#Roman Numerals Challenge
To build the program (assumes you have maven installed):
./build.sh
You can then use the program:
./numerals iv
4
The system will accept upper or lowercase input.
To perform the tasks:
$ ./tasks.sh
Part 1
MMDCDXLIV is 2944
Part 2
VIV is 9
MIX is 1009
LID is not valid because
I may not be used as a prefix subtraction from D
DIX is 509
LICX is not valid because
I may not be used as a prefix subtraction from C
CLIX is 159
MMDLIV is 2554
MMXDLIV is not valid because
X may not be used as a prefix subtraction from D
MCMXCX is 2000
MCMXCVI is 1996
Controversy
Roman numerals, unlike modern arabic numerals, are not a single thing.
They existed for a long period of time and had no single interpretation.
The example parsed in the tasks, MMDCDXLIV, is considered by some parsers
to be invalid as DCD can be represented as CM and brevity normally decides
between two representations, similarly for VIV which is better represented as IX.
Further Rules
The addition of further rules which checked whether the representation was canonical,
ie the most short by comparing with the output from a reverse transform could be used
to eliminate VIV and MCMXCX.
How to Read Roman Numerals
###Know the symbols and their values.
Reading Roman numerals is pretty easy once you have the basic symbols and their corresponding values down pat.
I=1
V=5
X=10
L=50
C=100
D=500
M=1000
There are seven basic symbols. With these seven symbols you can fashion pretty much any number (with the exception of exotic numbers like negatives, decimals, etc.).
When one or more numeral is used to form a number, the value of each symbol is (generally) added together from left to right.
The letters are arranged from left to right in descending order of value to form a number:
II = 2
XXX (10+10+10) = 30
LII (50+1+1) = 52
MMLVII (1,000+1,000+50+5+1+1) = 2,057
In some instances, a lower numeral placed in front of a larger numeral indicates that the lower numeral should be subtracted from the larger.
The subtraction rule (usually) kicks in when you’re getting close to a number that has a unique symbol. Take 4, for instance. It’s just one number away from 5, which has its own symbol (“V”). Instead of writing out four “I”s, you’d simply write “IV,” which indicates that you subtract 1 from 5 to get 4. Easy peasy.
How about 9? It’s just one digit away from 10, which has its own symbol (“X”). So instead of “VIIII” (5+1+1+1+1), you’d write “IX” (1 subtracted from 10).
And what about 40? It’s just 10 away from 50 which has its own symbol (“L”), so instead of writing out XXXX, you’d simply put XL (10 subtracted from 50). Just remember, when you see a lower value in front of a higher value, this rule kicks in. Note only 1, 10, 100 can be used in the subtraction, the use of 5, 50 or 500 is not correct.
Some more examples of the subtraction rule in action:
29 = XXIX (10+10+(10-1))
399 = CCCXCIX (100+100+100+(100-10)+(10-1))
444 = CDXLIV ((500-100)+(50-10)+(5-1))
I = 1
IV = 4
V =5
IX = 9
X = 10
XL = 40
L = 50
XC = 90
C = 100
CD = 400
D = 500
CM = 900
M = 1000