CS 2073
Computer Programming w/Eng.
Applications
Ch 4
Modular Programming With Functions
Turgay Korkmaz
Office: SB 4.01.13
Phone: (210) 458-7346
Fax: (210) 458-4437
e-mail: korkmaz@cs.utsa.edu
web: www.cs.utsa.edu/~korkmaz
1
Name Addr
Lecture++;
Lecture
Content
16
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
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
Structure Chart
Shows how the program
separated into tasks and which
tasks reference other tasks.
NOTE: It does NOT indicate the
sequence of steps in the
program!
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
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)
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;
}
7
Programmer-Defined
Functions Terminology

Function Prototype describes how a function is called
int my_add_func(int a, int b);

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!

8
Example: Pre-defined Functions
So far, we used several pre-defined functions!
#include <stdio.h> double sin(double radian);
#include <math.h>
double sin(double radian)
int main(void)
{
{
/* details of computing sin */
}
double angle;
printf(“Input angle in radians: \n“);
scanf(“%lf”, &angle);
printf(“The sine of the angle is %f\n“,
sin(angle) );
return 0;
}
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 x1,y1,x2,y2);
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));
}
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)
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
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
13
Exercise: void function

Write a program to
generate the
following output?
*
**
***
****
*****
for (i=1; i<=5; i++) {
for (j=1; j<=i; j++)
printf(“*”);
printf(“\n”);
}
#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;
}
14
Example: value returning
function
n!=n*(n-1)*…*1, 0! = 1 by definition
Return Type
Declarations
Statements
Function name
int fact(int n)
{
Parameter Declarations
int factres = 1;
while(n>1)
{
factres = factres*n;
n--;
}
return(factres);
}
15
Example – use fact()
#include <stdio.h>
int fact(int n); /* prototype */
int main(void)
{
int t= 5,s;
s = fact(t) + fact(t+1);
t=5
s=?
Function call
}
printf(“result is %d\n”, s);
return 0;
16
Example – execution of factorial
function (cont’d)
fact( 5 )
int fact(int n)
{
int factres = 1;
while(n>1)
{
factres = factres*n;
n--;
}
return(factres);
t=5
s=?
n=5
factres = 1
}
17
Example – execution of factorial
function (cont’d)
int fact(int n)
{
int factres = 1;
while(n>1)
{
factres = factres*n;
n--;
}
return(factres);
}
t=5
s=?
n=5 4 3 2 1
factres = 1 5 20
60 120
18
Example – execution of factorial
function (cont’d)
#include <stdio.h>
int fact(int n); /* prototype */
int main(void)
{
int t= 5,s;
s = 120 + fact(t+1);
t=5
s=?
Function call
}
printf(“result is %d\n”, s);
return 0;
19
Example – execution of factorial
function (cont’d)
fact( 6 )
t=5
int fact(int n)
{
int factres = 1;
s=?
t+1
while(n>1)
{
factres = factres*n;
n--;
}
return(factres);
n=6
factres = 1
}
20
Example – execution of factorial
function (cont’d)
int fact(int n)
{
int factres = 1;
while(n>1)
{
factres = factres*n;
n--;
}
return(factres);
}
t=5
s=?
n=6 5 4 3 2 1
factres = 1 6 30
120 360 720
21
Example – execution of
factorial function (cont’d)
#include <stdio.h>
int fact(int n); /* prototype */
int main(void)
{
int t= 5,s;
t=5
s = 840
s = 120 + 720;
}
printf(“result is %d\n”, s);
return 0;
result is 840
22
Example – reuse of factorial
function

Write a statement to compute
X ! Z !*5
y
K ! D!
Enter X, Z, K, D
…
y=(fact(X)+fact(Z)*5)/(fact(K)-fact(D));
23
Example – reuse of factorial
function in another function

Write a select function that takes n and k and
computes “n choose k” where
n
n!
  
 k  (n  k )!k!
int select(int n, int k)
{
return fact(n)/(fact(n-k)*fact(k));
}
24
Name Addr
Lecture++;
Lecture
Content
17
25
Function Examples
26
Exercise

Write a function to compute maximum and
minimum of two numbers
int max(int a, int b)
{
int min(int a, int b)
if (a > b)
{
return a;
if (a < b)
else
return a;
return b;
else
}
return b;
}
27
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));
}
28
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;
}
29
Exercise

Write a function that takes score as parameter and
computes and returns letter grade based on the scale
below.
80-100
60-79
40-59
0-39
A
B
C
D
30
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;
}
31
Exercise

Write a function to compute logba
log 10 a
log b a 
log 10 b
double log_any_base(double a, double b)
{
return log(a)/log(b);
}
32
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
33
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
In
In
In
function 2
function 1
function 3
function 2
34
Parameter Passing

Call by value



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
35
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
36
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=?
t=5
s=1
37
Scope

Local 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.
38
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();
printf("Z = %d\n",z);
z = z+a;
return 0;
}
z=2 5 9 12
a=4
a=3
Output
Z=5
Z=9
39
Storage Class - 4 types
Storage class refers to the lifetime of a variable
 automatic - key word auto - default for local variables


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


Memory set aside for local variables is not reserved when the block
in which the local variable was defined is exited.
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.
40
Skip

Study section 4.3 from the textbook
41
Name Addr
Lecture++;
Lecture
Content
18
42
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?
43
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?
44
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?
45
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
46
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;
}
*/
*/
47
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;
}
48
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;
49
}
Example: HiLo Game
/* Write a program that allows a user to play HiLo game.
User wins if he/she can guess the number between 1-100 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;
int secret;
/*
Declare variables */
printf("Enter a positive integer seed value: \n");
scanf("%u",&seed);
srand(seed);
while(1){
secret = rand_int(1,100);
playHiLo(secret);
}
return 0;
}
50
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");
return;
}
51
Exercise: Another “guess the
number game”




Computer selects a random number s between [1000
9999]
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
7436, 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
52
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;
}
53
4.5 Use of Floating-Point RNs:
Instrumentation Reliability



Reliability: the portion of
the time that the
component works
properly. For example,
0.8 means 80% of the
time the component is
OK
Given the reliability of
each component, can
you determine the
reliability of the whole
system?
Analytical vs. Simulation
54
Analytical vs. Simulation



Suppose the reliability for each component in previous
slide is the same and given by r
We can then analytically compute the overall reliability
for the systems in (a) and (b) as r3 and 3r-3r2+r3,
respectively. (how)
OR, we can simulate the system using RNs





Simulate each component by generating random numbers between 0 and 1.
If this number is less than r, then we consider the given component works properly.
If all three in (a) or at least one in (b) works properly, then we consider the whole
system works properly.
We repeat the above experiment (say) 1000 times and find that 600 times the
whole system worked properly. Then overall reliability is 600/1000=0.6.
Can you write a simulation program for any configuration where reliability of each
component could be different
55
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/*
Determine simulation reliability
estimates. */
for (k=1; k<=n; k++)
{
num1 = rand_float(0,1);
num2 = rand_float(0,1);
num3 = rand_float(0,1);
double rand_float(double a,double b);
int main(void)
{
unsigned int seed;
int n, k;
double component_reliability,
a_series, a_parallel,
series_success=0, parallel_success=0,
num1, num2, num3;
/* Get information for the simulation. */
printf("Enter individual \
component reliability: ");
scanf("%lf", &component_reliability);
printf("Enter number of trials: \n");
scanf("%i", &n);
printf("Enter unsigned integer seed: \n");
scanf("%u", &seed);
srand(seed);
printf("\n");
/* Compute Analytical reliabilities. */
a_series = pow(component_reliability,3);
a_parallel = 3*component_reliability
- 3*pow(component_reliability,2)
+ pow(component_reliability,3);
if (((num1<=component_reliability) &&
(num2<=component_reliability)) &&
(num3 <=component_reliability))
series_success++;
if (((num1<=component_reliability) ||
(num2<=component_reliability)) ||
(num3 <=component_reliability))
parallel_success++;
}
printf("Analytical Reliability \n");
printf("Series: %.3f Parallel: %.3f \n",
a_series,a_parallel);
printf("Simulation Reliability \n");
printf(" Number of trials %i \n",n);
printf("Series: %.3f Parallel: %.3f \n",
(double)series_success/n,
(double)parallel_success/n);
return 0;
}
double rand_float(double a,double b)
{
return ((double)rand()/RAND_MAX)*(b-a) + a;
}
56
Exercise

What will be the “if condition” in the
simulation code of the following system
Comp1, r1
Comp2, r2
Comp6, r6
Comp3, r3
Comp4, r4
Comp5, r5
if ( ( (num1<=r1 && num2<=r2) ||
(num4<=r4 && (num3<=r3||num5<=r5)) ) &&
(num6<=r6) )
success++;
57
SKIP REST

Study 4.6 and 4.7 from the textbook
58
4.8 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;
59
4.9 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)!
60
#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);
}
61
Fibonacci Numbers




Sequence {f0,f1,f2,…}. First two values (f0,f1)
are 1, each succeeding number is the sum of
previous two numbers.
1 1 2 3 5 8 13 21 34
F(0)=1, F(1) = 1
F(i) = F(i-1)+F(i-2)
62
Fibonacci Numbers
int fibonacci(int k)
{
int term;
term = 1;
if (k>1)
term = fibonacci(k-1)+fibonacci(k-2);
return term;
}
63
#include <stdio.h>
int fibonacci(int k)
{
int term = 1;
if (k>1)
term = fibonacci(k-1)+fibonacci(k-2);
/* 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);
}
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);
}
}
64
Extra examples
65
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);
}
66
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);
}
67
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
68
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;
}
69
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
min(a,c) = a
Max(a,b,a) = b
70
Solution
int median(int x, int y, int z)
{
return(max(min(x,y),min(x,z),min(y,z)));
}
71