From: simon Date: Mon, 9 Jun 2008 18:28:03 +0000 (+0000) Subject: New -A mode permitting even madder operators, and also -m to try to X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/commitdiff_plain/ed35622c0ee28dea11b975b9dbbbb66cdefadd2e New -A mode permitting even madder operators, and also -m to try to print all possible paths to a value. The latter has a lot of de-duplication left to be done, due to multiple evaluation orders. git-svn-id: svn://svn.tartarus.org/sgt/puzzles@8061 cda61777-01e9-0310-a592-d414129be87e --- diff --git a/unfinished/numgame.c b/unfinished/numgame.c index e6f0985..7e83fc4 100644 --- a/unfinished/numgame.c +++ b/unfinished/numgame.c @@ -37,8 +37,10 @@ */ #include +#include #include #include +#include #include "puzzles.h" #include "tree234.h" @@ -87,13 +89,19 @@ struct sets; +struct ancestor { + struct set *prev; /* index of ancestor set in set list */ + unsigned char pa, pb, po, pr; /* operation that got here from prev */ +}; + struct set { int *numbers; /* rationals stored as n,d pairs */ short nnumbers; /* # of rationals, so half # of ints */ short flags; /* SETFLAG_CONCAT only, at present */ - struct set *prev; /* index of ancestor set in set list */ - unsigned char pa, pb, po, pr; /* operation that got here from prev */ int npaths; /* number of ways to reach this set */ + struct ancestor a; /* primary ancestor */ + struct ancestor *as; /* further ancestors, if we care */ + int nas, assize; }; struct output { @@ -121,6 +129,8 @@ struct sets { #define OPFLAG_NEEDS_CONCAT 1 #define OPFLAG_KEEPS_CONCAT 2 +#define OPFLAG_UNARY 4 +#define OPFLAG_UNARYPFX 8 struct operation { /* @@ -195,7 +205,10 @@ struct rules { #define OUT(output, n, d) do { \ int g = gcd((n),(d)); \ + if (g < 0) g = -g; \ if ((d) < 0) g = -g; \ + if (g == -1 && (n) < -INT_MAX) return FALSE; \ + if (g == -1 && (d) < -INT_MAX) return FALSE; \ (output)[0] = (n)/g; \ (output)[1] = (d)/g; \ assert((output)[1] > 0); \ @@ -299,9 +312,10 @@ static int perform_concat(int *a, int *b, int *output) int t1, t2, p10; /* - * We can't concatenate anything which isn't an integer. + * We can't concatenate anything which isn't a non-negative + * integer. */ - if (a[1] != 1 || b[1] != 1) + if (a[1] != 1 || b[1] != 1 || a[0] < 0 || b[0] < 0) return FALSE; /* @@ -341,6 +355,78 @@ static int perform_concat(int *a, int *b, int *output) return TRUE; } +#define IPOW(ret, x, y) do { \ + int ipow_limit = (y); \ + if ((x) == 1 || (x) == 0) ipow_limit = 1; \ + else if ((x) == -1) ipow_limit &= 1; \ + (ret) = 1; \ + while (ipow_limit-- > 0) { \ + int tmp; \ + MUL(tmp, ret, x); \ + ret = tmp; \ + } \ +} while (0) + +static int perform_exp(int *a, int *b, int *output) +{ + int an, ad, xn, xd, limit, t, i; + + /* + * Exponentiation is permitted if the result is rational. This + * means that: + * + * - first we see whether we can take the (denominator-of-b)th + * root of a and get a rational; if not, we give up. + * + * - then we do take that root of a + * + * - then we multiply by itself (numerator-of-b) times. + */ + if (b[1] > 1) { + an = 0.5 + pow(a[0], 1.0/b[1]); + ad = 0.5 + pow(a[1], 1.0/b[1]); + IPOW(xn, an, b[1]); + IPOW(xd, ad, b[1]); + if (xn != a[0] || xd != a[1]) + return FALSE; + } else { + an = a[0]; + ad = a[1]; + } + if (b[0] >= 0) { + IPOW(xn, an, b[0]); + IPOW(xd, ad, b[0]); + } else { + IPOW(xd, an, -b[0]); + IPOW(xn, ad, -b[0]); + } + if (xd == 0) + return FALSE; + + OUT(output, xn, xd); + return TRUE; +} + +static int perform_factorial(int *a, int *b, int *output) +{ + int ret, t, i; + + /* + * Factorials of non-negative integers are permitted. + */ + if (a[1] != 1 || a[0] < 0) + return FALSE; + + ret = 1; + for (i = 1; i <= a[0]; i++) { + MUL(t, ret, i); + ret = t; + } + + OUT(output, ret, 1); + return TRUE; +} + const static struct operation op_add = { TRUE, "+", 0, 10, 0, TRUE, perform_add }; @@ -360,6 +446,12 @@ const static struct operation op_concat = { FALSE, "", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, 1000, 0, FALSE, perform_concat }; +const static struct operation op_exp = { + TRUE, "^", 0, 30, 1, FALSE, perform_exp +}; +const static struct operation op_factorial = { + TRUE, "!", OPFLAG_UNARY, 40, 0, FALSE, perform_factorial +}; /* * In Countdown, divisions resulting in fractions are disallowed. @@ -395,6 +487,17 @@ const static struct rules rules_four4s = { ops_four4s, TRUE }; +/* + * The most permissive ruleset I can think of. Permits + * exponentiation, and also silly unary operators like factorials. + */ +const static struct operation *const ops_anythinggoes[] = { + &op_add, &op_mul, &op_sub, &op_div, &op_concat, &op_exp, &op_factorial, NULL +}; +const static struct rules rules_anythinggoes = { + ops_anythinggoes, TRUE +}; + #define ratcmp(a,op,b) ( (long long)(a)[0] * (b)[1] op \ (long long)(b)[0] * (a)[1] ) @@ -480,7 +583,8 @@ static int outputfindcmp(void *av, void *bv) return 0; } -static void addset(struct sets *s, struct set *set, struct set *prev) +static void addset(struct sets *s, struct set *set, int multiple, + struct set *prev, int pa, int po, int pb, int pr) { struct set *s2; int npaths = (prev ? prev->npaths : 1); @@ -491,15 +595,36 @@ static void addset(struct sets *s, struct set *set, struct set *prev) /* * New set added to the tree. */ - set->prev = prev; + set->a.prev = prev; + set->a.pa = pa; + set->a.po = po; + set->a.pb = pb; + set->a.pr = pr; set->npaths = npaths; s->nsets++; s->nnumbers += 2 * set->nnumbers; + set->as = NULL; + set->nas = set->assize = 0; } else { /* - * Rediscovered an existing set. Update its npaths only. + * Rediscovered an existing set. Update its npaths. */ s2->npaths += npaths; + /* + * And optionally enter it as an additional ancestor. + */ + if (multiple) { + if (s2->nas >= s2->assize) { + s2->assize = s2->nas * 3 / 2 + 4; + s2->as = sresize(s2->as, s2->assize, struct ancestor); + } + s2->as[s2->nas].prev = prev; + s2->as[s2->nas].pa = pa; + s2->as[s2->nas].po = po; + s2->as[s2->nas].pb = pb; + s2->as[s2->nas].pr = pr; + s2->nas++; + } } } @@ -564,7 +689,8 @@ static int addoutput(struct sets *s, struct set *ss, int index, int *n) } static struct sets *do_search(int ninputs, int *inputs, - const struct rules *rules, int *target) + const struct rules *rules, int *target, + int multiple) { struct sets *s; struct set *sn; @@ -592,7 +718,7 @@ static struct sets *do_search(int ninputs, int *inputs, newnumber[1] = 1; addtoset(sn, newnumber); } - addset(s, sn, NULL); + addset(s, sn, multiple, NULL, 0, 0, 0, 0); /* * Now perform the breadth-first search: keep looping over sets @@ -627,13 +753,17 @@ static struct sets *do_search(int ninputs, int *inputs, !(ss->flags & SETFLAG_CONCAT)) continue; /* can't use this operation here */ for (i = 0; i < ss->nnumbers; i++) { - for (j = 0; j < ss->nnumbers; j++) { + int jlimit = (ops[k]->flags & OPFLAG_UNARY ? 1 : ss->nnumbers); + for (j = 0; j < jlimit; j++) { int n[2]; + int pa, po, pb, pr; - if (i == j) - continue; /* can't combine a number with itself */ - if (i > j && ops[k]->commutes) - continue; /* no need to do this both ways round */ + if (!(ops[k]->flags & OPFLAG_UNARY)) { + if (i == j) + continue; /* can't combine a number with itself */ + if (i > j && ops[k]->commutes) + continue; /* no need to do this both ways round */ + } if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n)) continue; /* operation failed */ @@ -643,17 +773,21 @@ static struct sets *do_search(int ninputs, int *inputs, sn->flags &= ~SETFLAG_CONCAT; for (m = 0; m < ss->nnumbers; m++) { - if (m == i || m == j) + if (m == i || (!(ops[k]->flags & OPFLAG_UNARY) && + m == j)) continue; sn->numbers[2*sn->nnumbers] = ss->numbers[2*m]; sn->numbers[2*sn->nnumbers + 1] = ss->numbers[2*m + 1]; sn->nnumbers++; } - sn->pa = i; - sn->pb = j; - sn->po = k; - sn->pr = addtoset(sn, n); - addset(s, sn, ss); + pa = i; + if (ops[k]->flags & OPFLAG_UNARY) + pb = sn->nnumbers+10; + else + pb = j; + po = k; + pr = addtoset(sn, n); + addset(s, sn, multiple, ss, pa, po, pb, pr); } } } @@ -683,13 +817,15 @@ static void free_sets(struct sets *s) } /* - * Construct a text formula for producing a given output. + * Print a text formula for producing a given output. */ -void mkstring_recurse(char **str, int *len, - struct sets *s, struct set *ss, int index, - int priority, int assoc, int child) +void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, + int priority, int assoc, int child); +void print_recurse_inner(struct sets *s, struct set *ss, + struct ancestor *a, int pathindex, int index, + int priority, int assoc, int child) { - if (ss->prev && index != ss->pr) { + if (a->prev && index != a->pr) { int pi; /* @@ -698,17 +834,17 @@ void mkstring_recurse(char **str, int *len, * recurse to there. */ pi = index; - assert(pi != ss->pr); - if (pi > ss->pr) + assert(pi != a->pr); + if (pi > a->pr) pi--; - if (pi >= min(ss->pa, ss->pb)) { + if (pi >= min(a->pa, a->pb)) { pi++; - if (pi >= max(ss->pa, ss->pb)) + if (pi >= max(a->pa, a->pb)) pi++; } - mkstring_recurse(str, len, s, ss->prev, pi, priority, assoc, child); - } else if (ss->prev && index == ss->pr && - s->ops[ss->po]->display) { + print_recurse(s, a->prev, pathindex, pi, priority, assoc, child); + } else if (a->prev && index == a->pr && + s->ops[a->po]->display) { /* * This number was created by a displayed operator in the * transition from this set to its predecessor. Hence we @@ -722,66 +858,67 @@ void mkstring_recurse(char **str, int *len, /* * Determine whether we need parentheses. */ - thispri = s->ops[ss->po]->priority; - thisassoc = s->ops[ss->po]->assoc; + thispri = s->ops[a->po]->priority; + thisassoc = s->ops[a->po]->assoc; parens = (thispri < priority || (thispri == priority && (assoc & child))); - if (parens) { - if (str) - *(*str)++ = '('; - if (len) - (*len)++; - } - mkstring_recurse(str, len, s, ss->prev, ss->pa, thispri, thisassoc, 1); - for (op = s->ops[ss->po]->text; *op; op++) { - if (str) - *(*str)++ = *op; - if (len) - (*len)++; - } - mkstring_recurse(str, len, s, ss->prev, ss->pb, thispri, thisassoc, 2); - if (parens) { - if (str) - *(*str)++ = ')'; - if (len) - (*len)++; - } + if (parens) + putchar('('); + + if (s->ops[a->po]->flags & OPFLAG_UNARYPFX) + for (op = s->ops[a->po]->text; *op; op++) + putchar(*op); + + print_recurse(s, a->prev, pathindex, a->pa, thispri, thisassoc, 1); + + if (!(s->ops[a->po]->flags & OPFLAG_UNARYPFX)) + for (op = s->ops[a->po]->text; *op; op++) + putchar(*op); + + if (!(s->ops[a->po]->flags & OPFLAG_UNARY)) + print_recurse(s, a->prev, pathindex, a->pb, thispri, thisassoc, 2); + + if (parens) + putchar(')'); } else { /* * This number is either an original, or something formed * by a non-displayed operator (concatenation). Either way, * we display it as is. */ - char buf[80], *p; - int blen; - blen = sprintf(buf, "%d", ss->numbers[2*index]); + printf("%d", ss->numbers[2*index]); if (ss->numbers[2*index+1] != 1) - blen += sprintf(buf+blen, "/%d", ss->numbers[2*index+1]); - assert(blen < lenof(buf)); - for (p = buf; *p; p++) { - if (str) - *(*str)++ = *p; - if (len) - (*len)++; + printf("/%d", ss->numbers[2*index+1]); + } +} +void print_recurse(struct sets *s, struct set *ss, int pathindex, int index, + int priority, int assoc, int child) +{ + if (!ss->a.prev || pathindex < ss->a.prev->npaths) { + print_recurse_inner(s, ss, &ss->a, pathindex, + index, priority, assoc, child); + } else { + int i; + pathindex -= ss->a.prev->npaths; + for (i = 0; i < ss->nas; i++) { + if (pathindex < ss->as[i].prev->npaths) { + print_recurse_inner(s, ss, &ss->as[i], pathindex, + index, priority, assoc, child); + break; + } + pathindex -= ss->as[i].prev->npaths; } } } -char *mkstring(struct sets *s, struct output *o) +void print(int pathindex, struct sets *s, struct output *o) { - int len; - char *str, *p; - - len = 0; - mkstring_recurse(NULL, &len, s, o->set, o->index, 0, 0, 0); - str = snewn(len+1, char); - p = str; - mkstring_recurse(&p, NULL, s, o->set, o->index, 0, 0, 0); - assert(p - str <= len); - *p = '\0'; - return str; + print_recurse(s, o->set, pathindex, o->index, 0, 0, 0); } +/* + * gcc -g -O0 -o numgame numgame.c -I.. ../{malloc,tree234,nullfe}.c -lm + */ int main(int argc, char **argv) { int doing_opts = TRUE; @@ -791,6 +928,7 @@ int main(int argc, char **argv) int numbers[10], nnumbers = 0; int verbose = FALSE; int pathcounts = FALSE; + int multiple = FALSE; struct output *o; struct sets *s; @@ -816,12 +954,18 @@ int main(int argc, char **argv) case 'D': rules = &rules_four4s; break; + case 'A': + rules = &rules_anythinggoes; + break; case 'v': verbose = TRUE; break; case 'p': pathcounts = TRUE; break; + case 'm': + multiple = TRUE; + break; case 't': { char *v; @@ -860,7 +1004,7 @@ int main(int argc, char **argv) } if (!rules) { - fprintf(stderr, "%s: no rule set specified; use -C,-B,-D\n", pname); + fprintf(stderr, "%s: no rule set specified; use -C,-B,-D,-A\n", pname); return 1; } @@ -869,7 +1013,8 @@ int main(int argc, char **argv) return 1; } - s = do_search(nnumbers, numbers, rules, (got_target ? &target : NULL)); + s = do_search(nnumbers, numbers, rules, (got_target ? &target : NULL), + multiple); if (got_target) { o = findrelpos234(s->outputtree, &target, outputfindcmp, @@ -892,20 +1037,31 @@ int main(int argc, char **argv) } for (i = start; i < limit; i++) { + char buf[256]; + o = index234(s->outputtree, i); - printf("%d", o->number); + sprintf(buf, "%d", o->number); if (pathcounts) - printf(" [%d]", o->npaths); + sprintf(buf + strlen(buf), " [%d]", o->npaths); if (got_target || verbose) { - char *p = mkstring(s, o); - printf(" = %s", p); - sfree(p); - } + int j, npaths; - printf("\n"); + if (multiple) + npaths = o->npaths; + else + npaths = 1; + + for (j = 0; j < npaths; j++) { + printf("%s = ", buf); + print(j, s, o); + putchar('\n'); + } + } else { + printf("%s\n", buf); + } } free_sets(s);