// Part 1 about Roman Numerals+
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//=============================+
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+
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+
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abstract class RomanDigit +
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case object I extends RomanDigit +
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case object V extends RomanDigit +
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case object X extends RomanDigit +
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case object L extends RomanDigit +
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case object C extends RomanDigit +
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case object D extends RomanDigit +
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case object M extends RomanDigit +
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+
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type RomanNumeral = List[RomanDigit] +
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+
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// (1) First write a polymorphic function that recursively+
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// transforms a list of options into an option of a list.+
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// As soon as a None is inside the list, the result is None. +
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// Otherwise produce a list of all Some's appended.+
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+
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def optionlist[A](xs: List[Option[A]]): Option[List[A]] = +
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+
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// (2) Write a function first a function that converts a character+
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// into a roman digit (if possible). Then convert a string into+
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// a roman numeral (if possible). If this is not possible, the functions+
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// should return None.+
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+
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def Char2RomanDigit(c: Char): Option[RomanDigit] = +
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+
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def String2RomanNumeral(s: String) : Option[RomanNumeral] = +
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+
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+
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// some test cases+
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//String2RomanNumeral("IIII")+
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//String2RomanNumeral("IV")+
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//String2RomanNumeral("VI")+
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//String2RomanNumeral("IX")+
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//String2RomanNumeral("MCMLXXIX")+
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//String2RomanNumeral("MCMXLIV") +
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//String2RomanNumeral("M C M X L I V")  // None+
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+
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// (3) Write a recursive function RomanNumral2Int that converts a+
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// RomanNumeral into an integer.+
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+
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def RomanNumeral2Int(rs: RomanNumeral): Int = +
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+
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+
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// some test cases+
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RomanNumeral2Int(List(I,I,I,I))         // 4+
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RomanNumeral2Int(List(I,V))             // 4+
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RomanNumeral2Int(List(V,I))             // 6+
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RomanNumeral2Int(List(I,X))             // 9+
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RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979+
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RomanNumeral2Int(List(M,C,M,X,L,I,V))   // 1944+
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+
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// (4) Write a function that converts a string (containing+
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// a roman numeral) into an integer (if possible). If not+
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// this is not possible, the functions should return None.+
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+
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def String2Int(s: String): Option[Int] = +
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+
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// some test cases+
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String2Int("IIII")      // 4 (though invalid roman numeral)  +
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String2Int("IV")        // 4+
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String2Int("VI")        // 6+
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String2Int("IX")        // 9+
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String2Int("MCMLXXIX")  // 1979+
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String2Int("MCMXLIV")   // 1944+
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String2Int("")          // 0+
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String2Int("MDCLXI")    // 1661+
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String2Int("MMMCMXCIX") // 3999+
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String2Int("XLVIII")    // 48+
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String2Int("MMVIII")    // 2008+
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+
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String2Int("MMXI")      // 2011 +
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String2Int("MIM")       // 1999+
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String2Int("MCMLVI")    // 1956 +
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+
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String2Int("III") 	// 3+
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String2Int("XXX") 	// 30+
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String2Int("CCC") 	// 300+
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String2Int("MMM") 	// 3000+
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String2Int("VII") 	// 7+
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String2Int("LXVI") 	// 66+
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String2Int("CL") 	// 150+
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String2Int("MCC") 	// 1200+
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String2Int("IV") 	// 4+
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String2Int("IX") 	// 9+
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String2Int("XC") 	// 90+
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String2Int("MDCLXVI")	// 1666+
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+
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String2Int("VIV")       // 9 (but should be written as IX) +
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String2Int("IVX")       // 14 (also invalid)+
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+
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// error cases+
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String2Int("MC?I")+
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String2Int("abc")+
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+
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+
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// (5) The file roman.txt contains a list of roman numerals. +
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// Read in these numerals from the file, convert them into +
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// integers and then add them all up.+
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+
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import io.Source+
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import scala.util._+
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+
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// function for reading files:+
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// Source.fromFile("file_name")("ISO-8859-9")+
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+
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def addromanfile(filename: String) =+
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+
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//test case+
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addromanfile("roman.txt")+
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+
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+
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// Part 2 about Validation of Roman Numerals+
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//===========================================+
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+
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// (6) Write a function that validates roman numerals according+
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// to the rules given in the CW.+
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+
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def isValidNumeral(digitList: RomanNumeral): Boolean =+
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+
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+
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+
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// some test cases+
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val invalids = List("IXC", "XCX", "IIII", "IIIII", "DD", "VL", +
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                    "MIM", "XXCIII", "LXXIIX", "IIIIX", "IIXX", +
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                    "ICM", "CIM", "VIV", "IVX", "MCMC", "XIIX", "IIXX")+
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+
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val valids = List("IV", "VI", "IX", "MCMLXXIX", "MCMXLIV", "", "MDCLXI",+
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                  "MMMCMXCIX", "XLVIII", "MMVIII", "MMXI", "MCMLVI", "III",+
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                  "XXX", "CCC", "MMM", "VII", "LXVI", "CL", "MCC", "XC",+
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                  "MDCLXVI")+
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+
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// (7) Write a recursive function that converts an Integer into a+
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// a roman numeral. The input will be between 0 and 3999.+
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+
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def Int2Roman(n: Int): RomanNumeral =+
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+
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// (8) Write a function that reads a text file containing valid and +
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// invalid roman numerals. Convert all valid roman numerals into integers, +
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// add them up and produce the result as a roman numeral (using the +
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// function in (7)+
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+
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def addvalidromanfile(filename: String) =+
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+
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// a test case+
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//addvalidromanfile("roman2.txt")+
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