Another Task: Roman Numbers

Task:

We would like to write a function that will read the next number in the input in roman numerals, and return it as an integer. We will also write a driver program to test this function.

Unfortunately, C does not provide a "%R" conversion specifier, or anything like that, so we will have to write our own. The function will be similar to getchar(), in that it is given nothing and returns the next number in the input as an integer.

Where do we start?

As before, we need to design the overall program. We start with the five step process.

1. Understand the problem

What is this program supposed to do?

The program is supposed to read the next roman number from the input. The main objective is to write the function get_roman(), but we will also need a driver to test it.

What kind of information is it given? (What is the input?)

The number is to be read from the standard input, and consists of roman digits:

M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, I = 1

What kind of results is it to produce? (What is the output?)

The function should return the integer representation of the roman number. The driver should just print the result.

What formulas or techniques will be needed?

At first, the method seems straightforward; we just add up the values associated with each roman digit. However, roman numbers have an added twist - prefix digits. If a digit with a lower value precedes a digit with a larger value, the lower value should be subtract rather than added.

For example IV = 4 and IX = 9

2. Do a small example by hand

As an example, let's try the roman number representation of this year:

        M C M X C V

We process the number from left to right:

        M C M X C V

           1000

        M C M X C V

           1000 + 100  = 1100

        M C M X C V

           1100 - 100 + ( 1000 - 100 ) = 1900

                  undo

        M C M X C V

           1900 + 10   = 1910

        M C M X C V

           1910 - 10  + ( 100 - 10 )   = 1990

                 undo

        M C M X C V

           1990 + 5   = 1995

Write an algorithm for solving the problem

The Driver Algorithm:

    get the first number in roman numerals

    While there are more numbers

            print the number

            get the next number in roman numerals

The Roman Module Algorithm:

    Given: nothing

    Returns: an integer, converted from the input or EOF

    initialize previous digit

    get the first digit

    while we still have roman digits

            convert digit to its value

            if previous digit was a prefix

                adjust the total

            otherwise accumulate the total

            save this digit as previous

            get the next digit

    return the number of EOF

Translate the algorithm into a programming language (like C)

The code is shown in the Code for Lecture section under Roman. you can also find it in ~ee160/Code.lect/Roman