Daa Assignment

Assignment: 1 Q.1 what do you mean by Analysis of Algorithm? Write an Algorithm For Insertion Sort and Analyze it.

Q.2 E!lain strassen"s #atri #ulti!li$ation? %ri&e its time $om!leity why this better than ordinary #atri #ulti!li$ation? Q.' what is (reedy A!!roa$h? A!!roa$h? %oes it always gi&e o!timal solution? E!lain )rus*al"s algo to obtain #S+. Q., %es$ribe the &arious ty!es of notations with eam!le? Q.- finds the o!timal merge !attern for the gi&en &alues '- 1- 2/ ,/ 1/

Q.0 illustrate the o!eration of min hea! tree for gi&en &alues 1/ 2/ '/ 1 2 ' , 11 21 '1 ,1 Q. sol&es the following re$urren$e relations and find their $om!leities using #aster #ethod.

Q. E!ress the following fun$tion using asym!toti$ notations3 4i5 062n 7 n2 4ii5 86n4n915

Class Test: 1 Q.1 What is the di&ide and $on:uer #ethod? Sort the following se:uen$e using #erge Sort method - 2 ,  1 ' 2 0

Q2.$onsider the fi&e items along with their res!e$ti&e &alues and weights. I; ; <'/ 2/ 1// / 10= )na!sa$* has @a!a$ity W;0/. Find the o!timal solution of the  !roblem using $on$e!t of fra$tional )na!sa$*. Q.' E!lain the ob se:uen$ing !roblem with eam!le. Q., Bse strassen"s matri multi!li$ation algo to $om!ute the matri !rodu$t of the following matri$es3

A;

C;





2

-

'

2

-

-

Assignment: 2 Q1. 4a5 %efine how )na!sa$* Droblem is sol&ed by using dynami$  !rogramming a!!roa$h? 4b5 @onsider n;' 4w1w2 w' 5 ; 42  ' ' 5  4!1 !2 !'5 ; 41 2 ,5 and #;0 find o!timal solution for gi&en data Q.2 ; a a b a b G  H; b a b b G If  is an J@S of  and H then find  using %ynami$ Drogramming.

Q.' Sol&e the +SD Droblem ha&ing the following $ost matri using Cran$h and Cound A C @ %  1/ 12/   1/ 0 1'  12     A  C  @  % Q., E!lain the matri $hain multi!li$ation algorithm using dynami$ a!!roa$h.

Q.- find the order of !arenthesization for the o!timal $hain multi!li$ation A1 ; '/ 6 '- K A, ; - 6 1/K

A2 ; '- 61- K A' ; 1- 6 -K A- ; 1/ 6 2/ K A0 ; 2/ 6 2-K

Q.0 Write short note on following3 4i5 Ca$*tra$*ing algorithm 4ii5 Jower bound theory 4iii5 Queen"s !roblem

Q. use %ynami$ !rogramming a!!roa$h to sol&e the following instan$e of the !roblem. #aimum $a!a$ity3 11 units  Lo of items3 Weights3 1 2-0 Drofits3 1 0 1 22 2

Class Test: 2 Q1. Sol&e the +SD Droblem ha&ing the following $ost matri using Cran$h and Cound A  , , 

C  2 0

@ 2 2  

% ' ' ' 

A  C  @  %

Q.2 ; A C @ C % A C G  H; C % @ A C A G If  is an J@S of  and H then find  using %ynami$ Drogramming. Q.' %ifferentiate between (reedy algorithm and %ynami$ Drogramming

Assignment: 3 Q.1 E!lain the !refi fun$tion for a String with an eam!le and write )#D mat$her algorithm? Q.2 Write short note on the following3 4i5 Quadrati$ assignment !roblem 4ii5 Coyer #oore algorithm Q.' %es$ribe LaM&e string #at$hing algorithm in detail? Q., E!lain Nabin *ar! algorithm with suitable eam!le? Q.- Bsing )#D algorithm find whether the !attern D ;  1/1//111G is in tet +; 1//1/1/1//111G or not?

Q.0 Sol&e the following assignment !roblem using bran$h and  bound for whi$h $ost matri is gi&en below 1

2

'

,

11 1, 11 1

12 11 1,

1 1' 1 2/

,/ 22 2' 2

A  C  @  %

Class Test: 3 Q.1 Derform Nabin )ar! algorithm on gi&en tet +;  2 ' -  / 2 ' 1 , 1 - G D;  ' 1 , 1 - G and modulo :; Q.2 E!lain the Coyer #oore algorithm for !attern mat$hing using  bad $hara$ter heuristi$ and good suffi heuristi$s with eam!le? Q.' Write the )#D string mat$hing algorithm and also find the  !refi fun$tion for the following !attern 3 a b a b b a b a a and Im!lement the algorithm.

Assignment: 4 Q1. E!lain the Jas >egas and #onte @arlo algorithm with eam!le?

Q.2. E!lain the flow networ* and augmenting !aths?

Q'.show the formation of $uts augmentation !ath min9flow9ma9 $ut in the following gra!h.

Class Test: 4 Q.1 define flow networ* and sol&e the following flow networ* for maimum flow.

Q.2 what are the randomized algorithms? What are the ad&antages using this $on$e!t?

Q.'. E!lain Nandomized algorithm for #in $ut.

Assignment: 5 Q1. What is the use of $oo*"s theorem? Dro&e it with eam!le.

Q.2 define the terms D LD LD @om!lete and LD hard !roblems

Q.' E!lain set $o&er !roblem in detail?

Q., assuming '9 @LF satisfiability !roblem to be LD9@om!lete  !ro&e that $li:ue !roblem is also LD9$om!lete !roblem.

Class Test: 5

Q.1 E!lain >erte $o&er and set $o&er !roblem is LD9@om!lete  !roblem.

Q.2 !ro&e that +SD !roblem is LD O$om!lete !roblem.

Q.' E!lain the relation between LDLD9@om!lete  LD9hard  !roblem