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1 | /* -*-c-*- |
2 | * | |
3 | * $Id$ | |
4 | * | |
5 | * Simple mastermind game | |
6 | * | |
7 | * (c) 2006 Mark Wooding | |
8 | */ | |
9 | ||
10 | /*----- Licensing notice --------------------------------------------------* | |
11 | * | |
12 | * This file is part of mm: a simple Mastermind game. | |
13 | * | |
14 | * mm is free software; you can redistribute it and/or modify | |
15 | * it under the terms of the GNU General Public License as published by | |
16 | * the Free Software Foundation; either version 2 of the License, or | |
17 | * (at your option) any later version. | |
18 | * | |
19 | * mm is distributed in the hope that it will be useful, | |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
22 | * GNU General Public License for more details. | |
23 | * | |
24 | * You should have received a copy of the GNU General Public License | |
25 | * along with mm; if not, write to the Free Software Foundation, | |
26 | * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. | |
27 | */ | |
28 | ||
29 | /*----- Header files ------------------------------------------------------*/ | |
30 | ||
31 | #include <ctype.h> | |
32 | #include <stdio.h> | |
33 | #include <stdlib.h> | |
34 | #include <string.h> | |
35 | #include <time.h> | |
36 | ||
37 | #include <mLib/alloc.h> | |
38 | #include <mLib/mdwopt.h> | |
39 | #include <mLib/quis.h> | |
40 | #include <mLib/report.h> | |
41 | #include <mLib/sub.h> | |
42 | ||
43 | /*----- Data structures ---------------------------------------------------*/ | |
44 | ||
45 | /* --- Digits --- * | |
46 | * | |
47 | * The symbols which make up the code to be guessed. | |
48 | */ | |
49 | ||
50 | typedef unsigned char dig; | |
51 | ||
52 | /* --- The game parameters --- */ | |
53 | ||
54 | typedef struct mm { | |
55 | dig k; /* Number of symbols in the code */ | |
56 | dig n; /* Number of distinct symbols */ | |
57 | } mm; | |
58 | ||
59 | /*----- Rating guesses ----------------------------------------------------*/ | |
60 | ||
61 | /* --- Algorithm --- * | |
62 | * | |
63 | * Rating guesses efficiently is quite important. | |
64 | * | |
65 | * The rate context structure contains a copy of the game parameters, and | |
66 | * three arrays, @v@, @s@ and @t@ allocated from the same @malloc@ed block: | |
67 | * | |
68 | * * %$v_i$% counts occurrences of the symbol %$i$% in the code. | |
69 | * * %$s$% is a copy of the code. | |
70 | * * %$t$% is temporary work space for the rating function. | |
71 | * | |
72 | * The rating function works by taking a pass over the guess, computing a | |
73 | * count table %$v'$%; but for each guess symbol which matches the | |
74 | * correspondng code symbol, decrementing the count %$v_i$% for that symbol | |
75 | * (in a temporary copy of the table %$v$%). The black count is then the | |
76 | * number of such matches, and the white count is given by | |
77 | * | |
78 | * %$w = \displaystyle \sum_{0<i\le n} \min(v_i, v'_i).$% | |
79 | * | |
80 | * Thus, the work is %$O(k + n)$%, rather than the %$O(k^2)$% for a | |
81 | * %%na\"\i{}ve%% implementation. | |
82 | */ | |
83 | ||
84 | typedef struct ratectx { | |
85 | mm m; | |
86 | dig *v; | |
87 | dig *s; | |
88 | dig *t; | |
89 | } ratectx; | |
90 | ||
91 | static ratectx *rate_alloc(const mm *m) | |
92 | { | |
93 | ratectx *r; | |
94 | dig *v; | |
95 | ||
96 | r = CREATE(ratectx); | |
97 | v = xmalloc((3 * m->n + m->k) * sizeof(dig)); | |
98 | r->m = *m; | |
99 | r->v = v; | |
100 | r->s = r->v + m->n; | |
101 | r->t = r->s + m->k; | |
102 | return (r); | |
103 | } | |
104 | ||
105 | static void rate_init(ratectx *r, const dig *s) | |
106 | { | |
107 | unsigned i; | |
108 | ||
109 | memset(r->v, 0, r->m.n * sizeof(dig)); | |
110 | for (i = 0; i < r->m.k; i++) | |
111 | r->v[s[i]]++; | |
112 | memcpy(r->s, s, r->m.k * sizeof(dig)); | |
113 | } | |
114 | ||
115 | static ratectx *rate_new(const mm *m, const dig *s) | |
116 | { | |
117 | ratectx *r = rate_alloc(m); | |
409fd535 | 118 | |
7a869046 MW |
119 | rate_init(r, s); |
120 | return (r); | |
121 | } | |
122 | ||
123 | static void rate(const ratectx *r, const dig *g, unsigned *b, unsigned *w) | |
124 | { | |
125 | unsigned i; | |
126 | unsigned k = r->m.k, n = r->m.n; | |
127 | dig *v = r->t; | |
128 | dig *vv = v + n; | |
129 | const dig *s = r->s; | |
130 | unsigned bb = 0, ww = 0; | |
131 | ||
132 | memset(v, 0, n * sizeof(dig)); | |
133 | memcpy(vv, r->v, n * sizeof(dig)); | |
134 | for (i = 0; i < k; i++) { | |
135 | if (g[i] != s[i]) | |
136 | v[g[i]]++; | |
137 | else { | |
138 | vv[g[i]]--; | |
139 | bb++; | |
140 | } | |
141 | } | |
142 | for (i = 0; i < n; i++) | |
143 | ww += v[i] < vv[i] ? v[i] : vv[i]; | |
144 | *b = bb; | |
145 | *w = ww; | |
146 | } | |
147 | ||
409fd535 | 148 | static void rate_free(ratectx *r) { xfree(r->v); DESTROY(r); } |
7a869046 MW |
149 | |
150 | /*----- Computer player ---------------------------------------------------*/ | |
151 | ||
152 | /* --- About the algorithms --- * | |
153 | * | |
154 | * At each stage, we attampt to choose the guess which will give us the most | |
155 | * information, regardless of the outcome. For each guess candidate, we | |
156 | * count the remaining possible codes for each outcome, and choose the | |
157 | * candidate with the least square sum. There are wrinkles. | |
158 | * | |
159 | * Firstly the number of possible guesses is large, and the number of | |
160 | * possible codes is huge too; and our algorithm takes time proportional to | |
161 | * the product of the two. However, a symbol we've never tried before is as | |
162 | * good as any other, so we can narrow the list of candidate guesses by | |
163 | * considering only %%\emph{prototypes}%% where we use only the smallest | |
164 | * untried symbol at any point to represent introducing any new symbol. The | |
165 | * number of initial prototypes is quite small. For the four-symbol game, | |
166 | * they are 0000, 0001, 0011, 0012, 0111, 0112, 0122, and 0123. | |
167 | * | |
168 | * Secondly, when the number of possible codes become small, we want to bias | |
169 | * the guess selection algorithm towards possible codes (so that we win if | |
170 | * we're lucky). Since the algorithm chooses the first guess with the lowest | |
171 | * sum-of-squares value, we simply run through the possible codes before | |
172 | * enumerating the prototype guesses. | |
173 | */ | |
174 | ||
175 | typedef struct cpc { | |
176 | mm m; /* Game parameters */ | |
177 | dig *s; /* n^k * k */ /* Remaining guesses */ | |
178 | size_t ns; /* Number of remaining guesses */ | |
179 | dig *bg; /* k */ /* Current best guess */ | |
180 | dig *t; /* k */ /* Scratch-space for prototype */ | |
181 | double bmax; /* Best guess least-squares score */ | |
182 | dig x, bx; /* Next unused symbol index */ | |
183 | size_t *v; /* (k + 1)^2 */ /* Bin counts for least-squares */ | |
184 | ratectx *r; /* Rate context for search */ | |
185 | } cpc; | |
186 | ||
187 | static void print_guess(const mm *m, const dig *d) | |
188 | { | |
189 | unsigned k = m->k, i; | |
190 | ||
191 | for (i = 0; i < k; i++) { | |
192 | if (i) putchar(' '); | |
193 | printf("%u", d[i]); | |
194 | } | |
195 | } | |
196 | ||
197 | static void dofep(cpc *c, void (*fn)(cpc *c, const dig *g, unsigned x), | |
198 | unsigned k, unsigned n, unsigned i, unsigned x) | |
199 | { | |
200 | unsigned j; | |
201 | dig *t = c->t; | |
202 | ||
203 | if (i == k) | |
204 | fn(c, c->t, x); | |
205 | else { | |
206 | for (j = 0; j < x; j++) { | |
207 | t[i] = j; | |
208 | dofep(c, fn, k, n, i + 1, x); | |
209 | } | |
210 | if (x < n) { | |
211 | t[i] = x; | |
212 | dofep(c, fn, k, n, i + 1, x + 1); | |
213 | } | |
214 | } | |
215 | } | |
216 | ||
217 | static void foreach_proto(cpc *c, void (*fn)(cpc *c, | |
218 | const dig *g, | |
219 | unsigned x)) | |
220 | { | |
221 | unsigned k = c->m.k, n = c->m.n; | |
409fd535 | 222 | |
7a869046 MW |
223 | dofep(c, fn, k, n, 0, c->x); |
224 | } | |
225 | ||
226 | static void try_guess(cpc *c, const dig *g, unsigned x) | |
227 | { | |
228 | size_t i; | |
229 | unsigned b, w; | |
230 | const dig *s; | |
231 | unsigned k = c->m.k; | |
232 | size_t *v = c->v; | |
233 | size_t *vp; | |
234 | double max; | |
235 | ||
236 | rate_init(c->r, g); | |
237 | memset(v, 0, (k + 1) * (k + 1) * sizeof(size_t)); | |
238 | for (i = c->ns, s = c->s; i; i--, s += k) { | |
239 | rate(c->r, s, &b, &w); | |
240 | v[b * (k + 1) + w]++; | |
241 | } | |
242 | max = 0; | |
243 | for (i = (k + 1) * (k + 1), vp = v; i; i--, vp++) | |
244 | max += (double)*vp * (double)*vp; | |
245 | if (c->bmax < 0 || max < c->bmax) { | |
246 | memcpy(c->bg, g, k * sizeof(dig)); | |
247 | c->bmax = max; | |
248 | c->bx = x; | |
249 | } | |
250 | } | |
251 | ||
252 | static void best_guess(cpc *c) | |
253 | { | |
254 | c->bmax = -1; | |
255 | if (c->ns < 1024) { | |
256 | unsigned k = c->m.k; | |
257 | const dig *s; | |
258 | size_t i; | |
259 | ||
260 | for (i = c->ns, s = c->s; i; i--, s += k) | |
261 | try_guess(c, s, c->x); | |
262 | } | |
263 | foreach_proto(c, try_guess); | |
264 | c->x = c->bx; | |
265 | } | |
266 | ||
267 | static void filter_guesses(cpc *c, const dig *g, unsigned b, unsigned w) | |
268 | { | |
269 | unsigned k = c->m.k; | |
270 | size_t i; | |
271 | const dig *s; | |
272 | unsigned bb, ww; | |
273 | dig *ss; | |
274 | ||
275 | rate_init(c->r, g); | |
276 | for (i = c->ns, s = ss = c->s; i; i--, s += k) { | |
277 | rate(c->r, s, &bb, &ww); | |
278 | if (b == bb && w == ww) { | |
279 | memmove(ss, s, k * sizeof(dig)); | |
280 | ss += k; | |
281 | } | |
282 | } | |
283 | c->ns = (ss - c->s) / k; | |
284 | } | |
285 | ||
286 | static size_t ipow(size_t b, size_t x) | |
287 | { | |
288 | size_t a = 1; | |
289 | while (x) { | |
290 | if (x & 1) | |
291 | a *= b; | |
292 | b *= b; | |
293 | x >>= 1; | |
294 | } | |
295 | return (a); | |
296 | } | |
297 | ||
298 | static void all_guesses(dig **ss, unsigned k, unsigned n, | |
299 | unsigned i, const dig *b) | |
300 | { | |
301 | unsigned j; | |
302 | ||
303 | if (i == k) { | |
304 | (*ss) += k; | |
305 | return; | |
306 | } | |
307 | for (j = 0; j < n; j++) { | |
308 | dig *s = *ss; | |
309 | if (i) | |
310 | memcpy(*ss, b, i * sizeof(dig)); | |
311 | s[i] = j; | |
312 | all_guesses(ss, k, n, i + 1, s); | |
313 | } | |
314 | } | |
315 | ||
316 | #define THINK(what, how) do { \ | |
317 | clock_t _t0, _t1; \ | |
318 | fputs(what "...", stdout); \ | |
319 | fflush(stdout); \ | |
320 | _t0 = clock(); \ | |
321 | do how while (0); \ | |
322 | _t1 = clock(); \ | |
323 | printf(" done (%.2fs)\n", (_t1 - _t0)/(double)CLOCKS_PER_SEC); \ | |
324 | } while (0) | |
325 | ||
326 | static cpc *cpc_new(const mm *m) | |
327 | { | |
328 | cpc *c = CREATE(cpc); | |
329 | c->m = *m; | |
330 | c->ns = ipow(c->m.n, c->m.k); | |
331 | c->s = xmalloc((c->ns + 2) * c->m.k * sizeof(dig)); | |
332 | c->bg = c->s + c->ns * c->m.k; | |
333 | c->t = c->bg + c->m.k; | |
334 | c->x = 0; | |
335 | c->v = xmalloc((c->m.k + 1) * (c->m.k + 1) * sizeof(size_t)); | |
336 | c->r = rate_alloc(m); | |
337 | THINK("Setting up", { | |
338 | dig *ss = c->s; all_guesses(&ss, c->m.k, c->m.n, 0, 0); | |
339 | }); | |
340 | return (c); | |
341 | } | |
342 | ||
343 | static void cpc_free(cpc *c) | |
344 | { | |
345 | xfree(c->s); | |
346 | xfree(c->v); | |
347 | rate_free(c->r); | |
348 | DESTROY(c); | |
349 | } | |
350 | ||
351 | static void cp_rate(void *r, const dig *g, unsigned *b, unsigned *w) | |
409fd535 | 352 | { rate(r, g, b, w); } |
7a869046 MW |
353 | |
354 | static const dig *cp_guess(void *cc) | |
355 | { | |
356 | cpc *c = cc; | |
357 | ||
358 | if (c->ns == 0) { | |
359 | printf("Liar! All solutions ruled out.\n"); | |
360 | return (0); | |
361 | } | |
362 | if (c->ns == 1) { | |
363 | fputs("Done! Solution is ", stdout); | |
364 | print_guess(&c->m, c->s); | |
365 | putchar('\n'); | |
366 | return (c->s); | |
367 | } | |
368 | printf("(Possible solutions remaining = %lu)\n", | |
369 | (unsigned long)c->ns); | |
370 | if (c->ns < 32) { | |
371 | const dig *s; | |
372 | size_t i; | |
373 | for (i = c->ns, s = c->s; i; i--, s += c->m.k) { | |
374 | printf(" %2lu: ", (unsigned long)(c->ns - i + 1)); | |
375 | print_guess(&c->m, s); | |
376 | putchar('\n'); | |
377 | } | |
378 | } | |
379 | THINK("Pondering", { | |
380 | best_guess(c); | |
381 | }); | |
382 | return (c->bg); | |
383 | } | |
384 | ||
385 | static void cp_update(void *cc, const dig *g, unsigned b, unsigned w) | |
386 | { | |
387 | cpc *c = cc; | |
388 | fputs("My guess = ", stdout); | |
389 | print_guess(&c->m, g); | |
390 | printf("; rating = %u black, %u white\n", b, w); | |
391 | THINK("Filtering", { | |
392 | filter_guesses(c, g, b, w); | |
393 | }); | |
394 | } | |
395 | ||
396 | /*----- Human player ------------------------------------------------------*/ | |
397 | ||
398 | typedef struct hpc { | |
399 | mm m; | |
400 | dig *t; | |
401 | } hpc; | |
402 | ||
403 | static hpc *hpc_new(const mm *m) | |
404 | { | |
405 | hpc *h = CREATE(hpc); | |
406 | h->t = xmalloc(m->k * sizeof(dig)); | |
407 | h->m = *m; | |
408 | return (h); | |
409 | } | |
410 | ||
411 | static void hpc_free(hpc *h) | |
412 | { | |
413 | xfree(h->t); | |
414 | DESTROY(h); | |
415 | } | |
416 | ||
417 | static void hp_rate(void *mp, const dig *g, unsigned *b, unsigned *w) | |
418 | { | |
419 | mm *m = mp; | |
420 | fputs("Guess = ", stdout); | |
421 | print_guess(m, g); | |
422 | printf("; rating: "); | |
423 | fflush(stdout); | |
424 | scanf("%u %u", b, w); | |
425 | } | |
426 | ||
427 | static const dig *hp_guess(void *hh) | |
428 | { | |
429 | hpc *h = hh; | |
430 | unsigned i; | |
431 | ||
432 | fputs("Your guess: ", stdout); | |
433 | fflush(stdout); | |
434 | for (i = 0; i < h->m.k; i++) { | |
435 | unsigned x; | |
436 | scanf("%u", &x); | |
437 | h->t[i] = x; | |
438 | } | |
439 | return (h->t); | |
440 | } | |
441 | ||
442 | static void hp_update(void *cc, const dig *g, unsigned b, unsigned w) | |
443 | { | |
444 | printf("Rating = %u black, %u white\n", b, w); | |
445 | } | |
446 | ||
447 | /*----- Solver player -----------------------------------------------------*/ | |
448 | ||
449 | typedef struct spc { | |
450 | cpc *c; | |
451 | hpc *h; | |
452 | int i; | |
453 | } spc; | |
454 | ||
455 | static spc *spc_new(const mm *m) | |
456 | { | |
457 | spc *s = CREATE(spc); | |
458 | s->c = cpc_new(m); | |
459 | s->h = hpc_new(m); | |
460 | s->i = 0; | |
461 | return (s); | |
462 | } | |
463 | ||
464 | static void spc_free(spc *s) | |
465 | { | |
466 | cpc_free(s->c); | |
467 | hpc_free(s->h); | |
468 | DESTROY(s); | |
469 | } | |
470 | ||
471 | static const dig *sp_guess(void *ss) | |
472 | { | |
473 | spc *s = ss; | |
474 | hpc *h = s->h; | |
475 | unsigned i; | |
476 | int ch; | |
477 | ||
478 | again: | |
479 | if (s->i) | |
480 | return (cp_guess(s->c)); | |
481 | ||
482 | fputs("Your guess (dot for end): ", stdout); | |
483 | fflush(stdout); | |
484 | do ch = getchar(); while (isspace(ch)); | |
485 | if (!isdigit(ch)) { s->i = 1; goto again; } | |
486 | ungetc(ch, stdin); | |
487 | for (i = 0; i < h->m.k; i++) { | |
488 | unsigned x; | |
489 | scanf("%u", &x); | |
490 | h->t[i] = x; | |
491 | } | |
492 | return (h->t); | |
493 | } | |
494 | ||
495 | static void sp_update(void *ss, const dig *g, unsigned b, unsigned w) | |
409fd535 | 496 | { spc *s = ss; cp_update(s->c, g, b, w); } |
7a869046 MW |
497 | |
498 | /*----- Main game logic ---------------------------------------------------*/ | |
499 | ||
500 | static int play(const mm *m, | |
501 | void (*ratefn)(void *rr, const dig *g, | |
502 | unsigned *b, unsigned *w), | |
503 | void *rr, | |
504 | const dig *(*guessfn)(void *gg), | |
505 | void (*updatefn)(void *gg, const dig *g, | |
506 | unsigned b, unsigned w), | |
507 | void *gg) | |
508 | { | |
509 | unsigned b, w; | |
510 | const dig *g; | |
511 | unsigned i; | |
512 | ||
513 | i = 0; | |
514 | for (;;) { | |
515 | i++; | |
516 | g = guessfn(gg); | |
517 | if (!g) | |
518 | return (-1); | |
519 | ratefn(rr, g, &b, &w); | |
520 | if (b == m->k) | |
521 | return (i); | |
522 | updatefn(gg, g, b, w); | |
523 | } | |
524 | } | |
525 | ||
526 | int main(int argc, char *argv[]) | |
527 | { | |
528 | unsigned h = 0; | |
529 | void *rr = 0; | |
530 | void (*ratefn)(void *rr, const dig *g, unsigned *b, unsigned *w) = 0; | |
531 | mm m; | |
532 | int n; | |
533 | ||
534 | ego(argv[0]); | |
535 | for (;;) { | |
536 | static struct option opt[] = { | |
537 | { "computer", 0, 0, 'C' }, | |
538 | { "human", 0, 0, 'H' }, | |
539 | { "solver", 0, 0, 'S' }, | |
540 | { 0, 0, 0, 0 } | |
541 | }; | |
542 | int i = mdwopt(argc, argv, "CHS", opt, 0, 0, 0); | |
543 | if (i < 0) | |
544 | break; | |
545 | switch (i) { | |
546 | case 'C': h = 0; break; | |
547 | case 'H': h = 1; break; | |
548 | case 'S': h = 2; break; | |
549 | default: | |
550 | exit(1); | |
551 | } | |
552 | } | |
553 | if (argc - optind == 0) { | |
554 | m.k = 4; | |
555 | m.n = 6; | |
556 | } else if (argc - optind < 2) | |
557 | die(1, "bad parameters"); | |
558 | else { | |
559 | m.k = atoi(argv[optind++]); | |
560 | m.n = atoi(argv[optind++]); | |
561 | if (argc - optind >= m.k) { | |
562 | dig *s = xmalloc(m.k * sizeof(dig)); | |
563 | int i; | |
564 | for (i = 0; i < m.k; i++) | |
565 | s[i] = atoi(argv[optind++]); | |
566 | rr = rate_new(&m, s); | |
567 | ratefn = cp_rate; | |
568 | xfree(s); | |
569 | } | |
570 | if (argc != optind) | |
571 | die(1, "bad parameters"); | |
572 | } | |
573 | ||
574 | switch (h) { | |
575 | case 1: { | |
576 | hpc *hh = hpc_new(&m); | |
577 | if (!rr) { | |
578 | dig *s = xmalloc(m.k * sizeof(dig)); | |
579 | int i; | |
580 | srand(time(0)); | |
581 | for (i = 0; i < m.k; i++) | |
582 | s[i] = rand() % m.n; | |
583 | rr = rate_new(&m, s); | |
584 | ratefn = cp_rate; | |
585 | xfree(s); | |
586 | } | |
587 | n = play(&m, ratefn, rr, hp_guess, hp_update, hh); | |
588 | hpc_free(hh); | |
589 | } break; | |
590 | case 0: { | |
591 | cpc *cc = cpc_new(&m); | |
592 | if (rr) | |
593 | n = play(&m, ratefn, rr, cp_guess, cp_update, cc); | |
594 | else | |
595 | n = play(&m, hp_rate, &m, cp_guess, cp_update, cc); | |
596 | cpc_free(cc); | |
597 | } break; | |
598 | case 2: { | |
599 | spc *ss = spc_new(&m); | |
600 | n = play(&m, hp_rate, &m, sp_guess, sp_update, ss); | |
601 | spc_free(ss); | |
602 | } break; | |
603 | default: | |
604 | abort(); | |
605 | } | |
606 | if (n > 0) | |
607 | printf("Solved in %d guesses\n", n); | |
608 | else | |
609 | die(1, "gave up"); | |
610 | return (0); | |
611 | } | |
612 | ||
613 | /*----- That's all, folks -------------------------------------------------*/ |