roman number to decimal number

description

roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.

Symbol       Value
I             1
V             5
X             10
L             50
C             100
D             500
M             1000

for example, 2 is written as II in roman numeral, just two one's added together. 12 is written as XII, which is simply X + II. the number 27 is written as XXVII, which is XX + V + II.

roman numerals are usually written largest to smallest from left to right. however, the numeral for four is not IIII. instead, the number four is written as IV. because the one is before the five we subtract it making four. the same principle applies to the number nine, which is written as IX. there are six instances where subtraction is used:

• I can be placed before V (5) and X (10) to make 4 and 9.
• X can be placed before L (50) and C (100) to make 40 and 90.
• C can be placed before D (500) and M (1000) to make 400 and 900.

given a roman numeral, convert it to an integer.

constraints

• 1 <= s.length <= 15
• s contains only the characters (I, V, X, L, C, D, M).
• it is guaranteed that s is a valid roman numeral in the range [1, 3999].

solution

this time we are going to try to solve the challenge in 3 different ways. but firts, let's define two support Maps:

val symbolAndValue = Map(
    'I' -> 1,
    'V' -> 5,
    'X' -> 10,
    'L' -> 50,
    'C' -> 100,
    'D' -> 500,
    'M' -> 1000
  )

val specialSymbols = Map(
  "IV" -> 4,
  "IX" -> 9,
  "XL" -> 40,
  "XC" -> 90,
  "CD" -> 400,
  "CM" -> 900
)

scala as a better java

let's implement a function using scala as a better java). so, our function should:

• mutate state
• and, iterate not recurs

def romanToIntJavaLike(s: String): Int = {
  var sum = 0
  val size = s.length
  var i = 0
  while (i < size) {
    val a = s(i)

    // extracting next char
    val j = i + 1
    if (j < size) {
      val str = s"$a${s(j)}"

      // and finding if the pair of current and next is s special case
      specialSymbols.get(str) match {
        case Some(n) =>
          sum = sum + n
          i = i + 2
        case None =>
          symbolAndValue.get(a).foreach { n =>
            sum = sum + n
            i = i + 1
          }
      }
    } else {
      symbolAndValue.get(a).foreach { n =>
        sum = sum + n
        i = i + 1
      }
    }

  }

  sum
}

as you can see, ronamToIntJavaLike:

• defines a accumulator sum
• iterate its input string s char-by-char
• crusial part is checking if there is a next char from our current char so we can check if the pair is a special case

let's give it a try:

romanToIntJavaLike("III")     // 3
// res0: Int = 3     // 3
romanToIntJavaLike("LVIII")   // 58
// res1: Int = 58   // 58
romanToIntJavaLike("MCMXCIV") // 1994
// res2: Int = 1994

welp, implementation seems to work.

scala-ish?

the scala-ish solution should:

• be tail recursive
• leverage pattern matching

def romanToInt(s: String): Int = {
  val valueOfSymbol: Char => Int = symbolAndValue.getOrElse(_, 0)

  @tailrec
  def go(chars: List[Char], sum: Int): Int = {
    chars match {
      case c1 :: c2 :: tail =>
        specialSymbols.get(s"$c1$c2") match {
          case Some(n) => go(tail, sum + n)
          // note that if c1 and c2 pair was not an specil sumbol i.e. IV
          // we only discard c1 and c2 is part of our collection for the next
          // recursive call
          case None    => go(c2 :: tail, valueOfSymbol(c1) + sum)
        }
      case c1 :: tail => go(tail, valueOfSymbol(c1) + sum)
      case Nil        => sum
    }
  }

  go(s.toList, 0)
}

let's give it a try:

romanToInt("III")
// res3: Int = 3
romanToInt("LVIII")
// res4: Int = 58
romanToInt("MCMXCIV")
// res5: Int = 1994

welp, this implementation seem to work correctly too! yay!