1/27/12. Vectors: Outline and Reading. Chapter 6: Vectors, Lists and Sequences. The Vector ADT. Applications of Vectors. Array based Vector: Insertion

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1 Chater 6: ectors, Lists ad Sequeces ectors: Outlie ad Readig The ector ADT ( 6.1.1) Array-based imlemetatio ( 6.1.2) Nacy Amato Parasol Lab, Det. CSE, Texas A&M Uiversity Ackowledgemet: These slides are adated from slides rovided with Data Structures ad Algorithms i C++, Goodrich, Tamassia ad Mout (Wiley ) htt://arasol.tamu.edu ectors 2 The ector ADT The ector ADT exteds the otio of array by storig a sequece of arbitrary objects A elemet ca be accessed, iserted or removed by secifyig its rak (umber of elemets recedig it) A excetio is throw if a icorrect rak is secified (e.g., a egative rak) Mai vector oeratios: elematrak(it r): returs the elemet at rak r without removig it relaceatrak(it r, Object o): relace the elemet at rak r with o isertatrak(it r, Object o): isert a ew elemet o to have rak r removeatrak(it r): removes the elemet at rak r Additioal oeratios size() ad isemty() ectors 3 Alicatios of ectors Direct alicatios Sorted collectio of objects (elemetary database) Idirect alicatios Auxiliary data structure for algorithms Comoet of other data structures ectors 4 Array-based ector Use a array of size N A variable kees track of the size of the vector (umber of elemets stored) Oeratio elematrak(r) is imlemeted i O(1) time by returig [r] 0 N-1 ectors 5 Array based ector: Isertio I oeratio isertatrak(r,o) we eed to make room for the ew elemet by shiftig forward the r elemets [r],, [ 1] I the worst case (r = 0), this takes O() time o ectors 6 1

2 Deletio Performace I oeratio removeatrak(r) we eed to fill the hole left by the removed elemet by shiftig backward the r 1 elemets [r + 1],, [ 1] I the worst case (r = 0), this takes O() time o ectors 7 I the array based imlemetatio of a ector The sace used by the data structure is O() Size(), isemty(), elematrak(r) ad relaceatrak(r,o) ru i O(1) time isertatrak(r,o) ad removeatrak(r) ru i O() time If we use the array i a circular fashio, isertatrak(0,o) ad removeatrak(0) ru i O(1) time I a isertatrak(r,o) oeratio, whe the array is full, istead of throwig a excetio, we ca relace the array with a larger oe ectors 8 Exercise: Imlemet the Deque ADT usig ector fuctios Deque fuctios: first(), last(), isertfirst(e), isertlast(e), removefirst (), removelast(), size(), isemty() ector fuctios: elematrak( r), relaceatrak(r,e), isertatrak (r,e), removeatrak(r ), size(), isemty() ectors 9 Exercise Solutio: Imlemet the Deque ADT usig ector fuctios Deque fuctios: first(), last(), isertfirst(e), isertlast(e), removefirst(), removelast(), size(), isemty() ector fuctios: elematrak( r), relaceatrak(r,e), isertatrak(r,e), removeatrak (r ), size(), isemty() Deque fuctio : Realizatio usig ector Fuctios size() ad isemty() fcs ca simly call ector fcs directly first() => elematrak(0) last() => elematrak(size()-1) isertfirst(e) => isertatrak(0,e) isertlast(e) => isertatrak(size(), e) removefirst() => removeatrak(0) removelast() => removeatrak(size()-1) ectors 10 STL vector class Iterators Fuctios i the STL vector class (icomlete) Size(), caacity() - retur #elts i vector, #elts vector ca hold emty() - boolea Oerator[r] - returs referece to elt at rak r (o idex check) At( r) - returs referece to elt at rak r (idex checked) Frot(), back() - retur refereces to first/last elts ush_back(e) - isert e at ed of vector o_back() - remove last elt vector() - creates a vector of size Similarities & Differeces with book s ector ADT STL assigmet v[r]=e is equivalet to v.relaceatrak(r,e) No direct STL couerarts of isertatrak( r) & removeatrak( r) STL also rovides more geeratl fcs for isertig & removig from arbitrary ositios i the vector - these use iterators ectors 11 A iterator abstracts the rocess of scaig through a collectio of elemets Methods of the ObjectIterator ADT: boolea hasnext() object ext() reset() Exteds the cocet of ositio by addig a traversal caability May be imlemeted with a array or sigly liked list A iterator is tyically associated with a aother data structure We ca augmet the Stack, Queue, ector, ad other cotaier ADTs with method: ObjectIterator elemets() Two otios of iterator: sashot: freezes the cotets of the data structure at a give time dyamic: follows chages to the data structure ectors 12 2

3 Iterators Some fuctios suorted by STL cotaiers Begi(), ed() - retur iterators to begiig or ed of cotaier Isert(I,e) - isert e just before the ositio idicated by iterator I (aalogous to our isertbefore()) Erase(I) - removes the elt at the ositio idicated by I (aalogous to our remove()) The fuctios ca be used to isert/remove elts from arbitrary ositios i the STL vector ad list ector Summary ector Oeratio Comlexity for Differet Imlemetatios RemoveAtRak(r), IsertAtRak(r,o) elematrak(r), RelaceAtRak(r,o) Array Fixed-Size or Exadable O(1) Best Case (r=0,) O() Worst Case O() Average Case O(1)? Size(), isemty() O(1)? List Sigly or Doubly Liked? ectors 13 ectors 14 Outlie ad Readig Lists ad Sequeces Sigly liked list Positio ADT ( 6.2.1) List ADT ( 6.2.2) Doubly liked list ( 6.2.3) Sequece ADT ( 6.3.1) Imlemetatios of the sequece ADT ( ) Iterators ( 6.2.5) ectors 15 1/27/12 04:04 ectors 16 Positio ADT List ADT ( 5.2.2) The Positio ADT models the otio of lace withi a data structure where a sigle object is stored A secial ull ositio refers to o object. Positios rovide a uified view of diverse ways of storig data, such as a cell of a array a ode of a liked list Member fuctios: Object& elemet(): returs the elemet stored at this ositio bool isnull(): returs true if this is a ull ositio ectors 17 The List ADT models a sequece of ositios storig arbitrary objects establishes a before/after relatio betwee ositios It allows for isertio ad removal i the middle Query methods: isfirst(), islast() Geeric methods: size(), isemty() Accessor methods: first(), last() before(), after() Udate methods: relaceelemet(, o), swaelemets(, q) isertbefore(, o), isertafter(, o), isertfirst(o), isertlast(o) remove() 18 3

4 List ADT List ADT Query methods: isfirst(), islast() : retur boolea idicatig if the give ositio is the first or last, res. Accessor methods first(), last(): retur the ositio of the first or last, res., elemet of S a error occurs if S is emty before(), after(): retur the ositio of the elemet of S recedig or followig, res, the oe at ositio a error occurs if S is emty, or is the first or last, res., ositio ectors 19 Udate Methods relaceelemet(, o) Relace the elemet at ositio with e swaelemets(, q) Swa the elemets stored at ositios & q isertbefore(, o), isertafter(, o), Isert a ew elemet o ito S before or after, res., ositio Outut: ositio of the ewly iserted elemet isertfirst(o), isertlast(o) Isert a ew elemet o ito S as the first or last, res., elemet Outut: ositio of the ewly iserted elemet remove() Remove the elemet at ositio from S ectors 20 Exercise: Describe how to imlemet the followig list ADT oeratios usig a sigly-liked list list ADT oeratios: first(), last(), before(), after() For each oeratio, exlai how it is imlemeted ad rovide the ruig time A sigly liked list cocrete data structure cosists of a sequece of odes Each ode stores elemet lik to the ext ode elem ext ode A B C D ectors 1/27/ :58 Exercise: Describe how to imlemet the followig list ADT oeratios usig a doubly-liked list list ADT oeratios: first(), last(), before(), after() For each oeratio, exlai how it is imlemeted ad rovide the ruig time Doubly-Liked List Nodes imlemet Positio ad store: elemet header lik to revious ode lik to ext ode Secial trailer ad header odes rev elem ext ode trailer elemets ectors 1/27/ :58 Isertio Deletio We visualize oeratio isertafter(, X) which returs ositio q We visualize remove(), where = last() A B C A B C D A B q C A B C q X D A B X C ectors 23 A B C ectors 24 4

5 Performace I the imlemetatio of the List ADT by meas of a doubly liked list The sace used by a list with elemets is O() The sace used by each ositio of the list is O(1) All the oeratios of the List ADT ru i O(1) time Oeratio elemet() of the Positio ADT rus i O(1) time STL list class Fuctios i the STL list class Size() - retur #elts i list, emty() - boolea Frot(), back() - retur refereces to first/last elts Push_frot(e), ush_back(e) - isert e at frot/ed Po_frot(), o_back() - remove first/last elt List() - creates a emty list Similarities & Differeces with book s List ADT STL frot() & back() corresod to first() & last() excet the STL fuctios retur the elemet & ot its ositio STL ush() & o() are equiv to List ADT isert ad remove whe alied to the begiig & ed of the list STL also rovides fcs for isertig & removig from arbitrary ositios i the list - these use iterators ectors 25 ectors 26 List Summary List Oeratio Comlexity for differet imlemetatios first(), last(), after() isertafter(,o), relaceelemet(,o), swaelemets(,q) before(), isertbefore(,o), remove() List Sigly-Liked O(1) O() WC & AC O(1) BC List Doubly- Liked O(1) O(1) Size(), isemty() O(1) O(1) ectors 27 Sequece ADT The Sequece ADT is the uio of the ector ad List ADTs Elemets accessed by Rak, or Positio Geeric methods: size(), isemty() ector-based methods: elematrak(r), relaceatrak(r, o), isertatrak(r, o), removeatrak(r) List-based methods: first(), last(), before(), after(), relaceelemet(, o), swaelemets(, q), isertbefore(, o), isertafter(, o), isertfirst(o), isertlast (o), remove() Bridge methods: atrak(r), rakof() ectors 28 Alicatios of Sequeces Array-based Imlemetatio The Sequece ADT is a basic, geeralurose, data structure for storig a ordered collectio of elemets Direct alicatios: Geeric relacemet for stack, queue, vector, or list small database (e.g., address book) Idirect alicatios: Buildig block of more comlex data structures ectors 29 We use a circular array storig ositios A ositio object stores: Elemet Rak Idices f ad l kee track of first ad last ositios S f elemets ositios ectors 30 l 5

6 Sequece Imlemetatios Oeratio Array List size, isemty 1 1 atrak, rakof, elematrak 1 first, last, before, after 1 1 relaceelemet, swaelemets 1 1 relaceatrak 1 isertatrak, removeatrak isertfirst, isertlast 1 1 isertafter, isertbefore 1 remove 1 ectors 31 6