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Teach A level Compu/ng: Algorithms and Data

Structures

EliotWilliams

@MrEliotWilliams

Course Outline

1 Representa9onsofdatastructures:Arrays,tuples,Stacks,Queues,Lists

2 RecursiveAlgorithms(&listsaswedidn’tquitegettherelast9me…)

3 SearchingandSor9ng-EWwillbelate!

4 HashingandDic9onaries,GraphsandTrees

5 Depthandbreadthfirstsearching;treetraversals

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Procedures Towriterecursiveprogramsweneedagoodunderstandingof

procedures

Why Procedures?

• Codeorganisa9on•  Proceduresallowcodetobeorganisedinparts•  Top-downdevelopment

• Codereuse•  Thelibrary•  Procedureswithparameters:exis9ngcode,yourdata

• Recursion

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• Procedures:•  0ormoreinputs•  0ormoreoutputs•  Sideeffects(printstatements,globalvariablesetc)

•  Func9ons•  1ormoreinputs•  1output•  Nosideeffects

Procedures & Func/ons

Crea/ng a procedure in python

• Whatistheresult?•  Isvariableachanged?

def fun1(p):! p = p + 1! return p!!a = 1!b = fun1(a)!print("argument a =", a)!print("return value b =", b)!

Name

Parameter

Returnexpression

Func9oncall

Argument

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Procedures Call Tree • Onefunc9oncallsanother

def doub(p):! return p*2!!def quad(p):! d = doub(p)! return doub(d)!!n = int(input("Number: "))!print("4 x", n, "=", quad(n))!

main

quad

doub

call

call return

return

Procedures Scope •  Scope:dic9onaryofvariables

def doub(p):! return p*2!!def quad(p):! d = doub(p)! return doub(d)!!n = int(input("Number: "))!print("4 x", n, "=", quad(n))!

nàinteger(3)doubà…codequadà…code

pàinteger(3)dàinteger(6)

pàinteger(6)

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• Whatistheresult?•  Isthelistvariableachanged?

deffun1(thelist):thelist.append(41)myl=[2,3,4]fun1(myl)print("myl=",myl)

Pass by reference or by value

Justlikeassignmentalist:…variablereferstothelist…parameterreferstothelistNoglobal:referenceisreadAnymutableobjectwillwillbehavethisway…….

big

• Defineafunc9onbigthattakes2inputsandreturnsthebiggest!

defbig(a,b):ifprint(big(2,3))print(big(4,4))

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big

• Defineafunc9onbigthattakes2inputsandreturnsthebiggest!

defbig(a,b):ifa>b:returnareturnbprint(big(2,3))print(big(4,4))

big3

defbig3(a,b,c):ifa>b:ifa>c:returnaelse:returncelse:ifb>c:returnbelse:returnc

defbig(a,b):ifa>b:returnareturnb

defbig3(a,b,c):d=big(a,b)returnbig(d,c)

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Recursion Recursion

Recursion

• Recursionincomputerscienceisamethodwherethesolu9ontoaproblemdependsonsolu9onstosmallerinstancesofthesameproblem(asopposedtoitera9on).[1]Theapproachcanbeappliedtomanytypesofproblems,andrecursionisoneofthecentralideasofcomputerscience.[2]

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What do you need to write every possible computer program….. • Complexques9on–Babbage'sanaly9calEnginehad:•  Thearithme9cfunc9ons+,−,×where−indicates"proper"subtrac9onx−y=0ify≥x•  Anysequenceofopera9onsisanopera9on•  Itera9onofanopera9on(repea9ngn9mesanopera9onP)•  Condi9onalitera9on(repea9ngn9mesanopera9onPcondi9onalonthe"success"oftestT)•  Condi9onaltransfer(i.e.condi9onal"goto").

• Anotheranswerisprocedures,simplearithme9cwiththecomparisons,and"if"statements

Predict & Explain what will this do

importturtle

myTurtle=turtle.Turtle()

myWindow=turtle.Screen()

deffoo(bar):

ifbar>0:

myTurtle.forward(bar)

myTurtle.right(90)

foo(bar-5)

foo(100)

myWindow.exitonclick()

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Our first Example - Spiral

importturtle

myTurtle=turtle.Turtle()

myWindow=turtle.Screen()

defspiral(side):

ifside>0:

myTurtle.forward(side)

myTurtle.right(90)

spiral(side-5)

spiral(100)

myWindow.exitonclick()

Modify

•  Changetheanglebetweenthebranches•  ChangethethicknessofthebranchessothatasthebranchLengetssmaller,thelinegetsthinner.•  ChangethecolourofthebranchessothattheystartbrownandasthebranchLengetsveryshortitisgreen.•  ChangetherecursivecallbranchLensothatinsteadofalwayssubtrac9ngthesameamountyousubtractarandomamountinsomerange

Hints:turtle.width(width)turtle.color(“blue”)

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Our first recursive program: Factorial

•  Inmyopinionnumbersequencestendtobetoocomplexforafirstexample• Recursionisathresholdconcept•  Newconcept•  Differentwayofthinkingaboutrepe99on•  Newterminology

• Wewanttokeepitsimpleatfirst•  Cogni9veloadtheory

Our first recursive program

defwibbler():print("wibble“)returnwibbler()

wibbler()#whatsgoingtohappen?

• what'sgoingtohappen?

• Doesthisworklikealoop?• Whattypeofloopdoesitworklike?

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A slight modifica/on

defwibbler(n):print("Wibble",n)returnwibbler(n+1)print(wibbler(1))

• Howmany9mesdoesitrun?

An improved wibbler……

defwibbler(n):if(n>0):print("wibble")returnwibbler(n-1)wibbler(3)

• What’sgoingtohappen

• Whatloopstructureisthislike?

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What's the difference?

defwibbler(n):if(n>0):print("wibble")returnwibbler(n-1)

defwibble(n):if(n==1): return("wibble")return("wibble"+wibble(n-1))

What's the difference?

defwibbler(n):if(n>0):print("wibble")returnwibbler(n-1)wibbler(3)

defwibble(n):if(n==1): return("wibble")return("wibble"+wibble(n-1))

print(wibble(3))

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defwibble(n):if(n==1): return("wibble")return("wibble"+wibble(n-1))

• Definesomethingintermsofitself•  RecursiveCase–simplifiestheproblemandmovestowardsthebasecasewitharecursivecall•  BaseCase–smallestinstance(Youmayneedmorethanonebasecase)

BaseCase–stopcondi9onRecursiveCase

Task - allstar

•  Givenastring,computerecursivelyanewstringwherealltheadjacentcharsarenowseparatedbya"*".

•  allStar("hello")→"h*e*l*l*o"•  allStar("ab")→"a*b"•  allStar("a")→"a"Iden9fyawaytobreakaproblemuprecursively….LookforaRecursiveCaseandaBaseCasedefallStar(string):

if(??????): return???????return(?????????????)

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Task /me

• Reverse

What's going on………………………….

Achildcouldn'tsleep,sohermothertoldherastoryaboutalizlefrog,whocouldn'tsleep,sothefrog'smothertoldherastoryaboutalizlebear,

whocouldn'tsleep,sothebear'smothertoldherastoryaboutalizleweasel...

whofellasleepandthelizlebearfellasleep;

andthelizlefrogfellasleep;andthechildfellasleep.

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•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*f(3)f(3)=3*3f(3)=3*f(2)

Factorial revisted

f(2)=2*f(1)

f(1)=1

•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*f(3)f(3)=3*3f(3)=3*f(2)

Factorial revisted

f(2)=2*1

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•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*f(3)f(3)=3*3f(3)=3*f(2)

Factorial revisted

f(2)=2

•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*f(3)f(3)=3*3f(3)=3*2

Factorial revisted

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•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*f(3)f(3)=3*3f(3)=6

Factorial revisted

•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=4*6

Factorial revisited

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•  f(n)=n*f(n-1)•  f(1)=1

•  f(4)=24

Factorial revisted

Why use recursion

•  Recursionisamethodofsolvingproblemsbasedonthedivideandconquermentality•  Some9mesitseasiertosolvethinkofaproblemintermsofitself

•  Q:Doesusingrecursionusuallymakeyourcodefaster?•  A:No.•  Q:Doesusingrecursionusuallyuselessmemory?•  A:No.•  Q:Thenwhyuserecursion?•  A:Itsome9mesmakesyourcodemuchsimpler!

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Predict-Explain-Modify-Create

• Predict–givenaworkingprogram,whatdoyouthinkitwilldo?(atahighlevelofabstrac9on)• Run–runitandtestyourpredic9on•  Explain/Ar9culate–getintothenizygrizy.Whatdoeseachlineofcodemean?(lowlevelofabstrac9on).Lotsofac9vi9eshere:trace,annotate,explain,talkabout,iden9fyparts,etc….• Modify–edittheprogramtomakeitdodifferentthings(highandlowlevelsofabstrac9on)Design/Create–designanewprogramthatusesthesamenizygrizybutthatsolvesanewproblem.

Linked Lists Animplementa9onofthelistabstrac9ons

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Linked List Concept

•  Eachentryhas•  Avalue•  Apointertothenextentry

• Keepapointertothefrontentry•  ThepointerofthelastentryisNone

b c d e f

front back

•  Wecouldrepresentthisinpythonby•  list=[['James',2],['Bob',0],['Sarah',-1]]•  startpos=1•  length=3

•  Wewouldneedproceduresto•  findavaluesposi9on•  Findanpointersposi9on•  Add•  Delete(andupdatethepreviouspointer–usingfindapointer)•  Printinorder•  Insertanewvalue

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Exercise

• Redrawlista|er:•  appendinganewentryattheend•  inser9ngbeforeentryzero•  inser9ngbeforeentry3

b c d e f

front back

Linked List Index

• Countalongthelisttoentryi• Returnthevalue

pointer = front count = 0 while count < i: pointer ß next of current entry count = count + 1 return the value of current entry

myList.index(i)

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Linked List Update

• Countalongthelisttoentryindex• Replacevaluewithnewvalue

pointer = front count = 0 while count < idx: pointer ß next of currentEntry count = count = 1 currentEntry.value = newValue

myList.update(idx, newValue)

Linked List Insert

• Countalongthelisttoentryidx-1•  Insertanewentry•  Nextpointerofcurrententrypointstonewentry•  Nextpointerofnewentrypointstofollowingentry

myList.insert(idx, newValue)