g e s o r t ( a , q + 1 , r ) ;

10 a = m e r g e ( a , p , q , r ) ;

11 else

12 a 1 = a ;13 return ;

14 end

15 a 1 = a ;


17 function [ a 1 ] = m e r g e ( a , p , q , r )

18 n 1 = q - p + 1 ;

19 n 2 = r - q ;

20 l e f t = zeros ( n 1 + 1 ) ;

21 r i g h t = zeros ( n 2 + 1 ) ;

22 for i = 1 : n 123 l e f t ( i ) = a ( p + i - 1 ) ;

24 end

25 for i 1 = 1 : n 2

26 r i g h t ( i 1 ) = a ( q + i 1 ) ;

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27 end

28 l e f t ( n 1 + 1 ) = 9 9 9 9 9 9 9 9 9 ;29 r i g h t ( n 2 + 1 ) = 9 9 9 9 9 9 9 9 9 ;

30 i = 1 ;

31 j = 1 ;

32 k = p ;

33 for k = p : r

34 if ( l e f t ( i ) < = r i g h t ( j ) )

35 a ( k ) = l e f t ( i ) ;

36 i = i + 1 ;

37 else

38 a ( k ) = r i g h t ( j ) ;

39 j = j + 1 ;40 end

41 end

42 a 1 = a ;


44 / / C a l l i n g R o ut i n e :45 a =[26 5 77 1 61 11 59 15 48 19]

46 disp (a , G i ve n A rr a y ) ;47 a 1 = m e r g e s o r t ( a , 1 , 1 0 )



1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 7 . 7 ) ;4 function [ a 1 ] = s h e l l ( a , n , i n c r , n i c )

5 for i = 1 : n i c

6 s p a n = i n c r ( i ) ;7 for j = s p a n + 1 : n

8 y = a ( j ) ;

9 k = j - s p a n ;

10 while ( k > = 1 & y < a ( k ) )

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11 a ( k + s p a n ) = a ( k ) ;

12 k = k - s p a n ;13 end

14 a ( k + s p a n ) = y ;

15 end

16 end

17 a 1 = a ;


20 / / C a l l i n g R o ut i n e :21 a = [ 23 21 2 32 1 21 2 32 4 1 22 24 33 1 21 2]

22 disp (a , G i ve n A rr a y ) ;

23 i nc r =[ 5 3 1] // must a l wa y s end w it h 124 a1= shell(a ,7,incr ,3)


1 c l e ar a ll ;

2 clc ;

3 disp ( E xa mp le 7 . 7 ) ;

4 function [ a 1 ] = s h e l l ( a , n , i n c r , n i c )5 for i = 1 : n i c

6 s p a n = i n c r ( i ) ;

7 for j = s p a n + 1 : n

8 y = a ( j ) ;

9 k = j - s p a n ;

10 while ( k > = 1 & y < a ( k ) )

11 a ( k + s p a n ) = a ( k ) ;

12 k = k - s p a n ;

13 end

14 a ( k + s p a n ) = y ;15 end

16 end

17 a 1 = a ;


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20 / / C a l l i n g R o ut i n e :21 a = [ 23 21 2 32 1 21 2 32 4 1 22

Fundamentals of Data Structure in C_S. Sahni , S. Anderson-Freed and E. Horowitz (1)

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Transcript of Fundamentals of Data Structure in C_S. Sahni , S. Anderson-Freed and E. Horowitz (1)