#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 {
/*
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.
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;
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);
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
* - 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])
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);
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
};
/*
* 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
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;
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
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)) {
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;
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");
+ }
}
}
}
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);
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;
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;
multiple = TRUE;
break;
case 't':
+ case 'r':
{
char *v;
if (*p) {
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;
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,
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);
return 0;
}
+
+/* vim: set shiftwidth=4 tabstop=8: */
~mdw / sgt / puzzles / blobdiff