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 | /* |
91623748 |
145 | * Text display of the operator, in expressions and for |
146 | * debugging respectively. |
f278dcf4 |
147 | */ |
91623748 |
148 | char *text, *dbgtext; |
f278dcf4 |
149 | |
150 | /* |
151 | * Flags dictating when the operator can be applied. |
152 | */ |
153 | int flags; |
154 | |
155 | /* |
156 | * Priority of the operator (for avoiding unnecessary |
157 | * parentheses when formatting it into a string). |
158 | */ |
159 | int priority; |
160 | |
161 | /* |
162 | * Associativity of the operator. Bit 0 means we need parens |
163 | * when the left operand of one of these operators is another |
164 | * instance of it, e.g. (2^3)^4. Bit 1 means we need parens |
165 | * when the right operand is another instance of the same |
166 | * operator, e.g. 2-(3-4). Thus: |
167 | * |
168 | * - this field is 0 for a fully associative operator, since |
169 | * we never need parens. |
170 | * - it's 1 for a right-associative operator. |
171 | * - it's 2 for a left-associative operator. |
172 | * - it's 3 for a _non_-associative operator (which always |
173 | * uses parens just to be sure). |
174 | */ |
175 | int assoc; |
176 | |
177 | /* |
178 | * Whether the operator is commutative. Saves time in the |
179 | * search if we don't have to try it both ways round. |
180 | */ |
181 | int commutes; |
182 | |
183 | /* |
184 | * Function which implements the operator. Returns TRUE on |
185 | * success, FALSE on failure. Takes two rationals and writes |
186 | * out a third. |
187 | */ |
188 | int (*perform)(int *a, int *b, int *output); |
189 | }; |
190 | |
191 | struct rules { |
192 | const struct operation *const *ops; |
193 | int use_all; |
194 | }; |
195 | |
196 | #define MUL(r, a, b) do { \ |
197 | (r) = (a) * (b); \ |
198 | if ((b) && (a) && (r) / (b) != (a)) return FALSE; \ |
199 | } while (0) |
200 | |
201 | #define ADD(r, a, b) do { \ |
202 | (r) = (a) + (b); \ |
203 | if ((a) > 0 && (b) > 0 && (r) < 0) return FALSE; \ |
204 | if ((a) < 0 && (b) < 0 && (r) > 0) return FALSE; \ |
205 | } while (0) |
206 | |
207 | #define OUT(output, n, d) do { \ |
208 | int g = gcd((n),(d)); \ |
ed35622c |
209 | if (g < 0) g = -g; \ |
f278dcf4 |
210 | if ((d) < 0) g = -g; \ |
ed35622c |
211 | if (g == -1 && (n) < -INT_MAX) return FALSE; \ |
212 | if (g == -1 && (d) < -INT_MAX) return FALSE; \ |
f278dcf4 |
213 | (output)[0] = (n)/g; \ |
214 | (output)[1] = (d)/g; \ |
215 | assert((output)[1] > 0); \ |
216 | } while (0) |
217 | |
218 | static int gcd(int x, int y) |
219 | { |
220 | while (x != 0 && y != 0) { |
221 | int t = x; |
222 | x = y; |
223 | y = t % y; |
224 | } |
225 | |
226 | return abs(x + y); /* i.e. whichever one isn't zero */ |
227 | } |
228 | |
229 | static int perform_add(int *a, int *b, int *output) |
230 | { |
231 | int at, bt, tn, bn; |
232 | /* |
233 | * a0/a1 + b0/b1 = (a0*b1 + b0*a1) / (a1*b1) |
234 | */ |
235 | MUL(at, a[0], b[1]); |
236 | MUL(bt, b[0], a[1]); |
237 | ADD(tn, at, bt); |
238 | MUL(bn, a[1], b[1]); |
239 | OUT(output, tn, bn); |
240 | return TRUE; |
241 | } |
242 | |
243 | static int perform_sub(int *a, int *b, int *output) |
244 | { |
245 | int at, bt, tn, bn; |
246 | /* |
247 | * a0/a1 - b0/b1 = (a0*b1 - b0*a1) / (a1*b1) |
248 | */ |
249 | MUL(at, a[0], b[1]); |
250 | MUL(bt, b[0], a[1]); |
251 | ADD(tn, at, -bt); |
252 | MUL(bn, a[1], b[1]); |
253 | OUT(output, tn, bn); |
254 | return TRUE; |
255 | } |
256 | |
257 | static int perform_mul(int *a, int *b, int *output) |
258 | { |
259 | int tn, bn; |
260 | /* |
261 | * a0/a1 * b0/b1 = (a0*b0) / (a1*b1) |
262 | */ |
263 | MUL(tn, a[0], b[0]); |
264 | MUL(bn, a[1], b[1]); |
265 | OUT(output, tn, bn); |
266 | return TRUE; |
267 | } |
268 | |
269 | static int perform_div(int *a, int *b, int *output) |
270 | { |
271 | int tn, bn; |
272 | |
273 | /* |
274 | * Division by zero is outlawed. |
275 | */ |
276 | if (b[0] == 0) |
277 | return FALSE; |
278 | |
279 | /* |
280 | * a0/a1 / b0/b1 = (a0*b1) / (a1*b0) |
281 | */ |
282 | MUL(tn, a[0], b[1]); |
283 | MUL(bn, a[1], b[0]); |
284 | OUT(output, tn, bn); |
285 | return TRUE; |
286 | } |
287 | |
288 | static int perform_exact_div(int *a, int *b, int *output) |
289 | { |
290 | int tn, bn; |
291 | |
292 | /* |
293 | * Division by zero is outlawed. |
294 | */ |
295 | if (b[0] == 0) |
296 | return FALSE; |
297 | |
298 | /* |
299 | * a0/a1 / b0/b1 = (a0*b1) / (a1*b0) |
300 | */ |
301 | MUL(tn, a[0], b[1]); |
302 | MUL(bn, a[1], b[0]); |
303 | OUT(output, tn, bn); |
304 | |
305 | /* |
306 | * Exact division means we require the result to be an integer. |
307 | */ |
308 | return (output[1] == 1); |
309 | } |
310 | |
311 | static int perform_concat(int *a, int *b, int *output) |
312 | { |
313 | int t1, t2, p10; |
314 | |
315 | /* |
ed35622c |
316 | * We can't concatenate anything which isn't a non-negative |
317 | * integer. |
f278dcf4 |
318 | */ |
ed35622c |
319 | if (a[1] != 1 || b[1] != 1 || a[0] < 0 || b[0] < 0) |
f278dcf4 |
320 | return FALSE; |
321 | |
322 | /* |
323 | * For concatenation, we can safely assume leading zeroes |
324 | * aren't an issue. It isn't clear whether they `should' be |
325 | * allowed, but it turns out not to matter: concatenating a |
326 | * leading zero on to a number in order to harmlessly get rid |
327 | * of the zero is never necessary because unwanted zeroes can |
328 | * be disposed of by adding them to something instead. So we |
329 | * disallow them always. |
330 | * |
331 | * The only other possibility is that you might want to |
332 | * concatenate a leading zero on to something and then |
333 | * concatenate another non-zero digit on to _that_ (to make, |
334 | * for example, 106); but that's also unnecessary, because you |
335 | * can make 106 just as easily by concatenating the 0 on to the |
336 | * _end_ of the 1 first. |
337 | */ |
338 | if (a[0] == 0) |
339 | return FALSE; |
340 | |
341 | /* |
342 | * Find the smallest power of ten strictly greater than b. This |
343 | * is the power of ten by which we'll multiply a. |
344 | * |
345 | * Special case: we must multiply a by at least 10, even if b |
346 | * is zero. |
347 | */ |
348 | p10 = 10; |
349 | while (p10 <= (INT_MAX/10) && p10 <= b[0]) |
350 | p10 *= 10; |
351 | if (p10 > INT_MAX/10) |
352 | return FALSE; /* integer overflow */ |
353 | MUL(t1, p10, a[0]); |
354 | ADD(t2, t1, b[0]); |
355 | OUT(output, t2, 1); |
356 | return TRUE; |
357 | } |
358 | |
ed35622c |
359 | #define IPOW(ret, x, y) do { \ |
360 | int ipow_limit = (y); \ |
361 | if ((x) == 1 || (x) == 0) ipow_limit = 1; \ |
362 | else if ((x) == -1) ipow_limit &= 1; \ |
363 | (ret) = 1; \ |
364 | while (ipow_limit-- > 0) { \ |
365 | int tmp; \ |
366 | MUL(tmp, ret, x); \ |
367 | ret = tmp; \ |
368 | } \ |
369 | } while (0) |
370 | |
371 | static int perform_exp(int *a, int *b, int *output) |
372 | { |
373 | int an, ad, xn, xd, limit, t, i; |
374 | |
375 | /* |
376 | * Exponentiation is permitted if the result is rational. This |
377 | * means that: |
378 | * |
379 | * - first we see whether we can take the (denominator-of-b)th |
380 | * root of a and get a rational; if not, we give up. |
381 | * |
382 | * - then we do take that root of a |
383 | * |
384 | * - then we multiply by itself (numerator-of-b) times. |
385 | */ |
386 | if (b[1] > 1) { |
387 | an = 0.5 + pow(a[0], 1.0/b[1]); |
388 | ad = 0.5 + pow(a[1], 1.0/b[1]); |
389 | IPOW(xn, an, b[1]); |
390 | IPOW(xd, ad, b[1]); |
391 | if (xn != a[0] || xd != a[1]) |
392 | return FALSE; |
393 | } else { |
394 | an = a[0]; |
395 | ad = a[1]; |
396 | } |
397 | if (b[0] >= 0) { |
398 | IPOW(xn, an, b[0]); |
399 | IPOW(xd, ad, b[0]); |
400 | } else { |
401 | IPOW(xd, an, -b[0]); |
402 | IPOW(xn, ad, -b[0]); |
403 | } |
404 | if (xd == 0) |
405 | return FALSE; |
406 | |
407 | OUT(output, xn, xd); |
408 | return TRUE; |
409 | } |
410 | |
411 | static int perform_factorial(int *a, int *b, int *output) |
412 | { |
413 | int ret, t, i; |
414 | |
415 | /* |
416 | * Factorials of non-negative integers are permitted. |
417 | */ |
418 | if (a[1] != 1 || a[0] < 0) |
419 | return FALSE; |
420 | |
91623748 |
421 | /* |
422 | * However, a special case: we don't take a factorial of |
423 | * anything which would thereby remain the same. |
424 | */ |
425 | if (a[0] == 1 || a[0] == 2) |
426 | return FALSE; |
427 | |
ed35622c |
428 | ret = 1; |
429 | for (i = 1; i <= a[0]; i++) { |
430 | MUL(t, ret, i); |
431 | ret = t; |
432 | } |
433 | |
434 | OUT(output, ret, 1); |
435 | return TRUE; |
436 | } |
437 | |
f278dcf4 |
438 | const static struct operation op_add = { |
91623748 |
439 | TRUE, "+", "+", 0, 10, 0, TRUE, perform_add |
f278dcf4 |
440 | }; |
441 | const static struct operation op_sub = { |
91623748 |
442 | TRUE, "-", "-", 0, 10, 2, FALSE, perform_sub |
f278dcf4 |
443 | }; |
444 | const static struct operation op_mul = { |
91623748 |
445 | TRUE, "*", "*", 0, 20, 0, TRUE, perform_mul |
f278dcf4 |
446 | }; |
447 | const static struct operation op_div = { |
91623748 |
448 | TRUE, "/", "/", 0, 20, 2, FALSE, perform_div |
f278dcf4 |
449 | }; |
450 | const static struct operation op_xdiv = { |
91623748 |
451 | TRUE, "/", "/", 0, 20, 2, FALSE, perform_exact_div |
f278dcf4 |
452 | }; |
453 | const static struct operation op_concat = { |
91623748 |
454 | FALSE, "", "concat", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, |
f278dcf4 |
455 | 1000, 0, FALSE, perform_concat |
456 | }; |
ed35622c |
457 | const static struct operation op_exp = { |
91623748 |
458 | TRUE, "^", "^", 0, 30, 1, FALSE, perform_exp |
ed35622c |
459 | }; |
460 | const static struct operation op_factorial = { |
91623748 |
461 | TRUE, "!", "!", OPFLAG_UNARY, 40, 0, FALSE, perform_factorial |
ed35622c |
462 | }; |
f278dcf4 |
463 | |
464 | /* |
465 | * In Countdown, divisions resulting in fractions are disallowed. |
466 | * http://www.askoxford.com/wordgames/countdown/rules/ |
467 | */ |
468 | const static struct operation *const ops_countdown[] = { |
469 | &op_add, &op_mul, &op_sub, &op_xdiv, NULL |
470 | }; |
471 | const static struct rules rules_countdown = { |
472 | ops_countdown, FALSE |
473 | }; |
474 | |
475 | /* |
476 | * A slightly different rule set which handles the reasonably well |
477 | * known puzzle of making 24 using two 3s and two 8s. For this we |
478 | * need rational rather than integer division. |
479 | */ |
480 | const static struct operation *const ops_3388[] = { |
481 | &op_add, &op_mul, &op_sub, &op_div, NULL |
482 | }; |
483 | const static struct rules rules_3388 = { |
484 | ops_3388, TRUE |
485 | }; |
486 | |
487 | /* |
488 | * A still more permissive rule set usable for the four-4s problem |
489 | * and similar things. Permits concatenation. |
490 | */ |
491 | const static struct operation *const ops_four4s[] = { |
492 | &op_add, &op_mul, &op_sub, &op_div, &op_concat, NULL |
493 | }; |
494 | const static struct rules rules_four4s = { |
495 | ops_four4s, TRUE |
496 | }; |
497 | |
ed35622c |
498 | /* |
499 | * The most permissive ruleset I can think of. Permits |
500 | * exponentiation, and also silly unary operators like factorials. |
501 | */ |
502 | const static struct operation *const ops_anythinggoes[] = { |
503 | &op_add, &op_mul, &op_sub, &op_div, &op_concat, &op_exp, &op_factorial, NULL |
504 | }; |
505 | const static struct rules rules_anythinggoes = { |
506 | ops_anythinggoes, TRUE |
507 | }; |
508 | |
f278dcf4 |
509 | #define ratcmp(a,op,b) ( (long long)(a)[0] * (b)[1] op \ |
510 | (long long)(b)[0] * (a)[1] ) |
511 | |
512 | static int addtoset(struct set *set, int newnumber[2]) |
513 | { |
514 | int i, j; |
515 | |
516 | /* Find where we want to insert the new number */ |
517 | for (i = 0; i < set->nnumbers && |
518 | ratcmp(set->numbers+2*i, <, newnumber); i++); |
519 | |
520 | /* Move everything else up */ |
521 | for (j = set->nnumbers; j > i; j--) { |
522 | set->numbers[2*j] = set->numbers[2*j-2]; |
523 | set->numbers[2*j+1] = set->numbers[2*j-1]; |
524 | } |
525 | |
526 | /* Insert the new number */ |
527 | set->numbers[2*i] = newnumber[0]; |
528 | set->numbers[2*i+1] = newnumber[1]; |
529 | |
530 | set->nnumbers++; |
531 | |
532 | return i; |
533 | } |
534 | |
535 | #define ensure(array, size, newlen, type) do { \ |
536 | if ((newlen) > (size)) { \ |
537 | (size) = (newlen) + 512; \ |
538 | (array) = sresize((array), (size), type); \ |
539 | } \ |
540 | } while (0) |
541 | |
542 | static int setcmp(void *av, void *bv) |
543 | { |
544 | struct set *a = (struct set *)av; |
545 | struct set *b = (struct set *)bv; |
546 | int i; |
547 | |
548 | if (a->nnumbers < b->nnumbers) |
549 | return -1; |
550 | else if (a->nnumbers > b->nnumbers) |
551 | return +1; |
552 | |
553 | if (a->flags < b->flags) |
554 | return -1; |
555 | else if (a->flags > b->flags) |
556 | return +1; |
557 | |
558 | for (i = 0; i < a->nnumbers; i++) { |
559 | if (ratcmp(a->numbers+2*i, <, b->numbers+2*i)) |
560 | return -1; |
561 | else if (ratcmp(a->numbers+2*i, >, b->numbers+2*i)) |
562 | return +1; |
563 | } |
564 | |
565 | return 0; |
566 | } |
567 | |
568 | static int outputcmp(void *av, void *bv) |
569 | { |
570 | struct output *a = (struct output *)av; |
571 | struct output *b = (struct output *)bv; |
572 | |
573 | if (a->number < b->number) |
574 | return -1; |
575 | else if (a->number > b->number) |
576 | return +1; |
577 | |
578 | return 0; |
579 | } |
580 | |
581 | static int outputfindcmp(void *av, void *bv) |
582 | { |
583 | int *a = (int *)av; |
584 | struct output *b = (struct output *)bv; |
585 | |
586 | if (*a < b->number) |
587 | return -1; |
588 | else if (*a > b->number) |
589 | return +1; |
590 | |
591 | return 0; |
592 | } |
593 | |
ed35622c |
594 | static void addset(struct sets *s, struct set *set, int multiple, |
595 | struct set *prev, int pa, int po, int pb, int pr) |
f278dcf4 |
596 | { |
597 | struct set *s2; |
598 | int npaths = (prev ? prev->npaths : 1); |
599 | |
600 | assert(set == s->setlists[s->nsets / SETLISTLEN] + s->nsets % SETLISTLEN); |
601 | s2 = add234(s->settree, set); |
602 | if (s2 == set) { |
603 | /* |
604 | * New set added to the tree. |
605 | */ |
ed35622c |
606 | set->a.prev = prev; |
607 | set->a.pa = pa; |
608 | set->a.po = po; |
609 | set->a.pb = pb; |
610 | set->a.pr = pr; |
f278dcf4 |
611 | set->npaths = npaths; |
612 | s->nsets++; |
613 | s->nnumbers += 2 * set->nnumbers; |
ed35622c |
614 | set->as = NULL; |
615 | set->nas = set->assize = 0; |
f278dcf4 |
616 | } else { |
617 | /* |
ed35622c |
618 | * Rediscovered an existing set. Update its npaths. |
f278dcf4 |
619 | */ |
620 | s2->npaths += npaths; |
ed35622c |
621 | /* |
622 | * And optionally enter it as an additional ancestor. |
623 | */ |
624 | if (multiple) { |
625 | if (s2->nas >= s2->assize) { |
626 | s2->assize = s2->nas * 3 / 2 + 4; |
627 | s2->as = sresize(s2->as, s2->assize, struct ancestor); |
628 | } |
629 | s2->as[s2->nas].prev = prev; |
630 | s2->as[s2->nas].pa = pa; |
631 | s2->as[s2->nas].po = po; |
632 | s2->as[s2->nas].pb = pb; |
633 | s2->as[s2->nas].pr = pr; |
634 | s2->nas++; |
635 | } |
f278dcf4 |
636 | } |
637 | } |
638 | |
639 | static struct set *newset(struct sets *s, int nnumbers, int flags) |
640 | { |
641 | struct set *sn; |
642 | |
643 | ensure(s->setlists, s->setlistsize, s->nsets/SETLISTLEN+1, struct set *); |
644 | while (s->nsetlists <= s->nsets / SETLISTLEN) |
645 | s->setlists[s->nsetlists++] = snewn(SETLISTLEN, struct set); |
646 | sn = s->setlists[s->nsets / SETLISTLEN] + s->nsets % SETLISTLEN; |
647 | |
648 | if (s->nnumbers + nnumbers * 2 > s->nnumberlists * NUMBERLISTLEN) |
649 | s->nnumbers = s->nnumberlists * NUMBERLISTLEN; |
650 | ensure(s->numberlists, s->numberlistsize, |
651 | s->nnumbers/NUMBERLISTLEN+1, int *); |
652 | while (s->nnumberlists <= s->nnumbers / NUMBERLISTLEN) |
653 | s->numberlists[s->nnumberlists++] = snewn(NUMBERLISTLEN, int); |
654 | sn->numbers = s->numberlists[s->nnumbers / NUMBERLISTLEN] + |
655 | s->nnumbers % NUMBERLISTLEN; |
656 | |
657 | /* |
658 | * Start the set off empty. |
659 | */ |
660 | sn->nnumbers = 0; |
661 | |
662 | sn->flags = flags; |
663 | |
664 | return sn; |
665 | } |
666 | |
667 | static int addoutput(struct sets *s, struct set *ss, int index, int *n) |
668 | { |
669 | struct output *o, *o2; |
670 | |
671 | /* |
672 | * Target numbers are always integers. |
673 | */ |
674 | if (ss->numbers[2*index+1] != 1) |
675 | return FALSE; |
676 | |
677 | ensure(s->outputlists, s->outputlistsize, s->noutputs/OUTPUTLISTLEN+1, |
678 | struct output *); |
679 | while (s->noutputlists <= s->noutputs / OUTPUTLISTLEN) |
680 | s->outputlists[s->noutputlists++] = snewn(OUTPUTLISTLEN, |
681 | struct output); |
682 | o = s->outputlists[s->noutputs / OUTPUTLISTLEN] + |
683 | s->noutputs % OUTPUTLISTLEN; |
684 | |
685 | o->number = ss->numbers[2*index]; |
686 | o->set = ss; |
687 | o->index = index; |
688 | o->npaths = ss->npaths; |
689 | o2 = add234(s->outputtree, o); |
690 | if (o2 != o) { |
691 | o2->npaths += o->npaths; |
692 | } else { |
693 | s->noutputs++; |
694 | } |
695 | *n = o->number; |
696 | return TRUE; |
697 | } |
698 | |
699 | static struct sets *do_search(int ninputs, int *inputs, |
ed35622c |
700 | const struct rules *rules, int *target, |
91623748 |
701 | int debug, int multiple) |
f278dcf4 |
702 | { |
703 | struct sets *s; |
704 | struct set *sn; |
705 | int qpos, i; |
706 | const struct operation *const *ops = rules->ops; |
707 | |
708 | s = snew(struct sets); |
709 | s->setlists = NULL; |
710 | s->nsets = s->nsetlists = s->setlistsize = 0; |
711 | s->numberlists = NULL; |
712 | s->nnumbers = s->nnumberlists = s->numberlistsize = 0; |
713 | s->outputlists = NULL; |
714 | s->noutputs = s->noutputlists = s->outputlistsize = 0; |
715 | s->settree = newtree234(setcmp); |
716 | s->outputtree = newtree234(outputcmp); |
717 | s->ops = ops; |
718 | |
719 | /* |
720 | * Start with the input set. |
721 | */ |
722 | sn = newset(s, ninputs, SETFLAG_CONCAT); |
723 | for (i = 0; i < ninputs; i++) { |
724 | int newnumber[2]; |
725 | newnumber[0] = inputs[i]; |
726 | newnumber[1] = 1; |
727 | addtoset(sn, newnumber); |
728 | } |
ed35622c |
729 | addset(s, sn, multiple, NULL, 0, 0, 0, 0); |
f278dcf4 |
730 | |
731 | /* |
732 | * Now perform the breadth-first search: keep looping over sets |
733 | * until we run out of steam. |
734 | */ |
735 | qpos = 0; |
736 | while (qpos < s->nsets) { |
737 | struct set *ss = s->setlists[qpos / SETLISTLEN] + qpos % SETLISTLEN; |
738 | struct set *sn; |
739 | int i, j, k, m; |
740 | |
91623748 |
741 | if (debug) { |
742 | int i; |
743 | printf("processing set:"); |
744 | for (i = 0; i < ss->nnumbers; i++) { |
745 | printf(" %d", ss->numbers[2*i]); |
746 | if (ss->numbers[2*i+1] != 1) |
747 | printf("/%d", ss->numbers[2*i]+1); |
748 | } |
749 | printf("\n"); |
750 | } |
751 | |
f278dcf4 |
752 | /* |
753 | * Record all the valid output numbers in this state. We |
754 | * can always do this if there's only one number in the |
755 | * state; otherwise, we can only do it if we aren't |
756 | * required to use all the numbers in coming to our answer. |
757 | */ |
758 | if (ss->nnumbers == 1 || !rules->use_all) { |
759 | for (i = 0; i < ss->nnumbers; i++) { |
760 | int n; |
761 | |
762 | if (addoutput(s, ss, i, &n) && target && n == *target) |
763 | return s; |
764 | } |
765 | } |
766 | |
767 | /* |
768 | * Try every possible operation from this state. |
769 | */ |
770 | for (k = 0; ops[k] && ops[k]->perform; k++) { |
771 | if ((ops[k]->flags & OPFLAG_NEEDS_CONCAT) && |
772 | !(ss->flags & SETFLAG_CONCAT)) |
773 | continue; /* can't use this operation here */ |
774 | for (i = 0; i < ss->nnumbers; i++) { |
ed35622c |
775 | int jlimit = (ops[k]->flags & OPFLAG_UNARY ? 1 : ss->nnumbers); |
776 | for (j = 0; j < jlimit; j++) { |
f278dcf4 |
777 | int n[2]; |
ed35622c |
778 | int pa, po, pb, pr; |
f278dcf4 |
779 | |
ed35622c |
780 | if (!(ops[k]->flags & OPFLAG_UNARY)) { |
781 | if (i == j) |
782 | continue; /* can't combine a number with itself */ |
783 | if (i > j && ops[k]->commutes) |
784 | continue; /* no need to do this both ways round */ |
785 | } |
f278dcf4 |
786 | if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n)) |
787 | continue; /* operation failed */ |
788 | |
789 | sn = newset(s, ss->nnumbers-1, ss->flags); |
790 | |
791 | if (!(ops[k]->flags & OPFLAG_KEEPS_CONCAT)) |
792 | sn->flags &= ~SETFLAG_CONCAT; |
793 | |
794 | for (m = 0; m < ss->nnumbers; m++) { |
ed35622c |
795 | if (m == i || (!(ops[k]->flags & OPFLAG_UNARY) && |
796 | m == j)) |
f278dcf4 |
797 | continue; |
798 | sn->numbers[2*sn->nnumbers] = ss->numbers[2*m]; |
799 | sn->numbers[2*sn->nnumbers + 1] = ss->numbers[2*m + 1]; |
800 | sn->nnumbers++; |
801 | } |
ed35622c |
802 | pa = i; |
803 | if (ops[k]->flags & OPFLAG_UNARY) |
804 | pb = sn->nnumbers+10; |
805 | else |
806 | pb = j; |
807 | po = k; |
808 | pr = addtoset(sn, n); |
809 | addset(s, sn, multiple, ss, pa, po, pb, pr); |
91623748 |
810 | if (debug) { |
811 | int i; |
812 | printf(" %d %s %d ->", pa, ops[po]->dbgtext, pb); |
813 | for (i = 0; i < sn->nnumbers; i++) { |
814 | printf(" %d", sn->numbers[2*i]); |
815 | if (sn->numbers[2*i+1] != 1) |
816 | printf("/%d", sn->numbers[2*i]+1); |
817 | } |
818 | printf("\n"); |
819 | } |
f278dcf4 |
820 | } |
821 | } |
822 | } |
823 | |
824 | qpos++; |
825 | } |
826 | |
827 | return s; |
828 | } |
829 | |
830 | static void free_sets(struct sets *s) |
831 | { |
832 | int i; |
833 | |
834 | freetree234(s->settree); |
835 | freetree234(s->outputtree); |
836 | for (i = 0; i < s->nsetlists; i++) |
837 | sfree(s->setlists[i]); |
838 | sfree(s->setlists); |
839 | for (i = 0; i < s->nnumberlists; i++) |
840 | sfree(s->numberlists[i]); |
841 | sfree(s->numberlists); |
842 | for (i = 0; i < s->noutputlists; i++) |
843 | sfree(s->outputlists[i]); |
844 | sfree(s->outputlists); |
845 | sfree(s); |
846 | } |
847 | |
848 | /* |
ed35622c |
849 | * Print a text formula for producing a given output. |
f278dcf4 |
850 | */ |
ed35622c |
851 | void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, |
852 | int priority, int assoc, int child); |
853 | void print_recurse_inner(struct sets *s, struct set *ss, |
854 | struct ancestor *a, int pathindex, int index, |
855 | int priority, int assoc, int child) |
f278dcf4 |
856 | { |
ed35622c |
857 | if (a->prev && index != a->pr) { |
f278dcf4 |
858 | int pi; |
859 | |
860 | /* |
861 | * This number was passed straight down from this set's |
862 | * predecessor. Find its index in the previous set and |
863 | * recurse to there. |
864 | */ |
865 | pi = index; |
ed35622c |
866 | assert(pi != a->pr); |
867 | if (pi > a->pr) |
f278dcf4 |
868 | pi--; |
ed35622c |
869 | if (pi >= min(a->pa, a->pb)) { |
f278dcf4 |
870 | pi++; |
ed35622c |
871 | if (pi >= max(a->pa, a->pb)) |
f278dcf4 |
872 | pi++; |
873 | } |
ed35622c |
874 | print_recurse(s, a->prev, pathindex, pi, priority, assoc, child); |
875 | } else if (a->prev && index == a->pr && |
876 | s->ops[a->po]->display) { |
f278dcf4 |
877 | /* |
878 | * This number was created by a displayed operator in the |
879 | * transition from this set to its predecessor. Hence we |
880 | * write an open paren, then recurse into the first |
881 | * operand, then write the operator, then the second |
882 | * operand, and finally close the paren. |
883 | */ |
884 | char *op; |
885 | int parens, thispri, thisassoc; |
886 | |
887 | /* |
888 | * Determine whether we need parentheses. |
889 | */ |
ed35622c |
890 | thispri = s->ops[a->po]->priority; |
891 | thisassoc = s->ops[a->po]->assoc; |
f278dcf4 |
892 | parens = (thispri < priority || |
893 | (thispri == priority && (assoc & child))); |
894 | |
ed35622c |
895 | if (parens) |
896 | putchar('('); |
897 | |
898 | if (s->ops[a->po]->flags & OPFLAG_UNARYPFX) |
899 | for (op = s->ops[a->po]->text; *op; op++) |
900 | putchar(*op); |
901 | |
902 | print_recurse(s, a->prev, pathindex, a->pa, thispri, thisassoc, 1); |
903 | |
904 | if (!(s->ops[a->po]->flags & OPFLAG_UNARYPFX)) |
905 | for (op = s->ops[a->po]->text; *op; op++) |
906 | putchar(*op); |
907 | |
908 | if (!(s->ops[a->po]->flags & OPFLAG_UNARY)) |
909 | print_recurse(s, a->prev, pathindex, a->pb, thispri, thisassoc, 2); |
910 | |
911 | if (parens) |
912 | putchar(')'); |
f278dcf4 |
913 | } else { |
914 | /* |
915 | * This number is either an original, or something formed |
916 | * by a non-displayed operator (concatenation). Either way, |
917 | * we display it as is. |
918 | */ |
ed35622c |
919 | printf("%d", ss->numbers[2*index]); |
f278dcf4 |
920 | if (ss->numbers[2*index+1] != 1) |
ed35622c |
921 | printf("/%d", ss->numbers[2*index+1]); |
922 | } |
923 | } |
924 | void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, |
925 | int priority, int assoc, int child) |
926 | { |
927 | if (!ss->a.prev || pathindex < ss->a.prev->npaths) { |
928 | print_recurse_inner(s, ss, &ss->a, pathindex, |
929 | index, priority, assoc, child); |
930 | } else { |
931 | int i; |
932 | pathindex -= ss->a.prev->npaths; |
933 | for (i = 0; i < ss->nas; i++) { |
934 | if (pathindex < ss->as[i].prev->npaths) { |
935 | print_recurse_inner(s, ss, &ss->as[i], pathindex, |
936 | index, priority, assoc, child); |
937 | break; |
938 | } |
939 | pathindex -= ss->as[i].prev->npaths; |
f278dcf4 |
940 | } |
941 | } |
942 | } |
ed35622c |
943 | void print(int pathindex, struct sets *s, struct output *o) |
f278dcf4 |
944 | { |
ed35622c |
945 | print_recurse(s, o->set, pathindex, o->index, 0, 0, 0); |
f278dcf4 |
946 | } |
947 | |
ed35622c |
948 | /* |
949 | * gcc -g -O0 -o numgame numgame.c -I.. ../{malloc,tree234,nullfe}.c -lm |
950 | */ |
f278dcf4 |
951 | int main(int argc, char **argv) |
952 | { |
953 | int doing_opts = TRUE; |
954 | const struct rules *rules = NULL; |
955 | char *pname = argv[0]; |
956 | int got_target = FALSE, target = 0; |
957 | int numbers[10], nnumbers = 0; |
958 | int verbose = FALSE; |
959 | int pathcounts = FALSE; |
ed35622c |
960 | int multiple = FALSE; |
91623748 |
961 | int debug_bfs = FALSE; |
f278dcf4 |
962 | |
963 | struct output *o; |
964 | struct sets *s; |
965 | int i, start, limit; |
966 | |
967 | while (--argc) { |
968 | char *p = *++argv; |
969 | int c; |
970 | |
971 | if (doing_opts && *p == '-') { |
972 | p++; |
973 | |
974 | if (!strcmp(p, "-")) { |
975 | doing_opts = FALSE; |
976 | continue; |
91623748 |
977 | } else if (*p == '-') { |
978 | p++; |
979 | if (!strcmp(p, "debug-bfs")) { |
980 | debug_bfs = TRUE; |
981 | } else { |
982 | fprintf(stderr, "%s: option '--%s' not recognised\n", |
983 | pname, p); |
984 | } |
f278dcf4 |
985 | } else while (*p) switch (c = *p++) { |
986 | case 'C': |
987 | rules = &rules_countdown; |
988 | break; |
989 | case 'B': |
990 | rules = &rules_3388; |
991 | break; |
992 | case 'D': |
993 | rules = &rules_four4s; |
994 | break; |
ed35622c |
995 | case 'A': |
996 | rules = &rules_anythinggoes; |
997 | break; |
f278dcf4 |
998 | case 'v': |
999 | verbose = TRUE; |
1000 | break; |
1001 | case 'p': |
1002 | pathcounts = TRUE; |
1003 | break; |
ed35622c |
1004 | case 'm': |
1005 | multiple = TRUE; |
1006 | break; |
f278dcf4 |
1007 | case 't': |
1008 | { |
1009 | char *v; |
1010 | if (*p) { |
1011 | v = p; |
1012 | p = NULL; |
1013 | } else if (--argc) { |
1014 | v = *++argv; |
1015 | } else { |
1016 | fprintf(stderr, "%s: option '-%c' expects an" |
1017 | " argument\n", pname, c); |
1018 | return 1; |
1019 | } |
1020 | switch (c) { |
1021 | case 't': |
1022 | got_target = TRUE; |
1023 | target = atoi(v); |
1024 | break; |
1025 | } |
1026 | } |
1027 | break; |
1028 | default: |
1029 | fprintf(stderr, "%s: option '-%c' not" |
1030 | " recognised\n", pname, c); |
1031 | return 1; |
1032 | } |
1033 | } else { |
1034 | if (nnumbers >= lenof(numbers)) { |
1035 | fprintf(stderr, "%s: internal limit of %d numbers exceeded\n", |
1036 | pname, lenof(numbers)); |
1037 | return 1; |
1038 | } else { |
1039 | numbers[nnumbers++] = atoi(p); |
1040 | } |
1041 | } |
1042 | } |
1043 | |
1044 | if (!rules) { |
ed35622c |
1045 | fprintf(stderr, "%s: no rule set specified; use -C,-B,-D,-A\n", pname); |
f278dcf4 |
1046 | return 1; |
1047 | } |
1048 | |
1049 | if (!nnumbers) { |
1050 | fprintf(stderr, "%s: no input numbers specified\n", pname); |
1051 | return 1; |
1052 | } |
1053 | |
ed35622c |
1054 | s = do_search(nnumbers, numbers, rules, (got_target ? &target : NULL), |
91623748 |
1055 | debug_bfs, multiple); |
f278dcf4 |
1056 | |
1057 | if (got_target) { |
1058 | o = findrelpos234(s->outputtree, &target, outputfindcmp, |
1059 | REL234_LE, &start); |
1060 | if (!o) |
1061 | start = -1; |
1062 | o = findrelpos234(s->outputtree, &target, outputfindcmp, |
1063 | REL234_GE, &limit); |
1064 | if (!o) |
1065 | limit = -1; |
1066 | assert(start != -1 || limit != -1); |
1067 | if (start == -1) |
1068 | start = limit; |
1069 | else if (limit == -1) |
1070 | limit = start; |
1071 | limit++; |
1072 | } else { |
1073 | start = 0; |
1074 | limit = count234(s->outputtree); |
1075 | } |
1076 | |
1077 | for (i = start; i < limit; i++) { |
ed35622c |
1078 | char buf[256]; |
1079 | |
f278dcf4 |
1080 | o = index234(s->outputtree, i); |
1081 | |
ed35622c |
1082 | sprintf(buf, "%d", o->number); |
f278dcf4 |
1083 | |
1084 | if (pathcounts) |
ed35622c |
1085 | sprintf(buf + strlen(buf), " [%d]", o->npaths); |
f278dcf4 |
1086 | |
1087 | if (got_target || verbose) { |
ed35622c |
1088 | int j, npaths; |
f278dcf4 |
1089 | |
ed35622c |
1090 | if (multiple) |
1091 | npaths = o->npaths; |
1092 | else |
1093 | npaths = 1; |
1094 | |
1095 | for (j = 0; j < npaths; j++) { |
1096 | printf("%s = ", buf); |
1097 | print(j, s, o); |
1098 | putchar('\n'); |
1099 | } |
1100 | } else { |
1101 | printf("%s\n", buf); |
1102 | } |
f278dcf4 |
1103 | } |
1104 | |
1105 | free_sets(s); |
1106 | |
1107 | return 0; |
1108 | } |