Case Studies

1
Chapter 11

• Case Studies

2
Finding Maximum in List

• Init max
• While not end of list
• Read value
• If (valuegtmax)
• max ? value
• Report max

• Need to know range of values
• Need to assign sentinel, or use end-of-file
  (ctrl-d in UNIX) character.

3
Finding Maximum in List

• Assume data are positive integers.
• Set sentinel to -999 (or any non-positive
  integer).

Write a do-while loop.
4
Finding Maximum in List

• For the moment, to simplify matter, we assume
  first data is n, the number of elements in the
  list.

5
Finding Maximum in List

• We may initialise first data value to max.

6
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 gt 2.

7
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?

8
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.

9
Existential Universal Test

• Is there a black egg among all eggs?
• Data representation 'b' is black, 'w' is white.

10
Existential Universal Test

• What is wrong with this code?

11
Existential Universal Test

• What is wrong with this code?

12
Existential Universal Test

• Are all eggs white?

13
Existential Universal Test

• What is wrong with this code?

14
Existential Universal Test

• What is wrong with this code?

15
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 gt 0.
  (An empty list and a list of one element are
  trivially in strictly increasing order.)

16
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.

17
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.

18
Quadratic Equations

• Add a loop in your program so that you can enter
  many equations in a single run, as shown below.

19
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

20
Quadratic Equations

• Solve the quadratic equations in your program, if
  they have real roots.

21
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)

22
Factorisation

• Sample run.

23
Homework

• Try exercises in preceding slides.