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---
id: 5900f3c51000cf542c50fed7
title: 'Завдання 89: Римські цифри'
challengeType: 5
forumTopicId: 302204
dashedName: problem-89-roman-numerals
---
# --description--
Аби число, написане римськими цифрами, вважалося дійсним, необхідно дотримуватися основних правил. Попри те, що правила дозволяють виражати деякі числа кількома способами, завжди існує *best* спосіб написання певного числа.
- Цифри повинні бути розташовані в порядку спадання.
- М, С і Х не можуть бути виражені або перевищені меншими номіналами.
- D, L, і V можуть з'являтися тільки один раз.
На додаток до трьох правил, наведених вище, якщо використовуються від'ємні числа, необхідно дотримуватися наступних чотирьох правил.
- Тільки I, X та C можуть бути використані як початкова цифра у частині від’ємної пари.
- I можна розмістити лише перед V та X.
- X можна розмістити лише перед L та C.
- C можна розмістити лише перед D та M.
Наприклад, з'ясувалося, що існує принаймні шість способів написання числа шістнадцять:
<div style="margin-left: 4em; font-family: 'courier new', monospace;">
IIIIIIIIIIIIIIII<br>
VIIIIIIIIIII<br>
VVIIIIII<br>
XIIIIII<br>
VVVI<br>
XVI<br><br>
</div>
Проте, згідно із правилами лише XIIIIII та XVI є дійсними, а останній приклад вважається найбільш ефективним, оскільки він використовує найменшу кількість цифр.
Масив `roman` міститиме числа, написані дійсними, але не обов’язково мінімальними римськими цифрами.
Знайдіть кількість збережених символів, записавши кожен із них у мінімальній формі.
**Примітка:** Можна припустити, що всі римські цифри в масиві містять не більше чотирьох послідовних однакових одиниць.
# --hints--
`romanNumerals(testNumerals1)` має повертатись як число.
```js
assert(typeof romanNumerals(_testNumerals1) === 'number');
```
`romanNumerals(testNumerals1)` має повертатись як `19`.
```js
assert.strictEqual(romanNumerals(_testNumerals1), 19);
```
`romanNumerals(testNumerals2)` має повертатись як `743`.
```js
assert.strictEqual(romanNumerals(_testNumerals2), 743);
```
# --seed--
## --after-user-code--
```js
const _testNumerals1 = [
'XIIIIII', 'XVI', 'MMMCCLXVIIII', 'XXXXVI', 'MMMMXX', 'CCLI', 'CCCCXX', 'MMMMDCXXXXI', 'DCCCCIIII', 'MXVIIII'
];
const _testNumerals2 = [
'MMMMDCLXXII','MMDCCCLXXXIII','MMMDLXVIIII','MMMMDXCV','DCCCLXXII','MMCCCVI','MMMCDLXXXVII','MMMMCCXXI','MMMCCXX','MMMMDCCCLXXIII','MMMCCXXXVII','MMCCCLXXXXIX','MDCCCXXIIII','MMCXCVI','CCXCVIII','MMMCCCXXXII','MDCCXXX','MMMDCCCL','MMMMCCLXXXVI','MMDCCCXCVI','MMMDCII','MMMCCXII','MMMMDCCCCI','MMDCCCXCII','MDCXX','CMLXXXVII','MMMXXI','MMMMCCCXIV','MLXXII','MCCLXXVIIII','MMMMCCXXXXI','MMDCCCLXXII','MMMMXXXI','MMMDCCLXXX','MMDCCCLXXIX','MMMMLXXXV','MCXXI','MDCCCXXXVII','MMCCCLXVII','MCDXXXV','CCXXXIII','CMXX','MMMCLXIV','MCCCLXXXVI','DCCCXCVIII','MMMDCCCCXXXIV','CDXVIIII','MMCCXXXV','MDCCCXXXII','MMMMD','MMDCCLXIX','MMMMCCCLXXXXVI','MMDCCXLII','MMMDCCCVIIII','DCCLXXXIIII','MDCCCCXXXII','MMCXXVII','DCCCXXX','CCLXIX','MMMXI','MMMMCMLXXXXVIII','MMMMDLXXXVII','MMMMDCCCLX','MMCCLIV','CMIX','MMDCCCLXXXIIII','CLXXXII','MMCCCCXXXXV','MMMMDLXXXVIIII','MMMDCCCXXI','MMDCCCCLXXVI','MCCCCLXX','MMCDLVIIII','MMMDCCCLIX','MMMMCCCCXIX','MMMDCCCLXXV','XXXI','CDLXXXIII','MMMCXV','MMDCCLXIII','MMDXXX','MMMMCCCLVII','MMMDCI','MMMMCDLXXXIIII','MMMMCCCXVI','CCCLXXXVIII','MMMMCML','MMMMXXIV','MMMCCCCXXX','DCCX','MMMCCLX','MMDXXXIII','CCCLXIII','MMDCCXIII','MMMCCCXLIV','CLXXXXI','CXVI','MMMMCXXXIII','CLXX','DCCCXVIII','MLXVII','DLXXXX','MMDXXI','MMMMDLXXXXVIII','MXXII','LXI','DCCCCXLIII','MMMMDV','MMMMXXXIV','MDCCCLVIII','MMMCCLXXII','MMMMDCCXXXVI','MMMMLXXXIX','MDCCCLXXXI','MMMMDCCCXV','MMMMCCCCXI','MMMMCCCLIII','MDCCCLXXI','MMCCCCXI','MLXV','MMCDLXII','MMMMDXXXXII','MMMMDCCCXL','MMMMCMLVI','CCLXXXIV','MMMDCCLXXXVI','MMCLII','MMMCCCCXV','MMLXXXIII','MMMV','MMMV','DCCLXII','MMDCCCCXVI','MMDCXLVIII','CCLIIII','CCCXXV','MMDCCLXXXVIIII','MMMMDCLXXVIII','MMMMDCCCXCI','MMMMCCCXX','MMCCXLV','MMMDCCCLXIX','MMCCLXIIII','MMMDCCCXLIX','MMMMCCCLXIX','CMLXXXXI','MCMLXXXIX','MMCDLXI','MMDCLXXVIII','MMMMDCCLXI','MCDXXV','DL','CCCLXXII','MXVIIII','MCCCCLXVIII','CIII','MMMDCCLXXIIII','MMMDVIII','MMMMCCCLXXXXVII','MMDXXVII','MMDCCLXXXXV','MMMMCXLVI','MMMDCCLXXXII','MMMDXXXVI','MCXXII','CLI','DCLXXXIX','MMMCLI','MDCLXIII','MMMMDCCXCVII','MMCCCLXXXV','MMMDCXXVIII','MMMCDLX','MMMCMLII','MMMIV','MMMMDCCCLVIII','MMMDLXXXVIII','MCXXIV','MMMMLXXVI','CLXXIX','MMMCCCCXXVIIII','DCCLXXXV','MMMDCCCVI','LI','CLXXXVI','MMMMCCCLXXVI','MCCCLXVI','CCXXXIX','MMDXXXXI','MMDCCCXLI','DCCCLXXXVIII','MMMMDCCCIV','MDCCCCXV','MMCMVI','MMMMCMLXXXXV','MMDCCLVI','MMMMCCXLVIII','DCCCCIIII','MMCCCCIII','MMMDCCLXXXVIIII','MDCCCLXXXXV','DVII','MMMV','DCXXV','MMDCCCXCV','DCVIII','MMCDLXVI','MCXXVIII','MDCCXCVIII','MMDCLX','MMMDCCLXIV','MMCDLXXVII','MMDLXXXIIII','MMMMCCCXXII','MMMDCCCXLIIII','DCCCCLXVII','MMMCLXXXXIII','MCCXV','MMMMDCXI','MMMMDCLXXXXV','MMMCCCLII','MMCMIX','MMDCCXXV','MMDLXXXVI','MMMMDCXXVIIII','DCCCCXXXVIIII','MMCCXXXIIII','MMDCCLXXVIII','MDCCLXVIIII','MMCCLXXXV','MMMMDCCCLXXXVIII','MMCMXCI','MDXLII','MMMMDCCXIV','MMMMLI','DXXXXIII','MMDCCXI','MMMMCCLXXXIII','MMMDCCCLXXIII','MDCLVII','MMCD','MCCCXXVII','MMMMDCCIIII','MMMDCCXLVI','MMMCLXXXVII','MMMCCVIIII','MCCCCLXXIX','DL','DCCCLXXVI','MMDXCI','MMMMDCCCCXXXVI','MMCII','MMMDCCCXXXXV','MMMCDXLV','MMDCXXXXIV','MMD','MDCCCLXXXX','MMDCXLIII','MMCCXXXII','MMDCXXXXVIIII','DCCCLXXI','MDXCVIIII','MMMMCCLXXVIII','MDCLVIIII','MMMCCCLXXXIX','MDCLXXXV','MDLVIII','MMMMCCVII','MMMMDCXIV','MMMCCCLXIIII','MMIIII','MMMMCCCLXXIII','CCIII','MMMCCLV','MMMDXIII','MMMCCCXC','MMMDCCCXXI','MMMMCCCCXXXII','CCCLVI','MMMCCCLXXXVI','MXVIIII','MMMCCCCXIIII','CLXVII','MMMCCLXX','CCCCLXIV','MMXXXXII','MMMMCCLXXXX','MXL','CCXVI','CCCCLVIIII','MMCCCII','MCCCLVIII','MMMMCCCX','MCDLXXXXIV','MDCCCXIII','MMDCCCXL','MMMMCCCXXIII','DXXXIV','CVI','MMMMDCLXXX','DCCCVII','MMCMLXIIII','MMMDCCCXXXIII','DCCC','MDIII','MMCCCLXVI','MMMCCCCLXXI','MMDCCCCXVIII','CCXXXVII','CCCXXV','MDCCCXII','MMMCMV','MMMMCMXV','MMMMDCXCI','DXXI','MMCCXLVIIII','MMMMCMLII','MDLXXX','MMDCLXVI','CXXI','MMMDCCCLIIII','MMMCXXI','MCCIII','MMDCXXXXI','CCXCII','MMMMDXXXV','MMMCCCLXV','MMMMDLXV','MMMCCCCXXXII','MMMCCCVIII','DCCCCLXXXXII','MMCLXIV','MMMMCXI','MLXXXXVII','MMMCDXXXVIII','MDXXII','MLV','MMMMDLXVI','MMMCXII','XXXIII','MMMMDCCCXXVI','MMMLXVIIII','MMMLX','MMMCDLXVII','MDCCCLVII','MMCXXXVII','MDCCCCXXX','MMDCCCLXIII','MMMMDCXLIX','MMMMCMXLVIII','DCCCLXXVIIII','MDCCCLIII','MMMCMLXI','MMMMCCLXI','MMDCCCLIII','MMMDCCCVI','MMDXXXXIX','MMCLXXXXV','MMDXXX','MMMXIII','DCLXXIX','DCCLXII','MMMMDCCLXVIII','MDCCXXXXIII','CCXXXII','MMMMDCXXV','MMMCCCXXVIII','MDCVIII','MMMCLXXXXIIII','CLXXXI','MDCCCCXXXIII','MMMMDCXXX','MMMDCXXIV','MMMCCXXXVII','MCCCXXXXIIII','CXVIII','MMDCCCCIV','MMMMCDLXXV','MMMDLXIV','MDXCIII','MCCLXXXI','MMMDCCCXXIV','MCXLIII','MMMDCCCI','MCCLXXX','CCXV','MMDCCLXXI','MMDLXXXIII','MMMMDCXVII','MMMCMLXV','MCLXVIII','MMMMCCLXXVI','MMMDCCLXVIIII','MMMMDCCCIX','DLXXXXIX','DCCCXXII','MMMMIII','MMMMCCCLXXVI','DCCCXCIII','DXXXI','MXXXIIII','CCXII','MMMDCCLXXXIIII','MMMCXX','MMMCMXXVII','DCCCXXXX','MMCDXXXVIIII','MMMMDCCXVIII','LV','MMMDCCCCVI','MCCCII','MMCMLXVIIII','MDCCXI','MMMMDLXVII','MMCCCCLXI','MMDCCV','MMMCCCXXXIIII','MMMMDI','MMMDCCCXCV','MMDCCLXXXXI','MMMDXXVI','MMMDCCCLVI',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II','MCLXXXV','CDLXXXVII','DCVI','MMX','MMCCXIII','MMMMDCXX','MMMMXXVIII','DCCCLXII','MMMMCCCXLIII','MMMMCLXV','DXCI','MMMMCLXXX','MMMDCCXXXXI','MMMMXXXXVI','DCLX','MMMCCCXI','MCCLXXX','MMCDLXXII','DCCLXXI','MMMCCCXXXVI','MCCCCLXXXVIIII','CDLVIII','DCCLVI','MMMMDCXXXVIII','MMCCCLXXXIII','MMMMDCCLXXV','MMMXXXVI','CCCLXXXXIX','CV','CCCCXIII','CCCCXVI','MDCCCLXXXIIII','MMDCCLXXXII','MMMMCCCCLXXXI','MXXV','MMCCCLXXVIIII','MMMCCXII','MMMMCCXXXIII','MMCCCLXXXVI','MMMDCCCLVIIII','MCCXXXVII','MDCLXXV','XXXV','MMDLI','MMMCCXXX','MMMMCXXXXV','CCCCLIX','MMMMDCCCLXXIII','MMCCCXVII','DCCCXVI','MMMCCCXXXXV','MDCCCCXCV','CLXXXI','MMMMDCCLXX','MMMDCCCIII','MMCLXXVII','MMMDCCXXIX','MMDCCCXCIIII','MMMCDXXIIII','MMMMXXVIII','MMMMDCCCCLXVIII','MDCCCXX','MMMMCDXXI','MMMMDLXXXIX','CCXVI','MDVIII','MMCCLXXI','MMMDCCCLXXI','MMMCCCLXXVI','MMCCLXI','MMMMDCCCXXXIV','DLXXXVI','MMMMDXXXII','MMMXXIIII','MMMMCDIV','MMMMCCCXLVIII','MMMMCXXXVIII','MMMCCCLXVI','MDCCXVIII','MMCXX','CCCLIX','MMMMDCCLXXII','MDCCCLXXV','MMMMDCCCXXIV','DCCCXXXXVIII','MMMDCCCCXXXVIIII','MMMMCCXXXV','MDCLXXXIII','MMCCLXXXIV','MCLXXXXIIII','DXXXXIII','MCCCXXXXVIII','MMCLXXIX','MMMMCCLXIV','MXXII','MMMCXIX','MDCXXXVII','MMDCCVI','MCLXXXXVIII','MMMCXVI','MCCCLX','MMMCDX','CCLXVIIII','MMMCCLX','MCXXVIII','LXXXII','MCCCCLXXXI','MMMI','MMMCCCLXIV','MMMCCCXXVIIII','CXXXVIII','MMCCCXX','MMMCCXXVIIII','MCCLXVI','MMMCCCCXXXXVI','MMDCCXCIX','MCMLXXI','MMCCLXVIII','CDLXXXXIII','MMMMDCCXXII','MMMMDCCLXXXVII','MMMDCCLIV','MMCCLXIII','MDXXXVII','DCCXXXIIII','MCII','MMMDCCCLXXI','MMMLXXIII','MDCCCLIII','MMXXXVIII','MDCCXVIIII','MDCCCCXXXVII','MMCCCXVI','MCMXXII','MMMCCCLVIII','MMMMDCCCXX','MCXXIII','MMMDLXI','MMMMDXXII','MDCCCX','MMDXCVIIII','MMMDCCCCVIII','MMMMDCCCCXXXXVI','MMDCCCXXXV','MMCXCIV','MCMLXXXXIII','MMMCCCLXXVI','MMMMDCLXXXV','CMLXIX','DCXCII','MMXXVIII','MMMMCCCXXX','XXXXVIIII'
];
```
## --seed-contents--
```js
function romanNumerals(roman) {
return true;
}
// Only change code above this line
const testNumerals1 = [
'XIIIIII', 'XVI', 'MMMCCLXVIIII', 'XXXXVI', 'MMMMXX', 'CCLI', 'CCCCXX', 'MMMMDCXXXXI', 'DCCCCIIII', 'MXVIIII'
];
romanNumerals(testNumerals1);
```
# --solutions--
```js
function romanNumerals(roman) {
const numerals = [...roman];
const replaces = [
['VIIII', 'IX'],
['IIII', 'IV'],
['LXXXX', 'XC'],
['XXXX', 'XL'],
['DCCCC', 'CM'],
['CCCC', 'CD']
];
let savedChars = 0;
for (let i = 0; i < numerals.length; i++) {
const charsBefore = numerals[i].length;
for (let j = 0; j < replaces.length; j++) {
numerals[i] = numerals[i].replace(...replaces[j]);
}
const charsAfter = numerals[i].length;
savedChars += charsBefore - charsAfter;
}
return savedChars;
}
```