1. Modular Programming With Functions1 1

2. 4.1 Modularity How do you solve a big/complex problem?
Divide it into small tasks and solve each task. Then combine these solutions.
Divide and Conquer 2 2

3. 4.1 Modularity (cont’d)
In C we use functions also referred to as modules to perform specific tasks that we determined in our solution 3 3

4. Advantages of using modules
Modules can be written and tested separately
Modules can be reused
Large projects can be developed in parallel
Reduces length of program, making it more readable
Promotes the concept of abstraction
A module hides details of a task
We just need to know what this module does
We don’t need to know how it does it 4 4

5. 4.2 Programmer Defined Functions
Every C program starts with main()function
Additional functions are called or invoked when the program encounters function names
Functions could be
Pre-defined library functions (e.g., printf, sin, tan) or
Programmer-defined functions (e.g., my_printf, area)
Functions
Perform a specific task
May take arguments
May return a single value to the calling function
May change the value of the function arguments (call by reference) 5 5

6. Function definition return_type function_name (parameters) {
declarations;
statements; }
int my_add_func(int a, int b) {
int sum;
sum = a + b;
return sum; } 6 6

7. Programmer-Defined Functions Terminology
Function Prototype describes how a function is called
int my_add_func(int, int);
Function Call
result = my_add_func(5, X);
Function implementation
int my_add_func(int a, int b) { … }
Function parameters
Formal parameters
Actual parameter
Formal parameters must match with actual parameters in order, number and data type.
If the type is not the same, type conversion will be applied (coercion of arguments). But this might cause some errors (doubleint) so you need to be careful! 7 7

8. Example: Pre-defined Functions
So far, we used several pre-defined functions!
#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; }
double sin(double radian);
double sin(double radian) {
/* details of computing sin */ } 8 8

9. Example: Programmer-defined Functions
#include <stdio.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; }
#include <stdio.h>
double distance(double, double, double, double);
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 = distance(x1,y1,x2,y2);
printf(“Distance is %lf\n”, dist);
return 0; }
double distance(double x1, y1,x2,y2)
return sqrt(pow((x2-x1),2)
+ pow((y2-y1),2)); 9 9

10. Exercise
(6,8)
(-3,5)
(4,-1)
Suppose you are given the coordinate points of a triangle as shown above, write a program that can find the length of each edge…
User enters: (x1, y1), (x2, y2), and (x3, y3) 10

11. Value Returning Functions
Function returns a single value to the calling program
Function definition declares the type of value to be returned
A return expression; statement is required in the function definition
The value returned by a function can be assigned to a variable, printed, or used in an expression 11 11

12. Void Functions A void function may be called to
perform a particular task (clear the screen)
modify data
perform input and output
A void function does not return a value to the calling program
A return; statement can be used to exit from function without returning any value 12 12

13. Exercise: void function
#include <stdio.h>
void print_i_star(int i);
main() {
int i;
for (i=1; i<=5; i++) {
print_i_star( i ); }
void print_i_star(int i)
int j;
for (j=1; j<=i; j++)
printf(“*”);
printf(“\n”);
return;
Write a program to generate the following output? * **
***
****
*****
for (i=1; i<=5; i++) {
for (j=1; j<=i; j++)
printf(“*”);
printf(“\n”); } 13 13

14. Example: value returning function
n!=n*(n-1)*…*1, 0! = 1 by definition
Function name
Return Type
int fact(int n) {
int factres = 1;
while(n>1)
factres = factres*n;
n--; }
return(factres);
Parameter Declarations
Declarations
Statements 14 14

15. Example – use fact() t = 5 s = ? #include <stdio.h>
int fact(int n); /* prototype */
int main(void) {
int t= 5,s;
s = fact(t) + fact(t+1);
printf(“result is %d\n”, s);
return 0; }
t = 5
s = ?
Function call 15 15

16. Example – execution of factorial function (cont’d)
s = ?
n = 5
factres = 1
int fact(int n) {
int factres = 1;
while(n>1)
factres = factres*n;
n--; }
return(factres); 16 16

17. Example – execution of factorial function (cont’d)
s = ?
n =
factres =
int fact(int n) {
int factres = 1;
while(n>1)
factres = factres*n;
n--; }
return(factres); 17 17

18. Example – execution of factorial function (cont’d)
#include <stdio.h>
int fact(int n); /* prototype */
int main(void) {
int t= 5,s;
s = fact(t+1);
printf(“result is %d\n”, s);
return 0; }
t = 5
s = ?
Function call 18 18

19. Example – execution of factorial function (cont’d)
s = ?
n = 6
factres = 1
int fact(int n) {
int factres = 1;
while(n>1)
factres = factres*n;
n--; }
return(factres);
t+1 19 19

20. Example – execution of factorial function (cont’d)
s = ?
n =
factres =
int fact(int n) {
int factres = 1;
while(n>1)
factres = factres*n;
n--; }
return(factres); 20 20

21. Example – execution of factorial function (cont’d)
#include <stdio.h>
int fact(int n); /* prototype */
int main(void) {
int t= 5,s;
s = ;
printf(“result is %d\n”, s);
return 0; }
t = 5
s = 840
result is 840 21 21

22. Example – reuse of factorial function
Write a statement to compute
Enter X, Z, K, D …
y=(fact(X)+fact(Z)*5)/(fact(K)-fact(D)); 22 22

23. Example – reuse of factorial function in another function
Write a select function that takes n and k and computes “n choose k” where
int select(int n, int k) {
return fact(n)/(fact(n-k)*fact(k)); } 23 23

24. Function Examples 24 24

25. Exercise
Write a function to compute maximum and minimum of two numbers
int max(int a, int b) {
if (a > b)
return a;
else
return b; }
int min(int a, int b) {
if (a < b)
return a;
else
return b; } 25 25

26. Exercise Are following calls to max function valid?
What will be the result?
int max(int a, int b);
int min(int a, int b);
int main() {
int x = 2, y = 3, z = 7, temp;
temp = max(x,y);
temp = max(4,6);
temp = max(4,4+3*2);
temp = max(x,max(y,z)); } 26 26

27. Example for void function
void print_date(int mo, int day, int year) {
/*output formatted date */
printf(“%i/%i/%i\n”, mo, day, year );
return; } 27 27

28. Exercise
Write a function that takes score as parameter and computes and returns letter grade based on the scale below. A
60-79 B
40-59 C
0-39 D 28 28

29. Solution char get_letter_grade(int score) { char grade;
if ((score >= 80) && (score <=100))
grade = 'A';
else if ((score >= 60) && (score <= 79))
grade = 'B';
else if ((score >= 40) && (score <= 59))
grade = 'C';
else if ((score >= 0) && (score <= 39))
grade = 'D';
return grade; } 29 29

30. Exercise Write a function to compute logba
double log_any_base(double a, double b) {
return log(a)/log(b); } 30 30

31. Exercise: Trace functions
What is the output of the following program
#include <stdio.h>
int function1(int x) {
x = 2;
printf("Out1 = %d\n",x);
return(x+1); }
int main()
int x = 4, y;
y = function1(x);
printf("Out2 = %d\n",x);
printf("Out3 = %d\n",y);
return 0;
Output
Out1 = 2
Out2 = 4
Out3 = 3 31 31

32. Exercise What is the output of the following program
#include <stdio.h>
void function2() {
printf("In function 2\n"); }
void function1()
function2();
printf("In function 1\n");
void function3() {
printf("In function 3\n");
function2(); }
int main()
function1();
function3();
return 0;
Output
In function 2
In function 1
In function 3 32 32

33. Parameter Passing Call by value Call by reference
formal parameter receives the value of the actual parameter
function can NOT change the value of the actual parameter (arrays are an exception)
Call by reference
actual parameters are pointers (ch 5 and 6)
function can change the value of the actual parameter 33 33

34. Scope of a function or variable
Scope refers to the portion of the program in which
It is valid to reference the function or variable
The function or variable is visible or accessible
#include <stdio.h>
int fact(int n); /* prototype */
int main(void) {
int t= 5,s;
s = fact(t) + fact(t+1);
printf(“result is %d\n”, s);
return 0; }
int fact(int n)
int factres = 1;
while(n>1) {
factres = factres*n;
n--;
return(factres);
t = 5
s = ?
n = 5
factres = 1 34 34

35. Scope of a function or variable
Same variable name can be used in different functions
#include <stdio.h>
int fact(int n); /* prototype */
int main(void) {
int t= 5,s;
s = fact(t) + fact(t+1);
printf(“result is %d\n”, s);
return 0; }
int fact(int t)
int s = 1;
while(t>1) {
s = s*t;
t--;
return(s);
t = 5
s = ?
s = 1 35 35

36. Scope Local scope Global scope
a local variable is defined within a function or a block and can be accessed only within the function or block that defines it
Global scope
a global variable is defined outside the main function and can be accessed by any function within the program file. 36 36

37. Global vs Local Variable
#include <stdio.h>
int z = 2;
void function1()
{ int a = 4;
printf("Z = %d\n",z);
z = z+a; }
int main()
{ int a = 3;
z = z + a;
function1();
return 0; z=
a=4
a=3
Output
Z = 5
Z = 9 37 37

38. Storage Class - 4 types
Storage class refers to the lifetime of a variable
automatic - key word auto - default for local variables
Memory set aside for local variables is not reserved when the block in which the local variable was defined is exited.
external - key word extern - used for global variables
Memory is reserved for a global variable throughout the execution life of the program.
static - key word static
Requests that memory for a local variable be reserved throughout the execution life of the program. The static storage class does not affect the scope of the variable.
register - key word register
Requests that a variable should be placed in a high speed memory register. 38 38

39. Initial / default value
Storage Specifier
Storage place
Initial / default value
Scope
Life
auto
CPU Memory
Garbage value
local
Within the function only.
extern
CPU memory
Zero
Global
Till the end of the main program. Variable definition might be anywhere in the C program
static
Retains the value of the variable between different function calls.
register
Register memory
Within the function

40. void fun () {
int a=6; a = a + 1;
printf ("\nInside fun a = %d ", a); }
void fun1 () {
static int a;
a = a + 1;
printf ("\nInside fun1 a = %d ", a); }
void fun (void);
void fun1 (void);
void fun2 (void);
int count1=20;
int main () {
int count=5;
fun ();
fun1 ();
fun2 ();
printf ("\nIn main count = %d count1 = %d\n\n",count, count1);
return 0; }
void fun2 () {
int count=10;
count = count + 1;
count1 = count1 + 1;
printf ("\nInside fun2 count = %d count1=%d ",
count, count1); }

41. 4.4 Random Numbers What is a random number?
Tossing a coin (0, 1) Rolling a die (1, 2,…6)
Min, Max, Avg, possible outcomes are equally likely or not,
Engineering problems require use of random numbers
How can you compute the area of an irregular shape? 41 41

42. Uniform Random numbers
All outcomes are equally likely
For example fair die, where each outcome has the same probability of 1/6,
So we can generate uniform random numbers between 1 and 6 by rolling a die.
What if we need random numbers in another range? For example, 1 and 100? 42 42

43. Uniform Random numbers (cont’d)
In Standard C library, we have a function rand() to generate random numbers between 0 and RAND_MAX
RAND_MAX is a system dependent constant (e.g., 32,767) defined in stdlib.h
What will be the output of the following
printf(“%d %d %d\n”,rand(), rand(), rand());
What will be the output, if we re-run the same program? 43 43

44. Pseudo-random Numbers
Computers generate random numbers using a seed number and an algorithm.
So, if you give the same seed, you will always get the same sequence of pseudo-random numbers
In Standard C library, we have a function srand(int seed) to give a new seed number 44 44

45. Example: generate 10 RNs #include <stdio.h>
#include <stdlib.h>
int main(void) {
/* Declare variables. */
unsigned int seed;
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");
/* Exit program. */
return 0; } 45 45

46. RNs in a specified range [a b]
Generate a RN between 0 and 7
x = rand() % 8;
Generate a RN between 10 and 17
x = 10 + rand() % 8;
int rand_int(int a,int b) {
return rand()%(b-a+1) + a; } 46 46

47. Floating-Point RNs in a specified range [a b]
x = rand() / RAND_MAX will give a random number between 0.0 and 1.0
x = rand() / RAND_MAX *(b-a) will give a RN between 0.0 and b-a
The value is then shifted into range [a b] by adding a
double rand_float(double a,double b) {
return ((double)rand()/RAND_MAX)*(b-a)+a; } 47 47

48. Example: HiLo Game
/* Write a program that allows a user to play HiLo game.
User wins if he/she can guess the number between within
at most 6 iterations */
#include <stdio.h>
#include <stdlib.h>
int rand_int(int a,int b); /* prototype */
void playHiLo( int s);
int main(void) {
unsigned int seed; /* Declare variables */
int secret;
printf("Enter a positive integer seed value: \n");
scanf("%u",&seed);
srand(seed);
while(1){
secret = rand_int(1,100);
playHiLo(secret); }
return 0; 48 48

49. int rand_int(int a,int b) { return rand()%(b-a+1) + a; }
void playHiLo(int s)
int i, guess;
for(i=1; i <=6; i++){
printf("Enter your guess : ");
scanf("%d", &guess);
if (guess > s)
printf("It is Higher than secret\n");
else if (guess < s)
printf("It is Lower than secret\n");
else {
printf("Cong! you won\n");
return;
printf("Sorry! Try again\n"); 49 49

50. Exercise: Another “guess the number game”
Computer selects a random number s between [ ]
User tries to guess it by entering g
Computer tells how many digits are in place, out of place, not in secret number
For example, if s is 6234
User enters g as , then computer says
1 digit is in place
2 digits are out of place
1 digit is not in secret number
User keeps trying until he finds the secret number 50 50

51. Random Number Summary #include <stdlib.h> srand(seed);
rn = rand(); /* [0 RAND_MAX] (e.g., 32,767) */
int rand_int(int a,int b) {
return rand()%(b-a+1) + a; }
double rand_float(double a,double b)
return ((double)rand()/RAND_MAX)*(b-a)+a; 51 51

52. 4.5 Macros #define macro_name(parameters) macro_text
macro_text replaces macro_name in the program
Examples
#define area_tri(base,height) (0.5*(base)*(height))
#define PI 3.14
z=x * tri(3, 5) + y;  z=x * (0.5*(3)*(5)) + y;
k=2*PI*r;  k=2*3.14*r; 52 52

53. 4.6 Recursive Functions
A function that invokes itself is a recursive function.
int fact(int k) {
if (k == 0)
return 1;
else
return k*fact(k-1); }
k!=k*(k-1)! 53 53

54. #include <stdio.h> int fact(int k) { if (k == 0) return 1; else
return k*fact(k-1); }
int main()
int n;
int nf;
printf("Enter n\n");
scanf("%d",&n);
nf = fact(n);
printf("Factorial = %d\n", nf);
system("pause");
return(0); 54 54

55. Fibonacci Numbers
Sequence {f0,f1,f2,…}. First two values (f0,f1) are 1, each succeeding number is the sum of previous two numbers.
F(0)=1, F(1) = 1
F(i) = F(i-1)+F(i-2) 55 55

56. Fibonacci Numbers int fibonacci(int k) { int term; term = 1;
if (k>1)
term = fibonacci(k-1)+fibonacci(k-2);
return term; } 56 56

57. #include <stdio.h> int fibonacci(int k) { int term = 1;
if (k>1)
term = fibonacci(k-1)+fibonacci(k-2);
return(term); }
int main()
int n;
int nfib;
printf("Enter n\n");
scanf("%d",&n);
nfib = fibonacci(n);
printf("Fibonacci = %d\n",nfib);
system("pause");
return(0);
/* Iterative Version of Fibonacci Function */
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 = i + 1; }
return(c); 57 57

58. Extra examples 58 58

59. 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); } 59 59

60. Exercise
Given radius and height of a cylinder. Write a function to compute the volume.
V = pi*r2*h
#define PI 3.14
double volume(double radius, double height) {
return(PI*radius*radius*height); } 60 60

61. Exercise
Given radius and height of a cylinder. Write a function to compute the volume.
V = pi*r2*h
#define PI 3.14
double volume(double radius, double height) {
return(PI*radius*radius*height); } 61 61

62. 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 62 62

63. Solution 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;
else
return z; } 63 63

64. Exercise
Assume you have maximum and minimum functions implemented. Use these to find median of 3 numbers
a < b < c -> median is b
Consider 3 pairs (a,b),(b,c),(a,c)
min(a,b) = a
min(b,c) = b Max(a,b,a) = b
min(a,c) = a 64 64

65. Exercise
Assume you have maximum and minimum functions implemented. Use these to find median of 3 numbers
a < b < c -> median is b
Consider 3 pairs (a,b),(b,c),(a,c)
min(a,b) = a
min(b,c) = b Max(a,b,a) = b
min(a,c) = a 65 65

66. Solution int median(int x, int y, int z) {
return(max(min(x,y),min(x,z),min(y,z))); } 66 66