// Replacement Exam: Scala Part

//=======================================

// Roman Digits and 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]] = 

// some testcases

//optionlist(List(Some(1), Some(2), Some(3)))  // -> Some(List(1, 2, 3))

//optionlist(List(Some(1), None, Some(3)))     // -> None

//optionlist(List())                           // -> Some(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). In both  cases, if the conversion 

// 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 cases

//RomanNumeral2Int(List(I,I,I,I))         // 4

//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 

// this is not possible, the functions should return None.

//def String2Int(s: String): Option[Int] = 

// 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")       // 1999

//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

//String2Int("VIV")       // 9 (but should be written as IX) 

//String2Int("IVX")       // 14 (also invalid)

// error cases

//String2Int("I I I I")

//String2Int("MC?I")

//String2Int("abc")