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Jelly, 45 bytes L‘ḃ5MḢ;‘$œṖƲḅ5aị¥⁸N1¦Sṭ “¢¦½2d‘Çȷ6¡iḃ5ị“IVXLC Try it online! A pair of links that takes an integer as its argument and returns a string with the shortest generalised Roman num...
Answer
#3: Post edited
by
NikNakk
·
2023-11-30T09:34:43Z (12 months ago)
- # [Jelly], 45 bytes
- L‘ḃ5MḢ;‘$œṖƲḅ5aị¥⁸N1¦Sṭ
- “¢¦½2d‘Çȷ6¡iḃ5ị“IVXLC
- [Try it online!][TIO-lpkzui3t]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkzui3t]: https://tio.run/##y0rNyan8/9/nUcOMhzuaTX0f7lhkDWSrHJ38cOe0Y5se7mg1TXy4u/vQ0keNO/wMDy0LfrhzLdejhjmHFh1admivUQpQ7eH2E9tNDi3MBOkHKgVKeoZF@Dj////fxAQA "Jelly – Try It Online"
- A pair of links that takes an integer as its argument and returns a string with the shortest generalised Roman numeral. The TIO link is limited to finding the first 10,000 (rather than million) Roman numerals because it times out otherwise.
- Full explanation to follow, but this is a more efficient approach than the recursive one below because each substring of the Roman numerals is effectively memoised and used to calculate the longer ones. It also saves a couple of bytes which is nice!
- ## Previous version [Jelly], 47 bytes
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ?
“¢¦½2d‘ṗⱮ6ẎÇ€iị⁸ʋ%35ị“I LXVC- [Try it online!][TIO-lpkf59rf]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkf59rf]: https://tio.run/##y0rNyan8/9/34Y5F1o8aZqgcnfxw57Rjmw7Pf9S0xs/w0LLgY5uAUg93dNlzPWqYc2jRoWWH9hqlAFU@3Dn90cZ1Zg939R1uB6rNfLi7@1HjjlPdqsamIGbDHE8Fn4gw5////@saGgAA "Jelly – Try It Online"
(only checks Roman numerals up to length 6 since otherwise times out)- A full program that takes an integer argument and prints a string. Brute forces the answer by generating all possible Roman numerals with digits IVXLC up to length 8, evaluating them using the described method, and then finding the first which has the correct value.
- ## Explanation
- ```
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ? # Helper link: takes a Roman numeral (but made of the integer values of each digit) and returns its value
- Ʋ Ḋ? # If length >1 then following as a monad:
- Ʋ # - Following as a monad:
- Ḣ # - Head (get first index)
- M # - Indices of maximal values
- ;‘$ # - Concatenate to index plus 1
- œṖ # - Split the original Roman numeral at those two indices
- ߀ # - Call the helper link for each of the two or three groups generated
- N1¦ # - Negate first group
- S # - Sum
- Ḣ # Else: Head
-
- “¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC # Main link: takes an integer and returns the shortest numeral that evaluates to it
- “¢¦½2d‘ # Integers 1,5,10,50,100
- ṗⱮ8 # Cartesian power of these for each of 1 to 8
- Ẏ # Join outer lists
- ʋ # Following as a dyad using the list of lists of integers as the left argument and the main link’s argument as the right
- ǀ # - Call helper link for each of the list of lists of integers
- i # - Index of the original main link argument in these (so find the index of the shortest Roman numeral)
- ị⁸ # - Index into the list of lists of integers
- %35 # Mod 35
- ị“I LXVC # Modular index into "I LXVC" (Jelly will terminate the unterminated string at the end of the program)
- 💎
- ```
- Created with the help of [Luminespire](https://vyxal.github.io/Luminespire).
- # [Jelly], 45 bytes
- L‘ḃ5MḢ;‘$œṖƲḅ5aị¥⁸N1¦Sṭ
- “¢¦½2d‘Çȷ6¡iḃ5ị“IVXLC
- [Try it online!][TIO-lpkzui3t]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkzui3t]: https://tio.run/##y0rNyan8/9/nUcOMhzuaTX0f7lhkDWSrHJ38cOe0Y5se7mg1TXy4u/vQ0keNO/wMDy0LfrhzLdejhjmHFh1admivUQpQ7eH2E9tNDi3MBOkHKgVKeoZF@Dj////fxAQA "Jelly – Try It Online"
- A pair of links that takes an integer as its argument and returns a string with the shortest generalised Roman numeral. The TIO link is limited to finding the first 10,000 (rather than million) Roman numerals because it times out otherwise.
- Full explanation to follow, but this is a more efficient approach than the recursive one below because each substring of the Roman numerals is effectively memoised and used to calculate the longer ones. It also saves a couple of bytes which is nice!
- ## Previous version [Jelly], 47 bytes
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ?
- “¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC
- [Try it online!][TIO-lpkf59rf]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkf59rf]: https://tio.run/##y0rNyan8/9/34Y5F1o8aZqgcnfxw57Rjmw7Pf9S0xs/w0LLgY5uAUg93dNlzPWqYc2jRoWWH9hqlAFU@3Dn90cZ1Zg939R1uB6rNfLi7@1HjjlPdqsamIGbDHE8Fn4gw5////@saGgAA "Jelly – Try It Online"
- (TIO only checks Roman numerals up to length 6 since otherwise times out)
- A full program that takes an integer argument and prints a string. Brute forces the answer by generating all possible Roman numerals with digits IVXLC up to length 8, evaluating them using the described method, and then finding the first which has the correct value.
- ## Explanation
- ```
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ? # Helper link: takes a Roman numeral (but made of the integer values of each digit) and returns its value
- Ʋ Ḋ? # If length >1 then following as a monad:
- Ʋ # - Following as a monad:
- Ḣ # - Head (get first index)
- M # - Indices of maximal values
- ;‘$ # - Concatenate to index plus 1
- œṖ # - Split the original Roman numeral at those two indices
- ߀ # - Call the helper link for each of the two or three groups generated
- N1¦ # - Negate first group
- S # - Sum
- Ḣ # Else: Head
-
- “¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC # Main link: takes an integer and returns the shortest numeral that evaluates to it
- “¢¦½2d‘ # Integers 1,5,10,50,100
- ṗⱮ8 # Cartesian power of these for each of 1 to 8
- Ẏ # Join outer lists
- ʋ # Following as a dyad using the list of lists of integers as the left argument and the main link’s argument as the right
- ǀ # - Call helper link for each of the list of lists of integers
- i # - Index of the original main link argument in these (so find the index of the shortest Roman numeral)
- ị⁸ # - Index into the list of lists of integers
- %35 # Mod 35
- ị“I LXVC # Modular index into "I LXVC" (Jelly will terminate the unterminated string at the end of the program)
- 💎
- ```
- Created with the help of [Luminespire](https://vyxal.github.io/Luminespire).
#2: Post edited
by
NikNakk
·
2023-11-30T09:32:31Z (12 months ago)
# [Jelly], 47 bytes- MḢ;‘$œṖƲ߀N1¦SƲḢḊ?
- “¢¦½2d‘ṗⱮ6ẎÇ€iị⁸ʋ%35ị“I LXVC
- [Try it online!][TIO-lpkf59rf]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkf59rf]: https://tio.run/##y0rNyan8/9/34Y5F1o8aZqgcnfxw57Rjmw7Pf9S0xs/w0LLgY5uAUg93dNlzPWqYc2jRoWWH9hqlAFU@3Dn90cZ1Zg939R1uB6rNfLi7@1HjjlPdqsamIGbDHE8Fn4gw5////@saGgAA "Jelly – Try It Online"
- (only checks Roman numerals up to length 6 since otherwise times out)
- A full program that takes an integer argument and prints a string. Brute forces the answer by generating all possible Roman numerals with digits IVXLC up to length 8, evaluating them using the described method, and then finding the first which has the correct value.
- ## Explanation
- ```
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ? # Helper link: takes a Roman numeral (but made of the integer values of each digit) and returns its value
- Ʋ Ḋ? # If length >1 then following as a monad:
- Ʋ # - Following as a monad:
- Ḣ # - Head (get first index)
- M # - Indices of maximal values
- ;‘$ # - Concatenate to index plus 1
- œṖ # - Split the original Roman numeral at those two indices
- ߀ # - Call the helper link for each of the two or three groups generated
- N1¦ # - Negate first group
- S # - Sum
- Ḣ # Else: Head
-
- “¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC # Main link: takes an integer and returns the shortest numeral that evaluates to it
- “¢¦½2d‘ # Integers 1,5,10,50,100
- ṗⱮ8 # Cartesian power of these for each of 1 to 8
- Ẏ # Join outer lists
- ʋ # Following as a dyad using the list of lists of integers as the left argument and the main link’s argument as the right
- ǀ # - Call helper link for each of the list of lists of integers
- i # - Index of the original main link argument in these (so find the index of the shortest Roman numeral)
- ị⁸ # - Index into the list of lists of integers
- %35 # Mod 35
- ị“I LXVC # Modular index into "I LXVC" (Jelly will terminate the unterminated string at the end of the program)
- 💎
- ```
- Created with the help of [Luminespire](https://vyxal.github.io/Luminespire).
- # [Jelly], 45 bytes
- L‘ḃ5MḢ;‘$œṖƲḅ5aị¥⁸N1¦Sṭ
- “¢¦½2d‘Çȷ6¡iḃ5ị“IVXLC
- [Try it online!][TIO-lpkzui3t]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkzui3t]: https://tio.run/##y0rNyan8/9/nUcOMhzuaTX0f7lhkDWSrHJ38cOe0Y5se7mg1TXy4u/vQ0keNO/wMDy0LfrhzLdejhjmHFh1admivUQpQ7eH2E9tNDi3MBOkHKgVKeoZF@Dj////fxAQA "Jelly – Try It Online"
- A pair of links that takes an integer as its argument and returns a string with the shortest generalised Roman numeral. The TIO link is limited to finding the first 10,000 (rather than million) Roman numerals because it times out otherwise.
- Full explanation to follow, but this is a more efficient approach than the recursive one below because each substring of the Roman numerals is effectively memoised and used to calculate the longer ones. It also saves a couple of bytes which is nice!
- ## Previous version [Jelly], 47 bytes
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ?
- “¢¦½2d‘ṗⱮ6ẎÇ€iị⁸ʋ%35ị“I LXVC
- [Try it online!][TIO-lpkf59rf]
- [Jelly]: https://github.com/DennisMitchell/jelly
- [TIO-lpkf59rf]: https://tio.run/##y0rNyan8/9/34Y5F1o8aZqgcnfxw57Rjmw7Pf9S0xs/w0LLgY5uAUg93dNlzPWqYc2jRoWWH9hqlAFU@3Dn90cZ1Zg939R1uB6rNfLi7@1HjjlPdqsamIGbDHE8Fn4gw5////@saGgAA "Jelly – Try It Online"
- (only checks Roman numerals up to length 6 since otherwise times out)
- A full program that takes an integer argument and prints a string. Brute forces the answer by generating all possible Roman numerals with digits IVXLC up to length 8, evaluating them using the described method, and then finding the first which has the correct value.
- ## Explanation
- ```
- MḢ;‘$œṖƲ߀N1¦SƲḢḊ? # Helper link: takes a Roman numeral (but made of the integer values of each digit) and returns its value
- Ʋ Ḋ? # If length >1 then following as a monad:
- Ʋ # - Following as a monad:
- Ḣ # - Head (get first index)
- M # - Indices of maximal values
- ;‘$ # - Concatenate to index plus 1
- œṖ # - Split the original Roman numeral at those two indices
- ߀ # - Call the helper link for each of the two or three groups generated
- N1¦ # - Negate first group
- S # - Sum
- Ḣ # Else: Head
-
- “¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC # Main link: takes an integer and returns the shortest numeral that evaluates to it
- “¢¦½2d‘ # Integers 1,5,10,50,100
- ṗⱮ8 # Cartesian power of these for each of 1 to 8
- Ẏ # Join outer lists
- ʋ # Following as a dyad using the list of lists of integers as the left argument and the main link’s argument as the right
- ǀ # - Call helper link for each of the list of lists of integers
- i # - Index of the original main link argument in these (so find the index of the shortest Roman numeral)
- ị⁸ # - Index into the list of lists of integers
- %35 # Mod 35
- ị“I LXVC # Modular index into "I LXVC" (Jelly will terminate the unterminated string at the end of the program)
- 💎
- ```
- Created with the help of [Luminespire](https://vyxal.github.io/Luminespire).
#1: Initial revision
by
NikNakk
·
2023-11-30T00:29:07Z (12 months ago)
# [Jelly], 47 bytes
MḢ;‘$œṖƲ߀N1¦SƲḢḊ?
“¢¦½2d‘ṗⱮ6ẎÇ€iị⁸ʋ%35ị“I LXVC
[Try it online!][TIO-lpkf59rf]
[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-lpkf59rf]: https://tio.run/##y0rNyan8/9/34Y5F1o8aZqgcnfxw57Rjmw7Pf9S0xs/w0LLgY5uAUg93dNlzPWqYc2jRoWWH9hqlAFU@3Dn90cZ1Zg939R1uB6rNfLi7@1HjjlPdqsamIGbDHE8Fn4gw5////@saGgAA "Jelly – Try It Online"
(only checks Roman numerals up to length 6 since otherwise times out)
A full program that takes an integer argument and prints a string. Brute forces the answer by generating all possible Roman numerals with digits IVXLC up to length 8, evaluating them using the described method, and then finding the first which has the correct value.
## Explanation
```
MḢ;‘$œṖƲ߀N1¦SƲḢḊ? # Helper link: takes a Roman numeral (but made of the integer values of each digit) and returns its value
Ʋ Ḋ? # If length >1 then following as a monad:
Ʋ # - Following as a monad:
Ḣ # - Head (get first index)
M # - Indices of maximal values
;‘$ # - Concatenate to index plus 1
œṖ # - Split the original Roman numeral at those two indices
߀ # - Call the helper link for each of the two or three groups generated
N1¦ # - Negate first group
S # - Sum
Ḣ # Else: Head
“¢¦½2d‘ṗⱮ8ẎÇ€iị⁸ʋ%35ị“I LXVC # Main link: takes an integer and returns the shortest numeral that evaluates to it
“¢¦½2d‘ # Integers 1,5,10,50,100
ṗⱮ8 # Cartesian power of these for each of 1 to 8
Ẏ # Join outer lists
ʋ # Following as a dyad using the list of lists of integers as the left argument and the main link’s argument as the right
Ç€ # - Call helper link for each of the list of lists of integers
i # - Index of the original main link argument in these (so find the index of the shortest Roman numeral)
ị⁸ # - Index into the list of lists of integers
%35 # Mod 35
ị“I LXVC # Modular index into "I LXVC" (Jelly will terminate the unterminated string at the end of the program)
💎
```
Created with the help of [Luminespire](https://vyxal.github.io/Luminespire).