We want to realize a program for the administration of a parking lot formed by a collection of parking places. For each parking place the following information has to be stored:

• whether it is free of occupied;
• licence plate of the car, when occupied (a string);
• time since when it is occupied (two integers, for hours and minutes).

Part 1 Write a class ParkingPlace, for handling a parking place, that implements the following methods:

• ParkingPlace() : constructor without parameters that constructs a parking place that is initially free;
• String toString() : that returns "-------" if the parking place is free, and the licence plate of the car, if the parking place is occupied;
• void carArrives(String plate, int hour, int minutes) : modifies the state of the parking place by setting it to occupied, sets the plate of the car that occupies the place to plate, and sets the time since when it is occupied to hour and minutes; if the parking place is already occupied, the method does nothing;
• void carLeaves() : modifies the state of the parking place by setting it to free;
• boolean free() : returns true if the parking place is free, false otherwise;
• String getCar() : returns the plate of the car that occupies the parking place, if the place is occupied, null otherwise;
• int getHour() : returns the hour since when the parking place is occupied, if the place is occupied, -1 otherwise;
• int getMinutes() : returns the minutes since when the parking place is occupied, if the place is occupied, -1 otherwise;

Use the example program TestParkingPlace.Java to test the class you have developed.

Part 2 Write a class UseParkingPlace that contains various public static methods that are clients of ParkingPlace. In the description of all methods below, we assume that a parking lot is always represented as an array of parking places. The class should contain the following methods:

1. static int firstFreePlace(ParkingPlace[] p) : that, given a parking lot p, returns the index of the first free parking place in p;
2. static int countFreePlaces(ParkingPlace[] p) : that, given a parking lot p, returns the number of free parking places in p;
3. static int[] freePlaces(ParkingPlace[] p) : that, given a parking lot p, returns an array of integers containing the indices of all free parking places in p;
4. static void carEnters(ParkingPlace[] p, String a, int hour, int minutes) : that, given a parking lot p, modifies the array p by inserting the car a (represented by its plate) in the first free parking place available in p, assigning hour and minutes as arrival time; if there is no free parking place in p, the method does nothing;
5. static void carExits(ParkingPlace[] p, String a) : that, given a parking lot p, modifies the array p by freeing the parking place where the car a is parked; if the car a is not present in the parking lot, the method does nothing;
6. static int longestParkedCar(ParkingPlace[] p) : that, given a parking lot p, returns the index of the parking place in which the longest parked car is present; if there is more than one such car, the method should return one of the indexes (chosen arbitrarily); if there is no car parked in the parking lot, the method should return -1;
7. static String[] allParkedCars(ParkingPlace[] p) : that, given a parking lot p, returns an array of strings that represent the plates of all cars present in p;
8. static ParkingPlace[] readParkingLotFromFile(String filename) : that, given the name of a file containing parkingPlace records, constructs an array of ParkingPlace that represents the parking lot having exactly the parking places stored on the file. Each parkingPlace record has the following form:

   free
   license-plate
   hour
   minutes
   

   where
   • free is "true" or "false",
   • license-plate is the license plate of the car if the parking place is occupied, the empty string otherwise,
   • hour and minutes are two integers that represent the arrival time of the car, if the parking place is occupied, the empty string otherwise;
   Suggestion: introduce an auxiliary method for reading a single record;
9. static void writeParkingLotToFile(ParkingPlace[] p, String filename) : that, given a parking lot p and the name of a file, writes on the file the parkingPlace records (see above) corresponding to the entire parking lot.

Part 3 Realize a class ParkingLot to represent parking lots, and whose objects support the same functionalities as those implemented in UseParkingPlace through static methods. The class should export also a constructor that takes as parameter a positive integer n and constructs a parking lot with n parking places that initially are all empty. Notice that the method readParkingLotFromFile, that takes as parameter a string representing a filename containing parkingPlace records (see above), and constructs a parking lot having exactly the parking places stored on the file, should be implemented as a static method that creates and returns an object of the class ParkingLot.