$24
Lab #3: Rubik's Cube Solution
Problem Description
The Rubik's cube is a three-dimensional combination puzzle that is considered the world's best-selling toy.
The 3 × 3 rubik's cube above can be fattened so that all six faces are shown.
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 fnal cube is then output. As an example, the input
1
2
3
4
5 6 7
8
9
16
17
18
10
11
12
13 14 15
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
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
2/11
26/11/2021, 03:17 CodeCrunch
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 defnition of the clone method. This will be useful in a later level.
It is also worth noting that the Object class defnes a similar clone() method with a protected access modifer. 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.
$ 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
• ==>
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
Level 2
With the Face class ready, we can proceed to develop Rubik. We defne Rubik as a rubik's cube with one face that can be turned using the following methods:
right(): turns the face clockwise
left(): turns the face anti-clockwise
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
3/11
26/11/2021, 03:17 CodeCrunch
half(): turns the face half a revolution
RubikFront is a Rubik where the turns are applied to the front face. Defne 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.
$ 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
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
4/11
26/11/2021, 03:17
CodeCrunch
161728212019123536
......090807......
......404142......
......434445......
......464748......
......495051......
......525354......
jshell> s
s ==>
......010203......
......040506......
......070809......
101112192021282930
131415222324313233
161718252627343536
......373839......
......404142......
......434445......
......464748......
......495051......
......525354......
jshell> /exit
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
$ 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
......
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
5/11
26/11/2021, 03:17
CodeCrunch
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 fve 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
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
6/11
26/11/2021, 03:17 CodeCrunch
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.
$ 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
......
7/11
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
26/11/2021, 03:17
CodeCrunch
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......
8/11
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
26/11/2021, 03:17
CodeCrunch
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......
9/11
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079
26/11/2021, 03:17
CodeCrunch
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 fnal 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 frst RubikFront object. You will only need to modify the oneMove method to construct the appropriate Rubik object based on the frst character, and then invoke the correct turn.
import java.util.Scanner;
class Main {
static final int NFACES = 6;
static final int NROWS = 3;
static final int NCOLS = 3;
static Rubik oneMove(Rubik rubik, String move) {
System.out.print("Face " + move.charAt(0));
if (move.length() == 1) {
System.out.println(" right turn");
} else {
if (move.charAt(1) == '\'') {
System.out.println(" left turn");
} else {
System.out.println(" half turn");
}
}
return rubik;
}
public static void main(String[] args) {
int[][][] grid = new int[NFACES][NROWS][NCOLS];
Scanner sc = new Scanner(System.in);
for (int k = 0; k < NFACES; k++) {
for (int i = 0; i < NROWS; i++) {
for (int j = 0; j < NCOLS; j++) {
grid[k][i][j] = sc.nextInt();
}
}
}
Rubik rubik = new RubikFront(grid);
while (sc.hasNext()) {
rubik = oneMove(rubik, sc.next());
}
System.out.println(rubik);
}
}
The following is a sample run of the program. User input is underlined.
https://codecrunch.comp.nus.edu.sg/task_view.php?tid=5079 10/11
26/11/2021, 03:17
CodeCrunch
1
2
3
4 5
6
7
8 9
16 17
18
10 11
12
13
14 15
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
......
541518
......
......
510504
......
......
480201
......
303336455352101137
131438262306293235
161739272412070809
......
343119
......
......
404120
......
......
434421
......
......
464728
......
......
495042
......
......
032225
......
1
2
3
4 5
6
7
8 9
16 17
18
10 11
12
13
14 15
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
FRULBD
F' R' U' L'
B' D'
F2 R2
U2
L2
B2 D2
......
281118
......
......
220508
......
......
270648
......
211539342936452037
401451332344473253
014207192603543143
......
123830
......
......
354124
......
......
104916
......
......
521346
......
......
175002
......
......
090425
......
Check the format correctness of the output by typing the following Unix command
$ java Main < test5.in
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