CS 1401 Assignment #8

Date Assigned: Monday, October 22, or Tuesday, October 23, 2007.

Due Date: Monday, October 29, or Tuesday, October 30, 2007, before the beginning of your lab section.

Objective: The main objective of this assignment is to learn to design user-defined classes and ADTs.

Programming assignment: an interval [a, b] is characterized by its lower endpoint a and its upper endpoint b. A midpoint of the interval is defined as (a + b)/2, and its width is defined as b - a.

Arithmetic operations on the intervals are defined based on the following logic. For example, for addition, if I have between 5 and 8 dollars with me, and my friend has between 10 and 30, then the smallest amount we have together is 5 + 10 = 15, and the largest is 8 + 30 = 38.

For subtraction, if I have between 10 and 30 dollars, and I spend between 5 and 8 for lunch, then the smallest amount that will remain is when I had the smallest amount and spend the largest amount, i.e., 10 - 8 = 2. The largest remaining amount is when I had most money and spent the least amount of money, i.e., 30 - 5 = 25.

As a result, the arithmetic operations with intervals are defined as follows:

[a, b] + [c, d] = [a + c, b + d]
[a, b] - [c, d] = [a - d, b - c]
[a, b] * [c, d] = [min(a*c, a*d, b*c, b*d), max(a*c, a*d, b*c, b*d)]
1/[a, b] = [1/b, 1/a] if 0 is not in the interval [a, b]
  (and undefined otherwise)
[a, b]/[c, d] = [a, b] * (1/[c, d])

Describe a class whose elements are intervals, and methods include:

a constructor method,
methods to return (accessor) and to change (mutator) the values of the parameters,
methods for computing the midpoint and the width of an interval, and
method for the arithmetic operations.

Use your class in the main program to create the intervals [5, 8] and [10, 30] and to check that [5, 8] + [10, 30] = [15, 38] and [10, 30] - [5, 8] = [2, 25].

Homework assignment: on a separate sheet of paper, solve Ex. 6 from p. 520 and Ex. 16 from p. 522.

Deliverables: as instructed by your TA.