FOSS World News: Roman Numerals and Bash

Monday, November 26, 2018

Roman Numerals and Bash

Fun with retro-coding a Roman numeral converter—I head back to my college years and solve me homework anew!

I earned a bachelor's degree in computer science back in the dawn of computing. Well, maybe it wasn't quite that long ago, but we did talk about Ada and FORTRAN in class. As a UCSD alumnus, however, it's no surprise that UCSD Pascal was the programming language of choice. Don't worry; no punch cards and no paper tape were involved in my educational endeavors.

As with modern computer science study, we spent a lot of time coding algorithms and solving problems and puzzles. I'm a board-gamer, so I was quite happy to try to solve the "dining philosophers problem", the "four color problem" or the "traveling salesman problem". You might well have tried to solve the same darn problems.

One coding problem that has stuck with me is a Roman numeral conversion program. As part of my first programming class, I recall it being a pretty tricky problem, but we didn't have the internet or GitHub to scrounge around for smart solutions or inspiration.

So, in the spirit of retro-coding, let's build a script that can convert Roman numerals into regular decimal equivalent values.

Roman Numerals

I know, you're saying "um, remind me, what are Roman numerals?", even though you see them all the time in movies and books. You just ignore the MCMLXIII that shows up as a copyright notice. What's funny is that the general industry consensus is that studios use those Roman numerals instead of the more understandable "Copyright 1963" to obfuscate the age of the film (by the way, MCMLXIII = 1963).

It turns out that Roman numerals are interesting because they are essentially grouped into logical segments. At its most basic, each letter has a specific decimal value, so let's start there (see Table 1 for the values).

Table 1. Roman Numerals and Their Values

Symbol	I	V	X	L	C	D	M
Value	1	5	10	50	100	500	1000

If you wanted to write the value 60 as Roman numerals, that's easy: LX. Reverse the two values, however, and it's a completely different value: XL = 40. Why? Because when a lower value symbol appears before a higher value symbol, it's considered a reduction of that value. The fancy name for this is subtractive notation.

In other words, LX = 50 + 10, but XL = L – X = 50 – 10.

Now you can see how the earlier value breaks into clusters of values based on whether a subsequent value is higher or lower than the current value. Here's the logic: