I ! | 50); Mode <5 a Basteatng baal pyeobtene Hoon Backttadiing {% au algordiinite teebadgre for Solvtg j , One piece ot ed by boing to buill @ Solutio. Frcremreutatty a Bure, Keovtug Hore Solution Hat fe! fo Aattyy the Comtvertce q the problem a auy pout 4 thue , + Clunened Methed o| Backtwasktiq > Tie orden to opplug ? pkg toa Spealtc cleux of prorleece , Gre Mutt provide the dot het Le te be “PY Jove the asetteudase Fuattourte of dhe pocobtesee Sdled 8 Se procedural pastowetene, uthg Srate- Space “Tour. 9D There procedure Fhoutd tate Be Surtauce clete P ax o partow der & Showd do He oll A Mook cp? > tetunor the pasted Coudiate a& the ‘oot 4] Looe tone # Nefet pic) > Heke tere end 4] the pooctind Caucidate o% wot — wos: Coup letig, + Accept Cpe) > Geetonen true GC Le Solu of problem , & ake olenuwtce re Ghat Chic) > pomerate the (Put Sctiouin, of Gudtdate c. & Newt (pis) > quusenae She Newt csterinatthe Cxterator of a Counlidate , afte Hee Cxetecufon $. fk Cubkpuk Cp.c) —» Uke Fhe Solutten ¢ a pr we Appropedaae to Hie Appltcation. Hee, we will bfenun Hravee preobtewa wha Brcktockicg,a ae S$ £185,689 & d= td see Subecki 4 & utx G1 State Spoce tet D Fiualy, Add ott etruents “ad! shroud be quent Heui'e & fra eduuk Str] = shoud be Jer Stoun ‘A! - The Sohdton 3s £4,8,69 & $483 + No Sree pesto c- | The proton % te place “W? Queer Oe Mxm Chemboard So thet ao two Gueius attack Enol other by 4 Fu He Same tow, Sune Colum on Ge Scume og ome dhe Gelatin, would be 8 K Fou nat we For nea & nog there tk ne Solution beoauy ET CH 5 Ne place dee a Quen ‘uo place jor aesfou ve4 , ture ane two Solutfon a4 Shown below CH= Queen preteen ) | A ao Pt Houston Cyste ¢- Hauttodan Cte a Clore Joop en a weapls , wwluerce Eveney Mode Chester) th Visited Pratl Oue, so a Honut tod Cycbe fa patts tracdfig (vom a pofi bak to Shel), Vesting’ Eresey tide Ba soute:s® b> Cowtden Hie gol uudireeted qr whene 4! hk Sousece iz de Howutltetan cyeten one 1-a-X-3-4 1-3-4-a-2 + Aprly Bocktsodting to he protle of feltng 0 Hat ltonian Creutt fu He grep Shown below pc > Froutly Conteenet ce Spnee ~ es dow all Mearhabte Vesctfoter ee aah Veackex+ aout Houtlfoutou Ch) £ do © et Veetex (1)! j CxteJ= =0) Ketan! i Ck== %) pro Cx Dis): Hlaudlterdian (K+)! Swlatle (true)? & Newt Vest (1) t do £ weed = KOeIH) % Cut: 4 (xeel= 20) steturen} 3 Cevcx cei, CEL = 9) é fox fea te Kc! do a] Cxes) == x0) Baeak } 3 Cix= &) 5] Chen ot Cheah) ad ACKCHI, XCD) =0) qetvan! 3 while Ctrne)s 3sti) & Apply Bodlavachivg te dhe probtun of freeing Hawutltoud Coeutk Su dhe qr Shown bellows a wy) &) @ © © @ oe The Howuttterdan Clsccuth preceate cre 17293 DHOSPA 192959493891 1953949397294 lt Braet od Bowed t- Th an Farpuoved Veefon of Bacltwdtg «hens we dead caf opttiudzaton Crtestutgation on Martuulgatien) proteus, A “dente Solution I Lie ere ule Sartifta tre Conutscafiets a fre puoblem Fou & , 0 Subset of Wemu whore totot todlgt do not Cxcead re Copsatty 0} kapieiek. iAu “optimat Solute” a ferutbee Solution use tre bee Vatu > Greil cael Bavuel Hegutner bee add ieral Feu Carerpareed will: bracletncldg A fou Brey tuode of a State Space fran, a tony prose & bord CeHtten Jou os vppen ) Gx he but Value Of dhe ofjoetie function, & The Vatue 4| dhe Bet Solu gowns Bo fas. be 9 Hesce we wilt alfreuy 3 poco enue & Audiument Prolene & Knoprack probes * Treavelltg Sierra probleus # etayueue puotenn ¢- Heae, the Probleue % te Pautine “Ww goles to MU’ people so that tte tatal Cok o| He Ptguaeut & Miatrauu. IS Condes. dhe ou Cont Meisel > Pret Concpute She Jowese bovricd by odling Hee Srrattou Element “fy Soe ow «a) plow Bord would be Uk)= @ +341 44 = 107 > Now at Eveny Step» We haw te keep Pelt Mituak Solu veto Violating dhe Covudknorkcbs af the proton ° Qh atstiny alae = 6H es +6 7] ast aoe aoe 5 ab aah te= S34 te = 45 lit Bh Srine co 210 =20 | ae x rs Riser etry at lie ttornad a SolitPen >t, He Cork of Giver ae preobteae QB! & the Tob Allocatfen twwoutd be Pew A 9 Toha peruen B > Tob 4 perteou. C¢ SO TJob 3 peor D — TY + Solve the grew Peatgu recat presbeecan ee 13 a8 4 QB 3g 19 8 IS 9 86H JOj? Poets Coupute the Jowser Found by adda Dla Svcmate Eleuendia Su Euesuy tow i a Lower fond (2H) = BENET +10 #347 %, “8, Glu 2 Now o& Eveny Sip, ux howe to bop {frcttug Mardueedh wwillout Violating He Coustuafitr of Hee preoblewe, oO Afs a6 len 13: 88-4 26 83 19 18 IS 19 26 2H 10 lt-= S4+ES+ISHO 261 a ast Ler [Abe= BAH) Mee 2etHtistig 284 . D> The Core 4 aes is Tob fAllocatfor woutd be Iie = st ps#26) 2 53 FE fore ea 1s] Ht 26 2H 30 aolene “ 41" & He Penaon A > Jers peusrB 9 Tob 3 Perm ¢ > Toe > pesaon D> my—L s@® 4/4. byaprack vise Brequel § Bouud ¢- Thee ate UU Heau wk bts Why We ne Wy gh Veta Vi Va, Vi, “The tobe Cape petty of Kuaprack % WwW. Fhe prong te ty Martini Hee at punyrt Auch at ale totad lug of dle Phun 3 Se Aeowe ofc Equat te lo. 5 we Case Gere Crore “ov trot choore axe Stee , we have Ki Xr w-~ Xu, whene Xe> f1,03 A Xpet he Hew le ddeated HX, 0 Te Thur Ye tot duteeded Solve the fee Fraprack prtobteer + capacity w=JO 8 Ue ae cvee £44,533 8 Vatun axe FHo, 48, 2S, 123 => Faratly , Compute Vey, Catto) & place it x deasteauinig Odes Sten Wek uz P Next, Apply Crscacly Appecoaet, te Callealate Mera pref jee Uppert Boured Cus) flu Ty) Ta Gpriiianetaes Ls upparBeend (v8) = Hoy exe = by> Newt , Dew Gtede ~ Spoce ten wth Veo & Wao § Ub= 36 a Root Uode Nodecc) = 4a + BAL ub= $4 Wo oO % + Node Ce)= Apt es+ fH uk= gq Nee fete wis, Wo Ts @E A] form] © — * Node Cx) = #8 gee UBes2 ub= 58 Not eau He ‘Coluton vs The total preaftt qeteed Lh bY Meum added ate $1,, Ta y ¢ & Solve tee given Fuopiade pride Ubeg Breau ¢ Bond Ve G40, 10,128,183 We 68,4 6,93 & the Martane Capaetly ¢] Bropack We Is,<@) > Frratly » Compute Vee Cratie) & place ft Ne Secseeattug orden ve) we lune | Webglt | Value ae T = a as 3 a 4 a ud (VB: p Wnk, Apply Cerecdy Appreoacts te Cotcutote Uppert Bo ) ra uppenBovuel =lorioriad B42 387 Pp Net, Pusu a State~ Spoee tea wt Veo & Wro d UB= 38 ox Hoot oF NedeCO= 104JR+ SHA UBs 32 o& Node CE) = 10419 +442 ube 36 # Node CO) = lto+1OFlE UBE3 Solution Not Peale Couputation of Jousen - Boone dow Ter OG Bouud beebrdqe Frvolver ett Ltepe + Fou Gaal Cy 2, fad Siu & of clistacseee piers CHty F ky twe Measeck cera, i $ Compute Go S fou ant cibtes + Divide Lie tenat by 2 # FT] fu cote 4 faction Corocutt) dy the Nene Fusegen + Srhe dhe fo Tsp Wiha Becruch curd - Bovud Lord vp CL) Fhe Hautt Suc=A > Compute Hoe Gower Boru CLE), Sutlratty y choatng Min Cour eee fom Gash vente of total Suu shoud be dite! bY & LBe [clea + (3t6) + Ae Clad + CHE = gO* GO FEDS senda “Manly és(8)_ b> Nuk, Make Catenietes Loum Bovrd ChB) ax snot wode & Stack Check “Fug att pottditta oltle dudktug fhe Journ Booed CL8) gh pate Keip tre Vole of posh tliat you've Contded Some o& for Semceabiaiesy Veauttin , You Cau roore Mty Coe Edger. Sx Comtden pas "ABC", Hene Mre Corr of Vesetfeer ace Cape nse 4 Gains Cae + wud + SS + Cait Hal) Whene “tuti’ 9 defer cout eye frou Hak Verde 5 Ake State Srace- tren fx Coustrenateel uty Abe Cental UpuonBovid HA @ Medet axe Cumidbenedd Seqyeutiaity o st nedet)= C341) +(SH6 )¥CHa CH IY, =I # Node(B) = (S+1)+(346)4C11a) 1GE#SH CRAY 49.5 (16) G@). a * 4 NolecH) = (B41) + Cate) + CHa s)4COt9/9 =t9 #Node(s)= Cat I)+ (B+ 4 )4CGH) #43) C013) 16 Node C6): (gtd A(t +Ci4a)e( ees) Het) /a £6 z 4 NedeCA)= C341) CB49) dense) eCasde(adila Fig # Nole¢a) (812) (216)4 Coumscasayscanyy oy # Nece (2) (Sta DaCaeeys C649 D4 Cataiais ya £1q Noho: (843)4CziayeCesarecnsgyicotaye = a4 Asbod ,e st 3G “The cont of pases h Wy A Node): C143)4 C242 )4Cua)4C34a vac y/a =l6& P, Nps Nups Complete 8 Np = Havel Chayer 6 © Ala oettlonn fe told Ereny operation fh uulguely dived 4% Catied “Detorratuttte Algo”. PP The Ngowithe fe shi Eveay operation tot have Uuigre Uuutt , Hotlen Hrene Cau be Speeitied se | poutberbte fom Brevy operation Sur ae a 4% Cated “Noh Dekesruiicert ic ‘ge " > Trene ane tue qos flu woldn a protteut Cou ve Chawiified Cousputationcl Coniplent # Pa clam ¢- clonp & o class of deetifer prectteu Hat Cau fe Solved Fu * poly wowed” tue be Debeseududebye, Alacaitons. Nha claw o} protlen fk Cattedl * polyrouufet* ~ Some | dhe clax-p Ngosithoe Su elude Scuetfig Seascclitig 6, Muplicaton of twe Fntegeru Ek , : Teste ate Ngostitnnn Jou thie eo Polyseoveatad tare Algo Ven eeu fovrd & lence Carnot te Cate goaded ae chase -p ea Tep potter, knapa ack protec , Houuttterian Coteutt ee # Np- claw ¢~ clax- Np & a Clan | decbiton prcobteun Let Cae te Sobed ty Nou- detenuetudatic Poly wouutat Age « ques claw a problenn BH Cattled "Nou detenrenbaletre pol wat CNp)” Clan. J” | AM Ake Prottn ushkelr are 4 Clan~p ote che Sueuded tua Abe Clan-Np> "|s@) = Np. ake Conia kKrapraske protium, TSP provtene , -Haratth puke Cuter Ste , + NP- Complete proton ¢- A dediséen protleu ‘Dy t& aagd to be Np - Cousplete 4 9b belonge te Claw - NP 4 Bray protien Sa Mp H polyrondtatty deduat He t9 D. FNp-Hosed prcokteust ¢- A pnotlan $c Np-Hawd 8] au Agent jew Silvug FE cou be trcualatel Futo One for Soltng cay Np - prottun. Nip—Hesd tlemefone Menu Fatleaut ca hosed 4 day Np- prbltewi Np ~ Cormplete p-elaw prosteaa preodeus fig Retarfeaultp viv P, Np, NprComplete of up Hewtd 4 chatuan 0} Nuuesteal Apres ¢- Numerdeat Acton Atefese to Suehe Agar toe Frat ame ted dor Sig Moemedtcot probtem Suet on + Evatuat® Sux, Jog x Ete. * Evatattig Tictegree 8 Howeren , Yuuuesiour cletdecgn are ELecouuterted ustitle Sobfig Modtenedfocd preotleun uel ay + Mose Nowenfeal protea Gumot te Sohed "Czadly", Hoeyhave to be Shed “Approdivatayr, Tas & woally done by %epl asta an Su hut e objeat by a futte Apprortucation . Ber CMe at gery dy Le Bar ay oT + Due to Suh Apprortuation , “Truncation Eracore usoute Cove Bre of Fle Mager chatleuje fie ‘Nureaifead Avedigic % be Erefireate the tifude 0] Trtoucation Eran. Tuk te dene Ug Cateuta tool. * Othe type of Groen hat Could Oteuse fe He “Howud- off ~Ewnion", Tir %& Caused clue to Sutled Acouacy uotéle Hepreeutfig Heat Yor Su cligital Computer. Mert Cotsaputews peroutt 3 Jevede a precicton tauuly Siege prec ~thior, Doubte pretdion & Exkevded prectiion, Uatig Exterded preckion Slows ckwu lie Couputation, + Avotlen cliattage Hat May teoue fh ‘ourngiow” & tre * Ueides {lou pheronteccor, AaPMeuretfe opercatiCns Yells a Au oveaiflow Geousee eoleer Qe Hetult oetaide dle Mauge a Compidere fiecteg pote Now Uuder lene Geant tubeu au flncidlacctte Opestation yee a A{euut of Sucts & Fuertt Magutlule Abat Carnot be Heeprceceuted,