Fundamental of Programming (C)

Transcription

1 Borrowed from lecturer notes by Omid Jafarinezhad Fundamental of Programming (C) Lecturer: Vahid Khodabakhshi Lecture 6 Modular programming Department of Computer Engineering

2 Outline Introduction to pointer Introduction to function User define function Function prototype (declaration) Function definition Function call and return Formal and Actual Parameters Scope of Identifiers Storage classes Recursion Department of Computer Engineering 2/77

3 Pointer Fundamentals When a variable is defined the compiler (linker/loader actually) allocates a real memory address for the variable int x; x When a value is assigned to a variable, the value is actually placed to the memory that was allocated x=3; Department of Computer Engineering 3/77

4 Pointers When the value of a variable is used, the contents in the memory are used y=x; will read the contents in the 4 bytes of memory, and then assign it to variable y &x can get the address of x (referencing operator &) The address can be passed to a function: scanf("%d", &x); The address can also be stored in a variable Department of Computer Engineering 4/77

5 Pointers To declare a pointer variable type * pointername; For example: int x, k; int * p1; // (or p1 is a int pointer) char *p2; p1 = &x; /* Store the address in p1 */ Department of Computer Engineering 5/77

6 Using Pointers You can use pointers to access the values of other variables, i.e. the contents of the memory for other variables To do this, use the * operator (dereferencing operator) Depending on different context, * has different meanings For example: int n, m=3, *p; p=&m; n=*p; printf("%d\n", n); // 3 printf("%d\n",*p); // 3 Department of Computer Engineering 6/77

7 Using Pointers int i1; int i2; int *ptr1; 0x1014 ptr2: 0x1000 int *ptr2; 0x1010 i1 = 1; 0x100C ptr1: 0x1000 i2 = 2; 0x1008 ptr1 = &i1; ptr2 = ptr1; 0x1004 0x1000 i2: i1: *ptr1 = 3; i2 = *ptr2; Department of Computer Engineering 7/77

8 An Example int m=3, n=100, *p, *q; p=&m; printf("m is %d\n",*p); // 3 m++; printf("now m is %d\n",*p); // 4 m 3 m 3 m n 100 n 100 n p? p p q? q? q p=&n; printf("n is %d\n",*p); // 100 *p=500; printf("now n is %d\n", n); // 500 q=&m; *q = *p; printf("now m is %d\n", m); // m 4 m *p n 100 n 500 *p p p? q? q Department of Computer Engineering 8/77

9 Modular Programming Break a large problem into smaller pieces Smaller pieces sometimes called functions Why? Helps manage complexity Smaller blocks of code Easier to read Encourages re-use of code Divide and Conquer Within a particular program or across different programs Allows independent development of code Provides a layer of abstraction Department of Computer Engineering 9/77

10 Functions - Mathematical View f ( x) x 2 2x 3 What is f(2)? f (2) (2) 2 2(2) f (2) is 11 X Function Returned value 2 f (x) 11 Department of Computer Engineering 10/77

11 Functions Every C program starts with main() function Functions could be Pre-defined library functions e.g., printf, sin, tan Programmer-defined functions e.g., my_printf, area int main() Department of Computer Engineering 11/77

12 Pre-defined library functions The C standard library is a standardized collection of header files and library functions, which are used to implement common operations Department of Computer Engineering 12/77

13 Pre-defined library functions <math.h> Defines common mathematical functions e.g. sin, cos. sqrt, pow <stdio.h> Defines core input and output functions e.g. printf, scanf, puts, gets <time.h> Defines date and time handling functions e.g. time, clock <stdlib.h> Defines pseudo-random numbers generation functions e.g. rand, srand Department of Computer Engineering 13/77

14 C mathematical functions double fmod( double x, double y ); Computes the remainder of the division operation x/y double exp( double arg ); Computes the e (Euler's number, ) raised to the given power arg double log( double arg ); Computes the natural (base e) logarithm of arg double log10( double arg ); Computes the common (base 10) logarithm of arg double sqrt( double arg ); Computes square root of arg double pow( double base, double exp); Computes the value of base raised to the power exp Department of Computer Engineering 14/77

15 C mathematical functions double sin( double arg ); Computes sine of arg (representing angle in radians) double cos( double arg ); Computes cosine of arg (representing angle in radians) double tan( double arg ); Computes tangent of arg (representing angle in radians) overview of math functions in s#stdlib.h Department of Computer Engineering 15/77

16 An example #include <stdio.h> #include <math.h> int main(void) double angle; printf("input angle in radians: \n"); scanf("%lf", &angle); printf("the sine of the angle is %f\n", sin(angle) ); return 0; Department of Computer Engineering 16/77

17 An example #include <stdio.h> #include <math.h> int main(void) double x1,y1,x2,y2, dist; printf("enter x1 y1 x2 y2 :"); scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2); dist = sqrt(pow((x2-x1),2) + pow((y2-y1),2)); // printf("distance is %lf\n", dist); return 0; Department of Computer Engineering 17/77

18 Random numbers generation functions int rand(); Returns a uniformly distributed pseudo-random integral value between 0 and RAND_MAX (0 and RAND_MAX included) RAND_MAX : Expands to an integer constant expression equal to the maximum value returned by the function rand(). This value is implementation dependent. #define RAND_MAX /*implementation defined*/ srand() should be called before any calls to rand() to initialize the random number generator void srand( unsigned seed ); Initializes the built-in random number generator used to generate values for rand() with the seed value seed Department of Computer Engineering 18/77

19 An Example #include <stdio.h> #include <stdlib.h> int main(void) unsigned int seed; /* Declare variables. */ int k; /* Get seed value from the user. */ printf("enter a positive integer seed value: \n"); scanf("%u",&seed); srand(seed); /* Generate and print ten random numbers. */ printf("random Numbers: \n"); for (k=1; k<=10; k++) printf("%i ", rand()); printf("\n"); return 0; /* Exit program. */ Department of Computer Engineering 19/77

20 An Example #include <stdio.h> #include <stdlib.h> #include <time.h> int main(void) srand(time(0)); //use current time as seed for random generator /* Generate and print ten random numbers. */ printf("random Numbers: \n"); for (k=1; k<=10; k++) printf("%i ", rand()); printf("\n"); return 0; /* Exit program. */ Department of Computer Engineering 20/77

21 Random Numbers in [a b] Generate a random number [0.. 7] x = rand() % 8; Generate a random number [10..17] x = 10 + rand() % 8; rand() % (b-a+1) + a; Department of Computer Engineering 21/77 Sharif University of 21 Technology

22 User- defined OR Programmer-defined function Department of Computer Engineering 22/77

23 Functions - Definition Structure Function 'header' Return data type (if any) Name Descriptive Arguments (or parameter list) Notice: data type and name Statements Variable declaration Operations Return value (if any) type function_name (type arg1, type arg2 ) statements; double product(double x, double y) double result; result = x * y; return result; A function that calculates the product of two numbers Department of Computer Engineering 23/77

24 An Example Function prototype Like a variable declaration Tells compiler that the function will be defined later Helps detect program errors Note semicolon!! Function definition See previous slide Note, NO semicolon Function return return statement terminates execution of the current function Control returns to the calling function if return expression; then value of expression is returned as the value of the function call Only one value can be returned this way Function call main() is the 'calling function' product() is the 'called function' Control transferred to the function code Code in function definition is executed #include <stdio.h> /* function prototype */ double product(double x, double y); int main() double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans); return 0; /* function definition */ double product(double x, double y) double result; result = x * y; return result; Department of Computer Engineering 24/77

25 Function An Example Write a function named 'sum' sums two integers returns the sum Steps 1. Function header return data type function name argument list with data types 2. Statements in function definition variable declaration operations return value int sum_int(int x, int y) int result; result = x + y; return result; Department of Computer Engineering 25/77

26 Formal and Actual Parameters Formal parameter Variables declared in the formal list of the function header (written in function prototype & function definition) Actual parameter Constants, variables, or expression in a function call that correspond to its formal parameter The number of actual parameters in a function call must be the same as the number of formal parameters in the function definition A one-to-one correspondence must occur among the actual and formal parameters. The first actual parameter must correspond to the first formal parameter and the second to the second formal parameter, an so on The type of each actual parameter must be the same as that of the corresponding formal parameter Department of Computer Engineering 26/77

27 An Example #include <stdio.h> int calsum(int,int); Formal Parameters int main(void).... sum = calsum(num1,num2); /* function call */.. int calsum(int val1, int val2) /*function header*/ Formal Parameters /*function prototype*/ Actual Parameters Department of Computer Engineering 27/77

28 An Example If the function requires some arguments to be passed along, then the arguments need to be listed in the bracket ( ) according to the specified order void Calc(int, double, char, int); int main(void) int a, b; double c; char d; Calc(a, c, d, b); return (0); Function Call Department of Computer Engineering 28/77

29 Functions that do not return a value Use the return type of void void functionname( DataType arg_1, ) void functionname() void functionname( void) Department of Computer Engineering 29/77

30 Function Call An Example #include <stdio.h> //function prototype //global variable declaration int main(void) local variable declaration; statements; fn1( ); fn2( ); return (0); void fn1(void) local variable declaration; statements; void fn2(void) local variable declaration; statements; return; Department of Computer Engineering 30/77

31 Function Call An Example If the function returns a value, then the returned value need to be assigned to a variable so that it can be stored int GetUserInput (void); /* function prototype*/ int main(void) int input; input = GetUserInput( ); return(0); /* return 0; */ However, it is perfectly okay (syntax wise) to just call the function without assigning it to any variable if we want to ignore the returned value We can also call a function inside another function printf("user input is: %d", GetUserInput( )); Department of Computer Engineering 31/77

32 Receive nothing and return nothing #include <stdio.h> void greeting(void); /* function prototype */ int main(void) greeting( ); greeting( ); return(0); // return 0; Have fun!! Have fun!! Press any key to continue void greeting(void) printf("have fun!! \n"); Department of Computer Engineering 32/77

33 Receive nothing and return nothing #include <stdio.h> int getinput(void) /* ignore function prototype */ int number; printf("enter a number:"); scanf("%d",&number); return number; int main(void) int num1, num2, sum; num1 = getinput( ); num2 = getinput( ); sum = num1 + num2; printf("sum is %d\n",sum); return(0); Enter a number: 5 Enter a number: 4 Sum is 9 Press any key to continue Department of Computer Engineering 33/77

34 Receive parameter(s) and return nothing #include <stdio.h> int getinput(void); void displayoutput(int); int main(void) int num1, num2, sum; num1 = getinput(); num2 = getinput(); sum = num1 + num2; displayoutput(sum); return(0); int getinput(void) int number; printf("enter a number:"); scanf("%d",&number); return number; void displayoutput(int sum) printf("sum is %d \n",sum); Department of Computer Engineering 34/77 Enter a number: 5 Enter a number: 4 Sum is 9 Press any key to continue

35 Call by value And Call by reference Call by value In this method, only the copy of variable s value (copy of actual parameter s value) is passed to the function. Any modification to the passed value inside the function will not affect the actual value In all the examples that we have seen so far, this is the method that has been used Call by reference In this method, the reference (memory address) of the variable is passed to the function. Any modification passed done to the variable inside the function will affect the actual value To do this, we need to have knowledge about pointers and arrays Department of Computer Engineering 35/77

36 Call by value An Example How are the arguments passed into functions? 'Pass by value' function arguments are expressions In the function call: Expressions are evaluated and copies of their values are put into temporary memory locations The names of the corresponding parameters in the function definition are made to be the names of the copies The values of the expressions in the function call are not changed Department of Computer Engineering 36/77 #include <stdio.h> double product(double x, double y); int main() int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans); /* function definition */ double product(double A, double B) double result; result = A * B; return result;

37 Call by value An Example #include <stdio.h> int calsum(int,int); int main(void) int sum, num1, num2; /*function protototype*/ printf("enter two numbers to calculate its sum:\n"); scanf("%d%d",&num1,&num2); sum = calsum(num1,num2); /* function call */ printf("\n %d + %d = %d", num1, num2, sum); return(0); int calsum(int val1, int val2) /*function definition*/ int sum; sum = val1 + val2; val2 = 100; return sum; Department of Computer Engineering 37/77 num2 num1 sum val2 val1 sum Enter two numbers to calculate its sum: = 13 Press any key to continue 4? 9? 13? ?

38 Array and String Lecture 6 Call by reference #include <stdio.h> void CalByVal(a, b) a = 0; b = 10; void CalByRef(int *a, int *b) // CalByRef(int *p, int *q) *a = 0; *b = -5; // a = 0;!!!! int main(void) int a = 1, b = 5; printf("before cal CalByVal: a = %d, b = %d\n", a, b); CalByVal(a, b); printf("after cal CalByVal: a = %d, b = %d\n", a, b); b a b a b a CalByVal CalByRef main printf("before cal CalByRef: a = %d, b = %d\n", a, b); CalByRef(&a, &b); printf("after cal CalByRef: a = %d, b = %d\n", a, b); getch(); return 0; /* Exit program. */ Department of Computer Engineering 38

39 Array and String Lecture 6 Call by reference Instead of product() prod_sum() How can I get the function to give both product and sum? put * in front of variable name in prototype and function definition put & in front of variable names in function call Department of Computer Engineering 39 #include <stdio.h> void prod_sum(double x, double y, double *ptr1, double *ptr2); int main() double var1 = 3.0, var2 = 5.0; double prod, sum; prod_sum(var1, var2, &prod, &sum); printf("var1= %g\n" "var2= %g\n",var1, var2); printf("prod= %g\n" "sum= %g\n", prod, sum); /* function definition */ void prod_sum(double A, double B, double *rslt_prod, double *rslt_sum) *rslt_prod = A * B; *rslt_sum = A + B;

40 Array and String Lecture 6 Pointers and Arrays Recall that the value of an array name is also an address void main() int x[10]; ReOrder(x); // ReOrder(&x); void ReOrder(int *x) int i, j, t; for(i = 0; i < 9; i++) for(j = i + 1; i < 10; ++j) if(x[i] < x[j]) t = x[i]; x[i] = x[j]; x[j] = t; Department of Computer Engineering 40

41 Array and String Lecture 6 Organizing Multi-File Programs A large C program should be divided into multiple files // main.c #include <stdio.h> void Test() // int main() // return 0; // math.c double mathvar; double sin() double tempsin; // return tempsin; Department of Computer Engineering 41

42 Array and String Lecture 6 Identifiers and Scope Identifier The name of a variable, function, label, etc. int my_var1; /* a variable */ pow_table();/* a function */ start: /* a label */ Question: Does it make a difference where in a program an identifier is declared? YES! --> concept of scope Department of Computer Engineering 42

43 Array and String Lecture 6 Scope of Identifiers Scope of a declaration of an identifier The region of the program that the declaration is active (i.e., can access the variable, function, label, etc.) Five types of scope: Program (global scope) File Function prototype Function Block ("between the scope") Department of Computer Engineering 43

44 Scope of Identifiers - Program Scope Program (global) scope if declared outside of all functions "Visible" to all functions from point of declaration Visible to functions in other source files Use only when necessary and then very carefully!! If there exist a local variable and a global variable with the same name, the compiler will refer to the local variable #include <stdio.h> int a = 10; double product(double x, double y); int main() double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // /* function definition */ double product(double x, double y) double result; a = 20; result = x * y; return result; a = 10 a = 20 Department of Computer Engineering 44/77

45 An Example // File name: main.c #include <stdio.h> int a = 10; // File name: ExternFile.c extern int a = 10; /* function definition */ void TestExtern() // a = 90; // /* function definition */ double product(double x, double y) double result; // a = 70; return result; int main() a = 80; Department of Computer Engineering 45/77

46 Scope of Identifiers - File Scope File scope Keyword static Makes variable a visible only within this source file Use file scope to avoid naming conflict if multiple source files are used #include <stdio.h> static int a = 10; double product(double x, double y); int main() double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // /* function definition */ double product(double x, double y) double result; result = x * y; return result; Department of Computer Engineering 46/77

47 An Example // File name: main.c #include <stdio.h> static int a = 10; // File name: ExternFile.c extern int a = 10; /* function definition */ void TestExtern() // a = 90; // /* function definition */ double product(double x, double y) double result; // a = 70; return result; int main() a = 80; Department of Computer Engineering 47/77

48 Scope of Identifiers - Function Prototype Scope Function prototype scope Identifiers x and y are not visible outside the prototype Thus, names in the prototype do not have to match names in the function definition MUST match types, however! #include <stdio.h> double product(double x, double y); int main() int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans); /* function definition */ double product(double A, double B) double result; result = A * B; return result; Department of Computer Engineering 48/77

49 Scope of Identifiers - Function Scope Function scope Active from the beginning to the end of a function #include <stdio.h> int main() int a; // return 0; int FunctionScopeTest() int b; // return 0; Department of Computer Engineering 49/77

50 Scope of Identifiers - Block Scope Block (local) scope A block is a series of statements enclosed in braces The identifier scope is active from the point of declaration to the end of the block ( ) Nested blocks can both declare the same variable name and not interfere #include <stdio.h> double product(double x, double y); int main() int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // /* function definition */ double product(double x, double y) double result; // a = 60; Error result = x * y; return result; Department of Computer Engineering 50/77

51 An Example #include <stdio.h> int a = 10; int f1() int a; a = 70; int a; a = 100; return a; void main() a = 80; f1(); a =? a = 70 a = 100 a = 70 a = 10 a = 80 Department of Computer Engineering 51/77

52 Storage Classes Refers to the lifetime of a variable Local variables only exist within a function by default. When calling a function repeatedly, we might want to Start from scratch reinitialize the variables The storage class is auto Continue where we left off remember the last value The storage class is static Another two storage classes (seldomly used) register (ask to use hardware registers if available) extern (global variables are external) Department of Computer Engineering 52/77

53 Auto storage class Variables with automatic storage duration are created when the block in which they are declared is entered, exist when the block is active and destroyed when the block is exited. The keyword auto explicitly declares variables of automatic storage duration. It is rarely used because when we declare a local variable, by default it has class storage of type auto. int a, b; // is the same as auto int a, b; Department of Computer Engineering 53/77

54 Static storage class However the static keyword can be applied to a local variable so that the variable still exist even though the program has gone out of the function. As a result, whenever the program enters the function again, the value in the static variable still holds Department of Computer Engineering 54/77

55 Auto - Example #include <stdio.h> void auto_example(void); int main(void) int i; printf("auto example:\n"); auto_example( ); auto_example( ); auto_example( ); return(0); Auto example: Press any key to continue void auto_example(void) auto int num = 1; printf(" %d\n",num); num = num + 2; Department of Computer Engineering 55/77

56 Static - Example #include <stdio.h> void auto_example(void); int main(void) int i; printf("static example:\n"); static_example( ); static_example( ); static_example( ); return(0); void static_example(void) static int num = 1; Static example: Press any key to continue printf(" %d\n",num); num = num + 2; Department of Computer Engineering 56/77

57 Recursion Recursion is a technique that solves a problem by solving a smaller problem of the same type A recursive function is a function invoking itself, either directly or indirectly Recursion: A B C D A Concept of recursive function (generally): A recursive function is called to solve a problem The function only knows how to solve the simplest case of the problem. When the simplest case is given as an input, the function will immediately return with an answer However, if a more complex input is given, a recursive function will divide the problem into 2 (or more) pieces: a part that it knows how to solve and another part that it does not know how to solve if (stopping case) solve it else reduce the problem using recursion Department of Computer Engineering 57/77

58 Recursion Any problem that can be solved recursively can also be solved iteratively (using loop) Recursive functions are slow and takes a lot of memory space compared to iterative functions So why bother with recursion? There are 2 reasons: Recursion approach more naturally resembles the problem and therefore the program is easier to understand and debug Iterative solution might not be apparent Department of Computer Engineering 58/77

59 An Example: x y In this example, we want to calculate x to the power of y i.e. x y If we analyze the formula for x y, we could see that x y could be written as (x being multiplied to itself, y times) An example is 2 4, which can be written as 2 4 = 2 x 2 x 2 x 2 (in this case, x = 2, y = 4) 2 4 could also be rewritten as 2 4 = 2 1 x 2 3 where 2 1 = 2 (i.e the number itself) Therefore, we could divide the problem into two stage: Simplest case: when y = 1, the answer is x Recursive case, we need to solve for x * x (y-1) Department of Computer Engineering 59/77

60 Recursion solution of x y #include <stdio.h> double XpowerY(double, int); int main(void) double power, x; int y; printf("enter the value of x and y:\n"); scanf("%lf%d", &x, &y); power = XpowerY(x, y); printf("%.2f to the power of %d is %.2f\n\n", x, y, power); return(0); double XpowerY(double x, int y) if (y ==1) else return x; return x * XpowerY(x, y-1); Enter the value of x and y: to the power of 3 is 8.00 Press any key to continue Department of Computer Engineering 60/77

61 How C Maintains the Recursive Steps C keeps track of the values of variables by the stack data structure. Recall that stack is a data structure where the last item added is the first item processed There are two operations (push and pop) associated with stack a b c pop b c push d d b c Department of Computer Engineering 61/77 Sharif University of Technology

62 How C Maintains the Recursive Steps Each time a function is called, the execution state of the caller function (e.g., parameters, local variables, and memory address) are pushed onto the stack When the execution of the called function is finished, the execution can be restored by popping up the execution state from the stack Department of Computer Engineering 62/77

63 Recursive Steps of x y #include <stdio.h> double XpowerY(double, int); int main(void) double power, x; int y; printf("enter the value of x and y:\n"); scanf("%lf%d", &x, &y); power = XpowerY(x, y); printf("%.2f to the power of %d is %.2f\n\n", x, y, power); return(0); double XpowerY(double x, int y) if (y ==1) else return x; return x * XpowerY(x, y-1); 2 2 * 2 2 * 4 2 * 8 x = 2; y = 2; return x; x = 2; y = 2; x * XpowerY(2, 1) x = 2; y = 3; x * XpowerY(2, 2) x = 2; y = 4; x * XpowerY(2, 3) Department of Computer Engineering 63/77

64 Factorial Analysis: n!= n * (n-1) * (n-2) * (n-3) * (n-4) * 1 n! could be rewritten as n * (n-1)! Example: 5! = 5 * 4 * 3 * 2 * 1 = 5 * (4)!, where n = 5 Fact: 0! Or 1! is equal to 1 Therefore, we could divide this problem into two stages for n!: Simplest case: if (n <= 1), answer is 1 Recursive case: we need to solve for n * (n-1)! Department of Computer Engineering 64/77

65 Factorial #include <stdio.h> double fact(double); int main(void) double n, result; printf("please enter the value of n:"); scanf("%lf", &n); result = fact(n); printf(" %.f! = %.2f\n", n, result); return(0); double fact(double n) if (n <= 1) return 1; else return n * fact(n-1); int fact(int n) int factres = 1; while(n>1) factres = factres*n; n--; return (factres); Enter the value of n: 3 3! = 6.00 Press any key to continue Department of Computer Engineering 65/77

66 Reuse of factorial function Write a statement to compute y X! Z!*5 K! D! // Enter X, Z, K, D y = (fact(x) + fact(z) * 5) / (fact(k) - fact(d)); Department of Computer Engineering 66/77

67 Reuse of factorial function Write a select function that takes n and k and computes "n choose k" where n k ( n n! k)! k! int select(int n, int k) return fact(n) / (fact(n-k) * fact(k)); Department of Computer Engineering 67/77

68 Fibonacci Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th Fib(1) = 1 defined base case Fib(2) = 1 defined base case Fib(3) = 2 = Fib(2) + Fib(1) Fib(7) = 13 = Fib(6) + Fib(5) Fib(n) = Fib(n-1) + Fib(n-2) Department of Computer Engineering 68/77

69 Fibonacci int Fib (int n) int temp = 1; /* handles base cases */ if (n > 2) temp = Fib(n-1) + Fib(n-2); return temp; /* Iterative Version */ int fibonacci(int k) int a,b,c,i; if (k <= 1) return 1; else a = 1; b = 1; i = 2; while (i <= k) c = a + b; a = b; b = c; i++; return(c); Department of Computer Engineering 69/77

70 Fibonacci x = 1; temp = 1; return temp; x = 1; temp = 1; return temp; x = 1; temp = 1; return temp; x = 1; temp = 1; return temp; x = 5; temp = 1; temp = Fib(2) 1 + Fib(1); 1; + Fib(1); return temp; int Fib (int x) /* handles base cases of */ /* Fib(1) and Fib(2) */ int temp = 1; if (x > 2) /* other cases */ temp = Fib(x-1) + Fib(x-2); return temp; x = 1; temp = 1; return temp; x = 4; temp = 1; temp = Fib(3) 2 + 1; Fib(2); + Fib(2); return temp; x = 5; temp = 1; temp = Fib(2) 1 + Fib(1); 1; + Fib(1); return temp; x = 5; temp = 1; temp = Fib(4) 3 + 2; Fib(3); + Fib(3); return temp; Department of Computer Engineering 70/77

71 Fibonacci int Fib (int n) /* handles base cases of */ /* Fib(1) and Fib(2) */ int temp = 1; if (n > 2) /* other cases */ temp = Fib(n-1) + Fib(n-2); return temp; fib(4) fib(5) 3 2 fib(3) 1 1 fib(3) fib(2) fib(2) fib(1) 1 fib(2) 1 fib(1) Department of Computer Engineering 71/77

72 Exercise Write a function to compute log b a log b a log log a b # include <math.h> double log_any_base(double a, double b) return log(a) / log(b); Department of Computer Engineering 72/77

73 Exercise #include <stdio.h> int function1(int x) x = 2; return(x+1); int function2(int *x) *x = 2; return(*x+1); int main() int x = 4, y1, y2; y1 = x + function1(++x); // y1? y2 = ++x + function2(&x); // y2? return 0; Department of Computer Engineering 73/77

74 Exercise What is the output of the following program #include <stdio.h> // function prototypes void function3() printf("in function 3\n"); function2(); int main() function1(); function3(); return 0; Department of Computer Engineering 74/77 void function2() printf("in function 2\n"); void function1() function2(); printf("in function 1\n"); In function 2 In function 1 In function 3 In function 2

75 Exercise Given radius and height of a cylinder. Write a function to compute the surface area A = 2*pi*r*(r*h) #define PI 3.14 double area(double radius, double height) return 2 * PI * radius * (radius+height); Department of Computer Engineering 75/77

76 Exercise Write a function to compute the median of 3 numbers x, y and z Possible order of numbers x<y<z -> median y x<z<y -> median z y<x<z -> median x y<z<x -> median z z<x<y -> median x z<y<x -> median y int median(int x, int y, int z) if (((x < y) && (y < z)) ((z < y) && (y < x))) return y; else if (((y < x) && (x < z)) ((z < x) && (x < y))) return x; return z; Department of Computer Engineering 76/77

77 Exercise Recursive Definitions of gcd A: Euclid s algorithm makes use of the fact that gcd(x,y ) = gcd(y, x mod y) gcd( x, y) x, if y 0 gcd( y, x mod y), int gcd (unsigned int x, unsigned int y) if (y == 0 ) return x; return gcd(y, x % y); otherwise Department of Computer Engineering 77/77