roman

roman.js

// Converting to/from roman numerals (1-4999)

const map = {
  1: 'I',
  5: 'V',
  10: 'X',
  50: 'L',
  100: 'C',
  500: 'D',
  1000: 'M',
}

const imap = {
  I: 1,
  V: 5,
  X: 10,
  L: 50,
  C: 100,
  D: 500,
  M: 1000,
}

const subs = {
  5: 1,
  10: 1,
  50: 10,
  100: 10,
  1000: 100,
};

const sortNumeric = (a, b) => a - b; 
const amounts = Object.keys(map).map(Number).sort(sortNumeric);

const dec2roman = n => {

  // Zero.
  if (n === 0)
    return ''

  // Exact match
  if (n in map) 
    return map[n]

  // Larger than largest amount, so just prepend that symbol.
  if (n > 1000) {
    return 'M' + dec2roman(n - 1000);
  }

  // Find next highest symbol 
  let index;
  for (var i = 0; i < amounts.length; i++) {
    if (amounts[i] > n) {
      index = i;
      break;
    }
  }

  const highDec = amounts[index];
  const highRoman = map[highDec];

  const lowDec = amounts[index - 1];
  const lowRoman = map[lowDec];

  // Return a 2 character decremented roman symbol like 'IV' or 'CM'
  if (highDec in subs) {
    const sub = subs[highDec];
    if (n >= highDec - sub) {
      return map[sub] + highRoman + dec2roman(n - (highDec - sub));
    }
  }

  // Prepend the next lowest symbol e.g. 'V' if n = 6. Then recurse with the
  // remainder.
  return lowRoman + dec2roman(n - lowDec);
}

const roman2dec = s => {
  const digits = s.split('')

  if (digits.length === 0) 
    return 0;

  if (digits.length === 1)
    return imap[digits.pop()]

  const first = digits.pop();
  const second = digits.pop();

  if (imap[second] < imap[first]) {
    const delta = imap[first] - imap[second]
    return delta + roman2dec(digits.join(''))
  }

  digits.push(second);

  return imap[first] + roman2dec(digits.join('')) 

}

for (var i = 0; i <= 100; i++) {
  const roman = dec2roman(i)
  console.log(i, roman, roman2dec(roman))
}