X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/blobdiff_plain/ed35622c0ee28dea11b975b9dbbbb66cdefadd2e..HEAD:/unfinished/numgame.c diff --git a/unfinished/numgame.c b/unfinished/numgame.c index 7e83fc4..20861ca 100644 --- a/unfinished/numgame.c +++ b/unfinished/numgame.c @@ -130,7 +130,8 @@ struct sets { #define OPFLAG_NEEDS_CONCAT 1 #define OPFLAG_KEEPS_CONCAT 2 #define OPFLAG_UNARY 4 -#define OPFLAG_UNARYPFX 8 +#define OPFLAG_UNARYPREFIX 8 +#define OPFLAG_FN 16 struct operation { /* @@ -142,9 +143,10 @@ struct operation { int display; /* - * Text display of the operator. + * Text display of the operator, in expressions and for + * debugging respectively. */ - char *text; + char *text, *dbgtext; /* * Flags dictating when the operator can be applied. @@ -307,6 +309,26 @@ static int perform_exact_div(int *a, int *b, int *output) return (output[1] == 1); } +static int max_p10(int n, int *p10_r) +{ + /* + * Find the smallest power of ten strictly greater than n. + * + * Special case: we must return at least 10, even if n is + * zero. (This is because this function is used for finding + * the power of ten by which to multiply a number being + * concatenated to the front of n, and concatenating 1 to 0 + * should yield 10 and not 1.) + */ + int p10 = 10; + while (p10 <= (INT_MAX/10) && p10 <= n) + p10 *= 10; + if (p10 > INT_MAX/10) + return FALSE; /* integer overflow */ + *p10_r = p10; + return TRUE; +} + static int perform_concat(int *a, int *b, int *output) { int t1, t2, p10; @@ -337,18 +359,8 @@ static int perform_concat(int *a, int *b, int *output) if (a[0] == 0) return FALSE; - /* - * Find the smallest power of ten strictly greater than b. This - * is the power of ten by which we'll multiply a. - * - * Special case: we must multiply a by at least 10, even if b - * is zero. - */ - p10 = 10; - while (p10 <= (INT_MAX/10) && p10 <= b[0]) - p10 *= 10; - if (p10 > INT_MAX/10) - return FALSE; /* integer overflow */ + if (!max_p10(b[0], &p10)) return FALSE; + MUL(t1, p10, a[0]); ADD(t2, t1, b[0]); OUT(output, t2, 1); @@ -369,7 +381,7 @@ static int perform_concat(int *a, int *b, int *output) static int perform_exp(int *a, int *b, int *output) { - int an, ad, xn, xd, limit, t, i; + int an, ad, xn, xd; /* * Exponentiation is permitted if the result is rational. This @@ -383,8 +395,8 @@ static int perform_exp(int *a, int *b, int *output) * - 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]); + an = (int)(0.5 + pow(a[0], 1.0/b[1])); + ad = (int)(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]) @@ -417,6 +429,13 @@ static int perform_factorial(int *a, int *b, int *output) if (a[1] != 1 || a[0] < 0) return FALSE; + /* + * However, a special case: we don't take a factorial of + * anything which would thereby remain the same. + */ + if (a[0] == 1 || a[0] == 2) + return FALSE; + ret = 1; for (i = 1; i <= a[0]; i++) { MUL(t, ret, i); @@ -427,30 +446,151 @@ static int perform_factorial(int *a, int *b, int *output) return TRUE; } +static int perform_decimal(int *a, int *b, int *output) +{ + int p10; + + /* + * Add a decimal digit to the front of a number; + * fail if it's not an integer. + * So, 1 --> 0.1, 15 --> 0.15, + * or, rather, 1 --> 1/10, 15 --> 15/100, + * x --> x / (smallest power of 10 > than x) + * + */ + if (a[1] != 1) return FALSE; + + if (!max_p10(a[0], &p10)) return FALSE; + + OUT(output, a[0], p10); + return TRUE; +} + +static int perform_recur(int *a, int *b, int *output) +{ + int p10, tn, bn; + + /* + * This converts a number like .4 to .44444..., or .45 to .45454... + * The input number must be -1 < a < 1. + * + * Calculate the smallest power of 10 that divides the denominator exactly, + * returning if no such power of 10 exists. Then multiply the numerator + * up accordingly, and the new denominator becomes that power of 10 - 1. + */ + if (abs(a[0]) >= abs(a[1])) return FALSE; /* -1 < a < 1 */ + + p10 = 10; + while (p10 <= (INT_MAX/10)) { + if ((a[1] <= p10) && (p10 % a[1]) == 0) goto found; + p10 *= 10; + } + return FALSE; +found: + tn = a[0] * (p10 / a[1]); + bn = p10 - 1; + + OUT(output, tn, bn); + return TRUE; +} + +static int perform_root(int *a, int *b, int *output) +{ + /* + * A root B is: 1 iff a == 0 + * B ^ (1/A) otherwise + */ + int ainv[2], res; + + if (a[0] == 0) { + OUT(output, 1, 1); + return TRUE; + } + + OUT(ainv, a[1], a[0]); + res = perform_exp(b, ainv, output); + return res; +} + +static int perform_perc(int *a, int *b, int *output) +{ + if (a[0] == 0) return FALSE; /* 0% = 0, uninteresting. */ + if (a[1] > (INT_MAX/100)) return FALSE; + + OUT(output, a[0], a[1]*100); + return TRUE; +} + +static int perform_gamma(int *a, int *b, int *output) +{ + int asub1[2]; + + /* + * gamma(a) = (a-1)! + * + * special case not caught by perform_fact: gamma(1) is 1 so + * don't bother. + */ + if (a[0] == 1 && a[1] == 1) return FALSE; + + OUT(asub1, a[0]-a[1], a[1]); + return perform_factorial(asub1, b, output); +} + +static int perform_sqrt(int *a, int *b, int *output) +{ + int half[2] = { 1, 2 }; + + /* + * sqrt(0) == 0, sqrt(1) == 1: don't perform unary noops. + */ + if (a[0] == 0 || (a[0] == 1 && a[1] == 1)) return FALSE; + + return perform_exp(a, half, output); +} + const static struct operation op_add = { - TRUE, "+", 0, 10, 0, TRUE, perform_add + TRUE, "+", "+", 0, 10, 0, TRUE, perform_add }; const static struct operation op_sub = { - TRUE, "-", 0, 10, 2, FALSE, perform_sub + TRUE, "-", "-", 0, 10, 2, FALSE, perform_sub }; const static struct operation op_mul = { - TRUE, "*", 0, 20, 0, TRUE, perform_mul + TRUE, "*", "*", 0, 20, 0, TRUE, perform_mul }; const static struct operation op_div = { - TRUE, "/", 0, 20, 2, FALSE, perform_div + TRUE, "/", "/", 0, 20, 2, FALSE, perform_div }; const static struct operation op_xdiv = { - TRUE, "/", 0, 20, 2, FALSE, perform_exact_div + TRUE, "/", "/", 0, 20, 2, FALSE, perform_exact_div }; const static struct operation op_concat = { - FALSE, "", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, + FALSE, "", "concat", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, 1000, 0, FALSE, perform_concat }; const static struct operation op_exp = { - TRUE, "^", 0, 30, 1, FALSE, perform_exp + TRUE, "^", "^", 0, 30, 1, FALSE, perform_exp }; const static struct operation op_factorial = { - TRUE, "!", OPFLAG_UNARY, 40, 0, FALSE, perform_factorial + TRUE, "!", "!", OPFLAG_UNARY, 40, 0, FALSE, perform_factorial +}; +const static struct operation op_decimal = { + TRUE, ".", ".", OPFLAG_UNARY | OPFLAG_UNARYPREFIX | OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT, 50, 0, FALSE, perform_decimal +}; +const static struct operation op_recur = { + TRUE, "...", "recur", OPFLAG_UNARY | OPFLAG_NEEDS_CONCAT, 45, 2, FALSE, perform_recur +}; +const static struct operation op_root = { + TRUE, "v~", "root", 0, 30, 1, FALSE, perform_root +}; +const static struct operation op_perc = { + TRUE, "%", "%", OPFLAG_UNARY | OPFLAG_NEEDS_CONCAT, 45, 1, FALSE, perform_perc +}; +const static struct operation op_gamma = { + TRUE, "gamma", "gamma", OPFLAG_UNARY | OPFLAG_UNARYPREFIX | OPFLAG_FN, 1, 3, FALSE, perform_gamma +}; +const static struct operation op_sqrt = { + TRUE, "v~", "sqrt", OPFLAG_UNARY | OPFLAG_UNARYPREFIX, 30, 1, FALSE, perform_sqrt }; /* @@ -492,7 +632,8 @@ const static struct rules rules_four4s = { * 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 + &op_add, &op_mul, &op_sub, &op_div, &op_concat, &op_exp, &op_factorial, + &op_decimal, &op_recur, &op_root, &op_perc, &op_gamma, &op_sqrt, NULL }; const static struct rules rules_anythinggoes = { ops_anythinggoes, TRUE @@ -690,7 +831,7 @@ 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, - int multiple) + int debug, int multiple) { struct sets *s; struct set *sn; @@ -730,6 +871,17 @@ static struct sets *do_search(int ninputs, int *inputs, struct set *sn; int i, j, k, m; + if (debug) { + int i; + printf("processing set:"); + for (i = 0; i < ss->nnumbers; i++) { + printf(" %d", ss->numbers[2*i]); + if (ss->numbers[2*i+1] != 1) + printf("/%d", ss->numbers[2*i+1]); + } + printf("\n"); + } + /* * Record all the valid output numbers in this state. We * can always do this if there's only one number in the @@ -755,7 +907,7 @@ static struct sets *do_search(int ninputs, int *inputs, for (i = 0; i < ss->nnumbers; i++) { int jlimit = (ops[k]->flags & OPFLAG_UNARY ? 1 : ss->nnumbers); for (j = 0; j < jlimit; j++) { - int n[2]; + int n[2], newnn = ss->nnumbers; int pa, po, pb, pr; if (!(ops[k]->flags & OPFLAG_UNARY)) { @@ -763,11 +915,12 @@ static struct sets *do_search(int ninputs, int *inputs, continue; /* can't combine a number with itself */ if (i > j && ops[k]->commutes) continue; /* no need to do this both ways round */ + newnn--; } if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n)) continue; /* operation failed */ - sn = newset(s, ss->nnumbers-1, ss->flags); + sn = newset(s, newnn, ss->flags); if (!(ops[k]->flags & OPFLAG_KEEPS_CONCAT)) sn->flags &= ~SETFLAG_CONCAT; @@ -788,6 +941,21 @@ static struct sets *do_search(int ninputs, int *inputs, po = k; pr = addtoset(sn, n); addset(s, sn, multiple, ss, pa, po, pb, pr); + if (debug) { + int i; + if (ops[k]->flags & OPFLAG_UNARYPREFIX) + printf(" %s %d ->", ops[po]->dbgtext, pa); + else if (ops[k]->flags & OPFLAG_UNARY) + printf(" %d %s ->", pa, ops[po]->dbgtext); + else + printf(" %d %s %d ->", pa, ops[po]->dbgtext, pb); + for (i = 0; i < sn->nnumbers; i++) { + printf(" %d", sn->numbers[2*i]); + if (sn->numbers[2*i+1] != 1) + printf("/%d", sn->numbers[2*i+1]); + } + printf("\n"); + } } } } @@ -866,13 +1034,19 @@ void print_recurse_inner(struct sets *s, struct set *ss, if (parens) putchar('('); - if (s->ops[a->po]->flags & OPFLAG_UNARYPFX) + if (s->ops[a->po]->flags & OPFLAG_UNARYPREFIX) for (op = s->ops[a->po]->text; *op; op++) putchar(*op); + if (s->ops[a->po]->flags & OPFLAG_FN) + putchar('('); + print_recurse(s, a->prev, pathindex, a->pa, thispri, thisassoc, 1); - if (!(s->ops[a->po]->flags & OPFLAG_UNARYPFX)) + if (s->ops[a->po]->flags & OPFLAG_FN) + putchar(')'); + + if (!(s->ops[a->po]->flags & OPFLAG_UNARYPREFIX)) for (op = s->ops[a->po]->text; *op; op++) putchar(*op); @@ -929,6 +1103,8 @@ int main(int argc, char **argv) int verbose = FALSE; int pathcounts = FALSE; int multiple = FALSE; + int debug_bfs = FALSE; + int got_range = FALSE, rangemin = 0, rangemax = 0; struct output *o; struct sets *s; @@ -944,7 +1120,15 @@ int main(int argc, char **argv) if (!strcmp(p, "-")) { doing_opts = FALSE; continue; - } else while (*p) switch (c = *p++) { + } else if (*p == '-') { + p++; + if (!strcmp(p, "debug-bfs")) { + debug_bfs = TRUE; + } else { + fprintf(stderr, "%s: option '--%s' not recognised\n", + pname, p); + } + } else while (p && *p) switch (c = *p++) { case 'C': rules = &rules_countdown; break; @@ -967,6 +1151,7 @@ int main(int argc, char **argv) multiple = TRUE; break; case 't': + case 'r': { char *v; if (*p) { @@ -984,6 +1169,19 @@ int main(int argc, char **argv) got_target = TRUE; target = atoi(v); break; + case 'r': + { + char *sep = strchr(v, '-'); + got_range = TRUE; + if (sep) { + rangemin = atoi(v); + rangemax = atoi(sep+1); + } else { + rangemin = 0; + rangemax = atoi(v); + } + } + break; } } break; @@ -1013,8 +1211,19 @@ int main(int argc, char **argv) return 1; } + if (got_range) { + if (got_target) { + fprintf(stderr, "%s: only one of -t and -r may be specified\n", pname); + return 1; + } + if (rangemin >= rangemax) { + fprintf(stderr, "%s: range not sensible (%d - %d)\n", pname, rangemin, rangemax); + return 1; + } + } + s = do_search(nnumbers, numbers, rules, (got_target ? &target : NULL), - multiple); + debug_bfs, multiple); if (got_target) { o = findrelpos234(s->outputtree, &target, outputfindcmp, @@ -1031,6 +1240,15 @@ int main(int argc, char **argv) else if (limit == -1) limit = start; limit++; + } else if (got_range) { + if (!findrelpos234(s->outputtree, &rangemin, outputfindcmp, + REL234_GE, &start) || + !findrelpos234(s->outputtree, &rangemax, outputfindcmp, + REL234_LE, &limit)) { + printf("No solutions available in specified range %d-%d\n", rangemin, rangemax); + return 1; + } + limit++; } else { start = 0; limit = count234(s->outputtree); @@ -1068,3 +1286,5 @@ int main(int argc, char **argv) return 0; } + +/* vim: set shiftwidth=4 tabstop=8: */