We want to design a Java class for representing and manipulating lists of birthdays of persons.

Part 1. (4 points) For each Birthday object, the information of interest is:

• the day of the month (an integer between 1 and 31),
• the month (an integer between 1 and 12),
• the name of the person (a string).

• creation of a Birthday, given the day of the month, the month, and the name of the person;
• getDay: that returns the day of the month;
• getMonth: that returns the month;
• getName: that returns the name of the person.

Part 2. (16 points) Realize a Java class BirthdayList, to represent BirthdayList objects. Each birthday list is constituted by a sequence of birthdays, where each birthday is an instance of the class Birthday. A BirthdayList has also a size, which determines the maximum number of birthdays it can contain. The class BirthdayList should export the following functionalities:

• creation of a BirthdayList, given its size. Initially, the list is empty;
• numBirthdays: that returns the total number of birthdays in the list;
• numBirthdays: that, given a day d (an integer) and a month m (an integer), returns the number of persons in the list whose birthday is on day d and month m;
• getBirthday: that, given the name n of a person, returns the Birthday object for that person (i.e., for which the name is n), if such an object exists; and returns null otherwise;
• addBirthday: that, given a Birthday object b, inserts the birthday b in the list of birthdays, if a birthday with the same name as the one for b is not already present in the list. If such a birthday is already present in the list, an exception is thrown. If the birthday cannot be inserted because the number of birthdays in the list is already equal to the size of the list, an exception is thrown;
• addBirthday: that, given a day d (an integer), a month m (an integer), and a name n (a string), inserts a birthday with day d, month m, and name n in the list of birthdays, if a birthday for name n is not already present in the list. If such a birthday is already present in the list, an exception is thrown. If the birthday cannot be inserted because the number of birthdays in the list is already equal to the size of the list, an exception is thrown;
• removeBirthday: that, given a name n, removes the birthday for name n from the list of birthdays, if such a birthday is present in the list. If such a birthday is not present in the list, an exception is thrown;
• birthdaysOnDate: that, given a day d and a month m, returns an array of strings containing the names of all persons in the birthday list whose birthday is on day d and month m.
• nextBirthday: that, given a day d and a month m, returns the next birthday in the list after the date d/m. If there is more than one such birthday in the list, then a new birthday object is returned with the appropriate day and month and with name equal to null. Notice that a date after another one may refer to the following year. If the birthday list is empty, an exception is thrown.

Part 3. (6 points) Realize a static method personsWithBirthday, client of the class BirthdayList (i.e., external to such a class) that, given a BirthdayList object bl, a day d (an integer), a month m (an integer), and the name f of a file, writes on the file f the names of all those persons in the list whose birthday is on day d and month m, one name per line. The method should explicitly handle exceptions due to input/output errors that may occur.

Part 4. (4 points) Discuss the mechanism of dealing with errors in Java through exceptions. Give a complete example, where you show how a class for handling exceptions is defined, how an exception is thrown, and how an exception is handled by catching it.