Question $1(15$ pts$)$

For the IntArrayBag class discussed in class $($you can use IntArrayBag.java from the textbook$),$ implement

a new method called equals with a boolean return value and one parameter. The parameter, called $b,$ is

another IntArrayBag. The method returns true if $b$ and the bag that activates the method have exactly

the same number of every element. Otherwise, the method returns false. Notice that the locations of the

elements in the data arrays are not necessarily the same. It is only the number of occurrences of each

element that must be the same.

For example, for the two bags $a=\{1,2,2,3\}$ and $b=\{2,3,1,2\},$ they are equal because they have the

same number of every element: one $1,$ two $2s,$ and one $3.$

Question $2(85$ pts$)$

In this question, you will design a data structure that can be used to store some locations in a three$-$

dimensional space.

We will implement the Location $3$DSet class to store a set of locations. The Location$3$DSet class should

implement the functionality of a collection whose space can grow automatically when adding more locations.

The class Location$3$DSet should define proper instance variables and implement the following methods.

$(5$ pts$)$ This class should include proper instance variables to keep all location objects and the actual

number of locations.

$(5$ pts$)$ A no$-$argument constructor, which initializes a Location $3$ DSet instance, sets its capacity to

$10,$ and creates an array to store $10$ Location$3$D objects.

public Location$3$DSet$()$

$(5$ pts$)$ The following method which returns the actual number of elements in this collection.

public int size$()$

$(5$ pts$)$ The following method which returns the capacity of this collection instance.

public int capacity$()$

$(5$ pts$)$ A method which adds one given Location $3$D object to the first available space of the

Location$3$D array in this Location$3$DSet instance. When the collection space is sufficient to hold

the new location, this location object can be directly added to the collection. Otherwise, you need to

double the space of the instance array by implementing a method ensureCapacity $($defined

below$).$ The precondition is that the location object a should NOT be null.

public void add$($Location$3$D a$)$

$(5$ pts$)$ A method to remove from the collection the location with the given $x,y,z.$

public boolean remove $($double $x,$ double $y,$ double z$)$

$(5$ pts$)$ The following method guarantees the capacity of the collection. If this collection's capacity is

smaller than the input parameter, this method sets the capacity to minimumCapacity and enlarges

the array to hold minimumCapacity objects; otherwise, this collection is left unchanged. The

precondition is that the input parameter minimumCapacity should be positive.

private void ensureCapacity$($int minimumCapacity$)$

$(5$ pts$)$ A method which checks whether the collection contains a location with the given $x,y,z.$

public boolean contains $($double $x,$ double y$,$ double z$)$

$(10$ pts$)$ A method to save $x,y,z$ of all locations in the set to a $.$csv file. The content format of the

$.$csv file should be:

$x,y,z$

$1\mathrm{.}0,1\mathrm{.}5,3\mathrm{.}0$

$2\mathrm{.}0,4\mathrm{.}0,5\mathrm{.}0$

$2\mathrm{.}5,3\mathrm{.}5,2\mathrm{.}1$

$(15$ pts$)$ Write a method to calculate the $3$ nearest neighbors of each location and store those in the

location's nearest neighbor array. We will use Euclidean distance to calculate the distances between

points.

public void find$\_$nearest$\_$neighbors$()$

The Euclidean distance between a point $A(x_A,y_A,z_A)$ and a point $B(x_B,y_B,z_B)$ is computed as

follows:

$d(A,B)=\sqrt[\phantom{2}]{(x_A-x_B{)}^2+(y_A-y_B{)}^2+(z_A-z_B{)}^2}$

$(10$ pts$)$ main $()$ method to thoroughly test your code.

Design test cases, put them in your main method, run your program through the test cases. One test

case need to read all the location information from the data file $($sample$.$csv on Canvas$)$ and add

those locations to a location set. You should not use an array with fixed size to keep the location

information. You cannot use any Java built$-$in collections $($e$.$g$.,$ ArrayList$)$ either.

public static void main$($String$[]$ args$)$

$(10$ pts$)$ Properly run javadoc command to generate java documents for your class.