// Part 1 about Roman Numerals+ −
//=============================+ −
+ −
abstract class RomanDigit + −
case object I extends RomanDigit + −
case object V extends RomanDigit + −
case object X extends RomanDigit + −
case object L extends RomanDigit + −
case object C extends RomanDigit + −
case object D extends RomanDigit + −
case object M extends RomanDigit + −
+ −
type RomanNumeral = List[RomanDigit] + −
+ −
+ −
// (1) First write a polymorphic function that recursively+ −
// transforms a list of options into an option of a list.+ −
// As soon as a None is inside the list, the result is None. + −
// Otherwise produce a list of all Some's appended.+ −
+ −
def optionlist[A](xs: List[Option[A]]): Option[List[A]] = xs match {+ −
case Nil => Some(Nil)+ −
case x::xs => (x, optionlist(xs)) match {+ −
case (None, _) => None+ −
case (_, None) => None+ −
case (Some(y), Some(ys)) => Some(y::ys) + −
}+ −
}+ −
+ −
optionlist(List(Some(1), Some(2), Some(3)))+ −
optionlist(List(Some(1), None, Some(3)))+ −
optionlist(List())+ −
+ −
// (2) Write a function first a function that converts a character+ −
// into a roman digit (if possible). Then convert a string into+ −
// a roman numeral (if possible). If this is not possible, the functions+ −
// should return None.+ −
+ −
def Char2RomanDigit(c: Char): Option[RomanDigit] = c match {+ −
case 'I' => Some(I)+ −
case 'V' => Some(V)+ −
case 'X' => Some(X)+ −
case 'L' => Some(L)+ −
case 'C' => Some(C)+ −
case 'D' => Some(D)+ −
case 'M' => Some(M)+ −
case _ => None+ −
}+ −
+ −
def String2RomanNumeral(s: String) : Option[RomanNumeral] = + −
optionlist(s.toList.map(Char2RomanDigit))+ −
+ −
// some test cases+ −
String2RomanNumeral("IIII")+ −
String2RomanNumeral("IV")+ −
String2RomanNumeral("VI")+ −
String2RomanNumeral("IX")+ −
String2RomanNumeral("MCMLXXIX")+ −
String2RomanNumeral("MCMXLIV") + −
String2RomanNumeral("M C M X L I V") // None+ −
+ −
+ −
// (3) Write a recursive function RomanNumral2Int that converts a+ −
// RomanNumeral into an integer.+ −
+ −
def RomanNumeral2Int(rs: RomanNumeral): Int = rs match { + −
case Nil => 0+ −
case M::r => 1000 + RomanNumeral2Int(r) + −
case C::M::r => 900 + RomanNumeral2Int(r)+ −
case D::r => 500 + RomanNumeral2Int(r)+ −
case C::D::r => 400 + RomanNumeral2Int(r)+ −
case C::r => 100 + RomanNumeral2Int(r)+ −
case X::C::r => 90 + RomanNumeral2Int(r)+ −
case L::r => 50 + RomanNumeral2Int(r)+ −
case X::L::r => 40 + RomanNumeral2Int(r)+ −
case X::r => 10 + RomanNumeral2Int(r)+ −
case I::X::r => 9 + RomanNumeral2Int(r)+ −
case V::r => 5 + RomanNumeral2Int(r)+ −
case I::V::r => 4 + RomanNumeral2Int(r)+ −
case I::r => 1 + RomanNumeral2Int(r)+ −
}+ −
+ −
// some test cases+ −
RomanNumeral2Int(List(I,I,I,I)) // 4 (invalid roman number)+ −
RomanNumeral2Int(List(I,V)) // 4+ −
RomanNumeral2Int(List(V,I)) // 6+ −
RomanNumeral2Int(List(I,X)) // 9+ −
RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979+ −
RomanNumeral2Int(List(M,C,M,X,L,I,V)) // 1944+ −
+ −
+ −
// (4) Write a function that converts a string (containing+ −
// a roman numeral) into an integer (if possible). If not+ −
// this is not possible, the functions should return None.+ −
+ −
def String2Int(s: String): Option[Int] = + −
String2RomanNumeral(s).map(RomanNumeral2Int(_))+ −
+ −
// some test cases+ −
String2Int("IIII") // 4 (though invalid roman numeral) + −
String2Int("IV") // 4+ −
String2Int("VI") // 6+ −
String2Int("IX") // 9+ −
String2Int("MCMLXXIX") // 1979+ −
String2Int("MCMXLIV") // 1944+ −
String2Int("") // 0+ −
String2Int("MDCLXI") // 1661+ −
String2Int("MMMCMXCIX") // 3999+ −
String2Int("XLVIII") // 48+ −
String2Int("MMVIII") // 2008+ −
+ −
String2Int("MMXI") // 2011 + −
String2Int("MIM") // 2001+ −
String2Int("MCMLVI") // 1956 + −
+ −
String2Int("III") // 3+ −
String2Int("XXX") // 30+ −
String2Int("CCC") // 300+ −
String2Int("MMM") // 3000+ −
String2Int("VII") // 7+ −
String2Int("LXVI") // 66+ −
String2Int("CL") // 150+ −
String2Int("MCC") // 1200+ −
String2Int("IV") // 4+ −
String2Int("IX") // 9+ −
String2Int("XC") // 90+ −
String2Int("MDCLXVI") // 1666+ −
+ −
+ −
// error/none cases+ −
String2Int("MC?I") + −
String2Int("abc")+ −
+ −
+ −
+ −
// Part 2 about Validation of Roman Numerals+ −
//===========================================+ −
+ −
def Digit2Int(r: RomanDigit) = r match {+ −
case I => 1+ −
case V => 5+ −
case X => 10+ −
case L => 50+ −
case C => 100+ −
case D => 500+ −
case M => 1000+ −
}+ −
+ −
def runsAllowed(r: RomanDigit) = r match {+ −
case I | X | C | M => true+ −
case V | L | D => false+ −
}+ −
+ −
def subtractable(r1: RomanDigit, r2: RomanDigit) = (r1, r2) match {+ −
case (I, V) | (I, X) => true+ −
case (X, L) | (X, C) => true+ −
case (C, D) | (C, M) => true+ −
case _ => false+ −
}+ −
+ −
def isValidNumeral(digitList: RomanNumeral): Boolean = digitList match {+ −
+ −
// empty list is valid+ −
case Nil => true+ −
+ −
// no more than three runnables in succession+ −
case d1::d2::d3::d4::_ if (d1 == d2 && d1 == d3 && d1 == d4 && runsAllowed(d1)) => false+ −
+ −
// no more than one non-runnables in succession+ −
case d1::d2::_ if (d1 == d2 && !runsAllowed(d1)) => false+ −
+ −
// subtractable+ −
case d1::d2::_ if (Digit2Int(d1) < Digit2Int(d2) && !subtractable(d1, d2)) => false+ −
+ −
// followable1+ −
case d1::d2::d3::_ if (Digit2Int(d2) < Digit2Int(d3) && subtractable(d2,d3) && + −
Digit2Int(d1) < Digit2Int(d2) * 10) => false+ −
+ −
// followable2 + −
case d1::d2::d3::_ if (Digit2Int(d1) < Digit2Int(d2) && subtractable(d1,d2) && + −
Digit2Int(d1) <= Digit2Int(d3)) => false + −
+ −
// A single digit is always allowed+ −
case _::ds => isValidNumeral(ds) + −
+ −
}+ −
+ −
+ −
val invalids = List("IXC", "XCX", "IIII", "IIIII", "DD", "VL", "MIM", "XXCIII", "LXXIIX", "IIIIX",+ −
"IIXX", "ICM", "CIM", "VIV", "IVX", "MCMC", "XIIX", "IIXX")+ −
invalids.map(String2RomanNumeral(_)).flatten.map(isValidNumeral(_))+ −
invalids.map(String2RomanNumeral(_)).flatten.map((r) => (r, isValidNumeral(r)))+ −
+ −
+ −
val valids = List("IV", "VI", "IX", "MCMLXXIX", "MCMXLIV", "", "MDCLXI",+ −
"MMMCMXCIX", "XLVIII", "MMVIII", "MMXI", "MCMLVI", "III",+ −
"XXX", "CCC", "MMM", "VII", "LXVI", "CL", "MCC", "XC",+ −
"MDCLXVI")+ −
valids.map(String2RomanNumeral(_)).flatten.map(isValidNumeral(_))+ −
+ −
+ −
+ −
+ −
+ −
def Int2Roman(n: Int): RomanNumeral = n match {+ −
case 0 => Nil+ −
case n if (1000 <= n) => M :: Int2Roman(n - 1000)+ −
case n if (900 <= n) => C :: M :: Int2Roman(n - 900)+ −
case n if (500 <= n) => D :: Int2Roman(n - 500)+ −
case n if (400 <= n) => C :: D :: Int2Roman(n - 400)+ −
case n if (100 <= n) => C :: Int2Roman(n - 100)+ −
case n if (90 <= n) => X :: C :: Int2Roman(n - 90)+ −
case n if (50 <= n) => L :: Int2Roman(n - 50)+ −
case n if (40 <= n) => X :: L :: Int2Roman(n - 40)+ −
case n if (10 <= n) => X :: Int2Roman(n - 10)+ −
case n if (9 <= n) => I :: X :: Int2Roman(n - 9)+ −
case n if (5 <= n) => V :: Int2Roman(n - 5)+ −
case n if (4 <= n) => I :: V :: Int2Roman(n - 4)+ −
case n if (1 <= n) => I :: Int2Roman(n - 1)+ −
}+ −
+ −
+ −
Int2Roman(4)+ −
Int2Roman(6)+ −
Int2Roman(9)+ −
Int2Roman(1979)+ −
Int2Roman(1944)+ −
+ −
RomanNumeral2Int(List(I,V)) + −
RomanNumeral2Int(List(V,I)) + −
RomanNumeral2Int(List(I,X)) + −
RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) + −
RomanNumeral2Int(List(M,C,M,X,L,I,V))+ −
+ −
+ −