Decode and Encode Roman Numerals

[TorQ Guru]

Write two functions one, to encode, the other to decode all integers between 1 and 20000 from and to Roman Numerals. 

( https://en.wikipedia.org/wiki/Roman_numerals )

TM

[ryan sparks]

Here's one way, needs a bit of setup with dictionaries. I have encode expecting a list as the vectorised version is a lot faster than the atomic. However for decode just left it as atomic because making it work for lists just involved putting in a bunch of each's in and didn't really speed things up at all. 

/ make a&b dicts of nums->romans

/ and romans->nums respectively

k:13#,/(10*)\1 4 5 9

s:$`I`IV`V`IX`X`XL`L`XC`C`CD`D`CM`M

a:k!s

b:@[s;&1=#:'s;*:]!k

d:{+/@[r;-1+1_&:(>)':r:b x;-:]}

e:{*{(x[0],'a n;i-n:k k bin i:x 1)}/[((#x)#,"";x)]}

Here's a website I was testing the results on if anyone else wants it (the website has a blank line after 1491 for some reason, hence extra ugliness below)

test:t@\:<*t:0^@[;1;.q.trim]("J*";"=")0:2001#14_"\n"\:.Q.hg`:http://oeis.org/A006968/a006968.txt

e[!2001]~test 1

d'[test 1]~test 0

Cheers

Ryan

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[Muneish Adya]

Encoding is simple:

q)seed:([]I:1 4 5 9 10 40 50 90 100 400 500 900 1000;R:`I`IV`V`IX`X`XL`L`XC`X`CD`D`CM`M);

q)result:([I:`int$()]R:());

q)`result upsert {(x;1_{idx:seed[`I] bin x[0]; (x[0]-seed[`I]idx ; x[1],seed[`R]idx)}/[{x[0]};(x;`)][1])} each 1+til 20000

q)0N!result

or 

q)`result upsert {(x;`$raze string {idx:seed[`I] bin x[0]; (x[0]-seed[`I]idx ; x[1],seed[`R]idx)}/[{x[0]};(x;`)][1])} each 1+til 20000

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[Rahul Asati]

Encode:
v:1 4 5 9 10 40 50 90 100 400 500 900 1000; / value ranges
m:("I";"IV";"V";"IX";"X";"XL";"L";"XC";"C";"CD";"D";"CM";"M")   / corresponding roman number
encode:{first {(x[0],m i;x[1]-v i:v bin x 1);x) 1>x 1}/[(();x)]}

q) encode 15  / "XV"

Decode:

d:"IVXLCDM"!1 5 10 50 100 500 1000;
decode:{sum a*-1_1,?[a<=next a:reverse (),d x;1;-1]}

q) decode "XV"  / 15

Decode will convert all valid roman numbers to integers but side effect to that is it will also convert invalid roman numbers.
We can create a function to check validity of a roman number by applying all basic rules but I have used encode and decode functions to create one:

isValid:{x~encode decode x}
q) isValid "CCXIC"  / 0b


valid:{x~encode decode x}

[Ryan McCarron]

Encoding with the values from 1-10 and the symbols used in each order of magnitude:

b:(1+til 9)!("i";"ii";"iii";"iv";"v";"vi";"vii";"viii";"ix")

o:("xvi";"clx";"mdc";"XVm";"CLX";"MDC")

dr:{(raze reverse ((count a)#o)@'"xvi"?/:b reverse a:10 vs x) except " "}

Decoding by comparing number pairs:

nl:"ivxlcdmIVXLCDM"

n:nl!1 5 10 50 100 500 1000 1000 5000 10000 50000 100000 500000 1000000

rd:{{x+$[0>(-) . nl?"i"^y;neg n first y;n first y]}/[0;x,'next x]}

Note I've used the lowercase for normal numerals, and uppercase for 1000x that numeral (instead of the vinculum system on the wiki)

[Neill, Rolf]

(building on the work of others)

 

a:1 4 5 9 10 40 50 90 100 400 500 900 1000

b:("I";"IV";"V";"IX";"X";"XL";"L";"XC";"C";"CD";"D";"CM";"M")

e:{raze b a?-1*1_deltas -1_{x-a a bin x}\[x]}

d:{sum r*1+-2*next(>':)r:a b?x}

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[ryan sparks]

Cool, doing r*1 -2+ on the decode is nice. Inspired by this, and also using ryan's idea for lower/upper casing for big numbers (never knew roman numerals went beyond about 3000), another similar way for the decode (vector input/output):

k)b:("I";"IV";"V";"IX";"X";"XL";"L";"XC";"C";"CD";"D";"CM";"M";"Mv";"v";"Mx";"x")!17#,/(10*)\1 4 5 9

// k/q basically the same here: sum each <-> +/']

d:{sum each r*1 -1 r<1_'(r:b x),'0}

encoded:e til 20000  // e in earlier email

d encoded

Cheers

Ryan

On Thu, Mar 9, 2017 at 11:06 AM, Neill, Rolf <Rolf....@mlp.com> wrote:

(building on the work of others)

 

a:1 4 5 9 10 40 50 90 100 400 500 900 1000

b:("I";"IV";"V";"IX";"X";"XL";"L";"XC";"C";"CD";"D";"CM";"M")

e:{raze b a?-1*1_deltas -1_{x-a a bin x}\[x]}

d:{sum r*1+-2*next(>':)r:a b?x}

 

 

From: kdb...@googlegroups.com [mailto:kdbtorq@googlegroups.com] On Behalf Of TorQ Guru
Sent: Tuesday, February 28, 2017 5:26 AM
To: AquaQ kdb+/TorQ
Subject: [Aquaq kdbtorq] Decode and Encode Roman Numerals

 

Write two functions one, to encode, the other to decode all integers between 1 and 20000 from and to Roman Numerals. 

( https://en.wikipedia.org/wiki/Roman_numerals )

 

TM

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