// This class provides methods to convert between decimal integers and Roman numerals
// Learning Objectives:
//    1) problem decomposition
//    2) static methods
//
public class RomanNumerals
{
   //Class Variable: Largest allowable decimal number
   public static final int MAXIMUM = 5000;
   
   //Construct the Roman Numerals equivalent of a given positive integer
   // Exception thrown if the integer exceeds the defined MAXIMUM value
   // @param decimal: a positive integer
   // @return: the Roman Numerals equivalent of the parameter
   public static String roman(int decimal)
   {
      if (decimal <= 0 || decimal > MAXIMUM)
         throw new RuntimeException("Number out of range 1 .. 5000");
         
      return repeated('M', digit(3, decimal)) +
             pattern('C', 'D', 'M', digit(2, decimal) ) +
             pattern('X', 'L', 'C', digit(1, decimal) ) +
             pattern('I', 'V', 'X', digit(0, decimal) ) ;
   }
   
   //Interpret a Roman Numerals String to get its decimal value
   // Error checking is limited to recognizing illegal numerals
   // @param roman: a Roman Numerals string
   // @return the decimal equivalent of the parameter
   public static int decimal(String roman)
   {
      int lastIndex = roman.length() - 1;
      int number = numeralValue( roman.charAt(lastIndex) );
      
      for (int i = 0; i < lastIndex; i++)
      {
         int one = numeralValue( roman.charAt(i) );
         int two = numeralValue( roman.charAt(i + 1) );
         if (one < two)
            number -= one;
         else
            number += one;
      }
      return number;
   }
   
   //Helper Method
   // @param numeral: a Roman Numeral - I, V, X, L, C, D, M
   // @return the decimal value associated with the parameter
   // Exception thrown is the parameter is invalid
   private static int numeralValue(char numeral)
   {
      switch ( numeral )
      {
         case 'I':  return 1;
         case 'V':  return 5;
         case 'X':  return 10;
         case 'L':  return 50;
         case 'C':  return 100;
         case 'D':  return 500;
         case 'M':  return 1000;
         default :  throw new RuntimeException("Invalid Numeral " + numeral);
      }
   }
   
   //Helper Method
   // @param symbol: any character
   // @param count: any non-negative integer
   // @return the String formed by catenating symbol count times
   private static String repeated(char symbol, int count)
   {
      String image = "";
      for ( int k = 1; k <= count; k++ )
         image += symbol;
         
      return image;
   }
   
   //Helper Method
   // @param index: the index of a desired digit from a given integer
   // @param number: an integer from which a digit is to be selected
   // @return the digit at the given index of the given integer
   private static int digit(int index, int number)
   {
      for ( int i = 1; i <= index; i++ )
         number /= 10;
      return number % 10;
   }
   
   //Helper Method
   // Compose a Roman-numeral sequence to represent a given single digit
   // @param i: a one's symbol  - I(units) or X(tens) or C(hundreds)
   // @param v: a five's symbol - V(units) or L(tens) or D(hundreds)
   // @param x: a ten's symbol  - X(units) or C(tens) or M(hundreds)
   // @param digit: a single-digit integer
   // @return the Roman Numerals string representing the given digit
   private static String pattern(char i, char v, char x, int digit)
   {
      switch ( digit )
      {
         case 0:  return "";
         case 1:  return "" + i;
         case 2:  return "" + i + i;
         case 3:  return "" + i + i + i;
         case 4:  return "" + i + v;
         case 5:  return "" + v;
         case 6:  return "" + v + i; 
         case 7:  return "" + v + i + i;
         case 8:  return "" + v + i + i + i;
         case 9:  return "" + i + x;
         default: throw new RuntimeException("Single Digit expected");
      }
   }
}