-
Notifications
You must be signed in to change notification settings - Fork 0
/
Cube.py
155 lines (138 loc) · 5.12 KB
/
Cube.py
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
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as npimg
import copy
class RubiksCube:
facesdict = dict([("F",0),("U",1),("D",2),("L",3),("R",4),("B",5)])
def __init__(self,n=3,state = None):
'''
Intialises a Rubik's cube object
n: Dimension of the n x n x n cube
state: An optional initial cube state. A cube state contains six boolean arrays representing the colours of each index.
'''
self.n=n
self.cube_indices = np.arange(6*n**2).reshape((6,n,n))
self.solved_cube = np.zeros((6,n**2*6),dtype=bool)
for i,row in enumerate(self.solved_cube):
self.solved_cube[i,i*n**2:(i+1)*n**2] = True
if state is None:
self._cube = self._initialize()
else:
self._cube = state
self.face_array = self.build_face_array(n)
self.z_slice = self.build_z_slice(n)
self.move_list = []
self.rots=self.rotations_list()
def rotations_list(self):
'''
Creates a list of tuples which represents each possible move
'''
rots = []
for row_index in range(self.n):
for col_index in range(self.n):
for direction in [-1,1]:
rots.append((row_index,col_index,direction))
return rots
def build_face_array(self,n):
'''
Creates an array which specifies the index of the fact
'''
face_array = np.zeros((n,3),dtype=int)
face_array.fill(-1)
face_array[0,0] = 3
face_array[n-1,0] = 4
face_array[0,1] = 1
face_array[n-1,1]= 2
face_array[0,2] = 0
face_array[n-1,2] = 5
return face_array
def build_z_slice(self,n):
'''
Builds an array which specifies the indices of elements on each face that rotate when rotating on the z-axis
'''
z_slice=[]
for i in range(n):
u_row = self.cube_indices[1,n-1-i,:]
d_row = self.cube_indices[2,i,:]
l_row = self.cube_indices[3,:,n-1-i]
r_row = self.cube_indices[4,:,i]
z_slice.append(np.array([u_row,l_row,d_row,r_row]))
return np.array(z_slice)
def cube_colours(self):
'''
Maps the boolean cube array onto on array of indices for each colour.
cube: a reshaped cube to represent each face
'''
colour_map = np.zeros(6*self.n**2)
for i,row in enumerate(self._cube):
args = np.argwhere(row)
colour_map[args] = i
cube = colour_map.reshape((6,self.n,self.n))
return cube
def show_layout(self):
'''
Shows the layout of the cube
'''
cube = self.cube_colours()
titles = ["F","B","U","D","L","R"]
ix = [0,5,1,2,3,4]
fig = plt.figure()
self.patches = []
for i in range(1,7):
fig.add_subplot(3,2,i)
patch=plt.imshow(cube[ix[i-1]], vmin=0, vmax=6, cmap='jet')
plt.axis('off')
plt.title(titles[i-1])
self.patches.append(patch)
return fig
def _initialize(self,n=None):
'''
Initializes a cube.
n: Number of random rotations of the cube
'''
if n is None:
return self.solved_cube.copy()
else:
self._cube = self.solved_cube.copy()
self.random_rotate(n)
return self._cube
def rotation(self,index):
'''
Performs a rotation using the index of the move in the rotation list
'''
self.rotate_cube(*self.rots[index])
def rotate_cube(self,row_index,ax_index,direction):
'''
Rotates the cube along a specified row and axis index.
'''
face_ix = self.face_array[row_index,ax_index]
rot = face_ix != -1
if ax_index == 0:
indices = self.cube_indices[:,:,row_index][[0,1,5,2]].flatten()
elif ax_index == 1:
indices = self.cube_indices[:,row_index,:][[0,3,5,4]].flatten()
else:
indices = self.z_slice[row_index].flatten()
self._cube[:,indices] = np.roll(self._cube[:,indices],direction*self.n,axis=1)
if rot:
init = self.cube_indices[face_ix].flatten()
fin = np.rot90(self.cube_indices[face_ix],direction).flatten()
self._cube[:,fin] = self._cube[:,init]
self.move_list.append((row_index,ax_index,direction))
def reset(self,seed):
self.move_list = []
self._cube = self._initialize(seed)
return self._cube
def score_similarity(self):
return np.sum(self._cube.reshape(6,6,self.n**2),axis=2)/self.n**2
def random_rotate(self,n=1,seed=None):
'''
Rotates the cube randomly. The cube can rotate either 90deg or 180deg
'''
if seed:
np.random.RandomState(seed)
ixs_ = np.random.choice(self.n,n)
axis_ = np.random.choice(self.n,n)
dirs_ = np.random.choice((-1,1),n)
for x,y,z in zip(ixs_,axis_,dirs_):
self.rotate_cube(x,y,z)