ref: 3633fec8ae2178782a59136049c1552c9c331556
parent: 83121fb826f8ce669aa1d02816bb6adaeee1257b
author: Simon Tatham <[email protected]>
date: Mon Jun 9 14:28:03 EDT 2008
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. [originally from svn r8061]
--- a/unfinished/numgame.c
+++ b/unfinished/numgame.c
@@ -37,8 +37,10 @@
*/
#include <stdio.h>
+#include <string.h>
#include <limits.h>
#include <assert.h>
+#include <math.h>
#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 @@
#define OPFLAG_NEEDS_CONCAT 1
#define OPFLAG_KEEPS_CONCAT 2
+#define OPFLAG_UNARY 4
+#define OPFLAG_UNARYPFX 8
struct operation {/*
@@ -195,7 +205,10 @@
#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 @@
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 @@
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 @@
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 @@
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 @@
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 @@
/*
* 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 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 @@
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 @@
!(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 @@
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 @@
}
/*
- * 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 @@
* 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
@@ -722,31 +858,29 @@
/*
* 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
@@ -753,35 +887,38 @@
* 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 numbers[10], nnumbers = 0;
int verbose = FALSE;
int pathcounts = FALSE;
+ int multiple = FALSE;
struct output *o;
struct sets *s;
@@ -816,6 +954,9 @@
case 'D':
rules = &rules_four4s;
break;
+ case 'A':
+ rules = &rules_anythinggoes;
+ break;
case 'v':
verbose = TRUE;
break;
@@ -822,6 +963,9 @@
case 'p':
pathcounts = TRUE;
break;
+ case 'm':
+ multiple = TRUE;
+ break;
case 't':
{char *v;
@@ -860,7 +1004,7 @@
}
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 @@
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 @@
}
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);