// 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]] = // (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] = def String2RomanNumeral(s: String) : Option[RomanNumeral] = // 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 = // some test casesRomanNumeral2Int(List(I,I,I,I)) // 4RomanNumeral2Int(List(I,V)) // 4RomanNumeral2Int(List(V,I)) // 6RomanNumeral2Int(List(I,X)) // 9RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979RomanNumeral2Int(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] = // some test casesString2Int("IIII") // 4 (though invalid roman numeral) String2Int("IV") // 4String2Int("VI") // 6String2Int("IX") // 9String2Int("MCMLXXIX") // 1979String2Int("MCMXLIV") // 1944String2Int("") // 0String2Int("MDCLXI") // 1661String2Int("MMMCMXCIX") // 3999String2Int("XLVIII") // 48String2Int("MMVIII") // 2008String2Int("MMXI") // 2011 String2Int("MIM") // 1999String2Int("MCMLVI") // 1956 String2Int("III") // 3String2Int("XXX") // 30String2Int("CCC") // 300String2Int("MMM") // 3000String2Int("VII") // 7String2Int("LXVI") // 66String2Int("CL") // 150String2Int("MCC") // 1200String2Int("IV") // 4String2Int("IX") // 9String2Int("XC") // 90String2Int("MDCLXVI") // 1666String2Int("VIV") // 9 (but should be written as IX) String2Int("IVX") // 14 (also invalid)// error casesString2Int("MC?I")String2Int("abc")// (5) The file roman.txt contains a list of roman numerals. // Read in these numerals, convert them into integers and then // add them all up.import io.Sourceimport scala.util._// function for reading files:// Source.fromFile("file_name")("ISO-8859-9")