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Your task is to write a program that reads the cube faces as input, followed by the turns. It then manipulates the cube by turning the faces clockwise (F/R/U/L/B/D), anti-clockwise (F’/R’/U’/L’/B’/D’) or halfway around (F2/R2/U2/L2/B2/D2). The final cube is then output. As an example, the input
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54
F
R’
U2
will give the output
……541518……
……510504……
……480201……
303336455352101137
131438262306293235
161739272412070809 ……343119……
……404120……
……434421……
……464728……
……495042……
……032225……
Take note of the following assumptions:
Input always begins with a set of 54 values specifying the face values of the 3 × 3 cube in order (top, left, front, right, down, back),
The numbers of the cube faces are positive (> 0) integers less than 100
Input turns are always valid
| $ javac *.java
$ jshell -q your_java_files_in_bottom-up_dependency_order < test1.jsh jshell> Face f = new Face(new int[][]{{1,2,3},{4,5,6},{7,8,9}}) jshell> Face g = f.clone() jshell> Cloneable c = g jshell> c.clone() $.. ==> 010203 040506 070809 jshell> f.right() $.. ==> 070401 080502 090603 jshell> f.left() $.. ==> 030609 020508 010407 jshell> f.half() $.. ==> 090807 060504 030201 jshell> g g ==> 010203 040506 070809 jshell> f.toIntArray() $.. ==> int[3][] { int[3] { 1, 2, 3 }, int[3] { 4, 5, 6 }, int[3] { 7, 8, 9 } } jshell> /exit |
This task is divided into several levels. Read through all the levels to see how the different levels are related. You need to complete all levels.
Level 1
Since a cube comprises six faces, let’s begin by developing the Face class. The cube face’s nine values can be represented using a 3 × 3 array of integers. Each face can also be rotated right or left.
Develop the following methods for the Face class:
Face(int[][] grid): the constructor that takes in the 3 × 3 array of integers
Face right(): performs a quarter rotation to the right and returns a new Face
Face left(): performs a quarter rotation to the left and returns a new Face
Face half(): performs a half rotation and returns a new Face
int[][] toIntArray(): returns the 3 × 3 integer grid of the Face object String toString(): returns a String representing the Face object
In addition, a Face object should be cloneable. That is, there is a clone() method that creates an immutable copy. Note that Face newFace.grid = this.grid is not enough, as both will reference the same grid. Write a Cloneable interface that enforces the definition of the clone method. This will be useful in a later level.
It is also worth noting that the Object class defines a similar clone() method with a protected access modifier. While we can override this with another clone() method in the Face class, the accessibility cannot be less restrictive than protected. Only by implementing the Cloneable interface, would the overriding clone() method be public accessible.
In addition, use String.format(“%02d”, …) to output the cube face’s values.
Level 2
With the Face class ready, we can proceed to develop Rubik. We define Rubik as a rubik’s cube with one face that can be turned using the following methods:
| $ javac *.java
$ jshell -q your_java_files_in_bottom-up_dependency_order < test2.jsh jshell> int[][][] grid = new int[6][3][3] jshell> int d = 1 jshell> for (int k = 0; k < 6; k++) …> for (int i = 0; i < 3; i++) …> for (int j = 0; j < 3; j++) grid[k][i][j] = d++; jshell> Rubik r = new Rubik(grid) | Error: | Rubik is abstract; cannot be instantiated | Rubik r = new Rubik(grid); | ^————-^ jshell> Rubik r = new RubikFront(grid) jshell> Rubik s = r.clone(); jshell> Cloneable c = s jshell> c.clone() $.. ==> ……010203…… ……040506…… ……070809…… 101112192021282930 131415222324313233 161718252627343536 ……373839…… ……404142…… ……434445…… ……464748…… ……495051…… ……525354……
jshell> r.left() $.. ==> ……010203…… ……040506…… ……283134…… 101109212427392930 131408202326383233 161707192225373536 ……121518…… ……404142…… ……434445…… ……464748…… ……495051…… ……525354……
jshell> r.right() $.. ==> ……010203…… ……040506…… ……181512…… 101137252219072930 131438262320083233 161739272421093536 ……343128…… ……404142…… ……434445…… ……464748…… ……495051…… ……525354……
jshell> r.half() $.. ==> ……010203…… ……040506…… ……393837…… 101134272625182930 131431242322153233 |
right(): turns the face clockwise left(): turns the face anti-clockwise half(): turns the face half a revolution
RubikFront is a Rubik where the turns are applied to the front face. Define the RubikFront constructor that takes in a three-dimensional (6 × 3 × 3) integer array of the six face’s values.
Since all turn methods return an immutable object, it should be cloneable too.
| 161728212019123536 ……090807……
……404142…… ……434445…… ……464748…… ……495051…… ……525354…… jshell> s s ==> ……010203…… ……040506…… ……070809…… 101112192021282930 131415222324313233 161718252627343536 ……373839…… ……404142…… ……434445…… ……464748…… ……495051…… ……525354……
jshell> /exit |
| $ javac *.java
$ jshell -q your_java_files_in_bottom-up_dependency_order < test3.jsh jshell> int[][][] grid = new int[6][3][3] jshell> int d = 1 jshell> for (int k = 0; k < 6; k++) …> for (int i = 0; i < 3; i++) …> for (int j = 0; j < 3; j++) grid[k][i][j] = d++; jshell> Rubik r = new RubikFront(grid) jshell> r.upView() $.. ==> ……464748…… ……495051…… ……525354…… 161310010203303336 171411040506293235 181512070809283134 ……192021…… ……222324…… ……252627…… ……373839…… ……404142…… ……434445……
jshell> r.rightView() $.. ==> ……070401…… ……080502…… ……090603…… 192021282930545352 222324313233515049 252627343536484746 ……394245…… ……384144…… ……374043…… ……181716…… ……151413…… |
Level 3
A Rubik can also be oriented to any one of the six sides using the following methods:
rightView(): orientates the cube so that the right-side faces front leftView(): orientates the cube so that the left-side faces front upView(): orientates the cube so that the top-side faces front downView(): orientates the cube so that the bottom-side faces front backView(): orientates the cube so that the back-side faces front. Although you can view the back of the cube by either orientating right/left or up/down, for ease of correctness checking, we stipulate that you can only orientate right/left
frontView(): no orientation needed
……121110……
jshell> r.downView()
$.. ==>
……192021……
……222324……
……252627……
121518373839343128
111417404142353229
101316434445363330 ……464748……
……495051……
……525354……
……010203……
……040506……
……070809……
jshell> r.leftView()
$.. ==>
……030609……
……020508……
……010407……
545352101112192021
515049131415222324
484746161718252627 ……434037……
……444138……
……454239……
……363534……
……333231……
……302928……
jshell> r.backView()
$.. ==>
……090807……
……060504……
……030201……
282930545352101112
313233515049131415
343536484746161718 ……454443……
……424140……
……393837……
……272625……
……242322……
……212019……
jshell> r.frontView()
$.. ==>
……010203……
……040506……
……070809……
101112192021282930
131415222324313233
161718252627343536 ……373839……
……404142……
……434445……
……464748……
……495051……
……525354……
jshell> /exit
Level 4
We are now really ready to turn the other faces. Just like RubikFront, we need to implement five other classes:
RubikLeft to turn the left face
RubikRight to turn the right face
RubikBack to turn the back face
RubikUp to turn the top face
RubikDown to turn the bottom face
| $ javac *.java
$ jshell -q your_java_files_in_bottom-up_dependency_order < test4.jsh jshell> int[][][] grid = new int[6][3][3] jshell> int d = 1 jshell> for (int k = 0; k < 6; k++) …> for (int i = 0; i < 3; i++) …> for (int j = 0; j < 3; j++) grid[k][i][j] = d++; jshell> Rubik rubik = new RubikFront(grid); jshell> ((Rubik) new RubikUp(rubik)).left() $.. ==> ……030609…… ……020508…… ……010407…… 545352101112192021 131415222324313233 161718252627343536 ……373839…… ……404142…… ……434445…… ……464748…… ……495051…… ……302928……
jshell> ((Rubik) new RubikUp(rubik)).right() $.. ==> ……070401…… ……080502…… ……090603…… 192021282930545352 131415222324313233 161718252627343536 ……373839…… ……404142…… ……434445…… ……464748…… ……495051…… ……121110……
jshell> ((Rubik) new RubikUp(rubik)).half() $.. ==> ……090807…… ……060504…… ……030201…… 282930545352101112 131415222324313233 161718252627343536 ……373839…… ……404142…… ……434445…… ……464748…… ……495051…… ……212019……
jshell> ((Rubik) new RubikRight(rubik)).left() $.. ==> ……010248…… ……040551…… ……070854…… 101112192003303336 131415222306293235 161718252609283134 ……373821…… ……404124…… ……434427…… ……464739…… ……495042…… ……525345…… |
You might think that you need to implement right, left and half turns separately for each of the above classes. However, there is no need to. With only front-face turns implemented in RubikFront, all you have to do is to orientate the turning side so that it is facing the front, make the front-face turn, and then orientate it back.
If the design has been done correctly, we can simply extend our implementation with left/right/half turns for each of the remaining classes.
jshell> ((Rubik) new RubikRight(rubik)).right()
$.. ==>
……010221……
……040524……
……070827……
101112192039343128
131415222342353229
161718252645363330 ……373848……
……404151……
……434454……
……464703……
……495006……
……525309……
jshell> ((Rubik) new RubikRight(rubik)).half()
$.. ==>
……010239……
……040542……
……070845……
101112192048363534
131415222351333231
161718252654302928 ……373803……
……404106……
……434409……
……464721……
……495024……
……525327……
jshell> ((Rubik) new RubikDown(rubik)).left()
$.. ==>
……010203……
……040506……
……070809……
101112192021282930
131415222324313233
252627343536484746 ……394245……
……384144……
……374043……
……181716……
……495051……
……525354……
jshell> ((Rubik) new RubikDown(rubik)).right()
$.. ==>
……010203……
……040506……
……070809……
101112192021282930
131415222324313233
484746161718252627 ……434037……
……444138……
……454239……
……363534……
……495051……
……525354……
jshell> ((Rubik) new RubikDown(rubik)).half()
$.. ==>
……010203……
……040506……
……070809……
101112192021282930
131415222324313233
343536484746161718 ……454443……
……424140……
……393837……
……272625……
……495051……
……525354……
jshell> ((Rubik) new RubikLeft(rubik)).left()
$.. ==>
……190203……
……220506……
……250809……
121518372021282930
111417402324313233
101316432627343536 ……463839……
……494142……
……524445……
……014748……
……045051……
……075354……
jshell> ((Rubik) new RubikLeft(rubik)).right()
$.. ==>
……460203……
……490506……
……520809……
161310012021282930
171411042324313233
181512072627343536 ……193839……
……224142……
……254445……
……374748……
……405051……
……435354……
jshell> ((Rubik) new RubikLeft(rubik)).half()
$.. ==>
……370203……
……400506……
……430809……
181716462021282930
151413492324313233
121110522627343536 ……013839……
……044142……
……074445……
……194748……
……225051……
……255354……
jshell> ((Rubik) new RubikBack(rubik)).left()
$.. ==>
……161310……
……040506……
……070809……
431112192021282901
441415222324313202
451718252627343503 ……373839……
……404142……
……363330……
……485154……
……475053……
……464952……
jshell> ((Rubik) new RubikBack(rubik)).right()
$.. ==>
……303336……
……040506……
……070809……
031112192021282945
021415222324313244
011718252627343543 ……373839……
……404142……
……101316……
……524946……
| ……535047……
……545148……
jshell> ((Rubik) new RubikBack(rubik)).half() $.. ==> ……454443…… ……040506…… ……070809…… 361112192021282916 331415222324313213 301718252627343510 ……373839…… ……404142…… ……030201…… ……545352…… ……515049…… ……484746……
jshell> /exit |
Level 5
Finally, read the Rubik’s cube as input, followed by the turns and output the final Rubik’s cube after all the turns have been made.
A skeleton Main class has been provided for you that parses the input and creates the first RubikFront object. You will only need to modify the oneMove method to construct the appropriate Rubik object based on the first character, and then invoke the correct turn.
The following is a sample run of the program. User input is underlined.
