Chapter 11
Case Studies
Chapter 11: Case Studies
1
Finding Maximum in List
Init max
While not end of list
Read value
If (value>max)
max  value
Report max
Chapter 11
Need to know range of
values
Need to assign
sentinel, or use endof-file (ctrl-d in UNIX)
character.
Finding Maximum in List
2
Finding Maximum in List
Assume data are positive integers.
Set sentinel to -999 (or any non-positive
integer).
Write a
do-while
loop.
Chapter 11
max = –1;
printf("Enter value (–999 to end): ");
scanf("%d", &value);
while (value != –999) {
if (value > max)
max = value;
printf("Enter value (–999 to end): ");
scanf("%d", &value);
}
printf("Maximum is %d\n", max);
Finding Maximum in List
3
Finding Maximum in List
For the moment, to simplify matter, we assume
first data is n, the number of elements in the list.
max = –1;
printf("Enter the size of the list: ");
scanf("%d", &n);
for (i = 0; i < n; i++) {
printf("Enter value: ");
scanf("%d", &value);
if (value > max)
max = value;
}
printf("Maximum is %d\n", max);
Chapter 11
Finding Maximum in List
4
Finding Maximum in List
We may initialise first data value to max.
printf("Enter the size of the list: ");
scanf("%d", &n);
printf("Enter value: ");
scanf("%d", &value);
max = value;
for (i = 1; i < n; i++) {
printf("Enter value: ");
scanf("%d", &value);
if (value > max)
max = value;
}
printf("Maximum is %d\n", max);
Chapter 11
Finding Maximum in List
5
Problem
Find the maximum and second maximum of a
list of integers.
Do not assume the range of values for list
elements.
Assume first data is list size n, where n >= 2.
Chapter 11
Problem
6
Existential & Universal Test
Sometimes, we need to test some property in a
list. Two common tests are:
Existentiality: is there an element with a certain
property?
Universality: do all elements have a certain
property?
Chapter 11
Existential & Universal Test
7
Existential & Universal Test
Test for existentiality versus test for universality.
Is there a black egg among all eggs? This employs
existentiality.
Are all eggs white? This employs universality.
Their codes are different.
Chapter 11
Existential & Universal Test
8
Existential & Universal Test
Is there a black egg among all eggs?
Data representation: 'b' is black, 'w' is white.
black_exists = 0;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'b') {
black_exists = 1;
break;
}
}
if (black_exists)
printf("Black egg exists.\n");
else
printf("Black egg does not exist.\n");
Chapter 11
Existential & Universal Test
9
Existential & Universal Test
What is wrong with this code?
black_exists = 0;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'b')
black_exists = 1;
}
if (black_exists)
printf("Black egg exists.\n");
else
printf("Black egg does not exist.\n");
Chapter 11
Existential & Universal Test
10
Existential & Universal Test
What is wrong with this code?
black_exists = 0;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'b')
black_exists = 1;
else
black_exists = 0;
}
if (black_exists)
printf("Black egg exists.\n");
else
printf("Black egg does not exist.\n");
Chapter 11
Existential & Universal Test
11
Existential & Universal Test
Are all eggs white?
all_white = 1;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'b') {
all_white = 0;
break;
}
}
if (all_white)
printf("All eggs are white.\n");
else
printf("Not all eggs are white.\n");
Chapter 11
Existential & Universal Test
12
Existential & Universal Test
What is wrong with this code?
all_white = 0;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'w') {
all_white = 1;
break;
}
}
if (all_white)
printf("All eggs are white.\n");
else
printf("Not all eggs are white.\n");
Chapter 11
Existential & Universal Test
13
Existential & Universal Test
What is wrong with this code?
all_white = 0;
for (i = 0; i < n; i++) {
scanf("%c", &egg);
if (egg == 'w')
all_white = 1;
else
all_white = 0;
}
if (all_white)
printf("All eggs are white.\n");
else
printf("Not all eggs are white.\n");
Chapter 11
Existential & Universal Test
14
Problem
Given a list of integers, determine if the list is in
strictly increasing order. For example, (-3, 0, 6,
17) is in strictly increasing order, but (-6, 2, 2, 5)
and (5, 7, 8, 6) are not.
Do not assume the range of values for list
elements.
Assume first data is list size n, where n >= 0.
(An empty list and a list of one element are
trivially in strictly increasing order.)
Chapter 11
Problem
15
Quadratic Equations
A quadratic equation in x is of this form:
ax2 + bx + c = 0
Assume that a, b, and c are integers, and a is not
equal to zero.
Examples:
2x2 - 3x -7 = 0; -3x2 + 8x -3 = 0; x2 + 4 = 0
But 4x + 5 = 0; x3 + 3x2 + 2 = 0 are not.
Chapter 11
Quadratic Equations
16
Quadratic Equations
Write a program to request for the values a, b, c
of a quadratic equation and display the equation.
See three sample runs below.
$ quadratic
Enter a, b, c: 3, -7, 2
Quadratic equation is 3x^2 – 7x + 2 = 0
$ quadratic
Enter a, b, c: 0, 2, 4
This is not a quadratic equation.
$ quadratic
Enter a, b, c: -1, 0, -3
Quadratic equation is -x^2 – 3 = 0
Chapter 11
Quadratic Equations
17
Quadratic Equations
Add a loop in your program so that you can enter
many equations in a single run, as shown below.
$ quadratic
Enter a, b, c: 3, -7, 2
Quadratic equation is 3x^2 – 7x + 2 = 0
Do you want to continue (y/n)? y
Enter a, b, c: 0, 2, 4
This is not a quadratic equation.
Do you want to continue (y/n)? y
Enter a, b, c: -1, 0, -3
Quadratic equation is -x^2 – 3 = 0
Do you want to continue (y/n)? n
Bye!
Chapter 11
Quadratic Equations
18
Quadratic Equations
Recall that the roots are:
[ -b ±  (b2 - 4ac) ] / 2a
The discriminant is (b2 - 4ac). If this is
positive, then there are two real roots
zero, then there is only one real root
negative, then there are imaginary roots
Chapter 11
Quadratic Equations
19
Quadratic Equations
Solve the quadratic equations in your program, if
they have real roots.
$ quadratic
Enter a, b, c: 3, -7, 2
Quadratic equation is 3x^2 – 7x + 2 = 0
Real roots are: 2.00 and 0.33
Do you want to continue (y/n)? y
Enter a, b, c: 0, 2, 4
This is not a quadratic equation.
Do you want to continue (y/n)? y
Enter a, b, c: -1, 0, -3
Quadratic equation is -x^2 – 3 = 0
There are imaginary roots.
Do you want to continue (y/n)? n
Bye!
Chapter 11
Quadratic Equations
20
Factorisation
Write a program to enter a list of positive
integers, using zero as a sentinel to end the
input.
For each positive integer entered, find out its
factors, and display the factors as shown in the
example, in increasing order of factors. (Factor 1
is listed only once)
Chapter 11
Factorisation
21
Factorisation
Sample run.
Enter a positive integer (0 to end): 1
1 = 1
Enter a positive integer (0 to end): 5
1 = 1 * 5
Enter a positive integer (0 to end): 8
1 = 1 * 2 * 2 * 2
Enter a positive integer (0 to end): 90
1 = 1 * 2 * 3 * 3 * 5
Enter a positive integer (0 to end): 91
1 = 1 * 7 * 13
Enter a positive integer (0 to end): 0
Bye!
Chapter 11
Factorisation
22
Homework
Try exercises in preceding slides.
Chapter 11
Homework
23