f278dcf4 |
1 | /* |
2 | * This program implements a breadth-first search which |
3 | * exhaustively solves the Countdown numbers game, and related |
4 | * games with slightly different rule sets such as `Flippo'. |
5 | * |
6 | * Currently it is simply a standalone command-line utility to |
7 | * which you provide a set of numbers and it tells you everything |
8 | * it can make together with how many different ways it can be |
9 | * made. I would like ultimately to turn it into the generator for |
10 | * a Puzzles puzzle, but I haven't even started on writing a |
11 | * Puzzles user interface yet. |
12 | */ |
13 | |
14 | /* |
15 | * TODO: |
16 | * |
17 | * - start thinking about difficulty ratings |
18 | * + anything involving associative operations will be flagged |
19 | * as many-paths because of the associative options (e.g. |
20 | * 2*3*4 can be (2*3)*4 or 2*(3*4), or indeed (2*4)*3). This |
21 | * is probably a _good_ thing, since those are unusually |
22 | * easy. |
23 | * + tree-structured calculations ((a*b)/(c+d)) have multiple |
24 | * paths because the independent branches of the tree can be |
25 | * evaluated in either order, whereas straight-line |
26 | * calculations with no branches will be considered easier. |
27 | * Can we do anything about this? It's certainly not clear to |
28 | * me that tree-structure calculations are _easier_, although |
29 | * I'm also not convinced they're harder. |
30 | * + I think for a realistic difficulty assessment we must also |
31 | * consider the `obviousness' of the arithmetic operations in |
32 | * some heuristic sense, and also (in Countdown) how many |
33 | * numbers ended up being used. |
34 | * - actually try some generations |
35 | * - at this point we're probably ready to start on the Puzzles |
36 | * integration. |
37 | */ |
38 | |
39 | #include <stdio.h> |
ed35622c |
40 | #include <string.h> |
f278dcf4 |
41 | #include <limits.h> |
42 | #include <assert.h> |
ed35622c |
43 | #include <math.h> |
f278dcf4 |
44 | |
45 | #include "puzzles.h" |
46 | #include "tree234.h" |
47 | |
48 | /* |
49 | * To search for numbers we can make, we employ a breadth-first |
50 | * search across the space of sets of input numbers. That is, for |
51 | * example, we start with the set (3,6,25,50,75,100); we apply |
52 | * moves which involve combining two numbers (e.g. adding the 50 |
53 | * and the 75 takes us to the set (3,6,25,100,125); and then we see |
54 | * if we ever end up with a set containing (say) 952. |
55 | * |
56 | * If the rules are changed so that all the numbers must be used, |
57 | * this is easy to adjust to: we simply see if we end up with a set |
58 | * containing _only_ (say) 952. |
59 | * |
60 | * Obviously, we can vary the rules about permitted arithmetic |
61 | * operations simply by altering the set of valid moves in the bfs. |
62 | * However, there's one common rule in this sort of puzzle which |
63 | * takes a little more thought, and that's _concatenation_. For |
64 | * example, if you are given (say) four 4s and required to make 10, |
65 | * you are permitted to combine two of the 4s into a 44 to begin |
66 | * with, making (44-4)/4 = 10. However, you are generally not |
67 | * allowed to concatenate two numbers that _weren't_ both in the |
68 | * original input set (you couldn't multiply two 4s to get 16 and |
69 | * then concatenate a 4 on to it to make 164), so concatenation is |
70 | * not an operation which is valid in all situations. |
71 | * |
72 | * We could enforce this restriction by storing a flag alongside |
73 | * each number indicating whether or not it's an original number; |
74 | * the rules being that concatenation of two numbers is only valid |
75 | * if they both have the original flag, and that its output _also_ |
76 | * has the original flag (so that you can concatenate three 4s into |
77 | * a 444), but that applying any other arithmetic operation clears |
78 | * the original flag on the output. However, we can get marginally |
79 | * simpler than that by observing that since concatenation has to |
80 | * happen to a number before any other operation, we can simply |
81 | * place all the concatenations at the start of the search. In |
82 | * other words, we have a global flag on an entire number _set_ |
83 | * which indicates whether we are still permitted to perform |
84 | * concatenations; if so, we can concatenate any of the numbers in |
85 | * that set. Performing any other operation clears the flag. |
86 | */ |
87 | |
88 | #define SETFLAG_CONCAT 1 /* we can do concatenation */ |
89 | |
90 | struct sets; |
91 | |
ed35622c |
92 | struct ancestor { |
93 | struct set *prev; /* index of ancestor set in set list */ |
94 | unsigned char pa, pb, po, pr; /* operation that got here from prev */ |
95 | }; |
96 | |
f278dcf4 |
97 | struct set { |
98 | int *numbers; /* rationals stored as n,d pairs */ |
99 | short nnumbers; /* # of rationals, so half # of ints */ |
100 | short flags; /* SETFLAG_CONCAT only, at present */ |
f278dcf4 |
101 | int npaths; /* number of ways to reach this set */ |
ed35622c |
102 | struct ancestor a; /* primary ancestor */ |
103 | struct ancestor *as; /* further ancestors, if we care */ |
104 | int nas, assize; |
f278dcf4 |
105 | }; |
106 | |
107 | struct output { |
108 | int number; |
109 | struct set *set; |
110 | int index; /* which number in the set is it? */ |
111 | int npaths; /* number of ways to reach this */ |
112 | }; |
113 | |
114 | #define SETLISTLEN 1024 |
115 | #define NUMBERLISTLEN 32768 |
116 | #define OUTPUTLISTLEN 1024 |
117 | struct operation; |
118 | struct sets { |
119 | struct set **setlists; |
120 | int nsets, nsetlists, setlistsize; |
121 | tree234 *settree; |
122 | int **numberlists; |
123 | int nnumbers, nnumberlists, numberlistsize; |
124 | struct output **outputlists; |
125 | int noutputs, noutputlists, outputlistsize; |
126 | tree234 *outputtree; |
127 | const struct operation *const *ops; |
128 | }; |
129 | |
130 | #define OPFLAG_NEEDS_CONCAT 1 |
131 | #define OPFLAG_KEEPS_CONCAT 2 |
ed35622c |
132 | #define OPFLAG_UNARY 4 |
133 | #define OPFLAG_UNARYPFX 8 |
f278dcf4 |
134 | |
135 | struct operation { |
136 | /* |
137 | * Most operations should be shown in the output working, but |
138 | * concatenation should not; we just take the result of the |
139 | * concatenation and assume that it's obvious how it was |
140 | * derived. |
141 | */ |
142 | int display; |
143 | |
144 | /* |
145 | * Text display of the operator. |
146 | */ |
147 | char *text; |
148 | |
149 | /* |
150 | * Flags dictating when the operator can be applied. |
151 | */ |
152 | int flags; |
153 | |
154 | /* |
155 | * Priority of the operator (for avoiding unnecessary |
156 | * parentheses when formatting it into a string). |
157 | */ |
158 | int priority; |
159 | |
160 | /* |
161 | * Associativity of the operator. Bit 0 means we need parens |
162 | * when the left operand of one of these operators is another |
163 | * instance of it, e.g. (2^3)^4. Bit 1 means we need parens |
164 | * when the right operand is another instance of the same |
165 | * operator, e.g. 2-(3-4). Thus: |
166 | * |
167 | * - this field is 0 for a fully associative operator, since |
168 | * we never need parens. |
169 | * - it's 1 for a right-associative operator. |
170 | * - it's 2 for a left-associative operator. |
171 | * - it's 3 for a _non_-associative operator (which always |
172 | * uses parens just to be sure). |
173 | */ |
174 | int assoc; |
175 | |
176 | /* |
177 | * Whether the operator is commutative. Saves time in the |
178 | * search if we don't have to try it both ways round. |
179 | */ |
180 | int commutes; |
181 | |
182 | /* |
183 | * Function which implements the operator. Returns TRUE on |
184 | * success, FALSE on failure. Takes two rationals and writes |
185 | * out a third. |
186 | */ |
187 | int (*perform)(int *a, int *b, int *output); |
188 | }; |
189 | |
190 | struct rules { |
191 | const struct operation *const *ops; |
192 | int use_all; |
193 | }; |
194 | |
195 | #define MUL(r, a, b) do { \ |
196 | (r) = (a) * (b); \ |
197 | if ((b) && (a) && (r) / (b) != (a)) return FALSE; \ |
198 | } while (0) |
199 | |
200 | #define ADD(r, a, b) do { \ |
201 | (r) = (a) + (b); \ |
202 | if ((a) > 0 && (b) > 0 && (r) < 0) return FALSE; \ |
203 | if ((a) < 0 && (b) < 0 && (r) > 0) return FALSE; \ |
204 | } while (0) |
205 | |
206 | #define OUT(output, n, d) do { \ |
207 | int g = gcd((n),(d)); \ |
ed35622c |
208 | if (g < 0) g = -g; \ |
f278dcf4 |
209 | if ((d) < 0) g = -g; \ |
ed35622c |
210 | if (g == -1 && (n) < -INT_MAX) return FALSE; \ |
211 | if (g == -1 && (d) < -INT_MAX) return FALSE; \ |
f278dcf4 |
212 | (output)[0] = (n)/g; \ |
213 | (output)[1] = (d)/g; \ |
214 | assert((output)[1] > 0); \ |
215 | } while (0) |
216 | |
217 | static int gcd(int x, int y) |
218 | { |
219 | while (x != 0 && y != 0) { |
220 | int t = x; |
221 | x = y; |
222 | y = t % y; |
223 | } |
224 | |
225 | return abs(x + y); /* i.e. whichever one isn't zero */ |
226 | } |
227 | |
228 | static int perform_add(int *a, int *b, int *output) |
229 | { |
230 | int at, bt, tn, bn; |
231 | /* |
232 | * a0/a1 + b0/b1 = (a0*b1 + b0*a1) / (a1*b1) |
233 | */ |
234 | MUL(at, a[0], b[1]); |
235 | MUL(bt, b[0], a[1]); |
236 | ADD(tn, at, bt); |
237 | MUL(bn, a[1], b[1]); |
238 | OUT(output, tn, bn); |
239 | return TRUE; |
240 | } |
241 | |
242 | static int perform_sub(int *a, int *b, int *output) |
243 | { |
244 | int at, bt, tn, bn; |
245 | /* |
246 | * a0/a1 - b0/b1 = (a0*b1 - b0*a1) / (a1*b1) |
247 | */ |
248 | MUL(at, a[0], b[1]); |
249 | MUL(bt, b[0], a[1]); |
250 | ADD(tn, at, -bt); |
251 | MUL(bn, a[1], b[1]); |
252 | OUT(output, tn, bn); |
253 | return TRUE; |
254 | } |
255 | |
256 | static int perform_mul(int *a, int *b, int *output) |
257 | { |
258 | int tn, bn; |
259 | /* |
260 | * a0/a1 * b0/b1 = (a0*b0) / (a1*b1) |
261 | */ |
262 | MUL(tn, a[0], b[0]); |
263 | MUL(bn, a[1], b[1]); |
264 | OUT(output, tn, bn); |
265 | return TRUE; |
266 | } |
267 | |
268 | static int perform_div(int *a, int *b, int *output) |
269 | { |
270 | int tn, bn; |
271 | |
272 | /* |
273 | * Division by zero is outlawed. |
274 | */ |
275 | if (b[0] == 0) |
276 | return FALSE; |
277 | |
278 | /* |
279 | * a0/a1 / b0/b1 = (a0*b1) / (a1*b0) |
280 | */ |
281 | MUL(tn, a[0], b[1]); |
282 | MUL(bn, a[1], b[0]); |
283 | OUT(output, tn, bn); |
284 | return TRUE; |
285 | } |
286 | |
287 | static int perform_exact_div(int *a, int *b, int *output) |
288 | { |
289 | int tn, bn; |
290 | |
291 | /* |
292 | * Division by zero is outlawed. |
293 | */ |
294 | if (b[0] == 0) |
295 | return FALSE; |
296 | |
297 | /* |
298 | * a0/a1 / b0/b1 = (a0*b1) / (a1*b0) |
299 | */ |
300 | MUL(tn, a[0], b[1]); |
301 | MUL(bn, a[1], b[0]); |
302 | OUT(output, tn, bn); |
303 | |
304 | /* |
305 | * Exact division means we require the result to be an integer. |
306 | */ |
307 | return (output[1] == 1); |
308 | } |
309 | |
310 | static int perform_concat(int *a, int *b, int *output) |
311 | { |
312 | int t1, t2, p10; |
313 | |
314 | /* |
ed35622c |
315 | * We can't concatenate anything which isn't a non-negative |
316 | * integer. |
f278dcf4 |
317 | */ |
ed35622c |
318 | if (a[1] != 1 || b[1] != 1 || a[0] < 0 || b[0] < 0) |
f278dcf4 |
319 | return FALSE; |
320 | |
321 | /* |
322 | * For concatenation, we can safely assume leading zeroes |
323 | * aren't an issue. It isn't clear whether they `should' be |
324 | * allowed, but it turns out not to matter: concatenating a |
325 | * leading zero on to a number in order to harmlessly get rid |
326 | * of the zero is never necessary because unwanted zeroes can |
327 | * be disposed of by adding them to something instead. So we |
328 | * disallow them always. |
329 | * |
330 | * The only other possibility is that you might want to |
331 | * concatenate a leading zero on to something and then |
332 | * concatenate another non-zero digit on to _that_ (to make, |
333 | * for example, 106); but that's also unnecessary, because you |
334 | * can make 106 just as easily by concatenating the 0 on to the |
335 | * _end_ of the 1 first. |
336 | */ |
337 | if (a[0] == 0) |
338 | return FALSE; |
339 | |
340 | /* |
341 | * Find the smallest power of ten strictly greater than b. This |
342 | * is the power of ten by which we'll multiply a. |
343 | * |
344 | * Special case: we must multiply a by at least 10, even if b |
345 | * is zero. |
346 | */ |
347 | p10 = 10; |
348 | while (p10 <= (INT_MAX/10) && p10 <= b[0]) |
349 | p10 *= 10; |
350 | if (p10 > INT_MAX/10) |
351 | return FALSE; /* integer overflow */ |
352 | MUL(t1, p10, a[0]); |
353 | ADD(t2, t1, b[0]); |
354 | OUT(output, t2, 1); |
355 | return TRUE; |
356 | } |
357 | |
ed35622c |
358 | #define IPOW(ret, x, y) do { \ |
359 | int ipow_limit = (y); \ |
360 | if ((x) == 1 || (x) == 0) ipow_limit = 1; \ |
361 | else if ((x) == -1) ipow_limit &= 1; \ |
362 | (ret) = 1; \ |
363 | while (ipow_limit-- > 0) { \ |
364 | int tmp; \ |
365 | MUL(tmp, ret, x); \ |
366 | ret = tmp; \ |
367 | } \ |
368 | } while (0) |
369 | |
370 | static int perform_exp(int *a, int *b, int *output) |
371 | { |
372 | int an, ad, xn, xd, limit, t, i; |
373 | |
374 | /* |
375 | * Exponentiation is permitted if the result is rational. This |
376 | * means that: |
377 | * |
378 | * - first we see whether we can take the (denominator-of-b)th |
379 | * root of a and get a rational; if not, we give up. |
380 | * |
381 | * - then we do take that root of a |
382 | * |
383 | * - then we multiply by itself (numerator-of-b) times. |
384 | */ |
385 | if (b[1] > 1) { |
386 | an = 0.5 + pow(a[0], 1.0/b[1]); |
387 | ad = 0.5 + pow(a[1], 1.0/b[1]); |
388 | IPOW(xn, an, b[1]); |
389 | IPOW(xd, ad, b[1]); |
390 | if (xn != a[0] || xd != a[1]) |
391 | return FALSE; |
392 | } else { |
393 | an = a[0]; |
394 | ad = a[1]; |
395 | } |
396 | if (b[0] >= 0) { |
397 | IPOW(xn, an, b[0]); |
398 | IPOW(xd, ad, b[0]); |
399 | } else { |
400 | IPOW(xd, an, -b[0]); |
401 | IPOW(xn, ad, -b[0]); |
402 | } |
403 | if (xd == 0) |
404 | return FALSE; |
405 | |
406 | OUT(output, xn, xd); |
407 | return TRUE; |
408 | } |
409 | |
410 | static int perform_factorial(int *a, int *b, int *output) |
411 | { |
412 | int ret, t, i; |
413 | |
414 | /* |
415 | * Factorials of non-negative integers are permitted. |
416 | */ |
417 | if (a[1] != 1 || a[0] < 0) |
418 | return FALSE; |
419 | |
420 | ret = 1; |
421 | for (i = 1; i <= a[0]; i++) { |
422 | MUL(t, ret, i); |
423 | ret = t; |
424 | } |
425 | |
426 | OUT(output, ret, 1); |
427 | return TRUE; |
428 | } |
429 | |
f278dcf4 |
430 | const static struct operation op_add = { |
431 | TRUE, "+", 0, 10, 0, TRUE, perform_add |
432 | }; |
433 | const static struct operation op_sub = { |
434 | TRUE, "-", 0, 10, 2, FALSE, perform_sub |
435 | }; |
436 | const static struct operation op_mul = { |
437 | TRUE, "*", 0, 20, 0, TRUE, perform_mul |
438 | }; |
439 | const static struct operation op_div = { |
440 | TRUE, "/", 0, 20, 2, FALSE, perform_div |
441 | }; |
442 | const static struct operation op_xdiv = { |
443 | TRUE, "/", 0, 20, 2, FALSE, perform_exact_div |
444 | }; |
445 | const static struct operation op_concat = { |
446 | FALSE, "", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, |
447 | 1000, 0, FALSE, perform_concat |
448 | }; |
ed35622c |
449 | const static struct operation op_exp = { |
450 | TRUE, "^", 0, 30, 1, FALSE, perform_exp |
451 | }; |
452 | const static struct operation op_factorial = { |
453 | TRUE, "!", OPFLAG_UNARY, 40, 0, FALSE, perform_factorial |
454 | }; |
f278dcf4 |
455 | |
456 | /* |
457 | * In Countdown, divisions resulting in fractions are disallowed. |
458 | * http://www.askoxford.com/wordgames/countdown/rules/ |
459 | */ |
460 | const static struct operation *const ops_countdown[] = { |
461 | &op_add, &op_mul, &op_sub, &op_xdiv, NULL |
462 | }; |
463 | const static struct rules rules_countdown = { |
464 | ops_countdown, FALSE |
465 | }; |
466 | |
467 | /* |
468 | * A slightly different rule set which handles the reasonably well |
469 | * known puzzle of making 24 using two 3s and two 8s. For this we |
470 | * need rational rather than integer division. |
471 | */ |
472 | const static struct operation *const ops_3388[] = { |
473 | &op_add, &op_mul, &op_sub, &op_div, NULL |
474 | }; |
475 | const static struct rules rules_3388 = { |
476 | ops_3388, TRUE |
477 | }; |
478 | |
479 | /* |
480 | * A still more permissive rule set usable for the four-4s problem |
481 | * and similar things. Permits concatenation. |
482 | */ |
483 | const static struct operation *const ops_four4s[] = { |
484 | &op_add, &op_mul, &op_sub, &op_div, &op_concat, NULL |
485 | }; |
486 | const static struct rules rules_four4s = { |
487 | ops_four4s, TRUE |
488 | }; |
489 | |
ed35622c |
490 | /* |
491 | * The most permissive ruleset I can think of. Permits |
492 | * exponentiation, and also silly unary operators like factorials. |
493 | */ |
494 | const static struct operation *const ops_anythinggoes[] = { |
495 | &op_add, &op_mul, &op_sub, &op_div, &op_concat, &op_exp, &op_factorial, NULL |
496 | }; |
497 | const static struct rules rules_anythinggoes = { |
498 | ops_anythinggoes, TRUE |
499 | }; |
500 | |
f278dcf4 |
501 | #define ratcmp(a,op,b) ( (long long)(a)[0] * (b)[1] op \ |
502 | (long long)(b)[0] * (a)[1] ) |
503 | |
504 | static int addtoset(struct set *set, int newnumber[2]) |
505 | { |
506 | int i, j; |
507 | |
508 | /* Find where we want to insert the new number */ |
509 | for (i = 0; i < set->nnumbers && |
510 | ratcmp(set->numbers+2*i, <, newnumber); i++); |
511 | |
512 | /* Move everything else up */ |
513 | for (j = set->nnumbers; j > i; j--) { |
514 | set->numbers[2*j] = set->numbers[2*j-2]; |
515 | set->numbers[2*j+1] = set->numbers[2*j-1]; |
516 | } |
517 | |
518 | /* Insert the new number */ |
519 | set->numbers[2*i] = newnumber[0]; |
520 | set->numbers[2*i+1] = newnumber[1]; |
521 | |
522 | set->nnumbers++; |
523 | |
524 | return i; |
525 | } |
526 | |
527 | #define ensure(array, size, newlen, type) do { \ |
528 | if ((newlen) > (size)) { \ |
529 | (size) = (newlen) + 512; \ |
530 | (array) = sresize((array), (size), type); \ |
531 | } \ |
532 | } while (0) |
533 | |
534 | static int setcmp(void *av, void *bv) |
535 | { |
536 | struct set *a = (struct set *)av; |
537 | struct set *b = (struct set *)bv; |
538 | int i; |
539 | |
540 | if (a->nnumbers < b->nnumbers) |
541 | return -1; |
542 | else if (a->nnumbers > b->nnumbers) |
543 | return +1; |
544 | |
545 | if (a->flags < b->flags) |
546 | return -1; |
547 | else if (a->flags > b->flags) |
548 | return +1; |
549 | |
550 | for (i = 0; i < a->nnumbers; i++) { |
551 | if (ratcmp(a->numbers+2*i, <, b->numbers+2*i)) |
552 | return -1; |
553 | else if (ratcmp(a->numbers+2*i, >, b->numbers+2*i)) |
554 | return +1; |
555 | } |
556 | |
557 | return 0; |
558 | } |
559 | |
560 | static int outputcmp(void *av, void *bv) |
561 | { |
562 | struct output *a = (struct output *)av; |
563 | struct output *b = (struct output *)bv; |
564 | |
565 | if (a->number < b->number) |
566 | return -1; |
567 | else if (a->number > b->number) |
568 | return +1; |
569 | |
570 | return 0; |
571 | } |
572 | |
573 | static int outputfindcmp(void *av, void *bv) |
574 | { |
575 | int *a = (int *)av; |
576 | struct output *b = (struct output *)bv; |
577 | |
578 | if (*a < b->number) |
579 | return -1; |
580 | else if (*a > b->number) |
581 | return +1; |
582 | |
583 | return 0; |
584 | } |
585 | |
ed35622c |
586 | static void addset(struct sets *s, struct set *set, int multiple, |
587 | struct set *prev, int pa, int po, int pb, int pr) |
f278dcf4 |
588 | { |
589 | struct set *s2; |
590 | int npaths = (prev ? prev->npaths : 1); |
591 | |
592 | assert(set == s->setlists[s->nsets / SETLISTLEN] + s->nsets % SETLISTLEN); |
593 | s2 = add234(s->settree, set); |
594 | if (s2 == set) { |
595 | /* |
596 | * New set added to the tree. |
597 | */ |
ed35622c |
598 | set->a.prev = prev; |
599 | set->a.pa = pa; |
600 | set->a.po = po; |
601 | set->a.pb = pb; |
602 | set->a.pr = pr; |
f278dcf4 |
603 | set->npaths = npaths; |
604 | s->nsets++; |
605 | s->nnumbers += 2 * set->nnumbers; |
ed35622c |
606 | set->as = NULL; |
607 | set->nas = set->assize = 0; |
f278dcf4 |
608 | } else { |
609 | /* |
ed35622c |
610 | * Rediscovered an existing set. Update its npaths. |
f278dcf4 |
611 | */ |
612 | s2->npaths += npaths; |
ed35622c |
613 | /* |
614 | * And optionally enter it as an additional ancestor. |
615 | */ |
616 | if (multiple) { |
617 | if (s2->nas >= s2->assize) { |
618 | s2->assize = s2->nas * 3 / 2 + 4; |
619 | s2->as = sresize(s2->as, s2->assize, struct ancestor); |
620 | } |
621 | s2->as[s2->nas].prev = prev; |
622 | s2->as[s2->nas].pa = pa; |
623 | s2->as[s2->nas].po = po; |
624 | s2->as[s2->nas].pb = pb; |
625 | s2->as[s2->nas].pr = pr; |
626 | s2->nas++; |
627 | } |
f278dcf4 |
628 | } |
629 | } |
630 | |
631 | static struct set *newset(struct sets *s, int nnumbers, int flags) |
632 | { |
633 | struct set *sn; |
634 | |
635 | ensure(s->setlists, s->setlistsize, s->nsets/SETLISTLEN+1, struct set *); |
636 | while (s->nsetlists <= s->nsets / SETLISTLEN) |
637 | s->setlists[s->nsetlists++] = snewn(SETLISTLEN, struct set); |
638 | sn = s->setlists[s->nsets / SETLISTLEN] + s->nsets % SETLISTLEN; |
639 | |
640 | if (s->nnumbers + nnumbers * 2 > s->nnumberlists * NUMBERLISTLEN) |
641 | s->nnumbers = s->nnumberlists * NUMBERLISTLEN; |
642 | ensure(s->numberlists, s->numberlistsize, |
643 | s->nnumbers/NUMBERLISTLEN+1, int *); |
644 | while (s->nnumberlists <= s->nnumbers / NUMBERLISTLEN) |
645 | s->numberlists[s->nnumberlists++] = snewn(NUMBERLISTLEN, int); |
646 | sn->numbers = s->numberlists[s->nnumbers / NUMBERLISTLEN] + |
647 | s->nnumbers % NUMBERLISTLEN; |
648 | |
649 | /* |
650 | * Start the set off empty. |
651 | */ |
652 | sn->nnumbers = 0; |
653 | |
654 | sn->flags = flags; |
655 | |
656 | return sn; |
657 | } |
658 | |
659 | static int addoutput(struct sets *s, struct set *ss, int index, int *n) |
660 | { |
661 | struct output *o, *o2; |
662 | |
663 | /* |
664 | * Target numbers are always integers. |
665 | */ |
666 | if (ss->numbers[2*index+1] != 1) |
667 | return FALSE; |
668 | |
669 | ensure(s->outputlists, s->outputlistsize, s->noutputs/OUTPUTLISTLEN+1, |
670 | struct output *); |
671 | while (s->noutputlists <= s->noutputs / OUTPUTLISTLEN) |
672 | s->outputlists[s->noutputlists++] = snewn(OUTPUTLISTLEN, |
673 | struct output); |
674 | o = s->outputlists[s->noutputs / OUTPUTLISTLEN] + |
675 | s->noutputs % OUTPUTLISTLEN; |
676 | |
677 | o->number = ss->numbers[2*index]; |
678 | o->set = ss; |
679 | o->index = index; |
680 | o->npaths = ss->npaths; |
681 | o2 = add234(s->outputtree, o); |
682 | if (o2 != o) { |
683 | o2->npaths += o->npaths; |
684 | } else { |
685 | s->noutputs++; |
686 | } |
687 | *n = o->number; |
688 | return TRUE; |
689 | } |
690 | |
691 | static struct sets *do_search(int ninputs, int *inputs, |
ed35622c |
692 | const struct rules *rules, int *target, |
693 | int multiple) |
f278dcf4 |
694 | { |
695 | struct sets *s; |
696 | struct set *sn; |
697 | int qpos, i; |
698 | const struct operation *const *ops = rules->ops; |
699 | |
700 | s = snew(struct sets); |
701 | s->setlists = NULL; |
702 | s->nsets = s->nsetlists = s->setlistsize = 0; |
703 | s->numberlists = NULL; |
704 | s->nnumbers = s->nnumberlists = s->numberlistsize = 0; |
705 | s->outputlists = NULL; |
706 | s->noutputs = s->noutputlists = s->outputlistsize = 0; |
707 | s->settree = newtree234(setcmp); |
708 | s->outputtree = newtree234(outputcmp); |
709 | s->ops = ops; |
710 | |
711 | /* |
712 | * Start with the input set. |
713 | */ |
714 | sn = newset(s, ninputs, SETFLAG_CONCAT); |
715 | for (i = 0; i < ninputs; i++) { |
716 | int newnumber[2]; |
717 | newnumber[0] = inputs[i]; |
718 | newnumber[1] = 1; |
719 | addtoset(sn, newnumber); |
720 | } |
ed35622c |
721 | addset(s, sn, multiple, NULL, 0, 0, 0, 0); |
f278dcf4 |
722 | |
723 | /* |
724 | * Now perform the breadth-first search: keep looping over sets |
725 | * until we run out of steam. |
726 | */ |
727 | qpos = 0; |
728 | while (qpos < s->nsets) { |
729 | struct set *ss = s->setlists[qpos / SETLISTLEN] + qpos % SETLISTLEN; |
730 | struct set *sn; |
731 | int i, j, k, m; |
732 | |
733 | /* |
734 | * Record all the valid output numbers in this state. We |
735 | * can always do this if there's only one number in the |
736 | * state; otherwise, we can only do it if we aren't |
737 | * required to use all the numbers in coming to our answer. |
738 | */ |
739 | if (ss->nnumbers == 1 || !rules->use_all) { |
740 | for (i = 0; i < ss->nnumbers; i++) { |
741 | int n; |
742 | |
743 | if (addoutput(s, ss, i, &n) && target && n == *target) |
744 | return s; |
745 | } |
746 | } |
747 | |
748 | /* |
749 | * Try every possible operation from this state. |
750 | */ |
751 | for (k = 0; ops[k] && ops[k]->perform; k++) { |
752 | if ((ops[k]->flags & OPFLAG_NEEDS_CONCAT) && |
753 | !(ss->flags & SETFLAG_CONCAT)) |
754 | continue; /* can't use this operation here */ |
755 | for (i = 0; i < ss->nnumbers; i++) { |
ed35622c |
756 | int jlimit = (ops[k]->flags & OPFLAG_UNARY ? 1 : ss->nnumbers); |
757 | for (j = 0; j < jlimit; j++) { |
f278dcf4 |
758 | int n[2]; |
ed35622c |
759 | int pa, po, pb, pr; |
f278dcf4 |
760 | |
ed35622c |
761 | if (!(ops[k]->flags & OPFLAG_UNARY)) { |
762 | if (i == j) |
763 | continue; /* can't combine a number with itself */ |
764 | if (i > j && ops[k]->commutes) |
765 | continue; /* no need to do this both ways round */ |
766 | } |
f278dcf4 |
767 | if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n)) |
768 | continue; /* operation failed */ |
769 | |
770 | sn = newset(s, ss->nnumbers-1, ss->flags); |
771 | |
772 | if (!(ops[k]->flags & OPFLAG_KEEPS_CONCAT)) |
773 | sn->flags &= ~SETFLAG_CONCAT; |
774 | |
775 | for (m = 0; m < ss->nnumbers; m++) { |
ed35622c |
776 | if (m == i || (!(ops[k]->flags & OPFLAG_UNARY) && |
777 | m == j)) |
f278dcf4 |
778 | continue; |
779 | sn->numbers[2*sn->nnumbers] = ss->numbers[2*m]; |
780 | sn->numbers[2*sn->nnumbers + 1] = ss->numbers[2*m + 1]; |
781 | sn->nnumbers++; |
782 | } |
ed35622c |
783 | pa = i; |
784 | if (ops[k]->flags & OPFLAG_UNARY) |
785 | pb = sn->nnumbers+10; |
786 | else |
787 | pb = j; |
788 | po = k; |
789 | pr = addtoset(sn, n); |
790 | addset(s, sn, multiple, ss, pa, po, pb, pr); |
f278dcf4 |
791 | } |
792 | } |
793 | } |
794 | |
795 | qpos++; |
796 | } |
797 | |
798 | return s; |
799 | } |
800 | |
801 | static void free_sets(struct sets *s) |
802 | { |
803 | int i; |
804 | |
805 | freetree234(s->settree); |
806 | freetree234(s->outputtree); |
807 | for (i = 0; i < s->nsetlists; i++) |
808 | sfree(s->setlists[i]); |
809 | sfree(s->setlists); |
810 | for (i = 0; i < s->nnumberlists; i++) |
811 | sfree(s->numberlists[i]); |
812 | sfree(s->numberlists); |
813 | for (i = 0; i < s->noutputlists; i++) |
814 | sfree(s->outputlists[i]); |
815 | sfree(s->outputlists); |
816 | sfree(s); |
817 | } |
818 | |
819 | /* |
ed35622c |
820 | * Print a text formula for producing a given output. |
f278dcf4 |
821 | */ |
ed35622c |
822 | void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, |
823 | int priority, int assoc, int child); |
824 | void print_recurse_inner(struct sets *s, struct set *ss, |
825 | struct ancestor *a, int pathindex, int index, |
826 | int priority, int assoc, int child) |
f278dcf4 |
827 | { |
ed35622c |
828 | if (a->prev && index != a->pr) { |
f278dcf4 |
829 | int pi; |
830 | |
831 | /* |
832 | * This number was passed straight down from this set's |
833 | * predecessor. Find its index in the previous set and |
834 | * recurse to there. |
835 | */ |
836 | pi = index; |
ed35622c |
837 | assert(pi != a->pr); |
838 | if (pi > a->pr) |
f278dcf4 |
839 | pi--; |
ed35622c |
840 | if (pi >= min(a->pa, a->pb)) { |
f278dcf4 |
841 | pi++; |
ed35622c |
842 | if (pi >= max(a->pa, a->pb)) |
f278dcf4 |
843 | pi++; |
844 | } |
ed35622c |
845 | print_recurse(s, a->prev, pathindex, pi, priority, assoc, child); |
846 | } else if (a->prev && index == a->pr && |
847 | s->ops[a->po]->display) { |
f278dcf4 |
848 | /* |
849 | * This number was created by a displayed operator in the |
850 | * transition from this set to its predecessor. Hence we |
851 | * write an open paren, then recurse into the first |
852 | * operand, then write the operator, then the second |
853 | * operand, and finally close the paren. |
854 | */ |
855 | char *op; |
856 | int parens, thispri, thisassoc; |
857 | |
858 | /* |
859 | * Determine whether we need parentheses. |
860 | */ |
ed35622c |
861 | thispri = s->ops[a->po]->priority; |
862 | thisassoc = s->ops[a->po]->assoc; |
f278dcf4 |
863 | parens = (thispri < priority || |
864 | (thispri == priority && (assoc & child))); |
865 | |
ed35622c |
866 | if (parens) |
867 | putchar('('); |
868 | |
869 | if (s->ops[a->po]->flags & OPFLAG_UNARYPFX) |
870 | for (op = s->ops[a->po]->text; *op; op++) |
871 | putchar(*op); |
872 | |
873 | print_recurse(s, a->prev, pathindex, a->pa, thispri, thisassoc, 1); |
874 | |
875 | if (!(s->ops[a->po]->flags & OPFLAG_UNARYPFX)) |
876 | for (op = s->ops[a->po]->text; *op; op++) |
877 | putchar(*op); |
878 | |
879 | if (!(s->ops[a->po]->flags & OPFLAG_UNARY)) |
880 | print_recurse(s, a->prev, pathindex, a->pb, thispri, thisassoc, 2); |
881 | |
882 | if (parens) |
883 | putchar(')'); |
f278dcf4 |
884 | } else { |
885 | /* |
886 | * This number is either an original, or something formed |
887 | * by a non-displayed operator (concatenation). Either way, |
888 | * we display it as is. |
889 | */ |
ed35622c |
890 | printf("%d", ss->numbers[2*index]); |
f278dcf4 |
891 | if (ss->numbers[2*index+1] != 1) |
ed35622c |
892 | printf("/%d", ss->numbers[2*index+1]); |
893 | } |
894 | } |
895 | void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, |
896 | int priority, int assoc, int child) |
897 | { |
898 | if (!ss->a.prev || pathindex < ss->a.prev->npaths) { |
899 | print_recurse_inner(s, ss, &ss->a, pathindex, |
900 | index, priority, assoc, child); |
901 | } else { |
902 | int i; |
903 | pathindex -= ss->a.prev->npaths; |
904 | for (i = 0; i < ss->nas; i++) { |
905 | if (pathindex < ss->as[i].prev->npaths) { |
906 | print_recurse_inner(s, ss, &ss->as[i], pathindex, |
907 | index, priority, assoc, child); |
908 | break; |
909 | } |
910 | pathindex -= ss->as[i].prev->npaths; |
f278dcf4 |
911 | } |
912 | } |
913 | } |
ed35622c |
914 | void print(int pathindex, struct sets *s, struct output *o) |
f278dcf4 |
915 | { |
ed35622c |
916 | print_recurse(s, o->set, pathindex, o->index, 0, 0, 0); |
f278dcf4 |
917 | } |
918 | |
ed35622c |
919 | /* |
920 | * gcc -g -O0 -o numgame numgame.c -I.. ../{malloc,tree234,nullfe}.c -lm |
921 | */ |
f278dcf4 |
922 | int main(int argc, char **argv) |
923 | { |
924 | int doing_opts = TRUE; |
925 | const struct rules *rules = NULL; |
926 | char *pname = argv[0]; |
927 | int got_target = FALSE, target = 0; |
928 | int numbers[10], nnumbers = 0; |
929 | int verbose = FALSE; |
930 | int pathcounts = FALSE; |
ed35622c |
931 | int multiple = FALSE; |
f278dcf4 |
932 | |
933 | struct output *o; |
934 | struct sets *s; |
935 | int i, start, limit; |
936 | |
937 | while (--argc) { |
938 | char *p = *++argv; |
939 | int c; |
940 | |
941 | if (doing_opts && *p == '-') { |
942 | p++; |
943 | |
944 | if (!strcmp(p, "-")) { |
945 | doing_opts = FALSE; |
946 | continue; |
947 | } else while (*p) switch (c = *p++) { |
948 | case 'C': |
949 | rules = &rules_countdown; |
950 | break; |
951 | case 'B': |
952 | rules = &rules_3388; |
953 | break; |
954 | case 'D': |
955 | rules = &rules_four4s; |
956 | break; |
ed35622c |
957 | case 'A': |
958 | rules = &rules_anythinggoes; |
959 | break; |
f278dcf4 |
960 | case 'v': |
961 | verbose = TRUE; |
962 | break; |
963 | case 'p': |
964 | pathcounts = TRUE; |
965 | break; |
ed35622c |
966 | case 'm': |
967 | multiple = TRUE; |
968 | break; |
f278dcf4 |
969 | case 't': |
970 | { |
971 | char *v; |
972 | if (*p) { |
973 | v = p; |
974 | p = NULL; |
975 | } else if (--argc) { |
976 | v = *++argv; |
977 | } else { |
978 | fprintf(stderr, "%s: option '-%c' expects an" |
979 | " argument\n", pname, c); |
980 | return 1; |
981 | } |
982 | switch (c) { |
983 | case 't': |
984 | got_target = TRUE; |
985 | target = atoi(v); |
986 | break; |
987 | } |
988 | } |
989 | break; |
990 | default: |
991 | fprintf(stderr, "%s: option '-%c' not" |
992 | " recognised\n", pname, c); |
993 | return 1; |
994 | } |
995 | } else { |
996 | if (nnumbers >= lenof(numbers)) { |
997 | fprintf(stderr, "%s: internal limit of %d numbers exceeded\n", |
998 | pname, lenof(numbers)); |
999 | return 1; |
1000 | } else { |
1001 | numbers[nnumbers++] = atoi(p); |
1002 | } |
1003 | } |
1004 | } |
1005 | |
1006 | if (!rules) { |
ed35622c |
1007 | fprintf(stderr, "%s: no rule set specified; use -C,-B,-D,-A\n", pname); |
f278dcf4 |
1008 | return 1; |
1009 | } |
1010 | |
1011 | if (!nnumbers) { |
1012 | fprintf(stderr, "%s: no input numbers specified\n", pname); |
1013 | return 1; |
1014 | } |
1015 | |
ed35622c |
1016 | s = do_search(nnumbers, numbers, rules, (got_target ? &target : NULL), |
1017 | multiple); |
f278dcf4 |
1018 | |
1019 | if (got_target) { |
1020 | o = findrelpos234(s->outputtree, &target, outputfindcmp, |
1021 | REL234_LE, &start); |
1022 | if (!o) |
1023 | start = -1; |
1024 | o = findrelpos234(s->outputtree, &target, outputfindcmp, |
1025 | REL234_GE, &limit); |
1026 | if (!o) |
1027 | limit = -1; |
1028 | assert(start != -1 || limit != -1); |
1029 | if (start == -1) |
1030 | start = limit; |
1031 | else if (limit == -1) |
1032 | limit = start; |
1033 | limit++; |
1034 | } else { |
1035 | start = 0; |
1036 | limit = count234(s->outputtree); |
1037 | } |
1038 | |
1039 | for (i = start; i < limit; i++) { |
ed35622c |
1040 | char buf[256]; |
1041 | |
f278dcf4 |
1042 | o = index234(s->outputtree, i); |
1043 | |
ed35622c |
1044 | sprintf(buf, "%d", o->number); |
f278dcf4 |
1045 | |
1046 | if (pathcounts) |
ed35622c |
1047 | sprintf(buf + strlen(buf), " [%d]", o->npaths); |
f278dcf4 |
1048 | |
1049 | if (got_target || verbose) { |
ed35622c |
1050 | int j, npaths; |
f278dcf4 |
1051 | |
ed35622c |
1052 | if (multiple) |
1053 | npaths = o->npaths; |
1054 | else |
1055 | npaths = 1; |
1056 | |
1057 | for (j = 0; j < npaths; j++) { |
1058 | printf("%s = ", buf); |
1059 | print(j, s, o); |
1060 | putchar('\n'); |
1061 | } |
1062 | } else { |
1063 | printf("%s\n", buf); |
1064 | } |
f278dcf4 |
1065 | } |
1066 | |
1067 | free_sets(s); |
1068 | |
1069 | return 0; |
1070 | } |