DSA NOTES POST MIDTERM, Cheat Sheet of Data Structures and Algorithms

Download DSA NOTES POST MIDTERM and more Cheat Sheet Data Structures and Algorithms in PDF only on Docsity! | la, Binary Search tree Bs) : 2 OST is a node -basel binary cke tee. cata slrucluaw whith bos the | | | | | | i Fol loan) \y po Vey: \ * The left suvtrec of @ peel contains only Hodes with lays lesser tan The pade’s key, ‘ us - KL svbPee_of a pode contains only noclos wrth bees gproceloy thew, the necte's lou. ‘ ‘ 6 . v 8 The elf and viQhl subbue each must ally og OS, | am | Or 7 Sh ©) x i @ 1 How 40 _seavch 9 oinarg Yuen — j 4 Start atl tht oot / a - (ar Securch the tee fovel by wel, gnltl you find the clement Yyoo_ano ||, sravening, for er you Foach altat. Pub Nope athe || & Searching inthis (5 rat better than linked LL as it tokts OCiogn), a Smallest clement at loft mest efomint. —_]L A Longest Clima nt ot not Sts Ate ea Ta ba a erin se Se Se Mow’ If * Stop ett tho_roo mas a Se ||. * Compary te volt of P tho. ‘ftw youu any seanchiing. hr fth || _4ho valeo stored at the rook $$ + OF tho value ord _eqeal , thon ttn founcl + » offanaxSe, if it_is_a lal nod, thon not fond. + TF it is lnc thon the vaio Gloted! of the root pan seam the eft subtree. i % OF itis opucitin than the bo vated ) etored “at te reat, thon _ e_ _— Search tho rficnt fubtrco, i + Rect sttps 9-6 for tx root. of ta see Chosen In the Pyevious cep Y orf.» ——__—— a “+ Fonction RETMEVETEM + a | What is the size of tie proslom~ Se - No.of nodis in tw Tease an ontinging ees eee) fa -Whatis— the hase case G)? _ a | _ fy whon the uy 1S found. oe | itn troteee is. empty Chat, wos not fours) __& What t the qoninal_ cage? 5 — S€arch in ths bétor ng sub Bites 5% Rulriove + 1B. us 2 js a Gupart 13 with!2: —__—— &mparw uwith 20: Compang 18 with 18 Choose right subir Cheese bef subbur _ Found}; Cuvant — wee oe mS Z Somat Sid Nie oR ara So ew Eee Con ‘ o : ‘Does the orcas of ns. Aum ne tree mrailtn? ) DA :PREACEG {8 —_ Oe - a - —— = bi brat BADCGFE LC) Enput : ABCD EEG. tree = @ ee fp Ye iy N. —_—_ Ls Yes | the ovdtr of ering ckmnts matters. a Code : : _ 7 Binowy Saath — Mee #inclede <stdibeh> | Binclude <sidlibeh> l struct _nodef int bag; - - —struet nado * loft? struct_nede * right, p ens struct _node * neaNocke Cit i) EE struct nado “tmp = (struct nedt *) malloc (siechiatract ald) 5 tt temp—> lea = Frm} TIMP > RES NUN return dps NULL? i veturn tmp j a void inordorCstruct nodg * rooE) (a FP Croot 5 = NUL £m (hordor-Croot->—lept)-2 $$$ printf ( eed >t tet ala); Ss inorder Crpot -» pe ; { ol J ee ingort (lruct nel * nod, int int it Prods = =NOH) __FEVEN nwNodMthap » tay <node > key) “Ue. = insert Cnode ot yo else Bele ais right “zinsert (redo > rig, kay) returns gq Struct node * minValeoNode (stud node “node f Struct node *cussunt = Noda,” Ty ico L=NuI tlie (omant 1 cwrant> WE T= NIE. a, — return [ss STS ite le Sitters rape el "tS CU PUNE > (OE, return frie return queunk? —_ : eat Ip a - || struck node “delely Nodo(str uct node *root, “int pt a JL fh Groot == WL) petumn_roote ih ches < Toot >kay) — ——— root-—>-eht— ole Node Cook Lope, lop Se Oise if tees —> root kee )— root rig Mt-= ciliedacooe- > i wy) alse ¢ if Creoto tet =Nuof “struct nedy “temp = reot ange $+ —Freecreot}3-— — — — return tmp: 4 Lad else Pret right == Nuit net struct node + tymp = foot > belt; free Croot); return tmp; struck ede tomp-=nuinVallutNade- Croat >-r'g hb); Yoot > key = arp key s root > (ignt= dululaivode (root: right, ttyr)-> key)s 4 yeturn root; eo + Replace thu data “of ae “rede to in elec with ede deta oe + delet re 2 decasser’s. dato. as _ dae No fe # Tnordin traversal. (LDQ will produce a sorlidl _ gta. in BST ae Cus) * Srordon Predacessor -» largest ve in lib subtree a || 4nordin Secessor Seals vole in. right subbup See — Re We. “replace thovilen predecessor ot Grover Sucensor | with the node with ttvo _chilcbwh oe cow-delaing. ee cer + a ee ee ee _ a = 1 L _ i 12 Companins Pinany seanch Dues _to Lislear Lists: Operation Viney Seonch hue CES ice IS itll @ OG) OG) OG) EsEmpty OC) Od) —O@ ae __ Retrievedizm _ Clog.) O(LoqNN) OCNS |, Grsert Stim OCwogN) OOD ____O@)__ Delete ftom OC04 Ny OM) ON) eLtnkad Lest? Pres = insert, dele ns ~ search ee ee . Array > fros =Seorch _ — — | + Binary yur 970s = insort cold — {i ON | «BST» Prox~ msert, delet , search Cons — Stoych | ort ~=-Ocny cm St =o Search — Average = OCleg,1) Ewha Skaused- BSP Chapln-?27 AVL Trees Balenced Bincay search Aree CAV. Arte) + Ralonee Factor = Hight “ae Subbiar) = edgy (Pig - svbbud) —t ic, © th Or li ted ety ©, @ —— helmed Gage) struct AVLNedlo £ - - 7 a a : _ 7 7 iL ot — —lint data; et be FI ih Me __|| ie nfo, _ —— Stud AVLNode” (ef tp —} Etude A Ned igs ee nee cE | a int tat Cotrack AVENode 3a P Te (== NULL) a i i return Oy ~vyetum n-3 = height —_— if ——— — ~ ~ - i ~~ get Balance CStroct Av Node “1n)f np lp mess NGL $$$ el RE returnO; oe a —— ——— rerum Cc hight (n>. left> = height. Castigh))F 2 $ eT ee i: iD RR- rotation ~ Single ett Rotition Mo: @,. Rigetod 2a Retati x C6 Tet siae _ @- RST 1 2(ug) + — 7 \ Le Newly Inserted | Struct _AVINCds* singleLeftRotation Cotruct AwNede” XP 1 gtruct AVLNedo *Y = a-rrighte | Struct AVL Neco * To = Y -e lefty oo 4H nt mid tet =a 3 a nee | a srs i = fo? — | retern yp | ame hee = rox. Creight Ge~ let) 3 height oe erighty De je Reger = _ Max Cheig hit yo) , heighet Gy-otight) 9, Jj chruct AVLNedo® eRstation Cstrodt AVE Node oc) f Ter left = singtektt Rotem Cae WF) return singleRightRotat (xc) a Pete whe ty) RL - Roterhon - x OQ, behild Cy) ©. aye Rota tt oe ‘ % f Rigne | ~~ i ast I \@ ‘ struct AVviNodo* Ri Rotetion (struct AVLNode” Df : &-r right = single Right Rotation (x right)? oe return—singleleft Rotel Cac).+— re cds | | | | | | | | | | | | | | | | | | ie Ensertion- _ —ot Struct AVLNode* insert Cetruct AVINGH@* root, int valu){ jf root == NULL ee —}—____allooat_menory for ‘nods | set. rede odie = = you sf root > bft = _ ee : ce return root; gor foot hoig ut = =f | ; a ees a value <reot » it > dat dh — root > bets insert (root af yale) ae root > night — | _ gm ~ insert (oot aright , valeg \ | root hugnt = EF moK Qght (reder 0") acgick Gan raha win bE GetBalerice (root)? 4 fo ket 1) otetion Pe Neb Ratan 9s seol ok ft Sobimevol A Cou tice treXld bF CB) = 4 Ceigt, 22 i = LR — Rotation __Choptir-3 M ult wor) Frees SUbbues - om key Avalus + me - J per Ney ae | * (nsort_x oe “AA a Ione fag Ade—ree=t = Lnsert 52 in aboes “rut _ Ey tel a rr « Eyer intrnol_pede. of Mau way secyich tre hes —__ sett 6 chile — a upto! M-1 “Hays MaMa a2 Ngaf 2 et ee ss &For a 1 Subbu te, 0.5 h chy el of a node, all. ago in Te ust be_ b/o ker ‘Gis, kt \ ees ee ken < key (4) < ke el ey k lydlaa> kos —— pe uoage ine forse seach + Ol L041) Worse — OCD OG) PETE vedecin _ es _ SP hte \* &a5 for ineriiory +m0 cong. same as Searcy + Onsertion Search , “Weleda. = OM). ee i | —Sotution—for—it—B—$- —Bdlencoel. M=way Search. bra so E ee, he Oren B- Gf ack, —» lft DE Lk | 4h0 node has _tewo childern =» right subbiue TE sess node has 9-childiens UO Racks a middly, sublig —£ a ky + right _subbiee ° Prserting~_Prserlion alanys dont at waf rode te Splitting oF node; P Cx a ig ehid i 52 pit FA pO EBA, 6 ® tp = = Sy ST A Ty pNe e S tehive e l eniealla 32 — Insert 39 32 ud U7 i - a ¢ alloy) a foe ee __Snvertid 42 _ fab, (voit) —_ ‘Greed 47 = _—— po fer [69 [90 a 99) * Debt 69 0 Replay jt with inorden_successer. =. [54] — el 135] yet eae a ninen No- of 4 veith —heigit = ~ gs ety [tte ttc ar Hey wt petty Er — os he eat ——— _ arch “t= Oe en) __ | —_ I qnvrt us ths nt ewe oe BTSs é —__faslisl 36 [45] , = : S\N + jefe jas}z2] mae — KEEN Ll siti a eS ——_——— Tr 1, Doltion in A Tree: OC!°9,")__ | | Brery-ne node should. cordeaio Bt ji a mm entldnen ——— tn ernie ondetlow ee _ | Deut 99 » cls Yodg tes) — ee ee | 2 mS ‘Delt BO: Uneterf loco check OFF sibling & vight siblings Right sibling rawr mere vel al ¢ po onalboay) So peli ir fron pig Stl from _pargnt_dewsn. me id 7 a panmen— se Troe] st ray F36Lus Eel uss Ee 422lio ficclus BS iby 21 _Chaptin- 9 Binony_teap Orating Systm SPAT Cshortist Remaining processing tine) = Data Bret for spRP= —_—_ 1 Unfinished jobs ot ang point of time se | ib we reed to maintoira tne remaining processing tim of | We nad to Find tha job with the sheetst SPRT ft Whon job finishes we should _rems yo 1 from oun —__ealkiction. : “Sy iv) Waren crow job arrives we neecl to add t te the cabochon, basic eperottions- nial Lat sere fray tae O57 7 mert C) ODF __ ON) odoe9N ) o find Min() a Ow) Oa) OCI69.v) i) remo NinC ) _ Nn) - - Oon) We wont- —_ _ Insert OGogN) fe ~ find OC) _ Priority Quy | Dew — O09) ah 4. Binary, Heap? | [Ce Ts binary Ve Crot_Bs7.) thet cctisfios tw Propenes. iy structural Property All Lugls excspt tock lovel cre ull £ (ase __tvell_is (ft-Filled.. Ccompltt_ Binary Bu) ee = compl Binary Tree i. Be il M tys ae than__or or equal. its chi Idecay Or _oveny nodes Grodin tnan_or equal to_its hula _ _ Qo mm G. @ a H— © _ _) Ce) _ @®oOo Min heap Max Hap ; chock Min) (Rect Max) + AEG, Representation | Max Hap) Vavergl will bec | (up & down) jt es Pace _yequivempnts. : I~ OE 9 9 3 _ Q bale {4} ula] sq | [ae A 2D we \ Pewnt nede= LO-) - © é e debt childs) ORE) Rigi duld = 2042 “Wclonoton = Struct Heap > f a > lat * arrays : — IME county No. of Clompnts mm Ab capacity : A Size of Heo? 1 heap type Max Min I - =. z | Crean a. beop- | Stet Heap Coat Cint epacitydé —___ hallecedy _a memory for heap P| ll set lop 2 count_=07 et nap > capacity = cepocity ’ ‘1 alloccts pitgrery Fox hee p-ariay 6S for te cePaciry ie | ———ye torn heap eas Ponent of Ned Rt Rarer Covuct Heap h, int PE IR (sco i t> h- cont) ren -1" eg ° veturn UDR; j HE chill oB right cid = wat Wltchid (DE eon ot fat; int vightchid¢ ~*~) { yeturn TC41} Oo G_O_ 4 oe theo a a | _ _____]@3) 5ul_eshalaef-—f Jf 9 | jsulaclusfo7! TT T | Oo. 23 | 5 67 — | ot 23 45 67 Void insert Cstpack Heap *h, int datat — — —if.Ch-+ cot wapeny et po —____ Pisize hea pCndz po a jp inte Sh COuMpe po herarragt’ = ded — —_h-comttt 3 ee while Ci>=0 84 hs arraylt7 > > bre orray Parenti JL | ___ —}--——swap Chhes re arayle] , bh-- arPc array) > poe t= Pom chide a An elimi ig aloes Aulited from ths. noe at fio hoap)-So, clin, an __ elonent from the hoop dong into Follewing J St Stops ® Roplace to Yode nede's valtg with the last node's valug so that tho tue is stil a complte binany: Bee i) Dele tne lest vieds WD Percolat Se Airst rst cenit. ~<————--- he e Ye ony ook peti oy ew U5 — eS 8 wD i eee od 2) ge ae a jak Dalett Max Crecp hf i mt dat eka _ ct | if Ch Count ==Q) Se | return 1 ee | | data = h= carraylods | a arraylo] = ho carra gnc yy ee i hh? coont=—j tt | fercolati Dean (ho SS _ - ie | return Dotas TCO HI adh we us t- - oe nelomonk —» Have _to_putt Hye elmauts jn cs onder. reat 0 heap a op erect ty till heap beeos empty = \| i ——fastiad_cse_eill bo On Jo. Ln Place Sort ee = a | (iaapeloTn ] “lat in | heap spo) geet Car [ig ast Hao . iy Unlforaify - Bnd = heey wash function of. nde = hy) oo A a Mapping the keys 40 appropri, locations Cindicis) in a hash table is cablecl as poshing. (ca) rCalision.+ whan to oF more lays map % He seme memory locotieny, ° WE Can cheese best “Hosh funtion. ee But it > te Birthday Pomadoy. * Hash function is the mochonediceob fornula which whan _ applied ona hey, produces an intigen euch ean be vsecl _ ais an Idee dor the Mey in Heshtable. Main aim > Flemtits shoud be rondenly 4 oniformly distributd.. Propertits of crcod Hash funchont |} Loco Cost. / a iy Dotarminism — Cunmated hosh_ value should _bo the sang. of fey whineven - cofcalat it. Bo Different Hash fonctions :— 1) Division Methad - Mis sizeof hash table hod = © mod M Don’t choo s- M29" or close to it Choos? ¥- MPa No. 3 Grew > he even oC» oddl => hod oad M<9? -_ _ =! eg haga3u> 1994 %97 =70 NC935) = \999%97 = 7) HG Potential’ Drowback—P Cconsecut! ve koalas Coe ipa ~to-aonsecutruehash-vadtas —