# "Singmaster" to "Cubestring" conversion

#### TheDuckCuber

##### Member
Background: Python coder (amateur at best) here, won't understand some of the coding jargon so please excuse me beforehand.

So I was trying to make a Rubik's cube application with python the other day, and I decided for the scrambler I'd use Kociemba's 2-phase solver for the scramble generator. But the program requires the cube state to be inputted with the colour of each sticker on the cube while I have the cube states saved in the Singmaster notation. i.e., the common notation used by the average cuber (RLUDFB etc.). Is there a way to convert the notation my cube states in a way that the program is not made significantly slower?

All answers welcome.

#### Mastermind2368

##### Member
I'm a little confused on how exactly your program is intended to store the cube state. Is it a single list? A list of lists? A 54 character string?

If it's something like that, you can create functions which are each defined as a different turn, and cycle the correct pieces for the corresponding rotation. If you wanted to rotate R, you would have to find the indexes of all the stickers in the R slice, and move each sticker to the next position.

I made something like this at one point (no scrambler though, just a 2d virtual cube) and I ended up doing that approach. Then to call the Singmaster notation, I made a function which takes a string and calls the other functions based upon the input.

#### Bruce MacKenzie

##### Member
Background: Python coder (amateur at best) here, won't understand some of the coding jargon so please excuse me beforehand.

So I was trying to make a Rubik's cube application with python the other day, and I decided for the scrambler I'd use Kociemba's 2-phase solver for the scramble generator. But the program requires the cube state to be inputted with the colour of each sticker on the cube while I have the cube states saved in the Singmaster notation. i.e., the common notation used by the average cuber (RLUDFB etc.). Is there a way to convert the notation my cube states in a way that the program is not made significantly slower?

All answers welcome.

I'm not sure what you mean by Singmaster notation. Kociemba's Cube Explorer accepts input in the form of a permutation of the identity string;

"UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"

This representation is composed of twenty groupings which name the twenty cubies which are rearranged by turns of the cube faces. The two letter groupings represent the edge cubies and the three letter groupings represent the corner cubies. The individual letters stand for the exposed facelets of the cubies using the Singmaster convention. UF stands for the cubie on the Up-Front edge of the solved cube. UFR stands for the cubie in the Up-Front-Right corner of the solved cube.

Arbitrary cube arrangements are encoded as a rearrangement of the identity representation. For example, a three way swap of the UF, UR and UB cubies would be shown as:

"UR UB UF UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"

This string specifies that the UR cubie has been moved to UF cubicle, the UB cubie has been moved to the UR cubicle and the UF cubie has been moved to the UB cubicle. Cubie orientation is encoded as a rearrangement of the letters in the letter groupings. A cube position having the UF and UR cubies flipped would be encoded as:

@ "FU RU UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"

Here the UF cubie is in the UF cubicle but with the Front facelet in the Up position. Corner cubie twist is encoded by rolling the three letter codes to the right or the left. If the UFR corner cubie is shown as FRU, the Front facelet has been rotated to the Up position and the cubie has a CW twist. If it is shown as RUF, the Right facelet has been rotated into the Up position and the cubie has a CCW twist. Note that swapping two letters of a corner cubie, ie FUR, represents the mirror image of the cubie and is not valid in a SCS representation.

Here's a screen shot of a cube state and its string representation:

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#### TheDuckCuber

##### Member
I'm a little confused on how exactly your program is intended to store the cube state. Is it a single list? A list of lists? A 54 character string?

If it's something like that, you can create functions which are each defined as a different turn, and cycle the correct pieces for the corresponding rotation. If you wanted to rotate R, you would have to find the indexes of all the stickers in the R slice, and move each sticker to the next position.

I made something like this at one point (no scrambler though, just a 2d virtual cube) and I ended up doing that approach. Then to call the Singmaster notation, I made a function which takes a string and calls the other functions based upon the input.
hmm yeah I'll see that. the programs stores the cube state based on the set of moves taken to reach that state

#### Bruce MacKenzie

##### Member
Ok, so you need to convert a generator turn sequence into a string representation suitable for input into Kociemba's 2 phase solver.

1. Represent the face turns as S54 permutations of the facelet positions. Kociemba gives the order he lists the facelets in the enums.py file.

2. Convert the generator turn sequence into a S54 permutation by compositing the face turn permutations using permutation multiplication;

3. Apply the composit permutation to the identity string: "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"

Addendum

I sat down and wrote some code to convert my cube representation to an S54 representation using Kociemba's numbering and printed out the face turns. Hope you find this useful.
The S54 reps may be used to composit turn sequences and permute the facelet color string. The GAP permutation rep is in 1 based canonical cycle notation suitable for GAP.

R UUFUUFUUFRRRRRRRRRFFDFFDFFDDDBDDBDDBLLLLLLLLLUBBUBBUBB

S54 = { 0, 1,20, 3, 4,23, 6, 7,26,15,12, 9,16,13,10,17,14,11,18,19,29,21,22,32,24,25,35,27,28,51,30,31,48,33,34,45,36,37,38,39,40,41,42,43,44, 8,46,47, 5,49,50, 2,52,53}

GAP: (3,21,30,52)(6,24,33,49)(9,27,36,46)(10,16,18,12)(11,13,17,15)
 _____UUF _____UUF _____UUF LLL FFD RRR UBB LLL FFD RRR UBB LLL FFD RRR UBB _____DDB _____DDB _____DDB

R' UUBUUBUUBRRRRRRRRRFFUFFUFFUDDFDDFDDFLLLLLLLLLDBBDBBDBB

S54 = { 0, 1,51, 3, 4,48, 6, 7,45,11,14,17,10,13,16, 9,12,15,18,19, 2,21,22, 5,24,25, 8,27,28,20,30,31,23,33,34,26,36,37,38,39,40,41,42,43,44,35,46,47,32,49,50,29,52,53}

GAP: (3,52,30,21)(6,49,33,24)(9,46,36,27)(10,12,18,16)(11,15,17,13)
 _____UUB _____UUB _____UUB LLL FFU RRR DBB LLL FFU RRR DBB LLL FFU RRR DBB _____DDF _____DDF _____DDF

U UUUUUUUUUBBBRRRRRRRRRFFFFFFDDDDDDDDDFFFLLLLLLLLLBBBBBB

S54 = { 6, 3, 0, 7, 4, 1, 8, 5, 2,45,46,47,12,13,14,15,16,17, 9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,39,40,41,42,43,44,36,37,38,48,49,50,51,52,53}

GAP: (1,7,9,3)(2,4,8,6)(10,46,37,19)(11,47,38,20)(12,48,39,21)
 _____UUU _____UUU _____UUU FFF RRR BBB LLL LLL FFF RRR BBB LLL FFF RRR BBB _____DDD _____DDD

U' UUUUUUUUUFFFRRRRRRLLLFFFFFFDDDDDDDDDBBBLLLLLLRRRBBBBBB

S54 = { 2, 5, 8, 1, 4, 7, 0, 3, 6,18,19,20,12,13,14,15,16,17,36,37,38,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,45,46,47,39,40,41,42,43,44, 9,10,11,48,49,50,51,52,53}

GAP: (1,3,9,7)(2,6,8,4)(10,19,37,46)(11,20,38,47)(12,21,39,48)
 _____UUU _____UUU _____UUU BBB LLL FFF RRR LLL FFF RRR BBB LLL FFF RRR BBB _____DDD _____DDD _____DDD

F UUUUUULLLURRURRURRFFFFFFFFFRRRDDDDDDLLDLLDLLDBBBBBBBBB

S54 = { 0, 1, 2, 3, 4, 5,44,41,38, 6,10,11, 7,13,14, 8,16,17,24,21,18,25,22,19,26,23,20,15,12, 9,30,31,32,33,34,35,36,37,27,39,40,28,42,43,29,45,46,47,48,49,50,51,52,53}

GAP: (7,45,30,10)(8,42,29,13)(9,39,28,16)(19,25,27,21)(20,22,26,24)
 _____UUU _____UUU _____LLL LLD FFF URR BBB LLD FFF URR BBB LLD FFF URR BBB _____RRR _____DDD _____DDD

F' UUUUUURRRDRRDRRDRRFFFFFFFFFLLLDDDDDDLLULLULLUBBBBBBBBB

S54 = { 0, 1, 2, 3, 4, 5, 9,12,15,29,10,11,28,13,14,27,16,17,20,23,26,19,22,25,18,21,24,38,41,44,30,31,32,33,34,35,36,37, 8,39,40, 7,42,43, 6,45,46,47,48,49,50,51,52,53}

GAP: (7,10,30,45)(8,13,29,42)(9,16,28,39)(19,21,27,25)(20,24,26,22)
 _____UUU _____UUU _____RRR LLU FFF DRR BBB LLU FFF DRR BBB LLU FFF DRR BBB _____LLL _____DDD _____DDD

L BUUBUUBUURRRRRRRRRUFFUFFUFFFDDFDDFDDLLLLLLLLLBBDBBDBBD

S54 = {53, 1, 2,50, 4, 5,47, 7, 8, 9,10,11,12,13,14,15,16,17, 0,19,20, 3,22,23, 6,25,26,18,28,29,21,31,32,24,34,35,42,39,36,43,40,37,44,41,38,45,46,33,48,49,30,51,52,27}

GAP: (1,54,28,19)(4,51,31,22)(7,48,34,25)(37,43,45,39)(38,40,44,42)
 _____BUU _____BUU _____BUU LLL UFF RRR BBD LLL UFF RRR BBD LLL UFF RRR BBD _____FDD _____FDD _____FDD

L' FUUFUUFUURRRRRRRRRDFFDFFDFFBDDBDDBDDLLLLLLLLLBBUBBUBBU

S54 = {18, 1, 2,21, 4, 5,24, 7, 8, 9,10,11,12,13,14,15,16,17,27,19,20,30,22,23,33,25,26,53,28,29,50,31,32,47,34,35,38,41,44,37,40,43,36,39,42,45,46, 6,48,49, 3,51,52, 0}

GAP: (1,19,28,54)(4,22,31,51)(7,25,34,48)(37,39,45,43)(38,42,44,40)
 _____FUU _____FUU _____FUU LLL DFF RRR BBU LLL DFF RRR BBU LLL DFF RRR BBU _____BDD _____BDD _____BDD

D UUUUUUUUURRRRRRFFFFFFFFFLLLDDDDDDDDDLLLLLLBBBBBBBBBRRR

S54 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,24,25,26,18,19,20,21,22,23,42,43,44,33,30,27,34,31,28,35,32,29,36,37,38,39,40,41,51,52,53,45,46,47,48,49,50,15,16,17}

GAP: (16,25,43,52)(17,26,44,53)(18,27,45,54)(28,34,36,30)(29,31,35,33)
 _____UUU _____UUU _____UUU LLL FFF RRR BBB LLL FFF RRR BBB BBB LLL FFF RRR _____DDD _____DDD _____DDD

D' UUUUUUUUURRRRRRBBBFFFFFFRRRDDDDDDDDDLLLLLLFFFBBBBBBLLL

S54 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,51,52,53,18,19,20,21,22,23,15,16,17,29,32,35,28,31,34,27,30,33,36,37,38,39,40,41,24,25,26,45,46,47,48,49,50,42,43,44}

GAP: (16,52,43,25)(17,53,44,26)(18,54,45,27)(28,30,36,34)(29,33,35,31)
 _____UUU _____UUU _____UUU LLL FFF RRR BBB LLL FFF RRR BBB FFF RRR BBB LLL _____DDD _____DDD _____DDD

B RRRUUUUUURRDRRDRRDFFFFFFFFFDDDDDDLLLULLULLULLBBBBBBBBB

S54 = {11,14,17, 3, 4, 5, 6, 7, 8, 9,10,35,12,13,34,15,16,33,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,39,42, 2,37,38, 1,40,41, 0,43,44,51,48,45,52,49,46,53,50,47}

GAP: (1,12,36,43)(2,15,35,40)(3,18,34,37)(46,52,54,48)(47,49,53,51)
 _____RRR _____UUU _____UUU ULL FFF RRD BBB ULL FFF RRD BBB ULL FFF RRD BBB _____DDD _____DDD _____LLL

B' LLLUUUUUURRURRURRUFFFFFFFFFDDDDDDRRRDLLDLLDLLBBBBBBBBB

S54 = {42,39,36, 3, 4, 5, 6, 7, 8, 9,10, 0,12,13, 1,15,16, 2,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,17,14,11,33,37,38,34,40,41,35,43,44,47,50,53,46,49,52,45,48,51}

GAP: (1,43,36,12)(2,40,35,15)(3,37,34,18)(46,48,54,52)(47,51,53,49)
 _____LLL _____UUU _____UUU DLL FFF RRU BBB DLL FFF RRU BBB DLL FFF RRU BBB _____DDD _____DDD _____RRR

R2 UUDUUDUUDRRRRRRRRRFFBFFBFFBDDUDDUDDULLLLLLLLLFBBFBBFBB

S54 = { 0, 1,29, 3, 4,32, 6, 7,35,17,16,15,14,13,12,11,10, 9,18,19,51,21,22,48,24,25,45,27,28, 2,30,31, 5,33,34, 8,36,37,38,39,40,41,42,43,44,26,46,47,23,49,50,20,52,53}

GAP: (3,30)(6,33)(9,36)(10,18)(11,17)(12,16)(13,15)(21,52)(24,49)(27,46)
 _____UUD _____UUD _____UUD LLL FFB RRR FBB LLL FFB RRR FBB LLL FFB RRR FBB _____DDU _____DDU _____DDU

U2 UUUUUUUUULLLRRRRRRBBBFFFFFFDDDDDDDDDRRRLLLLLLFFFBBBBBB

S54 = { 8, 7, 6, 5, 4, 3, 2, 1, 0,36,37,38,12,13,14,15,16,17,45,46,47,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35, 9,10,11,39,40,41,42,43,44,18,19,20,48,49,50,51,52,53}

GAP: (1,9)(2,8)(3,7)(4,6)(10,37)(11,38)(12,39)(19,46)(20,47)(21,48)
 _____UUU _____UUU _____UUU RRR BBB LLL FFF LLL FFF RRR BBB LLL FFF RRR BBB _____DDD _____DDD _____DDD

F2 UUUUUUDDDLRRLRRLRRFFFFFFFFFUUUDDDDDDLLRLLRLLRBBBBBBBBB

S54 = { 0, 1, 2, 3, 4, 5,29,28,27,44,10,11,41,13,14,38,16,17,26,25,24,23,22,21,20,19,18, 8, 7, 6,30,31,32,33,34,35,36,37,15,39,40,12,42,43, 9,45,46,47,48,49,50,51,52,53}

GAP: (7,30)(8,29)(9,28)(10,45)(13,42)(16,39)(19,27)(20,26)(21,25)(22,24)
 _____UUU _____UUU _____DDD LLR FFF LRR BBB LLR FFF LRR BBB LLR FFF LRR BBB _____UUU _____DDD _____DDD

L2 DUUDUUDUURRRRRRRRRBFFBFFBFFUDDUDDUDDLLLLLLLLLBBFBBFBBF

S54 = {27, 1, 2,30, 4, 5,33, 7, 8, 9,10,11,12,13,14,15,16,17,53,19,20,50,22,23,47,25,26, 0,28,29, 3,31,32, 6,34,35,44,43,42,41,40,39,38,37,36,45,46,24,48,49,21,51,52,18}

GAP: (1,28)(4,31)(7,34)(19,54)(22,51)(25,48)(37,45)(38,44)(39,43)(40,42)
 _____DUU _____DUU _____DUU LLL BFF RRR BBF LLL BFF RRR BBF LLL BFF RRR BBF _____UDD _____UDD _____UDD

D2 UUUUUUUUURRRRRRLLLFFFFFFBBBDDDDDDDDDLLLLLLRRRBBBBBBFFF

S54 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,42,43,44,18,19,20,21,22,23,51,52,53,35,34,33,32,31,30,29,28,27,36,37,38,39,40,41,15,16,17,45,46,47,48,49,50,24,25,26}

GAP: (16,43)(17,44)(18,45)(25,52)(26,53)(27,54)(28,36)(29,35)(30,34)(31,33)
 _____UUU _____UUU _____UUU LLL FFF RRR BBB LLL FFF RRR BBB RRR BBB LLL FFF _____DDD _____DDD _____DDD

B2 DDDUUUUUURRLRRLRRLFFFFFFFFFDDDDDDUUURLLRLLRLLBBBBBBBBB

S54 = {35,34,33, 3, 4, 5, 6, 7, 8, 9,10,42,12,13,39,15,16,36,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, 2, 1, 0,17,37,38,14,40,41,11,43,44,53,52,51,50,49,48,47,46,45}

GAP: (1,36)(2,35)(3,34)(12,43)(15,40)(18,37)(46,54)(47,53)(48,52)(49,51)
 _____DDD _____UUU _____UUU RLL FFF RRL BBB RLL FFF RRL BBB RLL FFF RRL BBB _____DDD _____DDD _____UUU

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