/usr/share/gnubik/scripts/mellor-solve.scm is in gnubik 2.4.1-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 | ;; Copyright (c) 2004 Dale Mellor
;;
;; This program is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 3 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program. If not, see <http://www.gnu.org/licenses/>.
;; I'm not normally one for global variables, but this is so pervasive
;; throughout this unit I couldn't resist. It is the scheme reflection of
;; GNUbik's own cube object.
(define cube '())
;; Whenever we access the cube, or perform moves on it, we call a function which
;; performs symbolic rotations about the sides l, r, b and f. This way, we only
;; have to work out one quarter of the total moves to solve the cube, and the
;; rest come by symmetry. The following variable gets a function which performs
;; the rotations (it will be a function which takes a string in and gives a
;; transformed string back).
(define rotated-flubrd-symbol '())
;; Function to create the procedure that gets assigned to the variable binding
;; above, given the number of turns required. For example, if one turn is
;; requested, then any algorithms which are centred around the front face will,
;; unwittingly, be applying themselves to the right face.
(define (rotated-flubrd-symbol-set! turns)
(set! rotated-flubrd-symbol
(lambda (s)
(do ((s (string-copy s))
(j 0 (+ 1 j)))
((eq? j turns) s)
(do ((i 0 (+ i 1))) ((eq? i (string-length s))
s)
(string-set! s i
(case (string-ref s i)
((#\l) #\f)
((#\f) #\r)
((#\r) #\b)
((#\b) #\l)
(else (string-ref s i)))))))))
;; So, if proc is designed to solve a block on the front face, we apply it to
;; four different rotations of the symbolic letters and have it solve a block on
;; four faces.
(define (repeat-for-all-rotations proc)
(do ((i 0 (+ i 1))) ((eq? i 4))
(rotated-flubrd-symbol-set! i)
(proc)))
;; Wrapper around get-colour-symbolic which applies the cube rotation first,
;; i.e. it is influenced by the script later setting rotated-flubrd-symbol by
;; calling rotated-flubrd-symbol-set!
(define (lookup-colour s)
(get-colour-symbolic cube (rotated-flubrd-symbol s)))
;; Wrapper around move-face which applies the cube rotation first. Note that
;; this takes a string consisting of multiple moves, each one represented by two
;; letters, e.g. "f+"; the single-letter symbols which move-face accepts cannot
;; be used here.
(define (do-moves moves)
(do ((moves moves (substring moves 2))) ((string-null? moves))
(move-face cube (rotated-flubrd-symbol (substring moves 0 2)))))
;; This introduces xsubstring, which allows us to perform cyclic rotations on
;; the characters of a string.
(use-modules ((srfi srfi-13)))
;; Think about fixing the uf block, but then apply the algorithms with the cube
;; symbolically rotated four times. Look for the required block in all possible
;; locations, and when it is found lookup the moves that are needed to bring it
;; to uf, without upsetting any of the other top edges.
(define (mellor-top-edge-solve)
(repeat-for-all-rotations
(lambda ()
(let ((u (lookup-colour "u"))
(f (lookup-colour "f")))
(let trial ((moves '(("fu" . "f-u+l-u-")
("ur" . "r-u-r+u+")
("ru" . "r-f-")
("bu" . "b-u-r-u+")
("ub" . "b-u-u-b+u-u-")
("ul" . "l+u+l-u-")
("lu" . "l+f+")
("fr" . "u-r+u+")
("rf" . "f-")
("rb" . "r+r+f-r-r-")
("br" . "u-r-u+")
("lb" . "l+l+f+l-l-")
("bl" . "u+l+u-")
("fl" . "u+l-u-")
("lf" . "f+")
("fd" . "d+r+f-r-")
("df" . "f+f+")
("rd" . "r+f-r-")
("dr" . "d-f+f+")
("db" . "d+d+f+f+")
("bd" . "d-r+f-r-")
("dl" . "d+f+f+")
("ld" . "l-f+l+"))))
(if (not (null? moves))
(if (and (eq? u (lookup-colour (caar moves)))
(eq? f (lookup-colour (xsubstring (caar moves) 1 3))))
(do-moves (cdar moves))
(trial (cdr moves)))))))))
;; Concentrate on getting the block ufr correct, but then apply the procedure to
;; all four sides of the cube. Look for the correct block in all locations, and
;; then lookup the moves required to get it to ufr.
(define (mellor-top-corner-solve)
(repeat-for-all-rotations
(lambda ()
(let ((top-colour (lookup-colour "u"))
(front-colour (lookup-colour "f"))
(right-colour (lookup-colour "r")))
(let loop ((moves '(("rfd" . "r-d-r+")
("fld" . "d+r-d-r+")
("lbd" . "f+d-d-f-")
("brd" . "f+d-f-")
("fdr" . "f+d+f-")
("rdb" . "d-f+d+f-")
("bdl" . "r-d-d-r+")
("ldf" . "r-d+r+")
("drf" . "r-d+r+f+d-d-f-")
("dfl" . "d+r-d+r+f+d-d-f-")
("dlb" . "d-d-r-d+r+f+d-d-f-")
("dbr" . "d-r-d+r+f+d-d-f-")
("fru" . "f+d-d-f-r-d-d-r+")
("ruf" . "r-d-d-r+f+d-d-f-")
("urb" . "b-d-d-b+r-d+r+")
("rbu" . "r+d+r-r-d-d-r+")
("bur" . "f+b-d-f-b+")
("ubl" . "b+d-b-r-d-d-r+")
("blu" . "b+r-d-d-r+b-")
("lub" . "l-f+d-d-f-l+")
("ulf" . "l+d-l-r-d+r+")
("lfu" . "l+r-d+r+l-")
("ful" . "f-d-f+f+d-d-f-"))))
(if (not (null? moves))
(if (and (eq? (lookup-colour (caar moves))
top-colour)
(eq? (lookup-colour (xsubstring (caar moves) 1 4))
front-colour)
(eq? (lookup-colour (xsubstring (caar moves) 2 5))
right-colour))
(do-moves (cdar moves))
(loop (cdr moves)))))))))
;; Consider the fr block. If the block is to be found in the bottom slice, get
;; it into one of two `starting positions' (either fd or rd) and then move it up
;; into fr by looping back. If the piece is not found here, it must be in one of
;; the other middle edge positions; for now we just check if we are holding a
;; middle edge block at fr and if so we drop it to the bottom slice, so that a
;; repeat of the algorithm will eventually put it in its correct place, and by
;; the time the repeat comes around our own block will hopefully have been
;; dropped down.
(define (mellor-middle-slice-solve)
(do ((i 0 (+ 1 i))) ((eq? i 3))
(repeat-for-all-rotations
(lambda ()
(let ((front-colour (lookup-colour "f"))
(right-colour (lookup-colour "r")))
(let loop ()
(cond ((and (eq? (lookup-colour "fd") front-colour)
(eq? (lookup-colour "df") right-colour))
(do-moves "d-r-d+r+d+f+d-f-"))
((and (eq? (lookup-colour "df") front-colour)
(eq? (lookup-colour "fd") right-colour))
(do-moves "d+") (loop))
((and (eq? (lookup-colour "rd") right-colour)
(eq? (lookup-colour "dr") front-colour))
(do-moves "d+f+d-f-d-r-d+r+"))
((and (eq? (lookup-colour "dr") right-colour)
(eq? (lookup-colour "rd") front-colour))
(do-moves "d-") (loop))
((and (eq? (lookup-colour "ld") front-colour)
(eq? (lookup-colour "dl") right-colour))
(do-moves "d+") (loop))
((and (eq? (lookup-colour "dl") front-colour)
(eq? (lookup-colour "ld") right-colour))
(do-moves "d+d+") (loop))
((and (eq? (lookup-colour "bd") front-colour)
(eq? (lookup-colour "db") right-colour))
(do-moves "d+d+") (loop))
((and (eq? (lookup-colour "db") front-colour)
(eq? (lookup-colour "bd") right-colour))
(do-moves "d-") (loop))
((and (eq? (lookup-colour "fr") front-colour)
(eq? (lookup-colour "rf") right-colour))
noop)
((let ((bottom-colour (lookup-colour "d")))
(and (not (eq? (lookup-colour "fr") bottom-colour))
(not (eq? (lookup-colour "rf") bottom-colour))))
(do-moves "d+f+d-f-d-r-d+r+") (loop)))))))))
;; Procedure which answers the question, `Is the fdr block located in the right
;; place (regardless of orientation)?'
(define (placed-fdr?)
(eq? (+ (ash 1 (lookup-colour "fdr"))
(ash 1 (lookup-colour "dfr"))
(ash 1 (lookup-colour "rdf")))
(+ (ash 1 (lookup-colour "f" ))
(ash 1 (lookup-colour "d" ))
(ash 1 (lookup-colour "r" )))))
;; We look at all the bottom corners, and set a bit in a bit-mask when one is in
;; the right place. There are six patterns to look for: four in which two
;; adjacent blocks are out of place, and two in which diagonal blocks are out of
;; place. When we find one of these, we apply a symbolic rotation to the cube so
;; that the missing pieces are in set positions, and then apply appriopriate set
;; moves. Otherwise, either all the pieces are already in place, or else we just
;; shift the bottom slice around and loop until we find a pattern.
(define (mellor-bottom-corner-place)
(let ((fix-2 (lambda () (do-moves "r-d-r+f+d+f-r-d+r+d-d-")))
(fix-d (lambda () (do-moves "r-d-r+f+d-d-f-r-d+r+d-"))))
(let loop ()
(case (do ((i 0 (+ i 1)) (a 0 a))
((eq? i 4) a)
(rotated-flubrd-symbol-set! i)
(set! a (+ a (if (placed-fdr?) (ash 1 i) 0))))
((3) (rotated-flubrd-symbol-set! 3) (fix-2))
((6) (rotated-flubrd-symbol-set! 0) (fix-2))
((12) (rotated-flubrd-symbol-set! 1) (fix-2))
((9) (rotated-flubrd-symbol-set! 2) (fix-2))
((5) (rotated-flubrd-symbol-set! 1) (fix-d))
((10) (rotated-flubrd-symbol-set! 0) (fix-d))
((15) noop)
(else (do-moves "d+") (loop))))))
;; Very similar methodology to the above; look for patterns of blocks with the
;; right orientation, and then apply set-piece moves (depending on whether three
;; or two pieces are out of position). In all cases, we loop until we have a
;; solution because sometimes it takes more than one effort to get things
;; correct (we could go for a more intelligent approach than this...)
(define (mellor-bottom-corner-orient)
(let ((base-colour (lookup-colour "d"))
(fix-2 (lambda () (do-moves "f-f-r-d+r+f+d+f-u-f+d-f-r-d-r+u+f-f-")))
(fix-3 (lambda () (do-moves "r-d-r+d-r-d-d-r+d-d-"))))
(let loop ()
(case (do ((i 0 (+ i 1)) (a 0 a))
((eq? i 4) a)
(rotated-flubrd-symbol-set! i)
(set! a (+ a (if (eq? (lookup-colour "dfr") base-colour)
(ash 1 i)
0))))
((0) (rotated-flubrd-symbol-set! 0) (fix-3) (loop))
((8) (rotated-flubrd-symbol-set! 0) (fix-3) (loop))
((1) (rotated-flubrd-symbol-set! 1) (fix-3) (loop))
((2) (rotated-flubrd-symbol-set! 2) (fix-3) (loop))
((4) (rotated-flubrd-symbol-set! 3) (fix-3) (loop))
((6) (rotated-flubrd-symbol-set! 0) (fix-2) (loop))
((12) (rotated-flubrd-symbol-set! 1) (fix-2) (loop))
((9) (rotated-flubrd-symbol-set! 2) (fix-2) (loop))
((3) (rotated-flubrd-symbol-set! 3) (fix-2) (loop))
((10 5) (fix-2) (loop))))))
;; Almost the same again; look at the pattern of correctly placed bottom edges,
;; and apply set-piece moves to a logically rotated cube so that the pieces are
;; in a certain pattern which we can solve. Again, it might take several efforts
;; to get this right, so we loop until a solution is found (again we could do
;; better than this if we tried!)
(define (mellor-bottom-edge-place)
(let ((fix (lambda () (do-moves "r+l-f+r-l+d-d-r+l-f+r-l+"))))
(let loop ()
(case (do ((i 0 (+ 1 i)) (a 0 a))
((eq? i 4) a)
(rotated-flubrd-symbol-set! i)
(let ((side-colour (lookup-colour "f")))
(set! a (+ a (if (or (eq? (lookup-colour "fd") side-colour)
(eq? (lookup-colour "df") side-colour))
(ash 1 i)
0)))))
((0) (fix) (loop))
((1) (rotated-flubrd-symbol-set! 0) (fix) (loop))
((2) (rotated-flubrd-symbol-set! 1) (fix) (loop))
((4) (rotated-flubrd-symbol-set! 2) (fix) (loop))
((8) (rotated-flubrd-symbol-set! 3) (fix) (loop))))))
;; A similar approach again, but looking for patterns and applying moves to get
;; the bottom edges in the correct orientation.
(define (mellor-bottom-edge-orient)
(let ((base-colour (get-colour-symbolic cube "d"))
(fix-adjacent (lambda () (do-moves "f-f-r-r-r-u-d+b-b-u-u-d-d-f-u-f+u-u-d-d-b+b+u+d-r+u+r-r-f-f-")))
(fix-opposite (lambda () (do-moves "r-r-l-l-r-u-d+b-b-u-u-d-d-f-u-u-f+u-u-d-d-b-b-u+d-r+u-u-r-r-l-l-"))))
(let loop ()
(case (do ((i 0 (+ i 1)) (a 0 a))
((eq? i 4) a)
(rotated-flubrd-symbol-set! i)
(set! a (+ a (if (eq? (lookup-colour "df") base-colour)
(ash 1 i)
0))))
((0) (fix-opposite) (loop))
((3) (rotated-flubrd-symbol-set! 2) (fix-adjacent))
((6) (rotated-flubrd-symbol-set! 3) (fix-adjacent))
((12) (rotated-flubrd-symbol-set! 0) (fix-adjacent))
((9) (rotated-flubrd-symbol-set! 1) (fix-adjacent))
((5) (rotated-flubrd-symbol-set! 0) (fix-opposite))
((10) (rotated-flubrd-symbol-set! 1) (fix-opposite))))))
;; Apply all the various stages for fixing a cube in order, but allow the user
;; to specify when to stop.
(define (mellor-solve stage)
(set! cube (gnubik-cube-state))
(if (check-cube-structure cube)
(do ((i 0 (+ i 1)) (stage-list (list mellor-top-edge-solve
mellor-top-corner-solve
mellor-middle-slice-solve
mellor-bottom-corner-place
mellor-bottom-corner-orient
mellor-bottom-edge-place
mellor-bottom-edge-orient)
(cdr stage-list)))
((eq? i stage) (execute-move-buffer!))
((car stage-list)))))
;; Provide plenty of menu entries to give the user some control over the solving
;; algorithm (he may want to perform part of the solution himself!)
(define _ gettext)
(define solvers (gnubik-create-menu (_ "_Solvers")))
(define m3 (gnubik-create-menu (_ "_3×3") solvers))
(define menu (gnubik-create-menu "_Mellor" m3))
(gnubik-register-script (_ "_Full cube")
'(mellor-solve 7) menu)
(gnubik-register-script (_ "Bottom _edge place")
'(mellor-solve 6) menu)
(gnubik-register-script (_ "Bottom _corner orient")
'(mellor-solve 5) menu)
(gnubik-register-script (_ "_Bottom corner place")
'(mellor-solve 4) menu)
(gnubik-register-script (_ "_Middle slice")
'(mellor-solve 3) menu)
(gnubik-register-script (_ "_Top slice")
'(mellor-solve 2) menu)
(gnubik-register-script (_ "_Top edges")
'(mellor-solve 1) menu)
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