BBM#101# #Introduc/on#to# Programming#I# Fall$2013,$Lecture$617$

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1 BBM#101# #Introduc/on#to# Programming#I# Fall$2013,$Lecture$617$ Instructors:AykutErdem,ErkutErdem,FuatAkal TAs:YasinSahin,AhmetSelmanBozkir,GultekinIsik, OguzhanGuclu Today# Func/ons# ParameterLists ReturnValues Prototypes Variable#Scopes# BlockStructure GlobalandLocalVariables Recursion# 1 2 Today# Func/ons# Defini@ons Invoca@on ParameterLists ReturnValues Prototypes Variable#Scopes# BlockStructure GlobalandLocalVariables Sta@cVariables Recursion# Introduc/on# Structured$ProgrammingisaproblemHsolvingstrategyanda programmingmethodologythatincludesthefollowingtwo guidelines: Theflowofcontrolinaprogramshouldbeassimpleas possible. Theconstruc@onofaprogramshouldembodytop1down$design. 3 4

2 TopBdown#Design# Top1down$design(stepwise$refinement,ordivide$and$conquer) consistsofrepeatedlydecomposingaproblemintosmaller problems. Aprogramisconstructedfromsmallerpieces(components, modules) Eachpieceismoremanageablethantheoriginalprogram Func/ons# Bossasksworkertocompletetask 5 6 Math#Library#Func/ons# Math#Library#Func/ons# Mathlibraryfunc@ons performcommonmathema@calcalcula@ons #include#<math.h># # Formatforcallingfunc@ons Func/onName(argument);# Ifmul@plearguments,usecommaHseparatedlist y = sqrt( ); Callsfunc@onsqrt,whichreturnsthesquarerootofitsargument ArgumentsmaybeanyrHvalue(constants,variables,or expressions) Func/on#Header# intabs(intnum) doublefabs(doublenum) doublepow(doublex,doubley) intrand(void) doublesin(doubleangle) doublecos(doubleangle) doublesqrt(doublenum) Descrip/on# Returnstheabsolutevalueofaninteger element Returnstheabsolutevalueofadoubleprecision element. Returnsxraisedtothepowerofy. Returnsarandomnumber Returnsthesineofanangle;theangleshouldbe inradius. Returnsthecosineofanangle;theangleshould beinradius. Returnsthethesquarerootofadouble 7 8

3 Math#Library#Func/ons#(Example)# Howtocodesquarerootof(x1#B#x2) 2 #+#(y1#b#y2) 2# byusing math.hlibraryfunc@ons? a = x1 x2; b = y1 y2; c = pow(a, 2) + pow(b, 2); d = sqrt(c); Func/ons# WehavealreadywriYen/calledsomefunc@onsbefore. /* Welcome to BBM 101 */ int main(void) { printf( Hello world\n ); mainisafunc@onthatmustexistineverycprogram. prinuisalibraryfunc@onwhichwehavealreadyusedinourprogram. Let s create and call our own functions now 9 10 Func/on#Defini/on# Syntax type name (parameters){ variables; statements; nameisthenameofthefunc@on typeisthetypeofthereturnedvaluebythefunc@on voidmeansthefunc@onreturnsnothing Func@onsreturnintvalueifnothingisspecified parametersspecifythetypesandnamesoftheparameters separatedbycomma Func/on#Returning#a#Value#(Example)# Let sdefineafunc@ontocomputethecubeofanumber: int cube ( int num ) { int result; result = num * num * num; return result; Thisfunc@oncanbecalledas: n = cube(5); 11 12

4 void#func/on#(example)# Func/on#Invoca/on# /* function definition */ void print_message(void){ printf( A message for you: ); printf( Have a nice day\n ); int main(void){ /* function invocation */ print_message(); Aprogramismadeupofoneor morefunc@ons,oneofthembeing main(). Whenaprogramencountersa func@on,thefunc@oniscalledor invoked. A\erthefunc@ondoesitswork, programcontrolispassedbackto thecallingenvironment,where programexecu@oncon@nues. Function1(){ return; Function2(){ return; int main(){ Function1(); Function2(); return; The#return#Statement# Whenareturnstatementisexecuted,theexecu@onofthe func@onisterminatedandtheprogramcontrolisimmediately passedbacktothecallingenvironment. Ifanexpressionfollowsthekeywordreturn,thevalueofthe expressionisreturnedtothecallingenvironmentaswell. Areturnstatementcanbeoneofthefollowingtwoforms: return; return expression; Examples:# # return; return 1.5; return result; return a+b*c; return x < y? x : y; The#return#Statement#(Example)# Defineafunc@ontocheckifaskedyearisaleapyear int IsLeapYear(int year){ return ( ((year % 4 == 0) && (year % 100 = 0)) Thisfunc@onmaybecalledas: if (IsLeapYear(2005)) else (year % 400 == 0) ); printf( 29 days in February.\n ); printf( 28 days in February.\n ); 15 16

5 Example:#Find#minimum#of#two#integers# Func/on#Parameters# int min(int a, int b){ if (a < b) return a; else return b; int main (void){ int j, k, m; printf( Input two integers: ); scanf( %d %d, &j, &k); m = min(j, k); Input two integers: 11 3 The mininum is 3. Afunc@oncanhavezeroormoreparameters. Theformal$parameter$list$indeclara@onheader int f (int x, double y, char c); Theactual$parameter$list$infunc@oncalling: value = f(age, 100*score, initial); Parameter variables and their types are declared here. Cannot be told what their types are from here. printf( \nthe minimum is %d.\n, m); Rules#for#Parameter#Lists# Thenumberofparametersintheactualandformalparameter listsmustbeconsistent. Parameterassocia@onisposiGonal:$thefirstactual$parameter matchesthefirstformal$parameter,thesecondmatchesthe second,andsoon. CallBbyBValue#Invoca/on# Eachargumentisevaluated,anditsvalueisusedlocallyinplace ofthecorrespondingformalparameter. Ifavariableispassedtoafunc@on,thestoredvalueofthat variableinthecallingenvironmentwillnotbechanged. InC,allcallsarecallHbyHvalue. Actual$parametersandformal$parametersmustbeof compa@ble$data$types. Actual$parametersmaybeavariable,constant,anyexpression matchingthetypeofthecorrespondingformalparameter

6 Func/on#Call# Func/on#Call#(Example)# # t = cubesum(i); j = cubesum(t); isequivalentto j = cubesum(cubesum(i)); int compute_sum (int n){ int sum = 0; for ( ; n > 0; --n) sum += n; printf( %d, n); return sum; int main (void){ int n = 3, sum; printf( %d, n); sum = compute_sum(n); printf( %d, n); printf( %d, sum); Example:#Find#maximum#of#three#integers# int maximum(int a, int b, int c){ int max = a; if (b > max) max = b; if (c > max) max = c; return max; int main (void){ int j, k, l, m; printf( Input three integers: ); scanf( %d %d %d, &j, &k, &l); Input three integers: The maxinum is 11. Func/on#Prototypes# Generalformforafunc@onprototypedeclara@on: return_type function_name (parameter-type-list) Usedtovalidatefunc@ons Prototypeonlyneedediffunc@ondefini@oncomesa\eruseinprogram Thefunc@onwiththeprototype int maximum( int, int, int ); #(Takesin3ints,returnsanint) printf( \nthe maximum is %d.\n, maximum(j, k, l)); 23 24

7 Using#Func/on#Prototypes# Today# int max (int a, int b){... int min (int a, int b){... int main(void){... min(x,y); max(u,v);... = int max(int,int); int min(int,int); int main(void){ min(x,y); max(u,v);... int max (int a, int b){... int min (int a, int b){... Func/ons# Defini@ons Invoca@on ParameterLists ReturnValues Prototypes Variable#Scopes# BlockStructure GlobalandLocalVariables Sta@cVariables Recursion# Block#Structure#and#Variable#Scope# int total, count; int main(int argc, const char * argv[]){ total = count = 0; { int count = 0; while (1) { if (count > 10) break; total += count; count++; printf("%d\n", count); count++; printf("%d\n", count); Global$countvariableis validinthewholeprogram. Local$countvariableis onlyvalidinthered blockhere External#Variables# Localvariablescanonlybeaccessedinthefunc@oninwhich theyaredefined. Ifavariableisdefinedoutsideanyfunc@onatthesamelevelas func@ondefini@ons,itisavailabletoallthefunc@onsdefined belowinthesamesourcefile "externalvariable Global#variablesareexternalvariablesdefinedbeforeany func@ondefini@on Theirscopewillbethewholeprogram 28

8 Local#Variables# void func1 (void){ int i = 5; printf( %d\n, i); i++; printf( %d\n, i); int main (void){ int i = 5; printf( %d \n, i); func1(); printf( %d \n,i); Sta/c#Variables# Avariableissaidtobesta/cifitisallocatedstorageatthe beginningoftheprogramexecu@onandthestorageremains allocatedun@ltheprogramexecu@onterminates. Externalvariablesarealwayssta@c. Withinablock,avariablecanbespecifiedtobesta@cbyusing thekeywordsta@cbeforeitstypedeclara@on: static type variable-name; Variabledeclaredsta@ccanbeini@alizedonlywithconstant expressions(if#not,#its#default#value#is#zero) Sta/c#Variables#(Example)# Sta/c#Variables#(ExampleBIni/al#Value)# void incr(void); int main(void){ int i; void incr(void); for (i=0; i<3; i++) incr(); void incr(void){ static int static_i = 0; printf( static_i = %d\n, static_i++); A#sta/c#variable#inside#a# func/on#keeps#its#value# between#invoca/ons.# Output: static_i = 0 static_i = 1 static_i = 2 31 void put_stars(int n){ static int static_n; int i; for (i=0; i<static_n; i++) printf( ); for (i=0; i<n; i++) printf( * ); printf( \n ); static_n+= n; int main(void){ put_stars(3); put_stars(2); put_stars(3); Output: *** ** *** 32

9 Today# Func/ons# ParameterLists ReturnValues Prototypes Variable#Scopes# BlockStructure GlobalandLocalVariables Recursion# Recursion# Recursionistheprocesswherebyaconstructoperatesonitself. thefirstone Recursionisaprogrammingtechniquethatnaturally implementsthedividehandhconquerproblemsolving methodology Recursive#Func/on# #How1does1it1Look1like?1 Computes#the#factorial#of#a#nonnega/ve#integer.# int fact(int n) { if (n == 0) return (1); else return (n * fact(n-1)); The#func/on#fact#calls#itself.# We#will#see#how#it#really#works#soon# # The#Nature#of#(direct)#Recursion# One or more simple cases of the problem(called the stopping$ cases$or$base$case)haveasimplenonhrecursivesolu@on. Theothercasesoftheproblemcanbereduced(using$recursion) toproblemsthatareclosertostoppingcases. Eventually the problem can be reduced to stopping cases only, whicharerela@velyeasytosolve. 1In1general:1 if(stopping$case) $$$$$$solve$it else$ $$$$$$reduce$the$problem$using$recursion 35 36

10 Recursive#Example#B#Palindrome# Apalindrome#isaword,phrase,numberorothersequenceof e.g.,radar,$level,$rotator,$ Steponnopets, EyEdipAdanadapideye, ,etc. Recursive#Defini/on: Ifthestringhasnoelements,thenit'sapalindrome. Ifthestringhasonlyoneelement,thenit'sapalindrome. Iftheelementsintheendpoints(thefirstandlastelements)arethesame, andtheinternalleyersareapalindrome,#thenit'sapalindrome. Four#Criteria#of#a#Recursive#Solu/on# Atestforthebasecaseenablestherecursivecallstostop. Theremustbeacaseoftheproblem(knownasbase$caseorstopping$case)that ishandleddifferentlyfromtheothercases(withoutrecursivelycallingitself.) Inthebasecase,therecursivecallsstopandtheproblemissolveddirectly. Eventually,oneofthesmallerproblemsmustbethebasecase. Themannerinwhichthesizeoftheproblemdiminishesensuresthatthebase caseiseventuallyisreached Factorial#Func/on# #Itera:ve1Defini:on1 Factorial#Func/on# #Recursive1Defini:on1 n=n*(nh1)*(nh2)* *2*1 0=1 Itera/ve#Defini/on#in#C: fval = 1; for (i = n; i >= 1; i--) fval = fval * i; for$any$integer$n$>$0$ Todefinenrecursively,nmustbedefinedintermsofthe factorialofasmallernumber. Observa@on(problemsizeisreduced): n=n*(nh1) Basecase"0#=#1# # Wecanreachthebasecase,bysubtrac@ng1fromnifnisa posi@veinteger. 1Recursive1Defini:on:1 $$$$n$=$1$ $ $if$n$=$0$ $$$$n$=$n*(n11)$ $if$n$>$0$ 39 40

11 Revisi/ng#the#Recursive#Factorial#Func/on# Defini/on#in#C1 /* Computes the factorial of a nonnegative integer. Precondition: n must be greater than or equal to 0. Postcondition: Returns the factorial of n; n is unchanged.*/ int fact(int n) { if (n == 0) return (1); else return (n * fact(n-1)); How#does#it#Compute?# printf( %d, fact (3)); 6# return#3#*#fact(2)# ###3#*#2## return#2#*#fact(1)# ###2#*#1## return#1#*#fact(0)# ###1#*#1# # return#1# Thisfactfunc@onsa@sfiesthefourcriteriaofarecursivesolu@on.# Tracing#a#Recursive#Func/on# Astackisusedtokeeptrackoffunc@oncalls. Wheneveranewfunc@oniscalled Foreachfunc@oncall,anac:va:on1record1(AR)iscreatedonthestack. ARconsistsofthefunc@on sparametersandlocalvariablesarepushed ontothestackalongwiththememoryaddressofthecallingstatement (returnpoint). Totracearecursivefunc@on,thebox1methodcanbeused. Theboxmethodisasystema@cwaytotracetheac@onsofarecursive func@on. Theboxmethodillustrateshowcompilersimplementrecursion. Eachboxintheboxmethodroughlycorrespondstoanac@va@onrecord. The#Box#Method# Labeleachrecursivecallinthebodyoftherecursivefunc@on. Theselabelshelpustokeeptrackofthecorrectplacetowhichwe mustreturna\erafunc@oncallcompletes. A\ereachrecursivecall,wereturntothelabeledloca@on,and subs@tutethatrecursivecallwithreturnedvalue. if (n ==0) else return (1); return (n * fact(n-1) ) A 43 44

12 The#Box#Method#(cont d.)# itslocalenvironment. Eachboxcontains: Thevaluesofthearguments slocalvariables Aplaceholderforthevaluereturnedfromeachrecursivecallfromthe currentbox(labelinthepreviousstep). The#Box#Method#(cont d.)# processtothefirstbox. Thendrawanarrowtoanewboxcreateda\erarecursivecall,puta labelonthatarrow. printf( %d, fact (3)); A The#Box#Method#(cont d.)# A\eranewboxiscreated,westarttoexecutethebodyofthe func@on. Onexi@ngafunc@on,crossoffthecurrentboxanfollowits arrowbacktotheboxthatcalledthefunc@on. Thisboxbecomesthecurrentbox. Subs@tutethevaluereturnedbythejustHterminatedfunc@oncallinto theappropriateiteminthecurrentbox. Con@nuetheexecu@onfromthereturnedpoint. Box#Trace#of#fact(3)1 Theini@alcallismade,andthefunc@onfactbeginsexecu@on. AtpointA,arecursivecallismade,andthenewinvoca@onoffactbeginsexecu@on. A AtpointA,arecursivecallismade,andthenewinvoca@onoffactbeginsexecu@on. A A 47 48

13 Box#Trace#of#fact(3)#(cont d.)# Box#Trace#of#fact(3)#(cont d.)# A A A Thisisthebasecase,sothisinvoca@onoffactcompletes. A A Thefunc@onvalueisreturnedtothecallingbox,whichcon@nuestheexecu@on. A A A Thecurrentinvoca@onoffactcompletes. A A A A 49 Thefunc@onvalueisreturnedtothecallingbox,whichcon@nuestheexecu@on. A Thecurrentinvoca@onoffactcompletes. A Thefunc@onvalueisreturnedtothecallingbox,whichcon@nuestheexecu@on. Thecurrentinvoca@onoffactcompletes. Thevalue6isreturnedtotheini@alcall. 50 Example:#Find#the#reverse#of#an#input#string# Trace#of#reverse(3)1 /* reads n characters and prints them in reverse order. */ void reverse(int n){ char next; if (n == 1) { /* stopping case */ scanf("%c", &next); printf("%c", next); else { scanf("%c", &next); reverse(n-1); printf("%c", next); return; int main(){ printf("enter a string: "); reverse(3); printf("\n"); reverse(3); /* Assume input is abc */ n=3 3 <= 1? false read next : a reverse(2) write a return n=2 2 <= 1? false read next : b reverse(1) write b return n=1 1 <= 1? true read next : c write c return 51 52

14 Example:#Fibonacci#Sequence# Itisthesequenceofintegers: t 0 t 1 t 2 t 3 t 4 t 5 t Eachelementinthissequenceisthesumofthetwopreceding elements. Thespecifica@onofthetermsintheFibonaccisequence: $ $$ $n $ $ifn$is$0or1 $ $t n $=$ $ $ $ $t n11$ +$t n12 otherwise$ Example:#Fibonacci#Sequence# int fib(int n){ if (n < 2) return n; else return(fib(n-2) + fib(n-1)); Thisisanexampleofnon1linear$recursion.Becausetotalnumberofrecursive callsgrowsexponen@ally. fib(n11)expressionmustbeevaluatedcompletelybeforeitsvaluecanbe addedtotheexpressionfib(n12)whichmustalsobeevaluatedcompletely RecursiontreeisusefulintracingthevaluesofvariablesduringnonHlinear recursion Recursion#Tree#for#Fibonacci#Sequence# =>7thFibonacci fib(6) number fib(5)+fib(4) fib(4)+fib(3) fib(3)+fib(2) fib(3)+fib(2) fib(2)+fib(1) fib(2)+fib(1) fib(2)+fib(1) # fib(1)+fib(0) Example:#Fibonacci#Sequence#(Itera/ve# Version)# int Fib(int n) { int Prev1, Prev2, Temp, j; if (n==0 n== 1) return n; else { Prev1=0; Prev2 = 1; for (j=1; j <= n; j++){ Temp = Prev1 + Prev2; Prev2 = Prev1; Prev1 = Temp; return Prev1; 55 56

15 Recursion#vs.#Itera/on# naturalandlogicalwayofsolvingaproblem. Conflict:machineefficiencyversusprogrammerefficiency. andastack(andviceversa). 57