CSc 120 Introduction to Computer Programming

II

Adapted from slides by Dr. Saumya Debray

14:StacksandQueues

linear data structures

2

Linear data structures Alineardatastructureisacollec6onofobjectswithastraight-lineorderingamongthem

‒ eachobjectinthecollec6onhasaposi*on‒  foreachobjectinthecollec6on,thereisano6onoftheobjectbeforeitora-erit

3

Data structures we've seen

Linear

• Pythonlists(akaarrays)•  Linkedlists

Notlinear

• Dic6onaries•  Sets

4

Today's topic

Linear

• Pythonlists(akaarrays)•  Linkedlists•  Stacks• Queues• Dequeues

Notlinear

• Dic6onaries•  Sets

5

Keyproperty:thewayinwhichobjectsareaddedto,andremovedfrom,thecollec6on

stacks

6

Stacks Astackisalineardatastructurewhereobjectsareinsertedorremovedonlyatoneend

‒ allinser6onsanddele6onshappenatonepar6cularendofthedatastructure

‒  thisendiscalledthetopofthestack‒  theotherendiscalledthebo1omofthestack

7

inser6onsanddele6onshappenatoneend

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

8

stackboRom

stacktop

None

None

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

9

stackboRom

stacktop

5

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

10

stackboRom

stacktop

517

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

11

stackboRom

stacktop

51733

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

12

stackboRom

stacktop

517339

Stacks: insertion of values Inser6onofasequenceofvaluesintoastack:

51733943

13

stackboRom

stacktop

51733943

Stacks: insertion of values

51733943

14

stackboRom

stacktop

51733943

orderinwhichvalueswereinserted

Stacks: removal of values

15

stackboRom

stacktop

51733943

51733943Removingvaluesfromthestack:

orderinwhichvalueswereinserted

Stacks: removal of values

16

stackboRom

stacktop

51733

43

51733943Removingvaluesfromthestack:

43

orderinwhichvalueswereinserted

9

Stacks: removal of values

17

stackboRom

stacktop

517

43

51733943Removingvaluesfromthestack:

439

orderinwhichvalueswereinserted

933

Stacks: removal of values

18

stackboRom

stacktop

5

43

51733943Removingvaluesfromthestack:

43933

orderinwhichvalueswereinserted

93317

Stacks: removal of values

19

stackboRom

stacktop

43

51733943Removingvaluesfromthestack:

4393317

orderinwhichvalueswereinserted

933175

Stacks: removal of values

20

stackboRom

stacktop

5

43

51733943Removingvaluesfromthestack:

43933175

orderinwhichvalueswereinserted

93317

None

None

Stacks: removal of values

21

51733943Removingvaluesfromthestack:

43933175

orderinwhichvalueswereinserted

orderinwhichvalueswereremoved

Stacks: LIFO property

22

51733943Removingvaluesfromthestack:

43933175

orderinwhichvalueswereinserted

orderinwhichvalueswereremoved

valuesareremovedinreverseorderfromtheorderofinser6on

"LIFOorder"Lastin,Firstout

Methods for a Stack class •  Stack():createsanewemptystack

• push(item):addsitemtothetopofthestack‒ returnsnothing‒ modifiesthestack

• pop():removesthetopitemfromthestack‒ returnstheremoveditem‒ modifiesthestack

•  is_empty():checkswhetherthestackisempty‒ returnsaBoolean

23

Implementing a Stack class classStack:#thetopofthestackisthelastiteminthelistdef__init__(self):self._items=[]

defpush(self,item):self._items.append(item)

defpop(self):returnself._items.pop()

24

removesandreturnsthelastiteminalist

EXERCISE >>>s=Stack()>>>s.push(4)>>>s.push(17)>>>s.push(5)>>>x=s.pop()>>>y=s.pop()

25

←whatdoesthestackslooklikehere?whatarethevaluesofxandy?

EXERCISE >>>s=Stack()>>>s.push(4)>>>s.push(17)>>>s.push(5)>>>x=s.pop()>>>y=s.pop()>>>s.push(x)>>>s.push(y)

26

←whatdoesthestackslooklikehere?

stacks: applications

27

An application: balancing parens

28

IDLE(thePythonshell)matchesupledandrightparens(),brackets[],andbraces{}

Howdoesitfigureouthowfarbacktohighlight?

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

29

Stack (empty)

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

30

[

Stack

âßtop

push

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

31

[

[â

Stack

[

ßtop

ßtop

push

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

32

[

[â

Stack

[

[

[

[

ßtop

ßtop

push

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

33

[

[â

Stack

[

[

[

[

ßtop

matches:pop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

34

[

[â

Stack

[

[

[

[

ßtop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

35

[

[â

Stack

[

[

[

[

ßtop

ßtop

push

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

36

[

[â

Stack

[

[

[

[

ßtop

ßtop

matches:pop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

37

[

[â

Stack

[

[

[

[

ßtop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

38

[

[

â

Stack

[

[

[

[

ßtop

matches:pop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

39

[

[

â

Stack

[

[

[

[ ßtop

An application: balancing parens Basicidea:Matcheach]withcorresponding[

‒ similarlyfor(…)and{…}pairs

‒  Idea:o maintainastacko  onseeing'[':pusho  onseeing']':popthematchingsymbolExample:[1,2,[3,[4],5,[7]]]

Elabora6on:Haveeachstackelementkeeptrackoftheposi6onofits[

40

[

[

Stack

[

[

[

[ ßtop

EXERCISE

41

Writeafunc*onbalanced(s) thatreturnsTrueifthestringsisbalancedwithrespectto‘[‘and’]’andFalseotherwise.

classStack:def__init__(self):self._items=[]

defpush(self,item):self._items.append(item)defpop(self):returnself._items.pop()defis_empty():returnself._items==[]

Related: Displaying web pages Webpage

42

Related: Displaying web pages Webpage Displayconsidera5ons

43

mainheader:largefont,bold

secondaryheader:mediumfont,bold

italicsfont

boldfont

Ques5on:howdoesthewebbrowserfigureouthowmuchagivendisplayformatshouldinclude?E.g.,whichtextisinboldface,howmuchisinitalics,etc.

Related: Displaying web pages Webpage HTMLsource

44

Related: Displaying web pages Webpage HTMLsource

45

Related: Displaying web pages Webpage HTMLsource

46

Related: Displaying web pages HTMLsource

47

"tags"

<h1>:"openheader1"</h1>:"closeheader1"<h2>:"openheader2"</h2>:"closeheader2"<i>:"openitalics"</i>:"closeitalics"

…

Related: Displaying web pages Webpage HTMLsource

48

Figuringouthowtodisplaydifferentpartsofthewebpagerequiresmatchingup“open-”and“close-”HTMLtags.Thisisessen6allythesameproblemasbalancingparens.

EXERCISE >>>s1=Stack()>>>s1.push(4)>>>s1.push(17)>>>s2=Stack()>>>s2.push(s1.pop())>>>s2.push(s1.pop())>>>s1.push(s2.pop())>>>s1.push(s2.pop())

49

←whatdoesthestacks1looklikehere?

Abstract Data Types

50

Abstract Data Types Anabstractdatatype(ADT)describesasetofdatavaluesandassociatedopera6onsthatarespecifiedindependentofanypar6cularimplementa6on.AnADTisalogicaldescrip6onofhowweviewthedataandtheopera6onsallowedonthatdata.

o describeswhatthedatarepresentso nothowisthedatarepresented

Thedataisencapsulated.

51

Abstract Data Types Becausethedataisencapsulatedwecanchangetheunderlyingimplementa6onwithoutaffec6ngthewaytheADTbehaves.

o thelogicaldescrip6onremainsthesameo theopera6onsremainthesame

52

EXERCISE

53

Hypothe*cal:Python7hasjustbeenreleasedandbuilt-inlistsareinefficient.Infact,allopera*onsareO(n2).Avoidtheseinefficienciesbyimplemen*ngtheStackclassusingLinkedLists.

queues

54

A Queue ADT Aqueueisalineardatastructurewhereinser6onsanddele6onshappenatdifferentends

‒  inser6onshappenatoneend(thequeue's"back“,or“tail”)

‒ dele6onshappenattheotherend(thequeue's"front“,or“head”)

55

dele6onsoccuratthisend(head)

inser6onsoccuratthisend

(tail)

Queues: insertion of values Inser6onofasequenceofvaluesintoaqueue:

56

NoneNonequeueback

queuefront

51733943

Queues: insertion of values

57

queueback

queuefront

5

Inser6onofasequenceofvaluesintoaqueue: 51733943

Queues: insertion of values

58

queueback

queuefront

17 5

Inser6onofasequenceofvaluesintoaqueue: 51733943

Queues: insertion of values

59

queueback

queuefront

33 17 5

Inser6onofasequenceofvaluesintoaqueue: 51733943

Queues: insertion of values

60

queueback

queuefront

9 33 17 5

Inser6onofasequenceofvaluesintoaqueue: 51733943

Queues: insertion of values

61

queueback

queuefront

43 9 33 17 5

Inser6onofasequenceofvaluesintoaqueue: 51733943

51733943

Queues: insertion of values

62

queueback

queuefront

43 9 33 17 5

orderofinser*on

51733943

Queues: removal of values

63

queueback

queuefront

43 9 33 17 5

orderofinser*on

Removingvaluesfromthisqueue:

51733943

Queues: removal of values

64

queueback

queuefront

43 9 33 5

orderofinser*on

Removingvaluesfromthisqueue: 5

17

51733943

Queues: removal of values

65

queueback

queuefront

43 9 17 5

orderofinser*on

Removingvaluesfromthisqueue: 517

33

51733943

Queues: removal of values

66

queueback

queuefront

43 33 17 5

orderofinser*on

Removingvaluesfromthisqueue: 51733

9

51733943

Queues: removal of values

67

queueback

queuefront

9 33 17 5

orderofinser*on

Removingvaluesfromthisqueue: 517339

43

51733943

Queues: removal of values

68

queueback

queuefront

43 9 33 17 5

orderofinser*on

Removingvaluesfromthisqueue: 51733943

NoneNone

Queues: removal of values

69

51733943

orderofinser*on

51733943orderofremoval

51733943

Queues: FIFO property

70

orderofinser*on

51733943orderofremoval

valuesareremovedinorderinwhichtheyareinserted

"FIFOorder"Firstin,Firstout

Methods for a queue class •  Queue():createsanewemptyqueue•  enqueue(item):addsitemtothebackofthequeue

‒ modifiesthequeue‒  returnsnothing

•  dequeue():removesandreturnstheitematthefrontofthequeue‒  returnstheremoveditem‒ modifiesthequeue

•  is_empty():checkswhetherthequeueisempty‒  returnsaBoolean

•  size():returnsthesizeofthequeue‒  returnsaninteger

71

Implementing a queue class • Useabuilt-inlistfortheinternalrepresenta6on

‒ Pythonlistscanbeaddedattothefrontorattheend•  Firstimplementa6on:

‒  theheadisthe0thelement‒  thetailisthenthelement

•  Secondimplementa6on‒  theheadisthenthelement‒  thetailisthe0thelement

72

Implementing a Queue class I classQueue:#thefrontofthequeueisthefirstiteminthelistdef__init__(self):self._items=[]

defenqueue(self,item):self._items.append(item)

defdequeue(self):returnself._items.pop(0)

73

removesandreturnsitem0fromthelist

0 1 2 3 4 5

�

head

�

tail

Implementing a Queue class II classQueue:#thefrontofthequeueisthelastiteminthelistdef__init__(self):self._items=[]

defenqueue(self,item):self._items.insert(0,item)

defdequeue(self):returnself._items.pop()

74

removesandreturnsthelastiteminthelist

0 1 2 3 4 5�

tail

�

head

EXERCISE >>>q=Queue()>>>q.enqueue(4)>>>q.enqueue(17)>>>x=q.dequeue()>>>q.enqueue(5)>>>y=q.dequeue()

75

←whatarethevaluesofxandy?

EXERCISE >>>q=Queue()>>>q.enqueue(4)>>>q.enqueue(17)>>>x=q.dequeue()>>>y=q.dequeue()>>>q.enqueue(y)>>>q.enqueue(x)>>>q.enqueue(y)

76

←whatdoesthequeueqlooklikehere?

queues: applications

77

Application 1: Simulation •  Typicalapplica6onssimulateproblemsthatrequiredatatobemanagedinaFIFOmanner‒ Hotpotato

o  Kidsstandinacircleandpassa“hotpotato”aroundun6ltoldtostop.Thepersonholdingthepotatoistakenoutofthecircle.Theprocessisrepeatedun6lonlyonepersonremains.

‒ Generalized:Givennelements,eliminateeverykthelementrepeatedlyun6lonly1elementisled.Whatwastheoriginalposi6onoftheremainingelement?

• Useasimula*ontodeterminewhichelementremains.

78

EXERCISE Problem:Givennelements,eliminateeverykthelementrepeatedlyun6lonly1elementisled.Whatwastheoriginalposi6onoftheremainingelement?useaqueuetosimulatethecirclenisthenumberofelementstoputintothequeuewhilethereismorethanoneelementinthequeueeliminateeverykthelement

Whatopera6onstakeanelementfromthefrontofthequeueandplaceitatthebackofthequeue?

79

General solution for k=2 •  Givennelements,eliminateeverykthelementrepeatedlyun6lonly1elementisled.Whatwastheoriginalposi6onoftheremainingelement?

•  Whenk=2,theoriginalposi6oncanbederivedfromthebinaryrepresenta6onofn.

Takethefirstdigitofthebinaryrepresenta6on.MoveittotheendTheresultistheoriginalposi6on.Ex:n=41,k=2Inbinaryn=101001Therefore,theoriginalposi6on(inbinary)is010011and010011=24+21+20=19hRps://en.wikipedia.org/wiki/Josephus_problem#CITEREFDowdyMays1989

80

Application 2 : Simulation •  Supposeweareopeningagrocerystore.Howmanycheckoutlinesshouldweputin?‒  toofew⇒longwait6mes,unhappycustomers‒  toomany⇒wastedmoney,space

• Usesimula*onsofthecheckoutprocesstoguidethedecision‒ studyexis6ngstorestofigureouttypicalshoppingandcheckout6mes

‒ es6mateno.ofcustomersexpectedatthenewloca6on‒ runsimula6onstodeterminecustomerwait6meandcheckoutlineu6liza6onunderdifferentscenarios

81

Discrete event simulation

82

…

queue

…

arrivalsdepartures

arrivalratedistribu6on

departureratedistribu6on

servers

customersByvaryingtheparametersofthesimula6on(arrivalanddeparturerates,no.ofservers)wecantryoutdifferentscenarios

Summary •  Stacksandqueuesareabstractdatatypes(ADTs)

‒ similarinthattheyarebothlineardatastructures‒  itemscanbethoughtofasarrangedinaline‒ eachitemhasaposi6onandabefore/aderrela6onshipwiththeotheritems

•  Theydifferinthewayitemsareaddedandremoved‒ stacks:itemsaddedandremovedatoneend

o  resultsinLIFObehavior‒ queues:itemsaddedatoneend,removedattheother

o  resultsinFIFObehavior

•  Theyfindawiderangeofapplica6onsincomputerscience

83

A Deque ADT

Adequeisalineardatastructurewhereinser6onsanddele6onshappenatbothends

84

inser6onsanddele6onsoccuratthisend(head)

inser6onsanddele6onsoccuratthisend

(tail)