graphgraphsearch

Assignment12SampleproblemsSampleproblemsGraphSearchGraphSearchInthefollowinggraphs,assumethatifthereiseverachoiceamongstmultiplenodes,boththeBFSandDFSalgorithmswillchoosetheleft-mostnodefirst.
Startingfromthegreennodeatthetop,whichalgorithmwillvisittheleastnumberofnodesbeforevisitingtheyellowgoalnodeA:BFSB:DFSC:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
C:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
D:BFSandDFSencountersamenumberofnodesbeforeencounterthegoalnodeA:BFSB:DFSC:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
C:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
D:BFSandDFSencountersamenumberofnodesbeforeencounterthegoalnodeTheanswerisBFSHowcanwegetForBFSalgorithm,visitinganode'ssiblingsbeforeitschildren,whileinDFSalgorithm,visitinganode'schildrenbeforeitssiblingsBeforecounteringgoalnodeBeforecounteringgoalnodeF:BFSalgorithmencountersnodes:ABCDEDFSalgorithmencountersnodes:ABDHLIEJMCInthefollowinggraphs,assumethatifthereiseverachoiceamongstmultiplenodes,boththeBFSandDFSalgorithmswillchoosetheleft-mostnodefirst.
Startingfromthegreennodeatthetop,whichalgorithmwillvisittheleastnumberofnodesbeforevisitingtheyellowgoalnodeA:BFSB:DFSC:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
C:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
D:BFSandDFSencountersamenumberofnodesbeforeencounterthegoalnodeA:BFSB:DFSC:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
C:NeitherBFSnorDFSwilleverencounterthegoalnodeinthisgraph.
D:BFSandDFSencountersamenumberofnodesbeforeencounterthegoalnodeTheanswerisDFSHowcanwegetForBFSalgorithm,visitinganode'ssiblingsbeforeitschildren,whileinDFSalgorithm,visitinganode'schildrenbeforeitssiblingsBeforecounteringgoalnodeBeforecounteringgoalnodeG:BFSalgorithmencountersnodes:ABCDEFDFSalgorithmencountersnodes:ABDConsiderthefollowinggraph.
IfthereiseveradecisionbetweenmultipleneighbornodesintheBFSorDFSalgorithms,assumewealwayschoosetheletterclosesttothebeginningofthealphabetfirst.
InwhatorderwillthenodesbevisitedusingaBreadthFirstSearchInwhatorderwillthenodesbevisitedusingaDepthFirstSearchConsiderthefollowinggraph.
IfthereiseveradecisionbetweenmultipleneighbornodesintheBFSorDFSalgorithms,assumewealwayschoosetheletterclosesttothebeginningofthealphabetfirst.
InwhatorderwillthenodesbevisitedusingaBreadthFirstSearchTheansweris:ABDCEGHFInwhatorderwillthenodesbevisitedusingaDepthFirstSearchTheansweris:ABCEHFGDHowcanwegetA->B->DB->C->E->GD->CC->AE->HE->HG->FH->F->GSoforBFS,theanswerisABDCEGHFforDFS,theanswerisABCEHFGDShootingballoonShootingballoonSupposeyouareplayinggameofshootingballoon.
Youexpecttoshootnballoonsintheboard,assumingyouaresharpshooter,100%hit.
Therearetwoscenarios,youneedfindtheappropriateBigOhnotationforeachscenario.
Intheseproblems,oneunitofworkisshootingoneballoon.
unitofworkisshootingoneballoon.
Scenario1:Forevery2balloonsyouareabletoshoot,onenewballoonisinsertedintheboard.
So,iftherewere20balloons,afteryoushootthefirst2,thereare19ontheboard.
Afteryoushootthenext2,thereare18ontheboard.
HowmanyballoonsdoyoushootbeforetheboardisemptybeforetheboardisemptyA:O(1)B:O(n)C:O(lgn)D:O(n)Scenario1:Forevery2balloonsyouareabletoshoot,onenewballoonisinsertedintheboard.
So,iftherewere20balloons,afteryoushootthefirst2,thereare19ontheboard.
Afteryoushootthenext2,thereare18ontheboard.
HowmanyballoonsdoyoushootbeforetheboardisemptyA:O(1)B:O(n)B:O(n)C:O(lgn)D:O(n)ifOneballoonontheboard,youshoot1balloonintotal,iftwoballoonsontheboard,youshoot3balloons,ifthreeballoonsontheboard,youshoot5balloonsintotal.
Sofollowit,youshoot2*n-1balloonsintotal.
Scenario2:Bythetimeyouhaveshootthefirstnballoons,n-1newballoonshavebeeninsertedontheboard.
Aftershootingthosen-1balloons,therearen-2newballoonsareinsertedontheboard.
Aftercheckingoutthosen-2balloons,therearen-3newballoonsontheboard.
Thissamepatterncontinuesuntilonnewballoonareinsertedontheboard.
Howmanytotalballoonsdoyouontheboard.
HowmanytotalballoonsdoyoushootbeforetheboardisemptyA:O(1)B:O(n)C:O(lgn)D:O(n)Scenario2:Bythetimeyouhaveshootthefirstnballoons,n-1newballoonshavebeeninsertedontheboard.
Aftershootingthosen-1balloons,therearen-2newballoonsareinsertedontheboard.
Aftercheckingoutthosen-2balloons,therearen-3newballoonsontheboard.
Thissamepatterncontinuesuntilonnewballoonareinsertedontheboard.
HowmanytotalballoonsdoyoushootbeforetheboardismanytotalballoonsdoyoushootbeforetheboardisemptyA:O(1)B:O(n)C:O(lgn)D:O(n)(n+n-1+n-2+n-3+……+n-(n-1)+n-(n))=(n*n-(n*(n+1)/2))