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. The class BirthdayList should export the following functionalities:

• creation of a BirthdayList that is initially 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;
• 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;
• 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.