1. Write a program that converts a number entered in Roman numerals to decimal form. Your program should consist of a class, say romanType. An object of romanType should do the following: a. Store the number as a Roman numeral. b. Convert and store the number into decimal form. c. Print the number as a Roman numeral or decimal number as requested by the user. (Write two separate functions-one to print the number as a Roman numeral and the other to print the number as a decimal number.) The decimal values of the Roman numerals are: M 1000 D 500 C 100 L 50 X 10 V 5 I 1 Remember, a larger numeral preceding a smaller numeral means addition, so LX is 60. A smaller numeral preceding a larger numeral means subtraction, so XL is 40. Any place in a decimal number, such as the is place, the 10s place, and so on, requires from zero to four Roman numerals. d. Test your program using the following Roman numerals: MCXIV, CCCLIX, and MDCLXVI.

2. Write the definition of the class dayType that implements the day of the week in a program. The class dayType should store the day, such as Sunday for Sunday. The program should be able to perform the following operations on an object of type dayType: a. Set the day. h. Print the day. c. Return the day. d. Return the next day. e. Return the previous day. f. Calculate and return the day by adding certain days to the current day. For example, if the current day is Monday and we add 4 days, the day to be returned is Friday. Similarly, if today is Tuesday and we add 13 days, the day to be returned is Monday. g. Add the appropriate constructors. -

3. Write the definitions of the functions to implement the operations for the Class dayType as defined in Programming Exercise 2. Also, write a program to test various operations on this class.

4. In this chapter, the class dateType was designed to implement the date in a program, but the member function setDate and the constructor do not check whether the date is valid before storing the date in the data members. Rewrite the definitions of the function setDate and the constructor so that the values for the month, day, and year are checked before storing the date into the data members. Add a function member, isLeapYear, to check whether a year is a leap year. Moreover, write a test program to test your class.

5. In Programming Exercise 2, the class dateType was designed and implemented to keep track of a date, but it has very limited operations. Redefine the class dateType so that it can perform the following operations on a date in addition to the operations already defined: a. Set the month. b. Set the day. c. Set the year. d. Return the month. e. Return the day. f. Return the year. g. Test whether the year is a leap year. h. Return the number of clays in the month. For example, if the date is 3-12-2011, the number of days to be returned is 31 because there are 31 days in March. I. Return the number of days passed in the year. For example, if the date is 3-18-2011, the number of days passed in the year is 77. Note that the number of days returned also includes the current day. 126 I Chapter 2: Object-Oriented Design (00D) and C++ I. Return the number of days remaining in the year. For example, if the date is 3-18-2011, the number of days remaining in the year is 288. k. Calculate the new date by adding a fixed number of days to the date. For example, if the date is 3-18-2011 and the days to be added 'are 25, the new date is 4-12-2011.

6. a. In Programming Exercise 1 in Chapter 1, we defined a class romanType to implement Roman numerals in a program. In that exercise, we also implemented a function, romanToDecimal, to convert a Roman numeral into its equivalent decimal number. Modify the definition of the class romanType so that the data members are declared as protected. Use the class string to manipulate the strings. Furthermore, overload the stream insertion and stream extraction operators for easy input and output. The stream insertion operator outputs the Roman numeral in the Roman format. Also, include a member function, decimalToRom'en, that converts the decimal number (the decimal number must be a positive integer) to an equivalent Roman numeral format. Write the definition of the member function decimalToRoman. For simplicity, we assume that only the letter I can appear in front of another letter and that it appears only in front of the letters v and X. For example, 4 is represented as IV, 9 is represented as Ix, 39 is represented as xxxix, and 49 is represented as xxxxix. Also, 40 will be represented as XXXX, 190 will be represented as CLXXXX, and so on. b. Derive a class extRomanType from the class romanType to do the following. In the class extRomanType, overload the arithmetic operators +, *, and / so that arithmetic operations can be performed on Roman numerals. Also, overload the pre- and postincrement and decrement operators as member functions of the class extRomanType. To add (subtract, multiply, or divide) Roman numerals, add (subtract, multiply, or divide, respectively) their decimal representations and then convert the result to the Roman numeral format. For subtraction, if the first number is smaller than the second number, output a message saying that, "Because the first number is smaller than the second, the numbers cannot be subtracted". Similarly, for division, the numerator must be larger than the denominator. Use similar conventions for the increment and decrement operators. c. Write the definitions of the functions to overload the operators described in part b. d. Write a program to test your class extRomanType.