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COMPREHENSIVE VIVA VOCE
Design And AnalysisOf Algorithm
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Divide And Conqer
Divide"ro#lem into several smaller s#"ro#lems Normally$ the s#"ro#lems are similar to the original
Conquerthe s#"ro#lems #y solving them re%rsively &ase %ase' solve small enogh "ro#lems #y #rte for%e
Combinethe soltions to get a soltion to thes#"ro#lems
And (nally a soltion to the orginal "ro#lem
Divide and Conqer algorithms are normally re%rsive
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)* Divide and Conqer +or,s ona- .o" do+n a""roa%h
#- &ottom " a""roa%h
%- &othd- None of these
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Ans is A
.he soltion to ato" level instan%e ofa "ro#lem is o#tained #y going do+nand o#taining soltions to smaller"ro#lems*
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/* Divide and %onqer is e0%ient fora- Sorting ,ind of "ro#lems
#- Mlti"lying large nm#ers
%- Synta%ti% analysisd- All the a#ove
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Ans is D
Sorting 1 merge sort$ qi%,sort
Mlti"li%ation 2 3arats#a algorithm isa fast mlti"li%ation algorithm$Strassen4s mlti"li%ation
Synta%ti% analysis 1 to" do+n "arsersAll the a#ove algorithms are designedsing d5% a""roa%h
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6* .he nm#er of %om"arisons made inan array %ontaining )7/8 entries sing#inary sear%h algorithm in the +orst%ase is
a- /9:
#- 9)/
%- )7d- )/
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Ans is )7
i- Co;$ at ea%h iteration half thenm#er of in"t is ignored* So it ta,esatmost )7 %om"arisons for the #inarysear%h algorithm to (nd the vale inan array of si;e )7/8
ii- i*e*$
log>)7/8-?)7-
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8* @hat are the %orre%t intermediateste"s of the follo+ing data set +hen itis #eing sorted +ith the Merge sort
a- )9$)B$)7$/7 22 )7$)B$)9$/7 22 )7$)9$)B$/7
#- )9$)7$/7$)B 22 )9$)7$)B$/7 22 )7$)9$)B$/7
%- )9$/7$)7$)B 22 )7$)9$/7$)B 22 )7$)9$)B$/7
d- )9$/7$)7$)B 22 )9$)7$/7$)B 22 )7$)9$/7$)B
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Ans is C
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9* @hi%h of the follo+ing is alse a#otmerge sort algorithm
a- It is a %om"arison sorting algorithm*
#- .he nsorted array is divided into s#lists$+hi%h are in trn divided into mores#lists*
%- .he nsorted array is divided into s#lists$
ea%h s#list is then sorted re%rsively #yre2a""lying the algorithm*
d- All of the a#ove statements are false
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Ans is #
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:* An array has indi%es ranging from =to =n the merge sort +old #ea""lied from % to =n$ +here % is
a- is the remainder of =F/$ if = is an oddnm#er
#- is the the non2integer "art of =F/
%- is the integer "art of =F/
d- is an integer %hosen ar#itrarily$ so long thatit is smaller than =n
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Ans is C
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G* In this seqen%e$ )) 8 /7 89 6/ :7B G7$ +hi%h element seems to #e the"ivot
a- G7
#- /7
%- B
d- 8
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Ans is &
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B* .he time %om"le=ity of Strassen4smlti"li%ation algorithm is
a- O>n/*B7G-
#- O>n/*6G6G-%- O>n6-
d- None of these
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Ans is A
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Jreedy Method
In a greedy method +e attem"t to%onstr%t an o"timal soltion instages* At ea%h stage +e ma,e a de%ision
that a""ears to #e the #est >nder some%riterion- at the time*
A de%ision made at one stage is not%hanged in a later stage$ so ea%hde%ision shold assre feasi#ility*
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A method that do not garantee ano"timal soltion #t hel" ma,ede%ision on lo%al o"timm at ea%h
stage ho"ing to lead to glo#alo"timm is
a- &a%, .ra%,ing
#- 3na"sa%,
%- Jreedy Method
d- Divide and Conqer
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Ans is C
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* or 7F) 3NAPSAC3 "ro#lem$ the algorithmta,es KKKKKKKK amont of time for memoryta#le$ and KKKKKKtime to determine the
o"timal load$ for N o#Le%ts and @ as the%a"a%ity of 3NAPSAC3*
a- O>N@-$ O>N@-
) >N@-$ O>N@-
%- O>N-$ O>N@-
d- O>N@-$ O>N-
e- O>N@-$ O>N@-*
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Ans+er ' >#-
i- the memory ta#le > / 1D matri= -%ontains N ro+s and @ %olmns$hen%e it is N@
ii- the %om"osition of the o"timal loadta,es " to N@ time
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)7* .he o"timality %ondition for 7F),na"sa%, "ro#lem is
a- "i =i 1 is ma=imm
#- +i =i %%- &oth
d- Only A
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Ans is C
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))* Identify the MS. o#tained sing "rims algorithm
a- >)$:-$>:$9-$ >9$8-$ >8$6-$ >6$/-$ >/$ G-
#- >)$:-$>:$9-$ >9$G-$ >G$/-$ >/$6-$ >6$ 8-
%- >)$:-$>:$9-$ >9$G-$ >G$8-$ >8$6-$ >6$ /-
d- >)$:-$>:$9-$ >9$8-$ >8$G-$ >G$/-$ >/$ 6-
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Ans is A
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)/* Identify the MS. o#tained sing 3rs,al4s algorithm
a- >)$:-$ >:$9-$ >9$8-$ >8$6-$ >6$/-$ >/$ G-
#- >)$:-$ >:$9-$ >/$G-$ >G$6-$ >6$8-$ >8$ 9-
%- >)$:-$ >6$8-$ >/$G-$ >/$6-$ >8$9-$ >9$:-*
d- >)$:-$ >:$9-$ >9$8-$ >8$G-$ >G$/-$ >/$ 6-
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Ans is C
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)6* DiL,stra4s algorithm may notterminate if the gra"h %ontainsnegative2+eight edges
.re
alse
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Ans is alse
It al+ays terminates$ #t may"rod%e in%orre%t reslts*
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)6* &ellman1ord algorithm %om"tesshortest "ath for gra"hs +ith only non2negative edges
a- .re
#- alse
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Ans is alse
&ellman1ord is sed "rimarily forgra"hs +ith negative edge +eights
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)8* @hi%h one is tre
I* In the 3rs,al4s algorithm$ for the %onstr%tion of minimals"anning tree for a gra"h$ the sele%ted edges al+ays form aforest*
II* In Prim4s algorithm$ for the %onstr%tion of minimal s"anning
tree for a gra"h$ the sele%ted edges al+ays form an or%hard*
III* DS$ &S algorithms al+ays ma,e se of a qee$ and sta%,res"e%tively*
>a- Only >I-
>#- Only >II-
>%- Only >III-
>d- &oth >I- and >III-
>e- &oth >II- and >III-
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Ans+er ' >a-
Reason' In the 3rs,al4s algorithm$for the %onstr%tion of minimals"anning tree for a gra"h$ thesele%ted edges al+ays form a forest*
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)9* Hmann tree are sed ina- niform length en%oding
#- Varia#le length en%oding
%- Com"ression algorithmsd- &oth # and %
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Ans is D
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Dynami% Programming
Dynamic programmingis a method forsolving %om"le= "ro#lems #y #rea,ing themdo+n into sim"ler s#"ro#lems*
a""li%a#le to "ro#lems e=hi#iting the"ro"erties of overla""ing s#"ro#lems ando"timal s#str%tre
overla""ing s#"ro#lems means those
"ro#lems that %an #e #ro,en do+n into s#2"ro#lems and the soltions for +hi%h are re2sed several times eg*$ i#ona%%i series
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O"timal S#Str%tre means o"timalsoltion to a "ro#lem is o#tained #ythe %om#ination of o"timal soltion
to its s# "ro#lem eg*$ .he shortest "ath #et+een t+o
verti%es also im"lies the shortest
"ath #et+een the intermediateverti%es too
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):* .he "ro#lem solving strategy that(nds the o"timal soltion #y ,ee"ingthe #est soltion fond " to the "oint
is %alled a- Divide and Conqer
#- Jreedy Methods
%- &a%,tra%,ing
d- Dynami% Programming
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Ans is D
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)G* Ho+ the Dynami% "rogrammingmethod diers from greedy method
a- De%ision seqen%e that hasgenerated
#- Prin%i"le of o"timality
%- #oth a 5 #
d- none
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Ans is A
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)B* @hi%h among the follo+ingalgorithm is sed to dete%t +hether areglar e="ression is a%%e"ted #y a
(nite ma%hine atomataa- Prim4s algorithm
#- 3rs,al4s algorithm
%- &ellmann and ord algorithm
d- @arshall4s and loyd algorithm
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Ans is D
@arshall and loyd algorithm is a,a all"air shortest "ath algorithm
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)* .he time %om"le=ity of o"timal#inary sear%h tree %onstr%ted singdynami% "rogramming is
a- O>n-
#- O>n/-
%- O>n6-
d- none
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Ans is C
O&S. is an algorithm that is sed forthe %onstr%tion of a tree +hi%h hasminimm sear%h %ost for ea%h ,eynode in the tree
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/7* An O>n/ /n- dynami%"rogramming is for +hi%h Pro#lem
a- &ran%h and #ond
#- 7F) 3na"sa%, "ro#lem
%- .ravelling Salesman "ro#lem
d- None
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Ans is C
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&a%,tra%,ing
&a%,tra%,ing is a general algorithmfor (nding all >or some- soltions tosome %om"tational "ro#lem$ that
in%rementally #ilds %andidates to thesoltions$ and a#andons ea%h "artial%andidate % >Q#a%,tra%,sQ- as soon as
it determines that % %annot "ossi#ly #e%om"leted to a valid soltion
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/)* Rles that restri%t ea%h i to ta,eon vales only from a given set is
a- Im"li%it %onstraint
#- E="li%it %onstraint
%- #oth
d- none
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Ans is &
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//* @hi%h algorithm determinessoltion #y systemati%ally sear%hingthe soltion s"a%e for the given
"ro#lem of instan%ea- &a%,tra%,ing
#- Dynami% "rogramming
%- &ran%h and #ondd- none
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Ans is A
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/6* .he sear%h for #a%,tra%,ing isfa%ilitated #y sing 2222222222 for soltions"a%e
a- leaf organi;ation
#- node organi;ation
%- tree organi;ation
d- s"a%e organi;ation
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Ans is C
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/8* B t"les is a soltion to +hi%h ofthe "ro#lem
a- 8 qeens
#- traveling salesman
%- B qeens
d- none
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Ans is C
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/9* @hi%h "ro#lem does the follo+ingline #elong to
Jiven n distin%t "ositive nm#ers and
+e desire to (nd all %om#ination ofthese nm#ers +hose sm is N
a- #a%,tra%,ing
#- traveling salesman%- sm of s#sets
d- gra"h %oloring
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Ans is C
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/:* @hen a gra"h J %an #e %olored ins%h a +ay no adLa%ent nodes havesame %olor yet only M %olors are sed*
@hat "ro#lem does the a#ove linerefer
a- %olora#ility de%ision
#- %olora#ility o"timi;ation%- #oth a and #
d- none
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Ans is A
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/G* @hi%h "ro#lem as,s for smallestinteger m for +hi%h the gra"h %an #e%olored
a- %olora#ility de%ision#- %olora#ility o"timi;ation
%- #oth a and #
d- none
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Ans is &
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/B* @hat is the smallest integerreferred to as in gra"h %oloring
a- %olora#ility de%ision
#- %olora#ility o"timi;ation%- %hromati% nm#er
d- none
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Ans is C
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/* .he soltion s"a%e for ,na"sa%,"ro#lem is
a-//
#-/:
%-/B
d-/n
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Ans is D
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&ran%h and &ond
ive node is a node that has #eengenerated #t +hose %hildren havenot yet #een generated*
E2node is a live node +hose %hildrenare %rrently #eing e="lored* In other
+ords$ an E2node is a node %rrently#eing e="anded*
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Dead node is a generated node that is notto #e e="anded or e="lored any frther*
All %hildren of a dead node have already#een e="anded*
&ran%h2and2#ond refers to all state s"a%esear%h methods in +hi%h all %hildren of an
E2node are generated #efore any otherlive node %an #e%ome the E2node*
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67* In a 82qeen "ro#lem the nodesnot leading to the soltion are ,illedsing +hi%h fn%tion
a- &ran%hing#- &a%,tra%,ing
%- Ran,ing
d- &onding
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Ans is D
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6)* 3na"sa%, "ro#lem is +hat ty"e of"ro#lem
a- Minimisation "ro#lem
#- Ma=imisation "ro#lem%- O"timal "ro#lem
d- None
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Ans is &
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66* In order to se "ro%edre C&& tosolve 3na"sa%, "ro#lem +e need tosatisfy +hi%h of the follo+ing %onditions
a- the str%tre of nodes in the states"a%e tree
#- ho+ to generate the %hildren node
%- ho+ to re%ogni;e a soltion noded- all the a#ove
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Ans is D
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68* In 7F) 3na"sa%, "ro#lem %>- isre%rsively de(ned to #eminT%>CHID>--$ %TRCHID>--U
a- feasi#le leaf node#- infeasi#le leaf node
%- nonleaf node
d- none
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Ans is C