Answer from Cubesolver

├── gui_client.jpg ├── .idea ├── encodings.xml ├── vcs.xml ├── misc.xml ├── modules.xml ├── inspectionProfiles │ └── Project_Default.xml └── RubiksCube-TwophaseSolver.iml ├── computer_vision.py ├── start_server.py ├── misc.py ├── .gitignore ├── vision_params.py ├── README.md ├── defs.py ├── sockets.py ├── enums.py ├── example.py ├── face.py ├── client_gui.py ├── moves.py ├── coord.py ├── symmetries.py ├── client_gui2.py ├── solver.py ├── vision2.py ├── pruning.py ├── cubie.py └── LICENSE /gui_client.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Tazeg/RubiksCube-TwophaseSolver/master/gui_client.jpg -------------------------------------------------------------------------------- /.idea/encodings.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /.idea/vcs.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | -------------------------------------------------------------------------------- /.idea/misc.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /.idea/modules.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | -------------------------------------------------------------------------------- /.idea/inspectionProfiles/Project_Default.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 10 | -------------------------------------------------------------------------------- /.idea/RubiksCube-TwophaseSolver.iml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 12 | -------------------------------------------------------------------------------- /computer_vision.py: -------------------------------------------------------------------------------- 1 | # ############################## Start the webserver, the opencv color grabber and the GUI ############################# 2 | 3 | import start_server 4 | from threading import Thread 5 | from vision2 import grab_colors 6 | background_thread = Thread(target=start_server.start, args=(8080, 20, 2)) 7 | background_thread.start() 8 | # Server listens now on port 8080, maxlength 20 moves, timeout 2 seconds 9 | 10 | thr = Thread(target=grab_colors, args=()) 11 | thr.start() 12 | # Run the opencv code and detect facelet colors 13 | 14 | import client_gui2 15 | # Start the GUI with several sliders to configure some opencv parameters 16 | 17 | -------------------------------------------------------------------------------- /start_server.py: -------------------------------------------------------------------------------- 1 | # ################# Start the server and listen for connections ######################################################## 2 | 3 | import sockets 4 | import sys 5 | 6 | 7 | if __name__ == '__main__': # file is executed 8 | if len(sys.argv) < 2: 9 | sys.argv.append(str(8080)) # Port 8080 default port 10 | if len(sys.argv) < 3: 11 | sys.argv.append(str(20)) # 20 moves default maximal return length of maneuver 12 | if len(sys.argv) < 4: 13 | sys.argv.append(str(3)) # 3 second default timeout for search 14 | print('startserver') 15 | sockets.server_start(sys.argv) 16 | else: 17 | def start(port, maxmoves, timeout): 18 | sockets.server_start((-1, port, maxmoves, timeout)) 19 | -------------------------------------------------------------------------------- /misc.py: -------------------------------------------------------------------------------- 1 | # ######################################## Miscellaneous functions ##################################################### 2 | 3 | def rotate_right(arr, l, r): 4 | """"Rotate array arr right between l and r. r is included.""" 5 | temp = arr[r] 6 | for i in range(r, l, -1): 7 | arr[i] = arr[i-1] 8 | arr[l] = temp 9 | 10 | 11 | def rotate_left(arr, l, r): 12 | """"Rotate array arr left between l and r. r is included.""" 13 | temp = arr[l] 14 | for i in range(l, r): 15 | arr[i] = arr[i+1] 16 | arr[r] = temp 17 | 18 | 19 | def c_nk(n, k): 20 | """Binomial coefficient [n choose k].""" 21 | if n < k: 22 | return 0 23 | if k > n // 2: 24 | k = n - k 25 | s, i, j = 1, n, 1 26 | while i != n - k: 27 | s *= i 28 | s //= j 29 | i -= 1 30 | j += 1 31 | return s 32 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | env/ 12 | build/ 13 | develop-eggs/ 14 | dist/ 15 | downloads/ 16 | eggs/ 17 | .eggs/ 18 | lib/ 19 | lib64/ 20 | parts/ 21 | sdist/ 22 | var/ 23 | *.egg-info/ 24 | .installed.cfg 25 | *.egg 26 | 27 | # PyInstaller 28 | # Usually these files are written by a python script from a template 29 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 30 | *.manifest 31 | *.spec 32 | 33 | # Installer logs 34 | pip-log.txt 35 | pip-delete-this-directory.txt 36 | 37 | # Unit test / coverage reports 38 | htmlcov/ 39 | .tox/ 40 | .coverage 41 | .coverage.* 42 | .cache 43 | nosetests.xml 44 | coverage.xml 45 | *,cover 46 | .hypothesis/ 47 | 48 | # Translations 49 | *.mo 50 | *.pot 51 | 52 | # Django stuff: 53 | *.log 54 | local_settings.py 55 | 56 | # Flask stuff: 57 | instance/ 58 | .webassets-cache 59 | 60 | # Scrapy stuff: 61 | .scrapy 62 | 63 | # Sphinx documentation 64 | docs/_build/ 65 | 66 | # PyBuilder 67 | target/ 68 | 69 | # IPython Notebook 70 | .ipynb_checkpoints 71 | 72 | # pyenv 73 | .python-version 74 | 75 | # celery beat schedule file 76 | celerybeat-schedule 77 | 78 | # dotenv 79 | .env 80 | 81 | # virtualenv 82 | venv/ 83 | ENV/ 84 | 85 | # Spyder project settings 86 | .spyderproject 87 | 88 | # Rope project settings 89 | .ropeproject 90 | -------------------------------------------------------------------------------- /vision_params.py: -------------------------------------------------------------------------------- 1 | # #################################### Computer vision parameters ###################################################### 2 | 3 | # The parameters are used by functions in vision2.py and can be changed from the GUI client_gui.py 4 | 5 | # default values for the parameters 6 | 7 | # black-filter 8 | rgb_L = 50 # threshold for r, g and b values. rgb-pixels with r,g,b< rgb_L are consider to be no facelet-pixel 9 | 10 | # white-filter 11 | sat_W = 60 # hsv-pixels with a saturation s > sat_W are considered not to be a white facelet-pixel 12 | val_W = 150 # hsv-pixels with a value v < sat_W are considered not to be a white facelet-pixel 13 | 14 | # this parameter cannot be changed by the GUI 15 | sigma_W = 300 # a grid square is considered part of a white facelet if the standard deviation of the hue is <= sigma_W 16 | 17 | # color-filter 18 | sigma_C = 5 # a grid square is considered part of a facelet if the standard deviation of the hue is <= sigma_C 19 | delta_C = 5 # pixels within the interval [hue-delta,hue+delta] are considered to belong to the same facelet 20 | 21 | # These parameters depend on the actually used cube colors and the lightning conditions 22 | orange_L = 6 # lowest allowed hue for color orange 23 | orange_H = 23 # highest allowed hue for color orange 24 | yellow_H = 50 # highest allowed hue for color yellow 25 | green_H = 100 # highest allowed hue for color green 26 | blue_H = 160 # highest allowed hue for color blue 27 | # hue values > blue_H and < orange_L describe the color red 28 | 29 | # The colors of a cube face are stored here by the function vision2.grabcolors 30 | face_col = [] # the colors (as text) of a cube face 31 | face_hsv = [] # the colors (as hsv-values) of a cube face 32 | 33 | # These dictionaries define the colors of all 6 faces and are filled by the client_gui2.transfer routine 34 | cube_col = {} # the colors (as text) of the 6 faces 35 | cube_hsv = {} # the colors (as hsv-values) of the 6 faces 36 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # RubiksCube-TwophaseSolver 2 | ## Overview 3 | This project implements the two-phase-algorithm in its fully developed form to solve Rubik's cube in Python. Though Python is much slower than for example C++ or even Java the implementation is sufficiently fast to solve random cubes in less than 20 moves on average on slow hardware like the Raspberry Pi3 within a few seconds. 4 | 5 | If you just want to solve Rubik's cube and play around with its patterns [Cube Explorer](http://kociemba.org/cube.htm) may be the better choice. But if you want to get a better understanding of the two-phase-algorithm details, you work on a project to build a cube solving robot or you write software for an NxNxN cube and use the reduction method this may be the right place to look. 6 | 7 | ## Usage 8 | There are several tables which must be created on the first run. These need about 80 MB disk space and it takes from about 1/2 to 6 hours to create them, depending on the hardware. Usually you start the cubesolving server which listens on a port of your choice and which accepts the cube definition string and returns the solving maneuver. The module example.py gives detailed examples how to start the server and a simple GUI-interface which interacts with the server. You can run the example file with 9 | 10 | "python example.py" or eventually "python3 example.py" 11 | 12 | Make sure that you use Python 3.4 or higher and you have the numpy package installed. 13 | 14 | ![](gui_client.jpg "") 15 | 16 | If you run the script "computer_vision.py" you have the possibility to enter the facelet colors with a webcam. There are several parameters which have an influence on the facelet detection quality. If you use a Raspberry Pi with the Raspberry Pi Camera Module and not an USB-webcam make sure you do "sudo modprobe bcm2835-v4l2" first. 17 | 18 | You can find some more information how to set the parameters here: 19 | [Computer vision and Rubik's cube](http://kociemba.org/computervision.html) 20 | -------------------------------------------------------------------------------- /defs.py: -------------------------------------------------------------------------------- 1 | # ###################################### some definitions and constants ################################################ 2 | 3 | from enums import Facelet as Fc, Color as Cl 4 | 5 | # Map the corner positions to facelet positions. 6 | cornerFacelet = [[Fc.U9, Fc.R1, Fc.F3], [Fc.U7, Fc.F1, Fc.L3], [Fc.U1, Fc.L1, Fc.B3], [Fc.U3, Fc.B1, Fc.R3], 7 | [Fc.D3, Fc.F9, Fc.R7], [Fc.D1, Fc.L9, Fc.F7], [Fc.D7, Fc.B9, Fc.L7], [Fc.D9, Fc.R9, Fc.B7] 8 | ] 9 | 10 | # Map the edge positions to facelet positions. 11 | edgeFacelet = [[Fc.U6, Fc.R2], [Fc.U8, Fc.F2], [Fc.U4, Fc.L2], [Fc.U2, Fc.B2], [Fc.D6, Fc.R8], [Fc.D2, Fc.F8], 12 | [Fc.D4, Fc.L8], [Fc.D8, Fc.B8], [Fc.F6, Fc.R4], [Fc.F4, Fc.L6], [Fc.B6, Fc.L4], [Fc.B4, Fc.R6] 13 | ] 14 | 15 | # Map the corner positions to facelet colors. 16 | cornerColor = [[Cl.U, Cl.R, Cl.F], [Cl.U, Cl.F, Cl.L], [Cl.U, Cl.L, Cl.B], [Cl.U, Cl.B, Cl.R], 17 | [Cl.D, Cl.F, Cl.R], [Cl.D, Cl.L, Cl.F], [Cl.D, Cl.B, Cl.L], [Cl.D, Cl.R, Cl.B] 18 | ] 19 | 20 | # Map the edge positions to facelet colors. 21 | edgeColor = [[Cl.U, Cl.R], [Cl.U, Cl.F], [Cl.U, Cl.L], [Cl.U, Cl.B], [Cl.D, Cl.R], [Cl.D, Cl.F], 22 | [Cl.D, Cl.L], [Cl.D, Cl.B], [Cl.F, Cl.R], [Cl.F, Cl.L], [Cl.B, Cl.L], [Cl.B, Cl.R] 23 | ] 24 | 25 | # ###################################### some "constants" ############################################################## 26 | N_PERM_4 = 24 27 | N_CHOOSE_8_4 = 70 28 | N_MOVE = 18 # number of possible face moves 29 | 30 | N_TWIST = 2187 # 3^7 possible corner orientations in phase 1 31 | N_FLIP = 2048 # 2^11 possible edge orientations in phase 1 32 | N_SLICE_SORTED = 11880 # 12*11*10*9 possible positions of the FR, FL, BL, BR edges in phase 1 33 | N_SLICE = N_SLICE_SORTED // N_PERM_4 # we ignore the permutation of FR, FL, BL, BR in phase 1 34 | N_FLIPSLICE_CLASS = 64430 # number of equivalence classes for combined flip+slice concerning symmetry group D4h 35 | 36 | N_U_EDGES_PHASE2 = 1680 # number of different positions of the edges UR, UF, UL and UB in phase 2 37 | # N_D_EDGES_PHASE2 = 1680 # number of different positions of the edges DR, DF, DL and DB in phase 2 38 | N_CORNERS = 40320 # 8! corner permutations in phase 2 39 | N_CORNERS_CLASS = 2768 # number of equivalence classes concerning symmetry group D4h 40 | N_UD_EDGES = 40320 # 8! permutations of the edges in the U-face and D-face in phase 2 41 | 42 | N_SYM = 48 # number of cube symmetries of full group Oh 43 | N_SYM_D4h = 16 # Number of symmetries of subgroup D4h 44 | ######################################################################################################################## 45 | -------------------------------------------------------------------------------- /sockets.py: -------------------------------------------------------------------------------- 1 | # ################## The code of the server socket which communicates with the client ################################## 2 | 3 | import socket 4 | import sys 5 | import threading 6 | import solver 7 | import time 8 | 9 | 10 | def client_thread(conn, maxlen, timeout): 11 | while True: # infinite loop only necessary for telnet client 12 | # Receiving from client 13 | data = [] 14 | while not (ord('\n') in data or ord('\r') in data): 15 | try: 16 | a = conn.recv(1024).upper() 17 | if len(a) == 0: 18 | conn.close() 19 | print('Connection closed', flush=True) 20 | return 21 | except: 22 | print('Connection closed', flush=True) 23 | conn.close() 24 | return 25 | for i in range(len(a)): 26 | if a[i] in [ord('\n'), ord('\r'), ord('G'), ord('E'), ord('T'), ord('U'), ord('R'), ord('F'), ord('D'), 27 | ord('L'), ord('B')]: 28 | data.append(a[i]) 29 | if data[0] == ord('X'): 30 | break 31 | defstr = ''.join(chr(i) for i in data if chr(i) > chr(32)) 32 | qpos = defstr.find('GET') 33 | if qpos >= 0: # in this case we suppose the client is a webbrowser 34 | defstr = defstr[qpos+3:qpos+57] 35 | reply = 'HTTP/1.1 200 OK' + '\n\n' + 'Answer from Cubesolver' + '\n' 36 | reply += solver.solve(defstr, maxlen, timeout) + '\n' + '' + '\n' 37 | conn.sendall(reply.encode()) 38 | conn.close() 39 | else: # other client, for example the GUI client or telnet 40 | reply = (solver.solve(defstr, maxlen, timeout)+'\n').encode() 41 | print(defstr) 42 | try: 43 | conn.sendall(reply) 44 | except: 45 | print('Error while sending data. Connection closed', flush=True) 46 | conn.close() 47 | return 48 | conn.close() 49 | 50 | 51 | def server_start(args): 52 | s = socket.socket(socket.AF_INET, socket.SOCK_STREAM) 53 | print('Server socket created') 54 | try: 55 | s.bind(('', int(args[1]))) # bind socket to local host and port 56 | except socket.error as e: 57 | print('Server socket bind failed. Error Code : ' + str(e.errno)) 58 | sys.exit() 59 | s.listen(10) 60 | print('Server now listening...') 61 | 62 | while 1: 63 | conn, addr = s.accept() 64 | print('Connected with ' + addr[0] + ':' + str(addr[1]) + ', ' + time.strftime("%Y.%m.%d %H:%M:%S")) 65 | threading.Thread(target=client_thread, args=(conn, int(args[2]), int(args[3]))).start() 66 | s.close() 67 | 68 | -------------------------------------------------------------------------------- /enums.py: -------------------------------------------------------------------------------- 1 | # #################### Enumerations which improve the readability of the code ######################################## 2 | 3 | from enum import IntEnum 4 | 5 | 6 | class Facelet(IntEnum): 7 | """"" 8 | The names of the facelet positions of the cube 9 | |************| 10 | |*U1**U2**U3*| 11 | |************| 12 | |*U4**U5**U6*| 13 | |************| 14 | |*U7**U8**U9*| 15 | |************| 16 | |************|************|************|************| 17 | |*L1**L2**L3*|*F1**F2**F3*|*R1**R2**R3*|*B1**B2**B3*| 18 | |************|************|************|************| 19 | |*L4**L5**L6*|*F4**F5**F6*|*R4**R5**R6*|*B4**B5**B6*| 20 | |************|************|************|************| 21 | |*L7**L8**L9*|*F7**F8**F9*|*R7**R8**R9*|*B7**B8**B9*| 22 | |************|************|************|************| 23 | |************| 24 | |*D1**D2**D3*| 25 | |************| 26 | |*D4**D5**D6*| 27 | |************| 28 | |*D7**D8**D9*| 29 | |************| 30 | A cube definition string "UBL..." means for example: In position U1 we have the U-color, in position U2 we have the 31 | B-color, in position U3 we have the L color etc. according to the order U1, U2, U3, U4, U5, U6, U7, U8, U9, R1, R2, 32 | R3, R4, R5, R6, R7, R8, R9, F1, F2, F3, F4, F5, F6, F7, F8, F9, D1, D2, D3, D4, D5, D6, D7, D8, D9, L1, L2, L3, L4, 33 | L5, L6, L7, L8, L9, B1, B2, B3, B4, B5, B6, B7, B8, B9 of the enum constants. 34 | """ 35 | U1 = 0 36 | U2 = 1 37 | U3 = 2 38 | U4 = 3 39 | U5 = 4 40 | U6 = 5 41 | U7 = 6 42 | U8 = 7 43 | U9 = 8 44 | R1 = 9 45 | R2 = 10 46 | R3 = 11 47 | R4 = 12 48 | R5 = 13 49 | R6 = 14 50 | R7 = 15 51 | R8 = 16 52 | R9 = 17 53 | F1 = 18 54 | F2 = 19 55 | F3 = 20 56 | F4 = 21 57 | F5 = 22 58 | F6 = 23 59 | F7 = 24 60 | F8 = 25 61 | F9 = 26 62 | D1 = 27 63 | D2 = 28 64 | D3 = 29 65 | D4 = 30 66 | D5 = 31 67 | D6 = 32 68 | D7 = 33 69 | D8 = 34 70 | D9 = 35 71 | L1 = 36 72 | L2 = 37 73 | L3 = 38 74 | L4 = 39 75 | L5 = 40 76 | L6 = 41 77 | L7 = 42 78 | L8 = 43 79 | L9 = 44 80 | B1 = 45 81 | B2 = 46 82 | B3 = 47 83 | B4 = 48 84 | B5 = 49 85 | B6 = 50 86 | B7 = 51 87 | B8 = 52 88 | B9 = 53 89 | 90 | 91 | class Color(IntEnum): 92 | """ The possible colors of the cube facelets. Color U refers to the color of the U(p)-face etc. 93 | Also used to name the faces itself.""" 94 | U = 0 95 | R = 1 96 | F = 2 97 | D = 3 98 | L = 4 99 | B = 5 100 | 101 | 102 | class Corner(IntEnum): 103 | """The names of the corner positions of the cube. Corner URF e.g. has an U(p), a R(ight) and a F(ront) facelet.""" 104 | URF = 0 105 | UFL = 1 106 | ULB = 2 107 | UBR = 3 108 | DFR = 4 109 | DLF = 5 110 | DBL = 6 111 | DRB = 7 112 | 113 | 114 | class Edge(IntEnum): 115 | """The names of the edge positions of the cube. Edge UR e.g. has an U(p) and R(ight) facelet.""" 116 | UR = 0 117 | UF = 1 118 | UL = 2 119 | UB = 3 120 | DR = 4 121 | DF = 5 122 | DL = 6 123 | DB = 7 124 | FR = 8 125 | FL = 9 126 | BL = 10 127 | BR = 11 128 | 129 | 130 | class Move(IntEnum): 131 | """The moves in the faceturn metric. Not to be confused with the names of the facelet positions in class Facelet.""" 132 | U1 = 0 133 | U2 = 1 134 | U3 = 2 135 | R1 = 3 136 | R2 = 4 137 | R3 = 5 138 | F1 = 6 139 | F2 = 7 140 | F3 = 8 141 | D1 = 9 142 | D2 = 10 143 | D3 = 11 144 | L1 = 12 145 | L2 = 13 146 | L3 = 14 147 | B1 = 15 148 | B2 = 16 149 | B3 = 17 150 | 151 | 152 | class BS(IntEnum): 153 | """Basic symmetries of the cube. All 48 cube symmetries can be generated by sequences of these 4 symmetries.""" 154 | ROT_URF3 = 0 155 | ROT_F2 = 1 156 | ROT_U4 = 2 157 | MIRR_LR2 = 3 158 | -------------------------------------------------------------------------------- /example.py: -------------------------------------------------------------------------------- 1 | # ############################ Examples how to use the cube solver ##################################################### 2 | 3 | cubestring = 'DUUBULDBFRBFRRULLLBRDFFFBLURDBFDFDRFRULBLUFDURRBLBDUDL' # cube definition string of cube we want to solve 4 | # See module enums.py for the format of the cube definition string 5 | 6 | # ######################### Method 1: directly call the solve routine# ################################################# 7 | # Advantage: No network layer needed. Disadvantage: Only local usage possible. # 8 | ######################################################################################################################## 9 | 10 | # Uncomment this part if you want to use method 1 11 | """ 12 | import solver as sv 13 | a = sv.solve(cubestring, 20, 2) # solve with a maximum of 20 moves and a timeout of 2 seconds for example 14 | print(a) 15 | a = sv.solve(cubestring, 18, 5) # solve with a maximum of 18 moves and a timeout of 5 seconds for example 16 | print(a) 17 | quit() 18 | """ 19 | ######################################################################################################################## 20 | 21 | 22 | # ############################### Method 2 a/b: Start the cubesolving-server# ########################################## 23 | # Advantage: Tables have to be loaded only once when the server starts. Disadvantage: Network layer must be present. # 24 | ######################################################################################################################## 25 | 26 | #---------------------------------------------------------------------------------------------------------------------- 27 | # Method 2a: Start the server from inside a Python script: 28 | import start_server 29 | from threading import Thread 30 | background_thread = Thread(target=start_server.start, args=(8080, 20, 2)) 31 | background_thread.start() 32 | # Server listens now on port 8080, maxlength 20 moves, timeout 2 seconds 33 | # ---------------------------------------------------------------------------------------------------------------------- 34 | 35 | # ---------------------------------------------------------------------------------------------------------------------- 36 | # Method 2b: Start the server from a terminal with parameters for port, maxlength and timeout: 37 | # python start_server.py 8080 20 2 38 | # ---------------------------------------------------------------------------------------------------------------------- 39 | 40 | 41 | # Once the server is started you can transfer the cube definition string to the server with different methods: 42 | 43 | # ---------------------------------------------------------------------------------------------------------------------- 44 | # 1. With a webbrowser, if the server runs on the same machine on port 8080 45 | # http://localhost:8080/DUUBULDBFRBFRRULLLBRDFFFBLURDBFDFDRFRULBLUFDURRBLBDUDL 46 | # With a webbrowser, if the server runs on server myserver.com, port 8081 47 | # http://myserver.com:8081/DUUBULDBFRBFRRULLLBRDFFFBLURDBFDFDRFRULBLUFDURRBLBDUDL 48 | # ---------------------------------------------------------------------------------------------------------------------- 49 | 50 | # ---------------------------------------------------------------------------------------------------------------------- 51 | # 2. With netcat, if the server runs on the same machine on port 8080 52 | # echo DUUBULDBFRBFRRULLLBRDFFFBLURDBFDFDRFRULBLUFDURRBLBDUDL | nc localhost 8080 53 | # ---------------------------------------------------------------------------------------------------------------------- 54 | 55 | # ---------------------------------------------------------------------------------------------------------------------- 56 | # 3. With this little graphical interface. 57 | # From within a Python script start the interface with 58 | 59 | import client_gui 60 | 61 | 62 | # From a terminal start the interface with 63 | # python client_gui.py 64 | # ---------------------------------------------------------------------------------------------------------------------- 65 | 66 | 67 | # ---------------------------------------------------------------------------------------------------------------------- 68 | # Computer vision 69 | 70 | # Start the interface, the server and the webcam from a terminal with 71 | 72 | # python computer_vision.py 73 | 74 | # ---------------------------------------------------------------------------------------------------------------------- 75 | ######################################################################################################################## 76 | 77 | -------------------------------------------------------------------------------- /face.py: -------------------------------------------------------------------------------- 1 | # ####### The cube on the facelet level is described by positions of the colored stickers. ############################# 2 | 3 | from defs import cornerFacelet, edgeFacelet, cornerColor, edgeColor 4 | from enums import Color, Corner, Edge 5 | from cubie import CubieCube 6 | 7 | 8 | class FaceCube: 9 | """Represent a cube on the facelet level with 54 colored facelets.""" 10 | def __init__(self): 11 | self.f = [] 12 | for i in range(9): 13 | self.f.append(Color.U) 14 | for i in range(9): 15 | self.f.append(Color.R) 16 | for i in range(9): 17 | self.f.append(Color.F) 18 | for i in range(9): 19 | self.f.append(Color.D) 20 | for i in range(9): 21 | self.f.append(Color.L) 22 | for i in range(9): 23 | self.f.append(Color.B) 24 | 25 | def __str__(self): 26 | return self.to_string() 27 | 28 | def from_string(self, s): 29 | """Construct a facelet cube from a string. See class Facelet(IntEnum) in enums.py for string format.""" 30 | if len(s) < 54: 31 | return 'Error: Cube definition string ' + s + ' contains less than 54 facelets.' 32 | elif len(s) > 54: 33 | return 'Error: Cube definition string ' + s + ' contains more than 54 facelets.' 34 | cnt = [0] * 6 35 | for i in range(54): 36 | if s[i] == 'U': 37 | self.f[i] = Color.U 38 | cnt[Color.U] += 1 39 | elif s[i] == 'R': 40 | self.f[i] = Color.R 41 | cnt[Color.R] += 1 42 | elif s[i] == 'F': 43 | self.f[i] = Color.F 44 | cnt[Color.F] += 1 45 | elif s[i] == 'D': 46 | self.f[i] = Color.D 47 | cnt[Color.D] += 1 48 | elif s[i] == 'L': 49 | self.f[i] = Color.L 50 | cnt[Color.L] += 1 51 | elif s[i] == 'B': 52 | self.f[i] = Color.B 53 | cnt[Color.B] += 1 54 | if all(x == 9 for x in cnt): 55 | return True 56 | else: 57 | return 'Error: Cube definition string ' + s + ' does not contain exactly 9 facelets of each color.' 58 | 59 | 60 | def to_string(self): 61 | """Give a string representation of the facelet cube.""" 62 | s = '' 63 | for i in range(54): 64 | if self.f[i] == Color.U: 65 | s += 'U' 66 | elif self.f[i] == Color.R: 67 | s += 'R' 68 | elif self.f[i] == Color.F: 69 | s += 'F' 70 | elif self.f[i] == Color.D: 71 | s += 'D' 72 | elif self.f[i] == Color.L: 73 | s += 'L' 74 | elif self.f[i] == Color.B: 75 | s += 'B' 76 | return s 77 | 78 | def to_2dstring(self): 79 | """Give a 2dstring representation of a facelet cube.""" 80 | s = self.to_string() 81 | r = ' ' + s[0:3] + '\n ' + s[3:6] + '\n ' + s[6:9] + '\n' 82 | r += s[36:39] + s[18:21] + s[9:12] + s[45:48] + '\n' + s[39:42] + s[21:24] + s[12:15] + s[48:51] \ 83 | + '\n' + s[42:45] + s[24:27] + s[15:18] + s[51:54] + '\n' 84 | r += ' ' + s[27:30] + '\n ' + s[30:33] + '\n ' + s[33:36] + '\n' 85 | return r 86 | 87 | def to_cubie_cube(self): 88 | """Return a cubie representation of the facelet cube.""" 89 | cc = CubieCube() 90 | cc.cp = [-1] * 8 # invalidate corner and edge permutation 91 | cc.ep = [-1] * 12 92 | for i in Corner: 93 | fac = cornerFacelet[i] # facelets of corner at position i 94 | for ori in range(3): 95 | if self.f[fac[ori]] == Color.U or self.f[fac[ori]] == Color.D: 96 | break 97 | col1 = self.f[fac[(ori + 1) % 3]] # colors which identify the corner at position i 98 | col2 = self.f[fac[(ori + 2) % 3]] 99 | for j in Corner: 100 | col = cornerColor[j] # colors of corner j 101 | if col1 == col[1] and col2 == col[2]: 102 | cc.cp[i] = j # we have corner j in corner position i 103 | cc.co[i] = ori 104 | break 105 | 106 | for i in Edge: 107 | for j in Edge: 108 | if self.f[edgeFacelet[i][0]] == edgeColor[j][0] and \ 109 | self.f[edgeFacelet[i][1]] == edgeColor[j][1]: 110 | cc.ep[i] = j 111 | cc.eo[i] = 0 112 | break 113 | if self.f[edgeFacelet[i][0]] == edgeColor[j][1] and \ 114 | self.f[edgeFacelet[i][1]] == edgeColor[j][0]: 115 | cc.ep[i] = j 116 | cc.eo[i] = 1 117 | break 118 | return cc 119 | -------------------------------------------------------------------------------- /client_gui.py: -------------------------------------------------------------------------------- 1 | # ################ A simple graphical interface which communicates with the server ##################################### 2 | 3 | from tkinter import * 4 | import socket 5 | import face 6 | import cubie 7 | 8 | 9 | # ################################## Some global variables and constants ############################################### 10 | DEFAULT_HOST = 'localhost' 11 | DEFAULT_PORT = '8080' 12 | width = 60 # width of a facelet in pixels 13 | facelet_id = [[[0 for col in range(3)] for row in range(3)] for face in range(6)] 14 | colorpick_id = [0 for i in range(6)] 15 | curcol = None 16 | t = ("U", "R", "F", "D", "L", "B") 17 | cols = ("yellow", "green", "red", "white", "blue", "orange") 18 | ######################################################################################################################## 19 | 20 | # ################################################ Diverse functions ################################################### 21 | 22 | 23 | def show_text(txt): 24 | """Display messages.""" 25 | print(txt) 26 | display.insert(INSERT, txt) 27 | root.update_idletasks() 28 | 29 | 30 | def create_facelet_rects(a): 31 | """Initialize the facelet grid on the canvas.""" 32 | offset = ((1, 0), (2, 1), (1, 1), (1, 2), (0, 1), (3, 1)) 33 | for f in range(6): 34 | for row in range(3): 35 | y = 10 + offset[f][1] * 3 * a + row * a 36 | for col in range(3): 37 | x = 10 + offset[f][0] * 3 * a + col * a 38 | facelet_id[f][row][col] = canvas.create_rectangle(x, y, x + a, y + a, fill="grey") 39 | if row == 1 and col == 1: 40 | canvas.create_text(x + width // 2, y + width // 2, font=("", 14), text=t[f], state=DISABLED) 41 | for f in range(6): 42 | canvas.itemconfig(facelet_id[f][1][1], fill=cols[f]) 43 | 44 | 45 | def create_colorpick_rects(a): 46 | """Initialize the "paintbox" on the canvas.""" 47 | global curcol 48 | global cols 49 | for i in range(6): 50 | x = (i % 3)*(a+5) + 7*a 51 | y = (i // 3)*(a+5) + 7*a 52 | colorpick_id[i] = canvas.create_rectangle(x, y, x + a, y + a, fill=cols[i]) 53 | canvas.itemconfig(colorpick_id[0], width=4) 54 | curcol = cols[0] 55 | 56 | 57 | def get_definition_string(): 58 | """Generate the cube definition string from the facelet colors.""" 59 | color_to_facelet = {} 60 | for i in range(6): 61 | color_to_facelet.update({canvas.itemcget(facelet_id[i][1][1], "fill"): t[i]}) 62 | s = '' 63 | for f in range(6): 64 | for row in range(3): 65 | for col in range(3): 66 | s += color_to_facelet[canvas.itemcget(facelet_id[f][row][col], "fill")] 67 | return s 68 | ######################################################################################################################## 69 | 70 | # ############################### Solve the displayed cube with a local or remote server ############################### 71 | 72 | 73 | def solve(): 74 | """Connect to the server and return the solving maneuver.""" 75 | display.delete(1.0, END) # clear output window 76 | try: 77 | s = socket.socket(socket.AF_INET, socket.SOCK_STREAM) 78 | except socket.error: 79 | show_text('Failed to create socket') 80 | return 81 | # host = 'f9f0b2jt6zmzyo6b.myfritz.net' # my RaspberryPi, if online 82 | host = txt_host.get(1.0, END).rstrip() # default is localhost 83 | port = int(txt_port.get(1.0, END)) # default is port 8080 84 | 85 | try: 86 | remote_ip = socket.gethostbyname(host) 87 | except socket.gaierror: 88 | show_text('Hostname could not be resolved.') 89 | return 90 | try: 91 | s.connect((remote_ip, port)) 92 | except: 93 | show_text('Cannot connect to server!') 94 | return 95 | show_text('Connected with ' + remote_ip + '\n') 96 | try: 97 | defstr = get_definition_string()+'\n' 98 | except: 99 | show_text('Invalid facelet configuration.\nWrong or missing colors.') 100 | return 101 | show_text(defstr) 102 | try: 103 | s.sendall((defstr+'\n').encode()) 104 | except: 105 | show_text('Cannot send cube configuration to server.') 106 | return 107 | show_text(s.recv(2048).decode()) 108 | ######################################################################################################################## 109 | 110 | # ################################# Functions to change the facelet colors ############################################# 111 | 112 | 113 | def clean(): 114 | """Restore the cube to a clean cube.""" 115 | for f in range(6): 116 | for row in range(3): 117 | for col in range(3): 118 | canvas.itemconfig(facelet_id[f][row][col], fill=canvas.itemcget(facelet_id[f][1][1], "fill")) 119 | 120 | 121 | def empty(): 122 | """Remove the facelet colors except the center facelets colors.""" 123 | for f in range(6): 124 | for row in range(3): 125 | for col in range(3): 126 | if row != 1 or col != 1: 127 | canvas.itemconfig(facelet_id[f][row][col], fill="grey") 128 | 129 | 130 | def random(): 131 | """Generate a random cube and set the corresponding facelet colors.""" 132 | cc = cubie.CubieCube() 133 | cc.randomize() 134 | fc = cc.to_facelet_cube() 135 | idx = 0 136 | for f in range(6): 137 | for row in range(3): 138 | for col in range(3): 139 | canvas.itemconfig(facelet_id[f][row][col], fill=cols[fc.f[idx]] ) 140 | idx += 1 141 | ######################################################################################################################## 142 | 143 | # ################################### Edit the facelet colors ########################################################## 144 | 145 | 146 | def click(event): 147 | """Define how to react on left mouse clicks.""" 148 | global curcol 149 | idlist = canvas.find_withtag("current") 150 | if len(idlist) > 0: 151 | if idlist[0] in colorpick_id: 152 | curcol = canvas.itemcget("current", "fill") 153 | for i in range(6): 154 | canvas.itemconfig(colorpick_id[i], width=1) 155 | canvas.itemconfig("current", width=5) 156 | else: 157 | canvas.itemconfig("current", fill=curcol) 158 | ######################################################################################################################## 159 | 160 | # ###################################### Generate and display the TK_widgets ########################################## 161 | root = Tk() 162 | root.wm_title("Solver Client") 163 | canvas = Canvas(root, width=12 * width + 20, height=9 * width + 20) 164 | canvas.pack() 165 | 166 | bsolve = Button(text="Solve", height=2, width=10, relief=RAISED, command=solve) 167 | bsolve_window = canvas.create_window(10 + 10.5 * width, 10 + 6.5 * width, anchor=NW, window=bsolve) 168 | bclean = Button(text="Clean", height=1, width=10, relief=RAISED, command=clean) 169 | bclean_window = canvas.create_window(10 + 10.5 * width, 10 + 7.5 * width, anchor=NW, window=bclean) 170 | bempty = Button(text="Empty", height=1, width=10, relief=RAISED, command=empty) 171 | bempty_window = canvas.create_window(10 + 10.5 * width, 10 + 8 * width, anchor=NW, window=bempty) 172 | brandom = Button(text="Random", height=1, width=10, relief=RAISED, command=random) 173 | brandom_window = canvas.create_window(10 + 10.5 * width, 10 + 8.5 * width, anchor=NW, window=brandom) 174 | display = Text(height=7, width=39) 175 | text_window = canvas.create_window(10 + 6.5 * width, 10 + .5 * width, anchor=NW, window=display) 176 | hp = Label(text=' Hostname and Port') 177 | hp_window = canvas.create_window(10 + 0 * width, 10 + 0.6 * width, anchor=NW, window=hp) 178 | txt_host = Text(height=1, width=20) 179 | txt_host_window = canvas.create_window(10 + 0 * width, 10 + 1 * width, anchor=NW, window=txt_host) 180 | txt_host.insert(INSERT, DEFAULT_HOST) 181 | txt_port = Text(height=1, width=20) 182 | txt_port_window = canvas.create_window(10 + 0 * width, 10 + 1.5 * width, anchor=NW, window=txt_port) 183 | txt_port.insert(INSERT, DEFAULT_PORT) 184 | canvas.bind("", click) 185 | create_facelet_rects(width) 186 | create_colorpick_rects(width) 187 | root.mainloop() 188 | ######################################################################################################################## 189 | 190 | -------------------------------------------------------------------------------- /moves.py: -------------------------------------------------------------------------------- 1 | # ################### Movetables describe the transformation of the coordinates by cube moves. ######################### 2 | 3 | from os import path 4 | import array as ar 5 | import cubie as cb 6 | import enums 7 | from defs import N_TWIST, N_FLIP, N_SLICE_SORTED, N_CORNERS, N_UD_EDGES, N_MOVE 8 | 9 | a = cb.CubieCube() 10 | # ######################################### Move table for the twists of the corners. ################################## 11 | 12 | # The twist coordinate describes the 3^7 = 2187 possible orientations of the 8 corners 13 | # 0 <= twist < 2187 in phase 1, twist = 0 in phase 2 14 | fname = "move_twist" 15 | if not path.isfile(fname): 16 | print("creating " + fname + " table...") 17 | twist_move = ar.array('H', [0 for i in range(N_TWIST * N_MOVE)]) 18 | for i in range(N_TWIST): 19 | a.set_twist(i) 20 | for j in enums.Color: # six faces U, R, F, D, L, B 21 | for k in range(3): # three moves for each face, for example U, U2, U3 = U' 22 | a.corner_multiply(cb.basicMoveCube[j]) 23 | twist_move[N_MOVE * i + 3 * j + k] = a.get_twist() 24 | a.corner_multiply(cb.basicMoveCube[j]) # 4. move restores face 25 | fh = open(fname, "wb") 26 | twist_move.tofile(fh) 27 | else: 28 | print("loading " + fname + " table...") 29 | fh = open(fname, "rb") 30 | twist_move = ar.array('H') 31 | twist_move.fromfile(fh, N_TWIST * N_MOVE) 32 | fh.close() 33 | ######################################################################################################################## 34 | 35 | # #################################### Move table for the flip of the edges. ########################################## 36 | 37 | # The flip coordinate describes the 2^11 = 2048 possible orientations of the 12 edges 38 | # 0 <= flip < 2048 in phase 1, flip = 0 in phase 2 39 | fname = "move_flip" 40 | if not path.isfile(fname): 41 | print("creating " + fname + " table...") 42 | flip_move = ar.array('H', [0 for i in range(N_FLIP * N_MOVE)]) 43 | for i in range(N_FLIP): 44 | a.set_flip(i) 45 | for j in enums.Color: 46 | for k in range(3): 47 | a.edge_multiply(cb.basicMoveCube[j]) 48 | flip_move[N_MOVE * i + 3 * j + k] = a.get_flip() 49 | a.edge_multiply(cb.basicMoveCube[j]) 50 | fh = open(fname, "wb") 51 | flip_move.tofile(fh) 52 | else: 53 | print("loading " + fname + " table...") 54 | fh = open(fname, "rb") 55 | flip_move = ar.array('H') 56 | flip_move.fromfile(fh, N_FLIP * N_MOVE) 57 | fh.close() 58 | ######################################################################################################################## 59 | 60 | # ###################### Move table for the four UD-slice edges FR, FL, Bl and BR. ##################################### 61 | 62 | # The slice_sorted coordinate describes the 12!/8! = 11880 possible positions of the FR, FL, BL and BR edges. 63 | # Though for phase 1 only the "unsorted" slice coordinate with Binomial(12,4) = 495 positions is relevant, using the 64 | # slice_sorted coordinate gives us the permutation of the FR, FL, BL and BR edges at the beginning of phase 2 for free. 65 | # 0 <= slice_sorted < 11880 in phase 1, 0 <= slice_sorted < 24 in phase 2, slice_sorted = 0 for solved cube 66 | fname = "move_slice_sorted" 67 | if not path.isfile(fname): 68 | print("creating " + fname + " table...") 69 | slice_sorted_move = ar.array('H', [0 for i in range(N_SLICE_SORTED * N_MOVE)]) 70 | for i in range(N_SLICE_SORTED): 71 | if i % 200 == 0: 72 | print('.', end='', flush=True) 73 | a.set_slice_sorted(i) 74 | for j in enums.Color: 75 | for k in range(3): 76 | a.edge_multiply(cb.basicMoveCube[j]) 77 | slice_sorted_move[N_MOVE * i + 3 * j + k] = a.get_slice_sorted() 78 | a.edge_multiply(cb.basicMoveCube[j]) 79 | fh = open(fname, "wb") 80 | slice_sorted_move.tofile(fh) 81 | print() 82 | else: 83 | print("loading " + fname + " table...") 84 | fh = open(fname, "rb") 85 | slice_sorted_move = ar.array('H') 86 | slice_sorted_move.fromfile(fh, N_SLICE_SORTED * N_MOVE) 87 | fh.close() 88 | ######################################################################################################################## 89 | 90 | # ################# Move table for the u_edges coordinate for transition phase 1 -> phase 2 ############################ 91 | 92 | # The u_edges coordinate describes the 12!/8! = 11880 possible positions of the UR, UF, UL and UB edges. It is needed at 93 | # the end of phase 1 to set up the coordinates of phase 2 94 | # 0 <= u_edges < 11880 in phase 1, 0 <= u_edges < 1680 in phase 2, u_edges = 1656 for solved cube.""" 95 | fname = "move_u_edges" 96 | if not path.isfile(fname): 97 | print("creating " + fname + " table...") 98 | u_edges_move = ar.array('H', [0 for i in range(N_SLICE_SORTED * N_MOVE)]) 99 | for i in range(N_SLICE_SORTED): 100 | if i % 200 == 0: 101 | print('.', end='', flush=True) 102 | a.set_u_edges(i) 103 | for j in enums.Color: 104 | for k in range(3): 105 | a.edge_multiply(cb.basicMoveCube[j]) 106 | u_edges_move[N_MOVE * i + 3 * j + k] = a.get_u_edges() 107 | a.edge_multiply(cb.basicMoveCube[j]) 108 | fh = open(fname, "wb") 109 | u_edges_move.tofile(fh) 110 | print() 111 | else: 112 | print("loading " + fname + " table...") 113 | fh = open(fname, "rb") 114 | u_edges_move = ar.array('H') 115 | u_edges_move.fromfile(fh, N_SLICE_SORTED * N_MOVE) 116 | fh.close() 117 | ######################################################################################################################## 118 | 119 | # ################# Move table for the d_edges coordinate for transition phase 1 -> phase 2 ############################ 120 | 121 | # The d_edges coordinate describes the 12!/8! = 11880 possible positions of the DR, DF, DL and DB edges. It is needed at 122 | # the end of phase 1 to set up the coordinates of phase 2 123 | # 0 <= d_edges < 11880 in phase 1, 0 <= d_edges < 1680 in phase 2, d_edges = 0 for solved cube. 124 | fname = "move_d_edges" 125 | if not path.isfile(fname): 126 | print("creating " + fname + " table...") 127 | d_edges_move = ar.array('H', [0 for i in range(N_SLICE_SORTED * N_MOVE)]) 128 | for i in range(N_SLICE_SORTED): 129 | if i % 200 == 0: 130 | print('.', end='', flush=True) 131 | a.set_d_edges(i) 132 | for j in enums.Color: 133 | for k in range(3): 134 | a.edge_multiply(cb.basicMoveCube[j]) 135 | d_edges_move[N_MOVE * i + 3 * j + k] = a.get_d_edges() 136 | a.edge_multiply(cb.basicMoveCube[j]) 137 | fh = open(fname, "wb") 138 | d_edges_move.tofile(fh) 139 | print() 140 | else: 141 | print("loading " + fname + " table...") 142 | fh = open(fname, "rb") 143 | d_edges_move = ar.array('H') 144 | d_edges_move.fromfile(fh, N_SLICE_SORTED * N_MOVE) 145 | fh.close() 146 | ######################################################################################################################## 147 | 148 | # ######################### # Move table for the edges in the U-face and D-face. ####################################### 149 | 150 | # The ud_edges coordinate describes the 40320 permutations of the edges UR, UF, UL, UB, DR, DF, DL and DB in phase 2 151 | # ud_edges undefined in phase 1, 0 <= ud_edges < 40320 in phase 2, ud_edges = 0 for solved cube. 152 | fname = "move_ud_edges" 153 | if not path.isfile(fname): 154 | print("creating " + fname + " table...") 155 | ud_edges_move = ar.array('H', [0 for i in range(N_UD_EDGES * N_MOVE)]) 156 | for i in range(N_UD_EDGES): 157 | if (i+1) % 600 == 0: 158 | print('.', end='', flush=True) 159 | if (i+1) % 48000 == 0: 160 | print('') 161 | a.set_ud_edges(i) 162 | for j in enums.Color: 163 | for k in range(3): 164 | a.edge_multiply(cb.basicMoveCube[j]) 165 | # only R2, F2, L2 and B2 in phase 2 166 | if j in [enums.Color.R, enums.Color.F, enums.Color.L, enums.Color.B] and k != 1: 167 | continue 168 | ud_edges_move[N_MOVE * i + 3 * j + k] = a.get_ud_edges() 169 | a.edge_multiply(cb.basicMoveCube[j]) 170 | fh = open(fname, "wb") 171 | ud_edges_move.tofile(fh) 172 | print() 173 | else: 174 | print("loading " + fname + " table...") 175 | fh = open(fname, "rb") 176 | ud_edges_move = ar.array('H') 177 | ud_edges_move.fromfile(fh, N_UD_EDGES * N_MOVE) 178 | fh.close() 179 | ######################################################################################################################## 180 | 181 | # ############################ Move table for the corners coordinate in phase 2 ######################################## 182 | 183 | # The corners coordinate describes the 8! = 40320 permutations of the corners. 184 | # 0 <= corners < 40320 defined but unused in phase 1, 0 <= corners < 40320 in phase 2, corners = 0 for solved cube 185 | fname = "move_corners" 186 | if not path.isfile(fname): 187 | print("creating " + fname + " table...") 188 | corners_move = ar.array('H', [0 for i in range(N_CORNERS * N_MOVE)]) 189 | for i in range(N_CORNERS): 190 | if (i+1) % 200 == 0: 191 | print('.', end='', flush=True) 192 | if(i+1) % 16000 == 0: 193 | print('') 194 | a.set_corners(i) 195 | for j in enums.Color: 196 | for k in range(3): 197 | a.corner_multiply(cb.basicMoveCube[j]) 198 | corners_move[N_MOVE * i + 3 * j + k] = a.get_corners() 199 | a.corner_multiply(cb.basicMoveCube[j]) 200 | fh = open(fname, "wb") 201 | corners_move.tofile(fh) 202 | fh.close() 203 | print() 204 | else: 205 | print("loading " + fname + " table...") 206 | fh = open(fname, "rb") 207 | corners_move = ar.array('H') 208 | corners_move.fromfile(fh, N_CORNERS * N_MOVE) 209 | fh.close() 210 | ######################################################################################################################## 211 | -------------------------------------------------------------------------------- /coord.py: -------------------------------------------------------------------------------- 1 | # ##### The cube on the coordinate level. It is described by a 3-tuple of natural numbers in phase 1 and phase 2. ###### 2 | 3 | from os import path 4 | import array as ar 5 | 6 | import cubie as cb 7 | import enums 8 | import moves as mv 9 | import pruning as pr 10 | import symmetries as sy 11 | from defs import N_U_EDGES_PHASE2, N_PERM_4, N_CHOOSE_8_4, N_FLIP, N_TWIST, N_UD_EDGES, N_MOVE 12 | from enums import Edge as Ed 13 | 14 | SOLVED = 0 # 0 is index of solved state (except for u_edges coordinate) 15 | u_edges_plus_d_edges_to_ud_edges = None # global variable 16 | 17 | 18 | class CoordCube: 19 | """Represent a cube on the coordinate level. 20 | 21 | In phase 1 a state is uniquely determined by the three coordinates flip, twist and slice. 22 | In phase 2 a state is uniquely determined by the three coordinates corners, ud_edges and slice_sorted. 23 | """ 24 | 25 | def __init__(self, cc=None): 26 | if cc is None: 27 | self.twist = SOLVED # twist of corners 28 | self.flip = SOLVED # flip of edges 29 | self.slice_sorted = SOLVED # Position of FR, FL, BL, BR edges. Valid in phase 1 (<11880) and phase 2 (<24) 30 | # The phase 1 slice coordinate is given by slice_sorted // 24 31 | 32 | self.u_edges = 1656 # Valid in phase 1 (<11880) and phase 2 (<1680). 1656 is the index of solved u_edges. 33 | self.d_edges = SOLVED # Valid in phase 1 (<11880) and phase 2 (<1680) 34 | self.corners = SOLVED # corner permutation. Valid in phase1 and phase2 35 | self.ud_edges = SOLVED # permutation of the ud-edges. Valid only in phase 2 36 | else: 37 | self.twist = cc.get_twist() 38 | self.flip = cc.get_flip() 39 | self.slice_sorted = cc.get_slice_sorted() 40 | self.u_edges = cc.get_u_edges() 41 | self.d_edges = cc.get_d_edges() 42 | self.corners = cc.get_corners() 43 | if self.slice_sorted < N_PERM_4: # phase 2 cube 44 | self.ud_edges = cc.get_ud_edges() 45 | else: 46 | self.ud_edges = -1 # invalid 47 | 48 | # symmetry reduced flipslice coordinate used in phase 1 49 | self.flipslice_classidx = sy.flipslice_classidx[N_FLIP * (self.slice_sorted // N_PERM_4) + self.flip] 50 | self.flipslice_sym = sy.flipslice_sym[N_FLIP * (self.slice_sorted // N_PERM_4) + self.flip] 51 | self.flipslice_rep = sy.flipslice_rep[self.flipslice_classidx] 52 | # symmetry reduced corner permutation coordinate used in phase 2 53 | self.corner_classidx = sy.corner_classidx[self.corners] 54 | self.corner_sym = sy.corner_sym[self.corners] 55 | self.corner_rep = sy.corner_rep[self.corner_classidx] 56 | 57 | def __str__(self): 58 | s = '(twist: ' + str(self.twist) + ', flip: ' + str(self.flip) + ', slice: ' + str(self.slice_sorted // 24) + \ 59 | ', U-edges: ' + str(self.u_edges) + ', D-edges: ' + str(self.d_edges) + ', E-edges: ' \ 60 | + str(self.slice_sorted) + ', Corners: ' + str(self.corners) + ', UD-Edges : ' + str(self.ud_edges) + ')' 61 | s = s + '\n' + str(self.flipslice_classidx) + ' ' + str(self.flipslice_sym) + ' ' + str(self.flipslice_rep) 62 | s = s + '\n' + str(self.corner_classidx) + ' ' + str(self.corner_sym) + ' ' + str(self.corner_rep) 63 | return s 64 | 65 | def phase1_move(self, m): 66 | self.twist = mv.twist_move[N_MOVE * self.twist + m] 67 | self.flip = mv.flip_move[N_MOVE * self.flip + m] 68 | self.slice_sorted = mv.slice_sorted_move[N_MOVE * self.slice_sorted + m] 69 | # optional: 70 | self.u_edges = mv.u_edges_move[N_MOVE * self.u_edges + m] # u_edges and d_edges retrieve ud_edges easily 71 | self.d_edges = mv.d_edges_move[N_MOVE * self.d_edges + m] # if phase 1 is finished and phase 2 starts 72 | self.corners = mv.corners_move[N_MOVE * self.corners + m] # Is needed only in phase 2 73 | 74 | self.flipslice_classidx = sy.flipslice_classidx[N_FLIP * (self.slice_sorted // N_PERM_4) + self.flip] 75 | self.flipslice_sym = sy.flipslice_sym[N_FLIP * (self.slice_sorted // N_PERM_4) + self.flip] 76 | self.flipslice_rep = sy.flipslice_rep[self.flipslice_classidx] 77 | 78 | self.corner_classidx = self.corner_classidx = sy.corner_classidx[self.corners] 79 | self.corner_sym = sy.corner_sym[self.corners] 80 | self.corner_rep = sy.corner_rep[self.corner_classidx] 81 | 82 | def phase2_move(self, m): 83 | self.slice_sorted = mv.slice_sorted_move[N_MOVE * self.slice_sorted + m] 84 | self.corners = mv.corners_move[N_MOVE * self.corners + m] 85 | self.ud_edges = mv.ud_edges_move[N_MOVE * self.ud_edges + m] 86 | 87 | def get_depth_phase1(self): 88 | slice_ = self.slice_sorted // N_PERM_4 89 | flip = self.flip 90 | twist = self.twist 91 | flipslice = N_FLIP * slice_ + flip 92 | classidx = sy.flipslice_classidx[flipslice] 93 | sym = sy.flipslice_sym[flipslice] 94 | depth_mod3 = pr.get_flipslice_twist_depth3(N_TWIST * classidx + sy.twist_conj[(twist << 4) + sym]) 95 | 96 | depth = 0 97 | while flip != SOLVED or slice_ != SOLVED or twist != SOLVED: 98 | if depth_mod3 == 0: 99 | depth_mod3 = 3 100 | for m in enums.Move: 101 | twist1 = mv.twist_move[N_MOVE * twist + m] 102 | flip1 = mv.flip_move[N_MOVE * flip + m] 103 | slice1 = mv.slice_sorted_move[N_MOVE * slice_ * N_PERM_4 + m] // N_PERM_4 104 | flipslice1 = N_FLIP * slice1 + flip1 105 | classidx1 = sy.flipslice_classidx[flipslice1] 106 | sym = sy.flipslice_sym[flipslice1] 107 | if pr.get_flipslice_twist_depth3( 108 | N_TWIST * classidx1 + sy.twist_conj[(twist1 << 4) + sym]) == depth_mod3 - 1: 109 | depth += 1 110 | twist = twist1 111 | flip = flip1 112 | slice_ = slice1 113 | depth_mod3 -= 1 114 | break 115 | return depth 116 | 117 | @staticmethod 118 | def get_depth_phase2(corners, ud_edges): 119 | # the slice coordinate is not included 120 | classidx = sy.corner_classidx[corners] 121 | sym = sy.corner_sym[corners] 122 | depth_mod3 = pr.get_corners_ud_edges_depth3(N_UD_EDGES * classidx + sy.ud_edges_conj[(ud_edges << 4) + sym]) 123 | if depth_mod3 == 3: # unfilled entry, depth >= 11 124 | return 11 125 | depth = 0 126 | while corners != SOLVED or ud_edges != SOLVED: 127 | if depth_mod3 == 0: 128 | depth_mod3 = 3 129 | # only iterate phase 2 moves 130 | for m in (enums.Move.U1, enums.Move.U2, enums.Move.U3, enums.Move.R2, enums.Move.F2, enums.Move.D1, 131 | enums.Move.D2, enums.Move.D3, enums.Move.L2, enums.Move.B2): 132 | corners1 = mv.corners_move[N_MOVE * corners + m] 133 | ud_edges1 = mv.ud_edges_move[N_MOVE * ud_edges + m] 134 | classidx1 = sy.corner_classidx[corners1] 135 | sym = sy.corner_sym[corners1] 136 | if pr.get_corners_ud_edges_depth3(N_UD_EDGES * classidx1 + sy.ud_edges_conj[(ud_edges1 << 4) + sym]) == \ 137 | depth_mod3 - 1: 138 | depth += 1 139 | corners = corners1 140 | ud_edges = ud_edges1 141 | depth_mod3 -= 1 142 | break 143 | return depth 144 | 145 | 146 | def create_phase2_edgemerge_table(): 147 | """phase2_edgemerge retrieves the initial phase 2 ud_edges coordinate from the u_edges and d_edges coordinates.""" 148 | fname = "phase2_edgemerge" 149 | global u_edges_plus_d_edges_to_ud_edges 150 | c_u = cb.CubieCube() 151 | c_d = cb.CubieCube() 152 | c_ud = cb.CubieCube() 153 | edge_u = [Ed.UR, Ed.UF, Ed.UL, Ed.UB] 154 | edge_d = [Ed.DR, Ed.DF, Ed.DL, Ed.DB] 155 | edge_ud = [Ed.UR, Ed.UF, Ed.UL, Ed.UB, Ed.DR, Ed.DF, Ed.DL, Ed.DB] 156 | 157 | if not path.isfile(fname): 158 | cnt = 0 159 | print("creating " + fname + " table...") 160 | u_edges_plus_d_edges_to_ud_edges = ar.array('H', [0 for i in range(N_U_EDGES_PHASE2 * N_PERM_4)]) 161 | for i in range(N_U_EDGES_PHASE2): 162 | c_u.set_u_edges(i) 163 | for j in range(N_CHOOSE_8_4): 164 | c_d.set_d_edges(j * N_PERM_4) 165 | invalid = False 166 | for e in edge_ud: 167 | c_ud.ep[e] = -1 # invalidate edges 168 | if c_u.ep[e] in edge_u: 169 | c_ud.ep[e] = c_u.ep[e] 170 | if c_d.ep[e] in edge_d: 171 | c_ud.ep[e] = c_d.ep[e] 172 | if c_ud.ep[e] == -1: 173 | invalid = True # edge collision 174 | break 175 | if not invalid: 176 | for k in range(N_PERM_4): 177 | c_d.set_d_edges(j * N_PERM_4 + k) 178 | for e in edge_ud: 179 | if c_u.ep[e] in edge_u: 180 | c_ud.ep[e] = c_u.ep[e] 181 | if c_d.ep[e] in edge_d: 182 | c_ud.ep[e] = c_d.ep[e] 183 | u_edges_plus_d_edges_to_ud_edges[N_PERM_4 * i + k] = c_ud.get_ud_edges() 184 | cnt += 1 185 | if cnt % 2000 == 0: 186 | print('.', end='', flush=True) 187 | print() 188 | fh = open(fname, "wb") 189 | u_edges_plus_d_edges_to_ud_edges.tofile(fh) 190 | fh.close() 191 | print() 192 | else: 193 | fh = open(fname, "rb") 194 | u_edges_plus_d_edges_to_ud_edges = ar.array('H') 195 | u_edges_plus_d_edges_to_ud_edges.fromfile(fh, N_U_EDGES_PHASE2 * N_PERM_4) 196 | 197 | 198 | ######################################################################################################################## 199 | 200 | 201 | create_phase2_edgemerge_table() 202 | -------------------------------------------------------------------------------- /symmetries.py: -------------------------------------------------------------------------------- 1 | # #################### Symmetry related functions. Symmetry considerations increase the performance of the solver.###### 2 | 3 | from os import path 4 | import numpy as np 5 | import array as ar 6 | import cubie as cb 7 | from defs import N_TWIST, N_SYM, N_SYM_D4h, N_FLIP, N_SLICE, N_CORNERS, N_UD_EDGES, N_MOVE, N_FLIPSLICE_CLASS, \ 8 | N_CORNERS_CLASS 9 | from enums import Corner as Co, Edge as Ed, Move as Mv, BS 10 | 11 | INVALID = 65535 12 | 13 | # #################### Permutations and orientation changes of the basic symmetries ################################### 14 | 15 | # 120° clockwise rotation around the long diagonal URF-DBL 16 | cpROT_URF3 = [Co.URF, Co.DFR, Co.DLF, Co.UFL, Co.UBR, Co.DRB, Co.DBL, Co.ULB] 17 | coROT_URF3 = [1, 2, 1, 2, 2, 1, 2, 1] 18 | epROT_URF3 = [Ed.UF, Ed.FR, Ed.DF, Ed.FL, Ed.UB, Ed.BR, Ed.DB, Ed.BL, Ed.UR, Ed.DR, Ed.DL, Ed.UL] 19 | eoROT_URF3 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1] 20 | 21 | # 180° rotation around the axis through the F and B centers 22 | cpROT_F2 = [Co.DLF, Co.DFR, Co.DRB, Co.DBL, Co.UFL, Co.URF, Co.UBR, Co.ULB] 23 | coROT_F2 = [0, 0, 0, 0, 0, 0, 0, 0] 24 | epROT_F2 = [Ed.DL, Ed.DF, Ed.DR, Ed.DB, Ed.UL, Ed.UF, Ed.UR, Ed.UB, Ed.FL, Ed.FR, Ed.BR, Ed.BL] 25 | eoROT_F2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 26 | 27 | # 90° clockwise rotation around the axis through the U and D centers 28 | cpROT_U4 = [Co.UBR, Co.URF, Co.UFL, Co.ULB, Co.DRB, Co.DFR, Co.DLF, Co.DBL] 29 | coROT_U4 = [0, 0, 0, 0, 0, 0, 0, 0] 30 | epROT_U4 = [Ed.UB, Ed.UR, Ed.UF, Ed.UL, Ed.DB, Ed.DR, Ed.DF, Ed.DL, Ed.BR, Ed.FR, Ed.FL, Ed.BL] 31 | eoROT_U4 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1] 32 | 33 | # reflection at the plane through the U, D, F, B centers 34 | cpMIRR_LR2 = [Co.UFL, Co.URF, Co.UBR, Co.ULB, Co.DLF, Co.DFR, Co.DRB, Co.DBL] 35 | coMIRR_LR2 = [3, 3, 3, 3, 3, 3, 3, 3] 36 | epMIRR_LR2 = [Ed.UL, Ed.UF, Ed.UR, Ed.UB, Ed.DL, Ed.DF, Ed.DR, Ed.DB, Ed.FL, Ed.FR, Ed.BR, Ed.BL] 37 | eoMIRR_LR2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 38 | 39 | basicSymCube = [cb.CubieCube()] * 4 40 | basicSymCube[BS.ROT_URF3] = cb.CubieCube(cpROT_URF3, coROT_URF3, epROT_URF3, eoROT_URF3) 41 | basicSymCube[BS.ROT_F2] = cb.CubieCube(cpROT_F2, coROT_F2, epROT_F2, eoROT_F2) 42 | basicSymCube[BS.ROT_U4] = cb.CubieCube(cpROT_U4, coROT_U4, epROT_U4, eoROT_U4) 43 | basicSymCube[BS.MIRR_LR2] = cb.CubieCube(cpMIRR_LR2, coMIRR_LR2, epMIRR_LR2, eoMIRR_LR2) 44 | # ###################################################################################################################### 45 | 46 | # ######################################## Fill SymCube list ########################################################### 47 | 48 | # 48 CubieCubes will represent the 48 cube symmetries 49 | symCube = [] 50 | cc = cb.CubieCube() # Identity cube 51 | idx = 0 52 | for urf3 in range(3): 53 | for f2 in range(2): 54 | for u4 in range(4): 55 | for lr2 in range(2): 56 | symCube.append(cb.CubieCube(cc.cp, cc.co, cc.ep, cc.eo)) 57 | idx += 1 58 | cc.multiply(basicSymCube[BS.MIRR_LR2]) 59 | cc.multiply(basicSymCube[BS.ROT_U4]) 60 | cc.multiply(basicSymCube[BS.ROT_F2]) 61 | cc.multiply(basicSymCube[BS.ROT_URF3]) 62 | ######################################################################################################################## 63 | 64 | # ########################################## Fill the inv_idx array #################################################### 65 | 66 | # Indices for the inverse symmetries: SymCube[inv_idx[idx]] == SymCube[idx]^(-1) 67 | inv_idx = [0] * N_SYM 68 | for j in range(N_SYM): 69 | for i in range(N_SYM): 70 | cc = cb.CubieCube(symCube[j].cp, symCube[j].co, symCube[j].ep, symCube[j].eo) 71 | cc.corner_multiply(symCube[i]) 72 | if cc.cp[Co.URF] == Co.URF and cc.cp[Co.UFL] == Co.UFL and cc.cp[Co.ULB] == Co.ULB: 73 | inv_idx[j] = i 74 | break 75 | ######################################################################################################################## 76 | 77 | # ################################# Generate the group table for the 48 cube symmetries ################################ 78 | mult_sym = np.empty([N_SYM, N_SYM], dtype=np.uint8) 79 | for i in range(N_SYM): 80 | for j in range(N_SYM): 81 | cc = cb.CubieCube(symCube[i].cp, symCube[i].co, symCube[i].ep, symCube[i].eo) 82 | cc.multiply(symCube[j]) 83 | for k in range(N_SYM): 84 | if cc == symCube[k]: # SymCube[i]*SymCube[j] == SymCube[k] 85 | mult_sym[i][j] = k 86 | break 87 | ######################################################################################################################## 88 | 89 | # #### Generate the table for the conjugation of a move m by a symmetry s. conj_move[m, s] = s*m*s^-1 ################## 90 | conj_move = np.empty([N_MOVE, N_SYM], dtype=np.uint8) 91 | for s in range(N_SYM): 92 | for m in Mv: 93 | ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube 94 | ss.multiply(cb.moveCube[m]) # s*m 95 | ss.multiply(symCube[inv_idx[s]]) # s*m*s^-1 96 | for m2 in Mv: 97 | if ss == cb.moveCube[m2]: 98 | conj_move[m][s] = m2 99 | ######################################################################################################################## 100 | 101 | # ###### Generate the phase 1 table for the conjugation of the twist t by a symmetry s. twist_conj[t, s] = s*t*s^-1 #### 102 | fname = "conj_twist" 103 | if not path.isfile(fname): 104 | print('On the first run, several tables will be created. This takes from 1/2 hour (e.g. PC) to 6 hours ' 105 | '(e.g. RaspberryPi3), depending on the hardware.') 106 | print("creating " + fname + " table...") 107 | twist_conj = ar.array('H', [0] * (N_TWIST * N_SYM_D4h)) 108 | for t in range(N_TWIST): 109 | cc = cb.CubieCube() 110 | cc.set_twist(t) 111 | for s in range(N_SYM_D4h): 112 | ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube 113 | ss.corner_multiply(cc) # s*t 114 | ss.corner_multiply(symCube[inv_idx[s]]) # s*t*s^-1 115 | twist_conj[N_SYM_D4h * t + s] = ss.get_twist() 116 | fh = open(fname, "wb") 117 | twist_conj.tofile(fh) 118 | else: 119 | print("loading " + fname + " table...") 120 | fh = open(fname, 'rb') 121 | twist_conj = ar.array('H') 122 | twist_conj.fromfile(fh, N_TWIST * N_SYM_D4h) 123 | 124 | fh.close() 125 | # ###################################################################################################################### 126 | 127 | # #################### Generate the phase 2 table for the conjugation of the URtoDB coordinate by a symmetrie ########## 128 | fname = "conj_ud_edges" 129 | if not path.isfile(fname): 130 | print("creating " + fname + " table...") 131 | ud_edges_conj = ar.array('H', [0] * (N_UD_EDGES * N_SYM_D4h)) 132 | for t in range(N_UD_EDGES): 133 | if (t + 1) % 400 == 0: 134 | print('.', end='', flush=True) 135 | if (t + 1) % 32000 == 0: 136 | print('') 137 | cc = cb.CubieCube() 138 | cc.set_ud_edges(t) 139 | for s in range(N_SYM_D4h): 140 | ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube 141 | ss.edge_multiply(cc) # s*t 142 | ss.edge_multiply(symCube[inv_idx[s]]) # s*t*s^-1 143 | ud_edges_conj[N_SYM_D4h * t + s] = ss.get_ud_edges() 144 | print('') 145 | fh = open(fname, "wb") 146 | ud_edges_conj.tofile(fh) 147 | else: 148 | print("loading " + fname + " table...") 149 | fh = open(fname, "rb") 150 | ud_edges_conj = ar.array('H') 151 | ud_edges_conj.fromfile(fh, N_UD_EDGES * N_SYM_D4h) 152 | fh.close() 153 | # ###################################################################################################################### 154 | 155 | # ############## Generate the tables to handle the symmetry reduced flip-slice coordinate in phase 1 ################## 156 | fname1 = "fs_classidx" 157 | fname2 = "fs_sym" 158 | fname3 = "fs_rep" 159 | if not (path.isfile(fname1) and path.isfile(fname2) and path.isfile(fname3)): 160 | print("creating " + "flipslice sym-tables...") 161 | flipslice_classidx = ar.array('H', [INVALID] * (N_FLIP * N_SLICE)) # idx -> classidx 162 | flipslice_sym = ar.array('B', [0] * (N_FLIP * N_SLICE)) # idx -> symmetry 163 | flipslice_rep = ar.array('L', [0] * N_FLIPSLICE_CLASS) # classidx -> idx of representant 164 | 165 | classidx = 0 166 | cc = cb.CubieCube() 167 | for slc in range(N_SLICE): 168 | cc.set_slice(slc) 169 | for flip in range(N_FLIP): 170 | cc.set_flip(flip) 171 | idx = N_FLIP * slc + flip 172 | if (idx + 1) % 4000 == 0: 173 | print('.', end='', flush=True) 174 | if (idx + 1) % 320000 == 0: 175 | print('') 176 | 177 | if flipslice_classidx[idx] == INVALID: 178 | flipslice_classidx[idx] = classidx 179 | flipslice_sym[idx] = 0 180 | flipslice_rep[classidx] = idx 181 | else: 182 | continue 183 | for s in range(N_SYM_D4h): # conjugate representant by all 16 symmetries 184 | ss = cb.CubieCube(symCube[inv_idx[s]].cp, symCube[inv_idx[s]].co, symCube[inv_idx[s]].ep, 185 | symCube[inv_idx[s]].eo) # copy cube 186 | ss.edge_multiply(cc) 187 | ss.edge_multiply(symCube[s]) # s^-1*cc*s 188 | idx_new = N_FLIP * ss.get_slice() + ss.get_flip() 189 | if flipslice_classidx[idx_new] == INVALID: 190 | flipslice_classidx[idx_new] = classidx 191 | flipslice_sym[idx_new] = s 192 | classidx += 1 193 | print('') 194 | fh = open(fname1, 'wb') 195 | flipslice_classidx.tofile(fh) 196 | fh.close() 197 | fh = open(fname2, 'wb') 198 | flipslice_sym.tofile(fh) 199 | fh.close() 200 | fh = open(fname3, 'wb') 201 | flipslice_rep.tofile(fh) 202 | fh.close() 203 | 204 | else: 205 | print("loading " + "flipslice sym-tables...") 206 | 207 | fh = open(fname1, 'rb') 208 | flipslice_classidx = ar.array('H') 209 | flipslice_classidx.fromfile(fh, N_FLIP * N_SLICE) 210 | fh.close() 211 | fh = open(fname2, 'rb') 212 | flipslice_sym = ar.array('B') 213 | flipslice_sym.fromfile(fh, N_FLIP * N_SLICE) 214 | fh.close() 215 | fh = open(fname3, 'rb') 216 | flipslice_rep = ar.array('L') 217 | flipslice_rep.fromfile(fh, N_FLIPSLICE_CLASS) 218 | fh.close() 219 | ######################################################################################################################## 220 | 221 | # ############ Generate the tables to handle the symmetry reduced corner permutation coordinate in phase 2 ############# 222 | fname1 = "co_classidx" 223 | fname2 = "co_sym" 224 | fname3 = "co_rep" 225 | if not (path.isfile(fname1) and path.isfile(fname2) and path.isfile(fname3)): 226 | print("creating " + "corner sym-tables...") 227 | corner_classidx = ar.array('H', [INVALID] * N_CORNERS) # idx -> classidx 228 | corner_sym = ar.array('B', [0] * N_CORNERS) # idx -> symmetry 229 | corner_rep = ar.array('H', [0] * N_CORNERS_CLASS) # classidx -> idx of representant 230 | 231 | classidx = 0 232 | cc = cb.CubieCube() 233 | for cp in range(N_CORNERS): 234 | cc.set_corners(cp) 235 | if (cp + 1) % 8000 == 0: 236 | print('.', end='', flush=True) 237 | 238 | if corner_classidx[cp] == INVALID: 239 | corner_classidx[cp] = classidx 240 | corner_sym[cp] = 0 241 | corner_rep[classidx] = cp 242 | else: 243 | continue 244 | for s in range(N_SYM_D4h): # conjugate representant by all 16 symmetries 245 | ss = cb.CubieCube(symCube[inv_idx[s]].cp, symCube[inv_idx[s]].co, symCube[inv_idx[s]].ep, 246 | symCube[inv_idx[s]].eo) # copy cube 247 | ss.corner_multiply(cc) 248 | ss.corner_multiply(symCube[s]) # s^-1*cc*s 249 | cp_new = ss.get_corners() 250 | if corner_classidx[cp_new] == INVALID: 251 | corner_classidx[cp_new] = classidx 252 | corner_sym[cp_new] = s 253 | classidx += 1 254 | print('') 255 | fh = open(fname1, 'wb') 256 | corner_classidx.tofile(fh) 257 | fh.close() 258 | fh = open(fname2, 'wb') 259 | corner_sym.tofile(fh) 260 | fh.close() 261 | fh = open(fname3, 'wb') 262 | corner_rep.tofile(fh) 263 | fh.close() 264 | 265 | else: 266 | print("loading " + "corner sym-tables...") 267 | 268 | fh = open(fname1, 'rb') 269 | corner_classidx = ar.array('H') 270 | corner_classidx.fromfile(fh,N_CORNERS) 271 | fh.close() 272 | fh = open(fname2, 'rb') 273 | corner_sym = ar.array('B') 274 | corner_sym.fromfile(fh, N_CORNERS) 275 | fh.close() 276 | fh = open(fname3, 'rb') 277 | corner_rep = ar.array('H') 278 | corner_rep.fromfile(fh, N_CORNERS_CLASS) 279 | fh.close() 280 | ######################################################################################################################## 281 | -------------------------------------------------------------------------------- /client_gui2.py: -------------------------------------------------------------------------------- 1 | # ################ A simple graphical interface which communicates with the server ##################################### 2 | 3 | # While client_gui only allows to set the facelets with the mouse, this file (client_gui2) also takes input from the 4 | # webcam and includes sliders for some opencv parameters. 5 | 6 | from tkinter import * 7 | import socket 8 | import face 9 | import cubie 10 | from threading import Thread 11 | from vision2 import grab_colors 12 | import vision_params 13 | 14 | 15 | import numpy as np 16 | 17 | # ################################## some global variables and constants ############################################### 18 | DEFAULT_HOST = 'localhost' 19 | DEFAULT_PORT = '8080' 20 | width = 60 # width of a facelet in pixels 21 | facelet_id = [[[0 for col in range(3)] for row in range(3)] for fc in range(6)] 22 | colorpick_id = [0 for i in range(6)] 23 | curcol = None 24 | t = ("U", "R", "F", "D", "L", "B") 25 | cols = ("yellow", "green", "red", "white", "blue", "orange") 26 | 27 | 28 | ######################################################################################################################## 29 | 30 | # ################################################ Diverse functions ################################################### 31 | 32 | 33 | def show_text(txt): 34 | """Display messages.""" 35 | print(txt) 36 | display.insert(INSERT, txt) 37 | root.update_idletasks() 38 | 39 | 40 | def create_facelet_rects(a): 41 | """Initialize the facelet grid on the canvas.""" 42 | offset = ((1, 0), (2, 1), (1, 1), (1, 2), (0, 1), (3, 1)) 43 | for f in range(6): 44 | for row in range(3): 45 | y = 10 + offset[f][1] * 3 * a + row * a 46 | for col in range(3): 47 | x = 10 + offset[f][0] * 3 * a + col * a 48 | facelet_id[f][row][col] = canvas.create_rectangle(x, y, x + a, y + a, fill="grey") 49 | if row == 1 and col == 1: 50 | canvas.create_text(x + width // 2, y + width // 2, font=("", 14), text=t[f], state=DISABLED) 51 | for f in range(6): 52 | canvas.itemconfig(facelet_id[f][1][1], fill=cols[f]) 53 | 54 | 55 | def create_colorpick_rects(a): 56 | """Initialize the "paintbox" on the canvas.""" 57 | global curcol 58 | global cols 59 | for i in range(6): 60 | x = (i % 3) * (a + 5) + 7 * a 61 | y = (i // 3) * (a + 5) + 7 * a 62 | colorpick_id[i] = canvas.create_rectangle(x, y, x + a, y + a, fill=cols[i]) 63 | canvas.itemconfig(colorpick_id[0], width=4) 64 | curcol = cols[0] 65 | 66 | 67 | def get_definition_string(): 68 | """Generate the cube definition string from the facelet colors.""" 69 | color_to_facelet = {} 70 | for i in range(6): 71 | color_to_facelet.update({canvas.itemcget(facelet_id[i][1][1], "fill"): t[i]}) 72 | s = '' 73 | for f in range(6): 74 | for row in range(3): 75 | for col in range(3): 76 | s += color_to_facelet[canvas.itemcget(facelet_id[f][row][col], "fill")] 77 | return s 78 | 79 | 80 | ######################################################################################################################## 81 | 82 | # ############################### Solve the displayed cube with a local or remote server ############################### 83 | 84 | 85 | def solve(): 86 | """Connect to the server and return the solving maneuver.""" 87 | display.delete(1.0, END) # clear output window 88 | try: 89 | s = socket.socket(socket.AF_INET, socket.SOCK_STREAM) 90 | except socket.error: 91 | show_text('Failed to create socket') 92 | return 93 | # host = 'f9f0b2jt6zmzyo6b.myfritz.net' # my RaspberryPi, if online 94 | host = txt_host.get(1.0, END).rstrip() # default is localhost 95 | port = int(txt_port.get(1.0, END)) # default is port 8080 96 | 97 | try: 98 | remote_ip = socket.gethostbyname(host) 99 | except socket.gaierror: 100 | show_text('Hostname could not be resolved.') 101 | return 102 | try: 103 | s.connect((remote_ip, port)) 104 | except: 105 | show_text('Cannot connect to server!') 106 | return 107 | show_text('Connected with ' + remote_ip + '\n') 108 | try: 109 | defstr = get_definition_string() + '\n' 110 | except: 111 | show_text('Invalid facelet configuration.\nWrong or missing colors.') 112 | return 113 | show_text(defstr) 114 | try: 115 | s.sendall((defstr + '\n').encode()) 116 | except: 117 | show_text('Cannot send cube configuration to server.') 118 | return 119 | show_text(s.recv(2048).decode()) 120 | 121 | 122 | ######################################################################################################################## 123 | 124 | # ################################# Functions to change the facelet colors ############################################# 125 | 126 | 127 | def clean(): 128 | """Restore the cube to a clean cube.""" 129 | for f in range(6): 130 | for row in range(3): 131 | for col in range(3): 132 | canvas.itemconfig(facelet_id[f][row][col], fill=canvas.itemcget(facelet_id[f][1][1], "fill")) 133 | 134 | 135 | def empty(): 136 | """Remove the facelet colors except the center facelets colors.""" 137 | for f in range(6): 138 | for row in range(3): 139 | for col in range(3): 140 | if row != 1 or col != 1: 141 | canvas.itemconfig(facelet_id[f][row][col], fill="grey") 142 | 143 | 144 | def random(): 145 | """Generate a random cube and sets the corresponding facelet colors.""" 146 | cc = cubie.CubieCube() 147 | cc.randomize() 148 | fc = cc.to_facelet_cube() 149 | idx = 0 150 | for f in range(6): 151 | for row in range(3): 152 | for col in range(3): 153 | canvas.itemconfig(facelet_id[f][row][col], fill=cols[fc.f[idx]]) 154 | idx += 1 155 | 156 | 157 | ######################################################################################################################## 158 | 159 | # ################################### Edit the facelet colors ########################################################## 160 | 161 | 162 | def click(event): 163 | """Define how to react on left mouse clicks""" 164 | global curcol 165 | idlist = canvas.find_withtag("current") 166 | if len(idlist) > 0: 167 | if idlist[0] in colorpick_id: 168 | curcol = canvas.itemcget("current", "fill") 169 | for i in range(6): 170 | canvas.itemconfig(colorpick_id[i], width=1) 171 | canvas.itemconfig("current", width=5) 172 | else: 173 | canvas.itemconfig("current", fill=curcol) 174 | 175 | 176 | ######################################################################################################################## 177 | 178 | 179 | # ######################################### functions to set the slider values ######################################### 180 | def set_rgb_L(val): 181 | vision_params.rgb_L = int(val) 182 | 183 | 184 | def set_orange_L(val): 185 | vision_params.orange_L = int(val) 186 | 187 | 188 | def set_orange_H(val): 189 | vision_params.orange_H = int(val) 190 | 191 | 192 | def set_yellow_H(val): 193 | vision_params.yellow_H = int(val) 194 | 195 | 196 | def set_green_H(val): 197 | vision_params.green_H = int(val) 198 | 199 | 200 | def set_blue_H(val): 201 | vision_params.blue_H = int(val) 202 | 203 | 204 | def set_sat_W(val): 205 | vision_params.sat_W = int(val) 206 | 207 | 208 | def set_val_W(val): 209 | vision_params.val_W = int(val) 210 | 211 | 212 | def set_sigma_C(val): 213 | vision_params.sigma_C = int(val) 214 | 215 | 216 | def set_delta_C(val): 217 | vision_params.delta_C = int(val) 218 | 219 | 220 | def transfer(): 221 | """Transfer the facelet colors detected by the opencv vision to the GUI editor.""" 222 | if len(vision_params.face_col) == 0: 223 | return 224 | centercol = vision_params.face_col[1][1] 225 | 226 | vision_params.cube_col[centercol] = vision_params.face_col 227 | vision_params.cube_hsv[centercol] = vision_params.face_hsv 228 | 229 | dc = {} 230 | for i in range(6): 231 | dc[canvas.itemcget(facelet_id[i][1][1], "fill")] = i # map color to face number 232 | for i in range(3): 233 | for j in range(3): 234 | canvas.itemconfig(facelet_id[dc[centercol]][i][j], fill=vision_params.face_col[i][j]) 235 | 236 | # ###################################################################################################################### 237 | 238 | # ###################################### Generate and display the TK_widgets ########################################## 239 | 240 | root = Tk() 241 | root.wm_title("Solver Client") 242 | canvas = Canvas(root, width=12 * width + 20, height=9 * width + 20) 243 | canvas.pack() 244 | bsolve = Button(text="Solve", height=2, width=10, relief=RAISED, command=solve) 245 | bsolve_window = canvas.create_window(10 + 10.5 * width, 10 + 6.5 * width, anchor=NW, window=bsolve) 246 | bclean = Button(text="Clean", height=1, width=10, relief=RAISED, command=clean) 247 | bclean_window = canvas.create_window(10 + 10.5 * width, 10 + 7.5 * width, anchor=NW, window=bclean) 248 | bempty = Button(text="Empty", height=1, width=10, relief=RAISED, command=empty) 249 | bempty_window = canvas.create_window(10 + 10.5 * width, 10 + 8 * width, anchor=NW, window=bempty) 250 | brandom = Button(text="Random", height=1, width=10, relief=RAISED, command=random) 251 | brandom_window = canvas.create_window(10 + 10.5 * width, 10 + 8.5 * width, anchor=NW, window=brandom) 252 | display = Text(height=7, width=39) 253 | text_window = canvas.create_window(10 + 6.5 * width, 10 + .5 * width, anchor=NW, window=display) 254 | hp = Label(text=' Hostname and Port') 255 | hp_window = canvas.create_window(10 + 0 * width, 10 + 0.6 * width, anchor=NW, window=hp) 256 | txt_host = Text(height=1, width=20) 257 | txt_host_window = canvas.create_window(10 + 0 * width, 10 + 1 * width, anchor=NW, window=txt_host) 258 | txt_host.insert(INSERT, DEFAULT_HOST) 259 | txt_port = Text(height=1, width=20) 260 | txt_port_window = canvas.create_window(10 + 0 * width, 10 + 1.5 * width, anchor=NW, window=txt_port) 261 | txt_port.insert(INSERT, DEFAULT_PORT) 262 | canvas.bind("", click) 263 | create_facelet_rects(width) 264 | create_colorpick_rects(width) 265 | 266 | s_orange_L = Scale(root, from_=1, to=14, length=width * 1.4, showvalue=0, label='red-orange', orient=HORIZONTAL, 267 | command=set_orange_L) 268 | canvas.create_window(10, 12 + 6.0 * width, anchor=NW, window=s_orange_L) 269 | s_orange_L.set(vision_params.orange_L) 270 | 271 | s_orange_H = Scale(root, from_=8, to=40, length=width * 1.4, showvalue=0, label='orange-yellow', orient=HORIZONTAL, 272 | command=set_orange_H) 273 | canvas.create_window(10, 12 + 6.6 * width, anchor=NW, window=s_orange_H) 274 | s_orange_H.set(vision_params.orange_H) 275 | 276 | s_yellow_H = Scale(root, from_=31, to=80, length=width * 1.4, showvalue=0, label='yellow-green', orient=HORIZONTAL, 277 | command=set_yellow_H) 278 | canvas.create_window(10, 12 + 7.2 * width, anchor=NW, window=s_yellow_H) 279 | s_yellow_H.set(vision_params.yellow_H) 280 | 281 | s_green_H = Scale(root, from_=70, to=120, length=width * 1.4, showvalue=0, label='green-blue', orient=HORIZONTAL, 282 | command=set_green_H) 283 | canvas.create_window(10, 12 + 7.8 * width, anchor=NW, window=s_green_H) 284 | s_green_H.set(vision_params.green_H) 285 | 286 | s_blue_H = Scale(root, from_=120, to=180, length=width * 1.4, showvalue=0, label='blue-red', orient=HORIZONTAL, 287 | command=set_blue_H) 288 | canvas.create_window(10, 12 + 8.4 * width, anchor=NW, window=s_blue_H) 289 | s_blue_H.set(vision_params.blue_H) 290 | 291 | s_rgb_L = Scale(root, from_=0, to=140, length=width * 1.4, showvalue=0, label='black-filter', orient=HORIZONTAL, 292 | command=set_rgb_L) 293 | canvas.create_window(10 + width * 1.5, 12 + 6 * width, anchor=NW, window=s_rgb_L) 294 | s_rgb_L.set(vision_params.rgb_L) 295 | 296 | s_sat_W = Scale(root, from_=120, to=0, length=width * 1.4, showvalue=0, label='white-filter s', orient=HORIZONTAL, 297 | command=set_sat_W) 298 | canvas.create_window(10 + width * 1.5, 12 + 6.6 * width, anchor=NW, window=s_sat_W) 299 | s_sat_W.set(vision_params.sat_W) 300 | 301 | s_val_W = Scale(root, from_=80, to=255, length=width * 1.4, showvalue=0, label='white-filter v', orient=HORIZONTAL, 302 | command=set_val_W) 303 | canvas.create_window(10 + width * 1.5, 12 + 7.2 * width, anchor=NW, window=s_val_W) 304 | s_val_W.set(vision_params.val_W) 305 | 306 | s_sigma_C = Scale(root, from_=30, to=0, length=width * 1.4, showvalue=0, label='color-filter \u03c3', orient=HORIZONTAL, 307 | command=set_sigma_C) 308 | canvas.create_window(10 + width * 1.5, 12 + 7.8 * width, anchor=NW, window=s_sigma_C) 309 | s_sigma_C.set(vision_params.sigma_C) 310 | 311 | s_delta_C = Scale(root, from_=10, to=0, length=width * 1.4, showvalue=0, label='color-filter \u03b4', orient=HORIZONTAL, 312 | command=set_delta_C) 313 | canvas.create_window(10 + width * 1.5, 12 + 8.4 * width, anchor=NW, window=s_delta_C) 314 | s_delta_C.set(vision_params.delta_C) 315 | 316 | btransfer = Button(text="Webcam import", height=2, width=13, relief=RAISED, command=transfer) 317 | canvas.create_window(10 + 0.5 * width, 10 + 2.1 * width, anchor=NW, window=btransfer) 318 | 319 | 320 | root.mainloop() 321 | 322 | ######################################################################################################################## 323 | -------------------------------------------------------------------------------- /solver.py: -------------------------------------------------------------------------------- 1 | # ################### The SolverThread class solves implements the two phase algorithm ################################# 2 | import face 3 | import threading as thr 4 | import cubie 5 | import symmetries as sy 6 | import coord 7 | import enums as en 8 | import moves as mv 9 | import pruning as pr 10 | import time 11 | 12 | 13 | class SolverThread(thr.Thread): 14 | 15 | def __init__(self, cb_cube, rot, inv, ret_length, timeout, start_time, solutions, terminated, shortest_length): 16 | """ 17 | :param cb_cube: The cube to be solved in CubieCube representation 18 | :param rot: Rotates the cube 120° * rot along the long diagonal before applying the two-phase-algorithm 19 | :param inv: 0: Do not invert the cube . 1: Invert the cube before applying the two-phase-algorithm 20 | :param ret_length: If a solution with length <= ret_length is found the search stops. 21 | The most efficient way to solve a cube is to start six threads in parallel with rot = 0, 1 and 2 and 22 | inv = 0, 1. The first thread which finds a solutions sets the terminated flag which signals all other threads 23 | to teminate. On average this solves a cube about 12 times faster than solving one cube with a single thread. 24 | And this despite of Pythons GlobalInterpreterLock GIL. 25 | :param timeout: Essentially the maximal search time in seconds. Essentially because the search does not return 26 | before at least one solution has been found. 27 | :param start_time: The time the search started. 28 | :param solutions: An array with the found solutions found by the six parallel threads 29 | :param terminated: An event shared by the six threads to signal a termination request 30 | :param shortest_length: The length of the shortes solutions in the solution array 31 | """ 32 | thr.Thread.__init__(self) 33 | self.cb_cube = cb_cube # CubieCube 34 | self.co_cube = None # CoordCube initialized in function run 35 | self.rot = rot 36 | self.inv = inv 37 | self.sofar_phase1 = None 38 | self.sofar_phase2 = None 39 | self.lock = thr.Lock() 40 | self.ret_length = ret_length 41 | self.timeout = timeout 42 | self.start_time = start_time 43 | 44 | self.cornersave = 0 45 | 46 | # these variables are shared by the six threads, initialized in function solve 47 | self.solutions = solutions 48 | self.terminated = terminated 49 | self.shortest_length = shortest_length 50 | 51 | def search_phase2(self, corners, ud_edges, slice_sorted, dist, togo_phase2): 52 | # ############################################################################################################## 53 | if self.terminated.is_set(): 54 | return 55 | ################################################################################################################ 56 | if togo_phase2 == 0 and slice_sorted == 0: 57 | self.lock.acquire() # phase 2 solved, store solution 58 | man = self.sofar_phase1 + self.sofar_phase2 59 | if len(self.solutions) == 0 or (len(self.solutions[-1]) > len(man)): 60 | 61 | if self.inv == 1: # we solved the inverse cube 62 | man = list(reversed(man)) 63 | man[:] = [en.Move((m // 3) * 3 + (2 - m % 3)) for m in man] # R1->R3, R2->R2, R3->R1 etc. 64 | man[:] = [en.Move(sy.conj_move[m, 16 * self.rot]) for m in man] 65 | self.solutions.append(man) 66 | self.shortest_length[0] = len(man) 67 | 68 | if self.shortest_length[0] <= self.ret_length: # we have reached the target length 69 | self.terminated.set() 70 | self.lock.release() 71 | else: 72 | for m in en.Move: 73 | if m in [en.Move.R1, en.Move.R3, en.Move.F1, en.Move.F3, 74 | en.Move.L1, en.Move.L3, en.Move.B1, en.Move.B3]: 75 | continue 76 | 77 | if len(self.sofar_phase2) > 0: 78 | diff = self.sofar_phase2[-1] // 3 - m // 3 79 | if diff in [0, 3]: # successive moves: on same face or on same axis with wrong order 80 | continue 81 | else: 82 | if len(self.sofar_phase1) > 0: 83 | diff = self.sofar_phase1[-1] // 3 - m // 3 84 | if diff in [0, 3]: # successive moves: on same face or on same axis with wrong order 85 | continue 86 | 87 | corners_new = mv.corners_move[18 * corners + m] 88 | ud_edges_new = mv.ud_edges_move[18 * ud_edges + m] 89 | slice_sorted_new = mv.slice_sorted_move[18 * slice_sorted + m] 90 | 91 | classidx = sy.corner_classidx[corners_new] 92 | sym = sy.corner_sym[corners_new] 93 | dist_new_mod3 = pr.get_corners_ud_edges_depth3( 94 | 40320 * classidx + sy.ud_edges_conj[(ud_edges_new << 4) + sym]) 95 | dist_new = pr.distance[3 * dist + dist_new_mod3] 96 | if max(dist_new, pr.cornslice_depth[24 * corners_new + slice_sorted_new]) >= togo_phase2: 97 | continue # impossible to reach solved cube in togo_phase2 - 1 moves 98 | 99 | self.sofar_phase2.append(m) 100 | self.search_phase2(corners_new, ud_edges_new, slice_sorted_new, dist_new, togo_phase2 - 1) 101 | self.sofar_phase2.pop(-1) 102 | 103 | def search(self, flip, twist, slice_sorted, dist, togo_phase1): 104 | # ############################################################################################################## 105 | if self.terminated.is_set(): 106 | return 107 | ################################################################################################################ 108 | if togo_phase1 == 0: # phase 1 solved 109 | 110 | if time.monotonic() > self.start_time + self.timeout and len(self.solutions) > 0: 111 | self.terminated.set() 112 | 113 | # compute initial phase 2 coordinates 114 | if self.sofar_phase1: # check if list is not empty 115 | m = self.sofar_phase1[-1] 116 | else: 117 | m = en.Move.U1 # value is irrelevant here, no phase 1 moves 118 | 119 | if m in [en.Move.R3, en.Move.F3, en.Move.L3, en.Move.B3]: # phase 1 solution come in pairs 120 | corners = mv.corners_move[18 * self.cornersave + m - 1] # apply R2, F2, L2 ord B2 on last ph1 solution 121 | else: 122 | corners = self.co_cube.corners 123 | for m in self.sofar_phase1: # get current corner configuration 124 | corners = mv.corners_move[18 * corners + m] 125 | self.cornersave = corners 126 | 127 | # new solution must be shorter and we do not use phase 2 maneuvers with length > 11 - 1 = 10 128 | togo2_limit = min(self.shortest_length[0] - len(self.sofar_phase1), 11) 129 | if pr.cornslice_depth[24 * corners + slice_sorted] >= togo2_limit: # this precheck speeds up the computation 130 | return 131 | 132 | u_edges = self.co_cube.u_edges 133 | d_edges = self.co_cube.d_edges 134 | for m in self.sofar_phase1: 135 | u_edges = mv.u_edges_move[18 * u_edges + m] 136 | d_edges = mv.d_edges_move[18 * d_edges + m] 137 | ud_edges = coord.u_edges_plus_d_edges_to_ud_edges[24 * u_edges + d_edges % 24] 138 | 139 | dist2 = self.co_cube.get_depth_phase2(corners, ud_edges) 140 | for togo2 in range(dist2, togo2_limit): # do not use more than togo2_limit - 1 moves in phase 2 141 | self.sofar_phase2 = [] 142 | self.search_phase2(corners, ud_edges, slice_sorted, dist2, togo2) 143 | 144 | else: 145 | for m in en.Move: 146 | # dist = 0 means that we are already are in the subgroup H. If there are less than 5 moves left 147 | # this forces all remaining moves to be phase 2 moves. So we can forbid these at the end of phase 1 148 | # and generate these moves in phase 2. 149 | if dist == 0 and togo_phase1 < 5 and m in [en.Move.U1, en.Move.U2, en.Move.U3, en.Move.R2, 150 | en.Move.F2, en.Move.D1, en.Move.D2, en.Move.D3, 151 | en.Move.L2, en.Move.B2]: 152 | continue 153 | 154 | if len(self.sofar_phase1) > 0: 155 | diff = self.sofar_phase1[-1] // 3 - m // 3 156 | if diff in [0, 3]: # successive moves: on same face or on same axis with wrong order 157 | continue 158 | 159 | flip_new = mv.flip_move[18 * flip + m] # N_MOVE = 18 160 | twist_new = mv.twist_move[18 * twist + m] 161 | slice_sorted_new = mv.slice_sorted_move[18 * slice_sorted + m] 162 | 163 | flipslice = 2048 * (slice_sorted_new // 24) + flip_new # N_FLIP * (slice_sorted // N_PERM_4) + flip 164 | classidx = sy.flipslice_classidx[flipslice] 165 | sym = sy.flipslice_sym[flipslice] 166 | dist_new_mod3 = pr.get_flipslice_twist_depth3(2187 * classidx + sy.twist_conj[(twist_new << 4) + sym]) 167 | dist_new = pr.distance[3 * dist + dist_new_mod3] 168 | if dist_new >= togo_phase1: # impossible to reach subgroup H in togo_phase1 - 1 moves 169 | continue 170 | 171 | self.sofar_phase1.append(m) 172 | self.search(flip_new, twist_new, slice_sorted_new, dist_new, togo_phase1 - 1) 173 | self.sofar_phase1.pop(-1) 174 | 175 | def run(self): 176 | cb = None 177 | if self.rot == 0: # no rotation 178 | cb = cubie.CubieCube(self.cb_cube.cp, self.cb_cube.co, self.cb_cube.ep, self.cb_cube.eo) 179 | elif self.rot == 1: # conjugation by 120° rotation 180 | cb = cubie.CubieCube(sy.symCube[32].cp, sy.symCube[32].co, sy.symCube[32].ep, sy.symCube[32].eo) 181 | cb.multiply(self.cb_cube) 182 | cb.multiply(sy.symCube[16]) 183 | elif self.rot == 2: # conjugation by 240° rotation 184 | cb = cubie.CubieCube(sy.symCube[16].cp, sy.symCube[16].co, sy.symCube[16].ep, sy.symCube[16].eo) 185 | cb.multiply(self.cb_cube) 186 | cb.multiply(sy.symCube[32]) 187 | if self.inv == 1: # invert cube 188 | tmp = cubie.CubieCube() 189 | cb.inv_cubie_cube(tmp) 190 | cb = tmp 191 | 192 | self.co_cube = coord.CoordCube(cb) # the rotated/inverted cube in coordinate representation 193 | 194 | dist = self.co_cube.get_depth_phase1() 195 | for togo1 in range(dist, 20): # iterative deepening, solution has at least dist moves 196 | self.sofar_phase1 = [] 197 | self.search(self.co_cube.flip, self.co_cube.twist, self.co_cube.slice_sorted, dist, togo1) 198 | #################################End class SolverThread################################################################# 199 | 200 | 201 | def solve(cubestring, max_length=20, timeout=3): 202 | """Solve a cube defined by its cube definition string. 203 | :param cubestring: The format of the string is given in the Facelet class defined in the file enums.py 204 | :param max_length: The function will return if a maneuver of length <= max_length has been found 205 | :param timeout: If the function times out, the best solution found so far is returned. If there has not been found 206 | any solution yet the computation continues until a first solution appears. 207 | """ 208 | fc = face.FaceCube() 209 | s = fc.from_string(cubestring) 210 | if s != cubie.CUBE_OK: 211 | return s # Error in facelet cube 212 | cc = fc.to_cubie_cube() 213 | s = cc.verify() 214 | if s != cubie.CUBE_OK: 215 | return s # Error in cubie cube 216 | 217 | my_threads = [] 218 | s_time = time.monotonic() 219 | 220 | # these mutable variables are modidified by all six threads 221 | s_length = [999] 222 | solutions = [] 223 | terminated = thr.Event() 224 | terminated.clear() 225 | syms = cc.symmetries() 226 | if len(list({16, 20, 24, 28} & set(syms))) > 0: # we have some rotational symmetry along a long diagonal 227 | tr = [0, 3] # so we search only one direction and the inverse 228 | else: 229 | tr = range(6) # This means search in 3 directions + inverse cube 230 | if len(list(set(range(48, 96)) & set(syms))) > 0: # we have some antisymmetry so we do not search the inverses 231 | tr = list(filter(lambda x: x < 3, tr)) 232 | for i in tr: 233 | th = SolverThread(cc, i % 3, i // 3, max_length, timeout, s_time, solutions, terminated, [999]) 234 | my_threads.append(th) 235 | th.start() 236 | for t in my_threads: 237 | t.join() # wait until all threads have finished 238 | s = '' 239 | if len(solutions) > 0: 240 | for m in solutions[-1]: # the last solution is the shortest 241 | s += m.name + ' ' 242 | return s + '(' + str(len(s)//3) + 'f)' 243 | ######################################################################################################################## -------------------------------------------------------------------------------- /vision2.py: -------------------------------------------------------------------------------- 1 | # ######################## analyse the webcam input and retrieve the facelet colors of a single cube face ############## 2 | 3 | 4 | # pip install opencv_python-3.2.0-cp36-cp36m-win_amd64.whl 5 | 6 | import cv2 7 | import numpy as np 8 | import vision_params 9 | 10 | grid_N = 25 # number of grid-squares in vertical direction 11 | 12 | 13 | def drawgrid(img, n): 14 | """Draw grid onto the webcam output. Only used for debugging purposes.""" 15 | h, w = img.shape[:2] 16 | sz = h // n 17 | border = 1 * sz 18 | for y in range(border, h - border, sz): 19 | for x in range(border, w - border, sz): 20 | cv2.rectangle(img, (x, y), (x + sz, y + sz), (0, 0, 0), 1) # plot small squares in black and white 21 | cv2.rectangle(img, (x - 1, y - 1), (x + 1 + sz, y + 1 + sz), (255, 255, 255), 1) 22 | 23 | 24 | def del_duplicates(pts): 25 | """Delete one of two potential facelet centers stored in pts if they are too close to each other.""" 26 | delta = width / 12 # width is defined global in grabcolors() 27 | dele = True 28 | while dele: 29 | dele = False 30 | r = range(len(pts)) 31 | for i in r: 32 | for j in r[i + 1:]: 33 | if np.linalg.norm(pts[i] - pts[j]) < delta: 34 | del pts[j] 35 | dele = True 36 | if dele: 37 | break 38 | if dele: 39 | break 40 | 41 | 42 | def medoid(pts): 43 | """The mediod is the point with the smallest summed distance from the other points. 44 | This is a candidate for the center facelet.""" 45 | res = np.array([0.0, 0.0]) 46 | smin = 100000 47 | for i in pts: 48 | s = 0 49 | for j in pts: 50 | s += np.linalg.norm(i - j) 51 | if s < smin: 52 | smin = s 53 | res = i 54 | 55 | return res 56 | 57 | 58 | def facelets(pts, med): 59 | """Separate the candidates into edge and corner facelets by their distance from the medoid.""" 60 | ed = [] 61 | co = [] 62 | if med[0] == 0: 63 | return co, ed # no edgefacelets detected 64 | # find shortest distance 65 | dmin = 10000 66 | for p in pts: 67 | d = np.linalg.norm(p - med) 68 | if 1 < d < dmin: 69 | dmin = d 70 | # edgefacelets should be in a distance not more than dmin*1.3 71 | for p in pts: 72 | d = np.linalg.norm(p - med) 73 | if dmin - 1 < d < dmin * 1.3: 74 | ed.append(p) 75 | # now find the corner facelets 76 | for p in pts: 77 | d = np.linalg.norm(p - med) 78 | if dmin * 1.3 < d < dmin * 1.7: 79 | co.append(p) 80 | return co, ed 81 | 82 | 83 | def mirr_facelet(co, ed, med): 84 | """If we have detected a facelet position, the point reflection at the center also gives a facelet position. 85 | We can use this position in case the other facelet was not detected directly.""" 86 | aef = [] 87 | acf = [] 88 | for p in ed: 89 | pa = 2 * med - p 90 | aef.append(pa) 91 | for p in co: 92 | pa = 2 * med - p 93 | acf.append(pa) 94 | 95 | # delete duplicates 96 | delta = width / 12 # width is defined global in grabcolors() 97 | for k in range(len(aef) - 1, -1, -1): 98 | for p in ed: 99 | if np.linalg.norm(aef[k] - p) < delta: 100 | del aef[k] 101 | break 102 | 103 | for k in range(len(acf) - 1, -1, -1): 104 | for p in co: 105 | if np.linalg.norm(acf[k] - p) < delta: 106 | del acf[k] 107 | break 108 | 109 | return acf, aef 110 | 111 | 112 | def display_colorname(bgrcap, p): 113 | """Display the colornames on the webcam picture.""" 114 | p = p.astype(np.uint16) 115 | _, col = getcolor(p) 116 | if col in ('blue', 'green', 'red'): 117 | txtcol = (255, 255, 255) 118 | else: 119 | txtcol = (0, 0, 0) 120 | font = cv2.FONT_HERSHEY_SIMPLEX 121 | tz = cv2.getTextSize(col, font, 0.4, 1)[0] 122 | cv2.putText( 123 | bgrcap, col, tuple(p - (tz[0] // 2, -tz[1] // 2)), font, 0.4, txtcol, 1) 124 | 125 | 126 | def getcolor(p): 127 | """Decide the color of a facelet by its h value (non white) or by s and v (white).""" 128 | sz = 10 129 | p = p.astype(np.uint16) 130 | rect = hsv[p[1] - sz:p[1] + sz, p[0] - sz:p[0] + sz] 131 | median = np.sum(rect, axis=(0, 1)) / sz / sz / 4 132 | mh, ms, mv = median 133 | if ms <= vision_params.sat_W and mv >= vision_params.val_W: 134 | return median, 'white' 135 | elif vision_params.orange_L <= mh < vision_params.orange_H: 136 | return median, 'orange' 137 | elif vision_params.orange_H <= mh < vision_params.yellow_H: 138 | return median, 'yellow' 139 | elif vision_params.yellow_H <= mh < vision_params.green_H: 140 | if ms < 150: 141 | return median, 'white' # green saturation is always higher 142 | else: 143 | return median, 'green' 144 | elif vision_params.green_H <= mh < vision_params.blue_H: 145 | if ms < 150: 146 | return median, 'white' # blue saturation is always higher 147 | else: 148 | return median, 'blue' 149 | else: 150 | return median, 'red' 151 | 152 | 153 | def getcolors(co, ed, aco, aed, m): 154 | """Find the colors of the 9 facelets and decide their position on the cube face.""" 155 | centers = [[m for x in range(3)] for x in range(3)] 156 | colors = [['' for x in range(3)] for x in range(3)] 157 | s = np.array([0., 0., 0.]) 158 | hsvs = [[s for x in range(3)] for x in range(3)] 159 | cocents = co + aco 160 | if len(cocents) != 4: 161 | return [], [] 162 | edcents = ed + aed 163 | if len(edcents) != 4: 164 | return [], [] 165 | for i in cocents: 166 | if i[0] < m[0] and i[1] < m[1]: 167 | centers[0][0] = i 168 | elif i[0] > m[0] and i[1] < m[1]: 169 | centers[0][2] = i 170 | elif i[0] < m[0] and i[1] > m[1]: 171 | centers[2][0] = i 172 | elif i[0] > m[0] and i[1] > m[1]: 173 | centers[2][2] = i 174 | 175 | for i in edcents: 176 | if i[1] < centers[0][1][1]: 177 | centers[0][1] = i 178 | for i in edcents: 179 | if i[0] < centers[1][0][0]: 180 | centers[1][0] = i 181 | for i in edcents: 182 | if i[0] > centers[1][2][0]: 183 | centers[1][2] = i 184 | for i in edcents: 185 | if i[1] > centers[2][1][1]: 186 | centers[2][1] = i 187 | for x in range(3): 188 | for y in range(3): 189 | hsv_, col = getcolor(centers[x][y]) 190 | colors[x][y] = col 191 | hsvs[x][y] = hsv_ 192 | 193 | return hsvs, colors 194 | 195 | 196 | def find_squares(bgrcap, n): 197 | """ Find the positions of squares in the webcam picture.""" 198 | global mask, color_mask, white_mask, black_mask 199 | 200 | h, s, v = cv2.split(hsv) 201 | h_sqr = np.square(h) 202 | 203 | sz = height // n 204 | border = 1 * sz 205 | 206 | varmax_edges = 20 207 | 208 | # iterate all grid squares 209 | for y in range(border, height - border, sz): 210 | for x in range(border, width - border, sz): 211 | 212 | # compute the standard deviation sigma of the hue in the square 213 | rect_h = h[y:y + sz, x:x + sz] 214 | rect_h_sqr = h_sqr[y:y + sz, x:x + sz] 215 | median_h = np.sum(rect_h) / sz / sz 216 | sqr_median_h = median_h * median_h 217 | median_h_sqr = np.sum(rect_h_sqr) / sz / sz 218 | var = median_h_sqr - sqr_median_h 219 | sigma = np.sqrt(var) 220 | 221 | delta = vision_params.delta_C 222 | 223 | # if sigma is small enough define a mask on the 3x3 square with the grid square in it's center 224 | if sigma < vision_params.sigma_W: 225 | rect3x3 = hsv[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz] 226 | mask = cv2.inRange(rect3x3, (0, 0, vision_params.val_W), 227 | (255, vision_params.sat_W, 255)) 228 | # and OR it to the white_mask 229 | white_mask[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz] = \ 230 | cv2.bitwise_or(mask, white_mask[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz]) 231 | 232 | # similar procedure for the color mask. Some issues because hues are computed modulo 180 233 | if sigma < vision_params.sigma_C: 234 | rect3x3 = h[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz] 235 | if median_h + delta >= 180: 236 | mask = cv2.inRange(rect3x3, 0, median_h + delta - 180) 237 | mask = cv2.bitwise_or(mask, cv2.inRange(rect3x3, median_h - delta, 180)) 238 | elif median_h - delta < 0: 239 | mask = cv2.inRange(rect3x3, median_h - delta + 180, 180) 240 | mask = cv2.bitwise_or(mask, cv2.inRange(rect3x3, 0, median_h + delta)) 241 | else: 242 | mask = cv2.inRange(rect3x3, median_h - delta, median_h + delta) 243 | color_mask[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz] = \ 244 | cv2.bitwise_or(mask, color_mask[y - 1 * sz:y + 2 * sz, x - 1 * sz:x + 2 * sz]) 245 | 246 | black_mask = cv2.inRange(bgrcap, (0, 0, 0), (vision_params.rgb_L, vision_params.rgb_L, vision_params.rgb_L)) 247 | black_mask = cv2.bitwise_not(black_mask) 248 | 249 | color_mask = cv2.bitwise_and(color_mask, black_mask) 250 | color_mask = cv2.blur(color_mask, (20, 20)) 251 | color_mask = cv2.inRange(color_mask, 240, 255) 252 | 253 | white_mask = cv2.bitwise_and(white_mask, black_mask) 254 | white_mask = cv2.blur(white_mask, (20, 20)) 255 | white_mask = cv2.inRange(white_mask, 240, 255) 256 | 257 | itr = iter([white_mask, color_mask]) # apply white filter first! 258 | 259 | # search for squares in the white_mask and in the color_mask 260 | for j in itr: 261 | # find contours 262 | # works for OpenCV 3.2 or higher. For versions < 3.2 omit im2 in the line below. 263 | im2, contours, hierarchy = cv2.findContours(j, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE) 264 | for n in range(len(contours)): 265 | approx = cv2.approxPolyDP(contours[n], sz // 2, True) 266 | # if the contour cannot be approximated by a quadrangle it is not a facelet square 267 | if approx.shape[0] != 4: 268 | continue 269 | corners = approx[:, 0] # get the corners of the potential facelet square 270 | 271 | # the edges of the square should have all about the same length 272 | edges = np.array( 273 | [cv2.norm(corners[0] - corners[1], cv2.NORM_L2), cv2.norm(corners[1] - corners[2], cv2.NORM_L2), 274 | cv2.norm(corners[2] - corners[3], cv2.NORM_L2), 275 | cv2.norm(corners[3] - corners[0], cv2.NORM_L2)]) 276 | edges_mean_sq = (np.sum(edges) / 4) ** 2 277 | edges_sq_mean = np.sum(np.square(edges)) / 4 278 | if edges_sq_mean - edges_mean_sq > varmax_edges: 279 | continue 280 | 281 | # cv2.drawContours(bgrcap, [approx], -1, (0, 0, 255), 8) 282 | middle = np.sum(corners, axis=0) / 4 # store the center of the potential facelet 283 | cent.append(np.asarray(middle)) 284 | 285 | 286 | def grab_colors(): 287 | """Find the cube in the webcam picture and grab the colors of the facelets.""" 288 | global cent, width, height, hsv, color_mask, white_mask 289 | cap = cv2.VideoCapture(0) 290 | _, bgrcap = cap.read() 291 | if bgrcap is None: 292 | print('Cannot connect to webcam!') 293 | print('If you use a Raspberry Pi and no USB-webcam you have to run "sudo modprobe bvm2835-v4l2" first!') 294 | return 295 | height, width = bgrcap.shape[:2] 296 | while 1: 297 | 298 | # Take each frame 299 | _, bgrcap = cap.read() # 300 | bgrcap = cv2.blur(bgrcap, (5, 5)) 301 | 302 | # now set all hue values >160 to 0. This is important since the color red often contains hue values 303 | # in this range *and* also hue values >0 and else we get a mess when we compute mean and variance 304 | hsv = cv2.cvtColor(bgrcap, cv2.COLOR_BGR2HSV) 305 | h, s, v = cv2.split(hsv) # 306 | h_mask = cv2.inRange(h, 0, 160) 307 | h = cv2.bitwise_and(h, h, mask=h_mask) 308 | hsv = cv2.merge((h, s, v)).astype(float) 309 | 310 | # define two empty masks for the white-filter and the color-filter 311 | color_mask = cv2.inRange(bgrcap, np.array([1, 1, 1]), np.array([0, 0, 0])) # mask for colors 312 | white_mask = cv2.inRange(bgrcap, np.array([1, 1, 1]), np.array([0, 0, 0])) # special mask for white 313 | 314 | cent = [] # the centers of the facelet-square candidates are stored in this global variable 315 | find_squares(bgrcap, grid_N) # find the candidates 316 | del_duplicates(cent) # delete candidates which are too close together 317 | 318 | # the medoid is the center which has the closest summed distances to the other centers 319 | # It should be the center facelet of the cube 320 | m = medoid(cent) 321 | 322 | cf, ef = facelets(cent, m) # identify the centers of the corner and edge facelets 323 | 324 | # compute the alternate corner and edges facelet centers. These are the point reflections of an already 325 | # known facelet center at the medoid center. Should some facelet center not be detected by itself it usually 326 | # still is detected in this way. 327 | acf, aef = mirr_facelet(cf, ef, m) 328 | 329 | display_colorname(bgrcap, m) 330 | for i in ef: 331 | display_colorname(bgrcap, i) 332 | for i in cf: 333 | display_colorname(bgrcap, i) 334 | for i in aef: 335 | display_colorname(bgrcap, i) 336 | for i in acf: 337 | display_colorname(bgrcap, i) 338 | 339 | # the results supplied by getcolors are used in client_gui2.py for the "Webcam import" 340 | vision_params.face_hsv, vision_params.face_col = getcolors(cf, ef, acf, aef, m) 341 | 342 | # drawgrid(bgrcap, grid_N) 343 | 344 | # show the windows 345 | cv2.imshow('color_filter mask', cv2.resize(color_mask, (width // 2, height // 2))) 346 | cv2.imshow('white_filter mask', cv2.resize(white_mask, (width // 2, height // 2))) 347 | cv2.imshow('black_filter mask', cv2.resize(black_mask, (width // 2, height // 2))) 348 | cv2.imshow('Webcam - type "x" to quit.', bgrcap) 349 | 350 | k = cv2.waitKey(5) & 0xFF 351 | if k == 120: # type x to exit 352 | break 353 | 354 | 355 | cv2.destroyAllWindows() 356 | -------------------------------------------------------------------------------- /pruning.py: -------------------------------------------------------------------------------- 1 | # ##################### The pruning tables cut the search tree during the search. ###################################### 2 | # ##################### The pruning values are stored modulo 3 which saves a lot of memory. ############################ 3 | 4 | import defs 5 | import enums 6 | import moves as mv 7 | import symmetries as sy 8 | import cubie as cb 9 | from os import path 10 | import time 11 | import array as ar 12 | 13 | flipslice_twist_depth3 = None # global variables, initialized during pruning table cration 14 | corners_ud_edges_depth3 = None 15 | cornslice_depth = None 16 | edgeslice_depth = None 17 | 18 | # ####################### functions to extract or set values in the pruning tables ##################################### 19 | 20 | 21 | def get_flipslice_twist_depth3(ix): 22 | """get_fst_depth3(ix) is *exactly* the number of moves % 3 to solve phase 1 of a cube with index ix""" 23 | y = flipslice_twist_depth3[ix // 16] 24 | y >>= (ix % 16) * 2 25 | return y & 3 26 | 27 | 28 | def get_corners_ud_edges_depth3(ix): 29 | """corners_ud_edges_depth3(ix) is *at least* the number of moves % 3 to solve phase 2 of a cube with index ix""" 30 | y = corners_ud_edges_depth3[ix // 16] 31 | y >>= (ix % 16) * 2 32 | return y & 3 33 | 34 | 35 | def set_flipslice_twist_depth3(ix, value): 36 | shift = (ix % 16) * 2 37 | base = ix >> 4 38 | flipslice_twist_depth3[base] &= ~(3 << shift) & 0xffffffff 39 | flipslice_twist_depth3[base] |= value << shift 40 | 41 | 42 | def set_corners_ud_edges_depth3(ix, value): 43 | shift = (ix % 16) * 2 44 | base = ix >> 4 45 | corners_ud_edges_depth3[base] &= ~(3 << shift) & 0xffffffff 46 | corners_ud_edges_depth3[base] |= value << shift 47 | 48 | ######################################################################################################################## 49 | 50 | 51 | def create_phase1_prun_table(): 52 | """Create/load the flipslice_twist_depth3 pruning table for phase 1.""" 53 | global flipslice_twist_depth3 54 | total = defs.N_FLIPSLICE_CLASS * defs.N_TWIST 55 | fname = "phase1_prun" 56 | if not path.isfile(fname): 57 | print("creating " + fname + " table...") 58 | print('This may take half an hour or even longer, depending on the hardware.') 59 | 60 | flipslice_twist_depth3 = ar.array('L', [0xffffffff] * (total // 16 + 1)) 61 | # #################### create table with the symmetries of the flipslice classes ############################### 62 | cc = cb.CubieCube() 63 | fs_sym = ar.array('H', [0] * defs.N_FLIPSLICE_CLASS) 64 | for i in range(defs.N_FLIPSLICE_CLASS): 65 | if (i + 1) % 1000 == 0: 66 | print('.', end='', flush=True) 67 | rep = sy.flipslice_rep[i] 68 | cc.set_slice(rep // defs.N_FLIP) 69 | cc.set_flip(rep % defs.N_FLIP) 70 | 71 | for s in range(defs.N_SYM_D4h): 72 | ss = cb.CubieCube(sy.symCube[s].cp, sy.symCube[s].co, sy.symCube[s].ep, 73 | sy.symCube[s].eo) # copy cube 74 | ss.edge_multiply(cc) # s*cc 75 | ss.edge_multiply(sy.symCube[sy.inv_idx[s]]) # s*cc*s^-1 76 | if ss.get_slice() == rep // defs.N_FLIP and ss.get_flip() == rep % defs.N_FLIP: 77 | fs_sym[i] |= 1 << s 78 | print() 79 | # ################################################################################################################## 80 | 81 | fs_classidx = 0 # value for solved phase 1 82 | twist = 0 83 | set_flipslice_twist_depth3(defs.N_TWIST * fs_classidx + twist, 0) 84 | done = 1 85 | depth = 0 86 | backsearch = False 87 | print('depth:', depth, 'done: ' + str(done) + '/' + str(total)) 88 | while done != total: 89 | depth3 = depth % 3 90 | if depth == 9: 91 | # backwards search is faster for depth >= 9 92 | print('flipping to backwards search...') 93 | backsearch = True 94 | if depth < 8: 95 | mult = 5 # controls the output a few lines below 96 | else: 97 | mult = 1 98 | idx = 0 99 | for fs_classidx in range(defs.N_FLIPSLICE_CLASS): 100 | if (fs_classidx + 1) % (200 * mult) == 0: 101 | print('.', end='', flush=True) 102 | if (fs_classidx + 1) % (16000 * mult) == 0: 103 | print('') 104 | 105 | twist = 0 106 | while twist < defs.N_TWIST: 107 | 108 | # ########## if table entries are not populated, this is very fast: ################################ 109 | if not backsearch and idx % 16 == 0 and flipslice_twist_depth3[idx // 16] == 0xffffffff \ 110 | and twist < defs.N_TWIST - 16: 111 | twist += 16 112 | idx += 16 113 | continue 114 | #################################################################################################### 115 | 116 | if backsearch: 117 | match = (get_flipslice_twist_depth3(idx) == 3) 118 | else: 119 | match = (get_flipslice_twist_depth3(idx) == depth3) 120 | 121 | if match: 122 | flipslice = sy.flipslice_rep[fs_classidx] 123 | flip = flipslice % 2048 # defs.N_FLIP = 2048 124 | slice_ = flipslice >> 11 # // defs.N_FLIP 125 | for m in enums.Move: 126 | twist1 = mv.twist_move[18 * twist + m] # defs.N_MOVE = 18 127 | flip1 = mv.flip_move[18 * flip + m] 128 | slice1 = mv.slice_sorted_move[432 * slice_ + m] // 24 # defs.N_PERM_4 = 24, 18*24 = 432 129 | flipslice1 = (slice1 << 11) + flip1 130 | fs1_classidx = sy.flipslice_classidx[flipslice1] 131 | fs1_sym = sy.flipslice_sym[flipslice1] 132 | twist1 = sy.twist_conj[(twist1 << 4) + fs1_sym] 133 | idx1 = 2187 * fs1_classidx + twist1 # defs.N_TWIST = 2187 134 | if not backsearch: 135 | if get_flipslice_twist_depth3(idx1) == 3: # entry not yet filled 136 | set_flipslice_twist_depth3(idx1, (depth + 1) % 3) 137 | done += 1 138 | # ####symmetric position has eventually more than one representation ############### 139 | sym = fs_sym[fs1_classidx] 140 | if sym != 1: 141 | for j in range(1, 16): 142 | sym >>= 1 143 | if sym % 2 == 1: 144 | twist2 = sy.twist_conj[(twist1 << 4) + j] 145 | # fs2_classidx = fs1_classidx due to symmetry 146 | idx2 = 2187 * fs1_classidx + twist2 147 | if get_flipslice_twist_depth3(idx2) == 3: 148 | set_flipslice_twist_depth3(idx2, (depth + 1) % 3) 149 | done += 1 150 | #################################################################################### 151 | 152 | else: # backwards search 153 | if get_flipslice_twist_depth3(idx1) == depth3: 154 | set_flipslice_twist_depth3(idx, (depth + 1) % 3) 155 | done += 1 156 | break 157 | twist += 1 158 | idx += 1 # idx = defs.N_TWIST * fs_class + twist 159 | 160 | depth += 1 161 | print() 162 | print('depth:', depth, 'done: ' + str(done) + '/' + str(total)) 163 | 164 | fh = open(fname, "wb") 165 | flipslice_twist_depth3.tofile(fh) 166 | else: 167 | print("loading " + fname + " table...") 168 | fh = open(fname, "rb") 169 | flipslice_twist_depth3 = ar.array('L') 170 | flipslice_twist_depth3.fromfile(fh, total // 16 + 1) 171 | fh.close() 172 | 173 | 174 | def create_phase2_prun_table(): 175 | """Create/load the corners_ud_edges_depth3 pruning table for phase 2.""" 176 | total = defs.N_CORNERS_CLASS * defs.N_UD_EDGES 177 | fname = "phase2_prun" 178 | global corners_ud_edges_depth3 179 | if not path.isfile(fname): 180 | print("creating " + fname + " table...") 181 | 182 | corners_ud_edges_depth3 = ar.array('L', [0xffffffff] * (total // 16)) 183 | # ##################### create table with the symmetries of the corners classes ################################ 184 | cc = cb.CubieCube() 185 | c_sym = ar.array('H', [0] * defs.N_CORNERS_CLASS) 186 | for i in range(defs.N_CORNERS_CLASS): 187 | if (i + 1) % 1000 == 0: 188 | print('.', end='', flush=True) 189 | rep = sy.corner_rep[i] 190 | cc.set_corners(rep) 191 | for s in range(defs.N_SYM_D4h): 192 | ss = cb.CubieCube(sy.symCube[s].cp, sy.symCube[s].co, sy.symCube[s].ep, 193 | sy.symCube[s].eo) # copy cube 194 | ss.corner_multiply(cc) # s*cc 195 | ss.corner_multiply(sy.symCube[sy.inv_idx[s]]) # s*cc*s^-1 196 | if ss.get_corners() == rep: 197 | c_sym[i] |= 1 << s 198 | print() 199 | ################################################################################################################ 200 | 201 | c_classidx = 0 # value for solved phase 2 202 | ud_edge = 0 203 | set_corners_ud_edges_depth3(defs.N_UD_EDGES * c_classidx + ud_edge, 0) 204 | done = 1 205 | depth = 0 206 | print('depth:', depth, 'done: ' + str(done) + '/' + str(total)) 207 | while depth < 10: # we fill the table only do depth 9 + 1 208 | depth3 = depth % 3 209 | idx = 0 210 | mult = 2 211 | if depth > 9: 212 | mult = 1 213 | for c_classidx in range(defs.N_CORNERS_CLASS): 214 | if (c_classidx + 1) % (20 * mult) == 0: 215 | print('.', end='', flush=True) 216 | if (c_classidx + 1) % (1600 * mult) == 0: 217 | print('') 218 | 219 | ud_edge = 0 220 | while ud_edge < defs.N_UD_EDGES: 221 | 222 | # ################ if table entries are not populated, this is very fast: ########################## 223 | if idx % 16 == 0 and corners_ud_edges_depth3[idx // 16] == 0xffffffff \ 224 | and ud_edge < defs.N_UD_EDGES - 16: 225 | ud_edge += 16 226 | idx += 16 227 | continue 228 | #################################################################################################### 229 | 230 | if get_corners_ud_edges_depth3(idx) == depth3: 231 | corner = sy.corner_rep[c_classidx] 232 | # only iterate phase 2 moves 233 | for m in (enums.Move.U1, enums.Move.U2, enums.Move.U3, enums.Move.R2, enums.Move.F2, 234 | enums.Move.D1, enums.Move.D2, enums.Move.D3, enums.Move.L2, enums.Move.B2): 235 | ud_edge1 = mv.ud_edges_move[18 * ud_edge + m] 236 | corner1 = mv.corners_move[18 * corner + m] 237 | c1_classidx = sy.corner_classidx[corner1] 238 | c1_sym = sy.corner_sym[corner1] 239 | ud_edge1 = sy.ud_edges_conj[(ud_edge1 << 4) + c1_sym] 240 | idx1 = 40320 * c1_classidx + ud_edge1 # N_UD_EDGES = 40320 241 | if get_corners_ud_edges_depth3(idx1) == 3: # entry not yet filled 242 | set_corners_ud_edges_depth3(idx1, (depth + 1) % 3) # depth + 1 <= 10 243 | done += 1 244 | # ######symmetric position has eventually more than one representation ############# 245 | sym = c_sym[c1_classidx] 246 | if sym != 1: 247 | for j in range(1, 16): 248 | sym >>= 1 249 | if sym % 2 == 1: 250 | ud_edge2 = sy.ud_edges_conj[(ud_edge1 << 4) + j] 251 | # c1_classidx does not change 252 | idx2 = 40320 * c1_classidx + ud_edge2 253 | if get_corners_ud_edges_depth3(idx2) == 3: 254 | set_corners_ud_edges_depth3(idx2, (depth + 1) % 3) 255 | done += 1 256 | #################################################################################### 257 | 258 | ud_edge += 1 259 | idx += 1 # idx = defs.N_UD_EDGEPERM * corner_classidx + ud_edge 260 | 261 | depth += 1 262 | print() 263 | print('depth:', depth, 'done: ' + str(done) + '/' + str(total)) 264 | 265 | print('remaining unfilled entries have depth >=11') 266 | fh = open(fname, "wb") 267 | corners_ud_edges_depth3.tofile(fh) 268 | else: 269 | print("loading " + fname + " table...") 270 | fh = open(fname, "rb") 271 | corners_ud_edges_depth3 = ar.array('L') 272 | corners_ud_edges_depth3.fromfile(fh, total // 16) 273 | 274 | fh.close() 275 | 276 | 277 | def create_phase2_cornsliceprun_table(): 278 | """Create/load the cornslice_depth pruning table for phase 2. With this table we do a fast precheck 279 | at the beginning of phase 2.""" 280 | fname = "phase2_cornsliceprun" 281 | global cornslice_depth 282 | if not path.isfile(fname): 283 | print("creating " + fname + " table...") 284 | cornslice_depth = ar.array('b', [-1] * (defs.N_CORNERS * defs.N_PERM_4)) 285 | corners = 0 # values for solved phase 2 286 | slice_ = 0 287 | cornslice_depth[defs.N_PERM_4 * corners + slice_] = 0 288 | done = 1 289 | depth = 0 290 | idx = 0 291 | while done != defs.N_CORNERS * defs.N_PERM_4: 292 | for corners in range(defs.N_CORNERS): 293 | for slice_ in range(defs.N_PERM_4): 294 | if cornslice_depth[defs.N_PERM_4 * corners + slice_] == depth: 295 | for m in (enums.Move.U1, enums.Move.U2, enums.Move.U3, enums.Move.R2, enums.Move.F2, 296 | enums.Move.D1, enums.Move.D2, enums.Move.D3, enums.Move.L2, enums.Move.B2): 297 | corners1 = mv.corners_move[18 * corners + m] 298 | slice_1 = mv.slice_sorted_move[18 * slice_ + m] 299 | idx1 = defs.N_PERM_4 * corners1 + slice_1 300 | if cornslice_depth[idx1] == -1: # entry not yet filled 301 | cornslice_depth[idx1] = depth + 1 302 | done += 1 303 | if done % 20000 == 0: 304 | print('.', end='', flush=True) 305 | 306 | depth += 1 307 | print() 308 | fh = open(fname, "wb") 309 | cornslice_depth.tofile(fh) 310 | else: 311 | print("loading " + fname + " table...") 312 | fh = open(fname, "rb") 313 | cornslice_depth = ar.array('b') 314 | cornslice_depth.fromfile(fh, defs.N_CORNERS * defs.N_PERM_4) 315 | fh.close() 316 | 317 | # array distance computes the new distance from the old_distance i and the new_distance_mod3 j. ######################## 318 | # We need this array because the pruning tables only store the distances mod 3. ######################################## 319 | distance = ar.array('b', [0 for i in range(60)]) 320 | for i in range(20): 321 | for j in range(3): 322 | distance[3*i + j] = (i // 3) * 3 + j 323 | if i % 3 == 2 and j == 0: 324 | distance[3 * i + j] += 3 325 | elif i % 3 == 0 and j == 2: 326 | distance[3 * i + j] -= 3 327 | 328 | create_phase1_prun_table() 329 | create_phase2_prun_table() 330 | create_phase2_cornsliceprun_table() 331 | -------------------------------------------------------------------------------- /cubie.py: -------------------------------------------------------------------------------- 1 | # ####### The cube on the cubie level is described by the permutation and orientations of corners and edges ############ 2 | 3 | from defs import cornerFacelet, edgeFacelet, cornerColor, edgeColor, N_SYM 4 | from enums import Color, Corner as Co, Edge as Ed 5 | import face 6 | from misc import c_nk, rotate_left, rotate_right 7 | from random import randrange 8 | 9 | 10 | # ################## The basic six cube moves described by permutations and changes in orientation ##################### 11 | 12 | # Up-move 13 | cpU = [Co.UBR, Co.URF, Co.UFL, Co.ULB, Co.DFR, Co.DLF, Co.DBL, Co.DRB] 14 | coU = [0, 0, 0, 0, 0, 0, 0, 0] 15 | epU = [Ed.UB, Ed.UR, Ed.UF, Ed.UL, Ed.DR, Ed.DF, Ed.DL, Ed.DB, Ed.FR, Ed.FL, Ed.BL, Ed.BR] 16 | eoU = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 17 | 18 | # Right-move 19 | cpR = [Co.DFR, Co.UFL, Co.ULB, Co.URF, Co.DRB, Co.DLF, Co.DBL, Co.UBR] # permutation of the corners 20 | coR = [2, 0, 0, 1, 1, 0, 0, 2] # changes of the orientations of the corners 21 | epR = [Ed.FR, Ed.UF, Ed.UL, Ed.UB, Ed.BR, Ed.DF, Ed.DL, Ed.DB, Ed.DR, Ed.FL, Ed.BL, Ed.UR] # permutation of the edges 22 | eoR = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # changes of the permutations of the edges 23 | 24 | # Front-move 25 | cpF = [Co.UFL, Co.DLF, Co.ULB, Co.UBR, Co.URF, Co.DFR, Co.DBL, Co.DRB] 26 | coF = [1, 2, 0, 0, 2, 1, 0, 0] 27 | epF = [Ed.UR, Ed.FL, Ed.UL, Ed.UB, Ed.DR, Ed.FR, Ed.DL, Ed.DB, Ed.UF, Ed.DF, Ed.BL, Ed.BR] 28 | eoF = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0] 29 | 30 | # Down-move 31 | cpD = [Co.URF, Co.UFL, Co.ULB, Co.UBR, Co.DLF, Co.DBL, Co.DRB, Co.DFR] 32 | coD = [0, 0, 0, 0, 0, 0, 0, 0] 33 | epD = [Ed.UR, Ed.UF, Ed.UL, Ed.UB, Ed.DF, Ed.DL, Ed.DB, Ed.DR, Ed.FR, Ed.FL, Ed.BL, Ed.BR] 34 | eoD = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 35 | 36 | # Left-move 37 | cpL = [Co.URF, Co.ULB, Co.DBL, Co.UBR, Co.DFR, Co.UFL, Co.DLF, Co.DRB] 38 | coL = [0, 1, 2, 0, 0, 2, 1, 0] 39 | epL = [Ed.UR, Ed.UF, Ed.BL, Ed.UB, Ed.DR, Ed.DF, Ed.FL, Ed.DB, Ed.FR, Ed.UL, Ed.DL, Ed.BR] 40 | eoL = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 41 | 42 | # Back-move 43 | cpB = [Co.URF, Co.UFL, Co.UBR, Co.DRB, Co.DFR, Co.DLF, Co.ULB, Co.DBL] 44 | coB = [0, 0, 1, 2, 0, 0, 2, 1] 45 | epB = [Ed.UR, Ed.UF, Ed.UL, Ed.BR, Ed.DR, Ed.DF, Ed.DL, Ed.BL, Ed.FR, Ed.FL, Ed.UB, Ed.DB] 46 | eoB = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1] 47 | ######################################################################################################################## 48 | 49 | CUBE_OK = True 50 | 51 | 52 | class CubieCube: 53 | """Represent a cube on the cubie level with 8 corner cubies, 12 edge cubies and the cubie orientations. 54 | 55 | Is also used to represent: 56 | 1. the 18 cube moves 57 | 2. the 48 symmetries of the cube. 58 | """ 59 | def __init__(self, cp=None, co=None, ep=None, eo=None): 60 | """ 61 | Initializes corners and edges. 62 | :param cp: corner permutation 63 | :param co: corner orientation 64 | :param ep: edge permutation 65 | :param eo: edge orientation 66 | """ 67 | if cp is None: 68 | self.cp = [Co(i) for i in range(8)] # You may not put this as the default two lines above! 69 | else: 70 | self.cp = cp[:] 71 | if co is None: 72 | self.co = [0]*8 73 | else: 74 | self.co = co[:] 75 | if ep is None: 76 | self.ep = [Ed(i) for i in range(12)] 77 | else: 78 | self.ep = ep[:] 79 | if eo is None: 80 | self.eo = [0] * 12 81 | else: 82 | self.eo = eo[:] 83 | 84 | def __str__(self): 85 | """Print string for a cubie cube.""" 86 | s = '' 87 | for i in Co: 88 | s = s + '(' + str(self.cp[i]) + ',' + str(self.co[i]) + ')' 89 | s += '\n' 90 | for i in Ed: 91 | s = s + '(' + str(self.ep[i]) + ',' + str(self.eo[i]) + ')' 92 | return s 93 | 94 | def __eq__(self, other): 95 | """Define equality of two cubie cubes.""" 96 | if self.cp == other.cp and self.co == other.co and self.ep == other.ep and self.eo == other.eo: 97 | return True 98 | else: 99 | return False 100 | 101 | def to_facelet_cube(self): 102 | """Return a facelet representation of the cube.""" 103 | fc = face.FaceCube() 104 | for i in Co: 105 | j = self.cp[i] # corner j is at corner position i 106 | ori = self.co[i] # orientation of C j at position i 107 | for k in range(3): 108 | fc.f[cornerFacelet[i][(k+ori) % 3]] = cornerColor[j][k] 109 | for i in Ed: 110 | j = self.ep[i] # similar for Es 111 | ori = self.eo[i] 112 | for k in range(2): 113 | fc.f[edgeFacelet[i][(k+ori) % 2]] = edgeColor[j][k] 114 | return fc 115 | 116 | def corner_multiply(self, b): 117 | """Multiply this cubie cube with another cubie cube b, restricted to the corners. Does not change b.""" 118 | c_perm = [0]*8 119 | c_ori = [0]*8 120 | ori = 0 121 | for c in Co: 122 | c_perm[c] = self.cp[b.cp[c]] 123 | ori_a = self.co[b.cp[c]] 124 | ori_b = b.co[c] 125 | if ori_a < 3 and ori_b < 3: # two regular cubes 126 | ori = ori_a + ori_b 127 | if ori >= 3: 128 | ori -= 3 129 | elif ori_a < 3 <= ori_b: # cube b is in a mirrored state 130 | ori = ori_a + ori_b 131 | if ori >= 6: 132 | ori -= 3 # the composition also is in a mirrored state 133 | elif ori_a >= 3 > ori_b: # cube a is in a mirrored state 134 | ori = ori_a - ori_b 135 | if ori < 3: 136 | ori += 3 # the composition is a mirrored cube 137 | elif ori_a >= 3 and ori_b >= 3: # if both cubes are in mirrored states 138 | ori = ori_a - ori_b 139 | if ori < 0: 140 | ori += 3 # the composition is a regular cube 141 | c_ori[c] = ori 142 | for c in Co: 143 | self.cp[c] = c_perm[c] 144 | self.co[c] = c_ori[c] 145 | 146 | def edge_multiply(self, b): 147 | """ Multiply this cubie cube with another cubiecube b, restricted to the edges. Does not change b.""" 148 | e_perm = [0]*12 149 | e_ori = [0]*12 150 | for e in Ed: 151 | e_perm[e] = self.ep[b.ep[e]] 152 | e_ori[e] = (b.eo[e] + self.eo[b.ep[e]]) % 2 153 | for e in Ed: 154 | self.ep[e] = e_perm[e] 155 | self.eo[e] = e_ori[e] 156 | 157 | def multiply(self, b): 158 | self.corner_multiply(b) 159 | self.edge_multiply(b) 160 | 161 | def inv_cubie_cube(self, d): 162 | """Store the inverse of this cubie cube in d.""" 163 | for e in Ed: 164 | d.ep[self.ep[e]] = e 165 | for e in Ed: 166 | d.eo[e] = self.eo[d.ep[e]] 167 | 168 | for c in Co: 169 | d.cp[self.cp[c]] = c 170 | for c in Co: 171 | ori = self.co[d.cp[c]] 172 | if ori >= 3: 173 | d.co[c] = ori 174 | else: 175 | d.co[c] = -ori 176 | if d.co[c] < 0: 177 | d.co[c] += 3 178 | 179 | def corner_parity(self): 180 | """Give the parity of the corner permutation.""" 181 | s = 0 182 | for i in range(Co.DRB, Co.URF, -1): 183 | for j in range(i - 1, Co.URF - 1, -1): 184 | if self.cp[j] > self.cp[i]: 185 | s += 1 186 | return s % 2 187 | 188 | def edge_parity(self): 189 | """Give the parity of the edge permutation. A solvable cube has the same corner and edge parity.""" 190 | s = 0 191 | for i in range(Ed.BR, Ed.UR, -1): 192 | for j in range(i - 1, Ed.UR - 1, -1): 193 | if self.ep[j] > self.ep[i]: 194 | s += 1 195 | return s % 2 196 | 197 | def symmetries(self): 198 | """Generate a list of the symmetries and antisymmetries of the cubie cube.""" 199 | from symmetries import symCube, inv_idx # not nice here but else we have circular imports 200 | s = [] 201 | d = CubieCube() 202 | for j in range(N_SYM): 203 | c = CubieCube(symCube[j].cp, symCube[j].co, symCube[j].ep, symCube[j].eo) 204 | c.multiply(self) 205 | c.multiply(symCube[inv_idx[j]]) 206 | if self == c: 207 | s.append(j) 208 | c.inv_cubie_cube(d) 209 | if self == d: # then we have antisymmetry 210 | s.append(j + N_SYM) 211 | return s 212 | 213 | # ###################################### coordinates for phase 1 and 2 ################################################# 214 | def get_twist(self): 215 | """Get the twist of the 8 corners. 0 <= twist < 2187 in phase 1, twist = 0 in phase 2.""" 216 | ret = 0 217 | for i in range(Co.URF, Co.DRB): 218 | ret = 3 * ret + self.co[i] 219 | return ret 220 | 221 | def set_twist(self, twist): 222 | twistparity = 0 223 | for i in range(Co.DRB - 1, Co.URF - 1, -1): 224 | self.co[i] = twist % 3 225 | twistparity += self.co[i] 226 | twist //= 3 227 | self.co[Co.DRB] = ((3 - twistparity % 3) % 3) 228 | 229 | def get_flip(self): 230 | """Get the flip of the 12 edges. 0 <= flip < 2048 in phase 1, flip = 0 in phase 2.""" 231 | ret = 0 232 | for i in range(Ed.UR, Ed.BR): 233 | ret = 2 * ret + self.eo[i] 234 | return ret 235 | 236 | def set_flip(self, flip): 237 | flipparity = 0 238 | for i in range(Ed.BR - 1, Ed.UR - 1, -1): 239 | self.eo[i] = flip % 2 240 | flipparity += self.eo[i] 241 | flip //= 2 242 | self.eo[Ed.BR] = ((2 - flipparity % 2) % 2) 243 | 244 | def get_slice(self): 245 | """Get the location of the UD-slice edges FR,FL,BL and BR ignoring their permutation. 246 | 0<= slice < 495 in phase 1, slice = 0 in phase 2.""" 247 | a = x = 0 248 | # Compute the index a < (12 choose 4) 249 | for j in range(Ed.BR, Ed.UR - 1, -1): 250 | if Ed.FR <= self.ep[j] <= Ed.BR: 251 | a += c_nk(11 - j, x + 1) 252 | x += 1 253 | return a 254 | 255 | def set_slice(self, idx): 256 | slice_edge = list(range(Ed.FR, Ed.BR + 1)) 257 | other_edge = [Ed.UR, Ed.UF, Ed.UL, Ed.UB, Ed.DR, Ed.DF, Ed.DL, Ed.DB] 258 | a = idx # Location 259 | for e in Ed: 260 | self.ep[e] = -1 # Invalidate all edge positions 261 | 262 | x = 4 # set slice edges 263 | for j in Ed: 264 | if a - c_nk(11 - j, x) >= 0: 265 | self.ep[j] = slice_edge[4 - x] 266 | a -= c_nk(11 - j, x) 267 | x -= 1 268 | 269 | x = 0 # set the remaining edges UR..DB 270 | for j in Ed: 271 | if self.ep[j] == -1: 272 | self.ep[j] = other_edge[x] 273 | x += 1 274 | 275 | def get_slice_sorted(self): 276 | """Get the permutation and location of the UD-slice edges FR,FL,BL and BR. 277 | 0 <= slice_sorted < 11880 in phase 1, 0 <= slice_sorted < 24 in phase 2, slice_sorted = 0 for solved cube.""" 278 | a = x = 0 279 | edge4 = [0]*4 280 | # First compute the index a < (12 choose 4) and the permutation array perm. 281 | for j in range(Ed.BR, Ed.UR - 1, -1): 282 | if Ed.FR <= self.ep[j] <= Ed.BR: 283 | a += c_nk(11 - j, x + 1) 284 | edge4[3 - x] = self.ep[j] 285 | x += 1 286 | # Then compute the index b < 4! for the permutation in edge4 287 | b = 0 288 | for j in range(3, 0, -1): 289 | k = 0 290 | while edge4[j] != j + 8: 291 | rotate_left(edge4, 0, j) 292 | k += 1 293 | b = (j + 1)*b + k 294 | return 24*a + b 295 | 296 | def set_slice_sorted(self, idx): 297 | slice_edge = [Ed.FR, Ed.FL, Ed.BL, Ed.BR] 298 | other_edge = [Ed.UR, Ed.UF, Ed.UL, Ed.UB, Ed.DR, Ed.DF, Ed.DL, Ed.DB] 299 | b = idx % 24 # Permutation 300 | a = idx // 24 # Location 301 | for e in Ed: 302 | self.ep[e] = -1 # Invalidate all edge positions 303 | 304 | j = 1 # generate permutation from index b 305 | while j < 4: 306 | k = b % (j + 1) 307 | b //= j + 1 308 | while k > 0: 309 | rotate_right(slice_edge, 0, j) 310 | k -= 1 311 | j += 1 312 | 313 | x = 4 # set slice edges 314 | for j in Ed: 315 | if a - c_nk(11 - j, x) >= 0: 316 | self.ep[j] = slice_edge[4 - x] 317 | a -= c_nk(11 - j, x) 318 | x -= 1 319 | 320 | x = 0 # set the remaining edges UR..DB 321 | for j in Ed: 322 | if self.ep[j] == -1: 323 | self.ep[j] = other_edge[x] 324 | x += 1 325 | 326 | def get_u_edges(self): 327 | """Get the permutation and location of edges UR, UF, UL and UB. 328 | 0 <= u_edges < 11880 in phase 1, 0 <= u_edges < 1680 in phase 2, u_edges = 1656 for solved cube.""" 329 | a = x = 0 330 | edge4 = [0]*4 331 | ep_mod = self.ep[:] 332 | for j in range(4): 333 | rotate_right(ep_mod, 0, 11) 334 | # First compute the index a < (12 choose 4) and the permutation array perm. 335 | for j in range(Ed.BR, Ed.UR - 1, -1): 336 | if Ed.UR <= ep_mod[j] <= Ed.UB: 337 | a += c_nk(11 - j, x + 1) 338 | edge4[3 - x] = ep_mod[j] 339 | x += 1 340 | # Then compute the index b < 4! for the permutation in edge4 341 | b = 0 342 | for j in range(3, 0, -1): 343 | k = 0 344 | while edge4[j] != j: 345 | rotate_left(edge4, 0, j) 346 | k += 1 347 | b = (j + 1)*b + k 348 | return 24*a + b 349 | 350 | def set_u_edges(self, idx): 351 | slice_edge = [Ed.UR, Ed.UF, Ed.UL, Ed.UB] 352 | other_edge = [Ed.DR, Ed.DF, Ed.DL, Ed.DB, Ed.FR, Ed.FL, Ed.BL, Ed.BR] 353 | b = idx % 24 # Permutation 354 | a = idx // 24 # Location 355 | for e in Ed: 356 | self.ep[e] = -1 # Invalidate all edge positions 357 | 358 | j = 1 # generate permutation from index b 359 | while j < 4: 360 | k = b % (j + 1) 361 | b //= j + 1 362 | while k > 0: 363 | rotate_right(slice_edge, 0, j) 364 | k -= 1 365 | j += 1 366 | 367 | x = 4 # set slice edges 368 | for j in Ed: 369 | if a - c_nk(11 - j, x) >= 0: 370 | self.ep[j] = slice_edge[4 - x] 371 | a -= c_nk(11 - j, x) 372 | x -= 1 373 | 374 | x = 0 # set the remaining edges UR..DB 375 | for j in Ed: 376 | if self.ep[j] == -1: 377 | self.ep[j] = other_edge[x] 378 | x += 1 379 | for j in range(4): 380 | rotate_left(self.ep, 0, 11) 381 | 382 | def get_d_edges(self): 383 | """Get the permutation and location of the edges DR, DF, DL and DB. 384 | 0 <= d_edges < 11880 in phase 1, 0 <= d_edges < 1680 in phase 2, d_edges = 0 for solved cube.""" 385 | a = x = 0 386 | edge4 = [0] * 4 387 | ep_mod = self.ep[:] 388 | for j in range(4): 389 | rotate_right(ep_mod, 0, 11) 390 | # First compute the index a < (12 choose 4) and the permutation array perm. 391 | for j in range(Ed.BR, Ed.UR - 1, -1): 392 | if Ed.DR <= ep_mod[j] <= Ed.DB: 393 | a += c_nk(11 - j, x + 1) 394 | edge4[3 - x] = ep_mod[j] 395 | x += 1 396 | # Then compute the index b < 4! for the permutation in edge4 397 | b = 0 398 | for j in range(3, 0, -1): 399 | k = 0 400 | while edge4[j] != j + 4: 401 | rotate_left(edge4, 0, j) 402 | k += 1 403 | b = (j + 1) * b + k 404 | return 24 * a + b 405 | 406 | def set_d_edges(self, idx): 407 | slice_edge = [Ed.DR, Ed.DF, Ed.DL, Ed.DB] 408 | other_edge = [Ed.FR, Ed.FL, Ed.BL, Ed.BR, Ed.UR, Ed.UF, Ed.UL, Ed.UB] 409 | b = idx % 24 # Permutation 410 | a = idx // 24 # Location 411 | for e in Ed: 412 | self.ep[e] = -1 # Invalidate all edge positions 413 | 414 | j = 1 # generate permutation from index b 415 | while j < 4: 416 | k = b % (j + 1) 417 | b //= j + 1 418 | while k > 0: 419 | rotate_right(slice_edge, 0, j) 420 | k -= 1 421 | j += 1 422 | 423 | x = 4 # set slice edges 424 | for j in Ed: 425 | if a - c_nk(11 - j, x) >= 0: 426 | self.ep[j] = slice_edge[4 - x] 427 | a -= c_nk(11 - j, x) 428 | x -= 1 429 | 430 | x = 0 # set the remaining edges UR..DB 431 | for j in Ed: 432 | if self.ep[j] == -1: 433 | self.ep[j] = other_edge[x] 434 | x += 1 435 | for j in range(4): 436 | rotate_left(self.ep, 0, 11) 437 | 438 | def get_corners(self): 439 | """Get the permutation of the 8 corners. 440 | 0 <= corners < 40320 defined but unused in phase 1, 0 <= corners < 40320 in phase 2, 441 | corners = 0 for solved cube""" 442 | perm = list(self.cp) # duplicate cp 443 | b = 0 444 | for j in range(Co.DRB, Co.URF, -1): 445 | k = 0 446 | while perm[j] != j: 447 | rotate_left(perm, 0, j) 448 | k += 1 449 | b = (j + 1) * b + k 450 | return b 451 | 452 | def set_corners(self, idx): 453 | self.cp = [i for i in Co] 454 | for j in Co: 455 | k = idx % (j + 1) 456 | idx //= j + 1 457 | while k > 0: 458 | rotate_right(self.cp, 0, j) 459 | k -= 1 460 | 461 | def get_ud_edges(self): 462 | """Get the permutation of the 8 U and D edges. 463 | ud_edges undefined in phase 1, 0 <= ud_edges < 40320 in phase 2, ud_edges = 0 for solved cube.""" 464 | perm = self.ep[0:8] # duplicate first 8 elements of ep 465 | b = 0 466 | for j in range(Ed.DB, Ed.UR, -1): 467 | k = 0 468 | while perm[j] != j: 469 | rotate_left(perm, 0, j) 470 | k += 1 471 | b = (j + 1) * b + k 472 | return b 473 | 474 | def set_ud_edges(self, idx): 475 | # positions of FR FL BL BR edges are not affected 476 | for i in list(Ed)[0:8]: 477 | self.ep[i] = i 478 | for j in list(Ed)[0:8]: 479 | k = idx % (j + 1) 480 | idx //= j + 1 481 | while k > 0: 482 | rotate_right(self.ep, 0, j) 483 | k -= 1 484 | # ###################################### end coordinates for phase 1 and 2 ############################################# 485 | 486 | # ############################################ other usefull functions ################################################# 487 | def randomize(self): 488 | """Generate a random cube. The probability is the same for all possible states.""" 489 | def set_edges(idx): 490 | """The permutation of the 12 edges. 0 <= idx < 12!.""" 491 | self.ep = [i for i in Ed] 492 | for j in Ed: 493 | k = idx % (j + 1) 494 | idx //= j + 1 495 | while k > 0: 496 | rotate_right(self.ep, 0, j) 497 | k -= 1 498 | set_edges(randrange(479001600)) # 12! 499 | p = self.edge_parity() 500 | while True: 501 | self.set_corners(randrange(40320)) # 8! 502 | if p == self.corner_parity(): # parities of edge and corner permutations must be the same 503 | break 504 | self.set_flip(randrange(2048)) # 2^11 505 | self.set_twist(randrange(2187)) # 3^7 506 | 507 | def verify(self): 508 | """Check if cubiecube is valid.""" 509 | edge_count = [0]*12 510 | for i in Ed: 511 | edge_count[self.ep[i]] += 1 512 | for i in Ed: 513 | if edge_count[i] != 1: 514 | return 'Error: Some edges are undefined.' 515 | 516 | s = 0 517 | for i in Ed: 518 | s += self.eo[i] 519 | if s % 2 != 0: 520 | return 'Error: Total edge flip is wrong.' 521 | 522 | corner_count = [0] * 8 523 | for i in Co: 524 | corner_count[self.cp[i]] += 1 525 | for i in Co: 526 | if corner_count[i] != 1: 527 | return 'Error: Some corners are undefined.' 528 | 529 | s = 0 530 | for i in Co: 531 | s += self.co[i] 532 | if s % 3 != 0: 533 | return 'Error: Total corner twist is wrong.' 534 | 535 | if self.edge_parity() != self.corner_parity(): 536 | return 'Error: Wrong edge and corner parity' 537 | 538 | return CUBE_OK 539 | ######################################################################################################################## 540 | 541 | # ################################## these cubes represent the basic cube moves ######################################## 542 | basicMoveCube = [0] * 6 543 | basicMoveCube[Color.U] = CubieCube(cpU, coU, epU, eoU) 544 | basicMoveCube[Color.R] = CubieCube(cpR, coR, epR, eoR) 545 | basicMoveCube[Color.F] = CubieCube(cpF, coF, epF, eoF) 546 | basicMoveCube[Color.D] = CubieCube(cpD, coD, epD, eoD) 547 | basicMoveCube[Color.L] = CubieCube(cpL, coL, epL, eoL) 548 | basicMoveCube[Color.B] = CubieCube(cpB, coB, epB, eoB) 549 | ######################################################################################################################## 550 | 551 | # ################################# these cubes represent the all 18 cube moves ######################################## 552 | 553 | moveCube = [0] * 18 554 | for c1 in Color: 555 | cc = CubieCube() 556 | for k1 in range(3): 557 | cc.multiply(basicMoveCube[c1]) 558 | moveCube[3 * c1 + k1] = CubieCube(cc.cp, cc.co, cc.ep, cc.eo) 559 | ######################################################################################################################## 560 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. 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"Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------