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New -A mode permitting even madder operators, and also -m to try to

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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]
This commit is contained in:
Simon Tatham
2008-06-09 18:28:03 +00:00
parent 83121fb826
commit 3633fec8ae
1 changed files with 241 additions and 85 deletions
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318
unfinished/numgame.c
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@ -37,8 +37,10 @@
*/ */
#include <stdio.h> #include <stdio.h>
#include <string.h>
#include <limits.h> #include <limits.h>
#include <assert.h> #include <assert.h>
#include <math.h>
#include "puzzles.h" #include "puzzles.h"
#include "tree234.h" #include "tree234.h"
@ -87,13 +89,19 @@
struct sets; 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 { struct set {
int *numbers; /* rationals stored as n,d pairs */ int *numbers; /* rationals stored as n,d pairs */
short nnumbers; /* # of rationals, so half # of ints */ short nnumbers; /* # of rationals, so half # of ints */
short flags; /* SETFLAG_CONCAT only, at present */ 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 */ 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 { struct output {
@ -121,6 +129,8 @@ struct sets {
#define OPFLAG_NEEDS_CONCAT 1 #define OPFLAG_NEEDS_CONCAT 1
#define OPFLAG_KEEPS_CONCAT 2 #define OPFLAG_KEEPS_CONCAT 2
#define OPFLAG_UNARY 4
#define OPFLAG_UNARYPFX 8
struct operation { struct operation {
/* /*
@ -195,7 +205,10 @@ struct rules {
#define OUT(output, n, d) do { \ #define OUT(output, n, d) do { \
int g = gcd((n),(d)); \ int g = gcd((n),(d)); \
if (g < 0) g = -g; \
if ((d) < 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)[0] = (n)/g; \
(output)[1] = (d)/g; \ (output)[1] = (d)/g; \
assert((output)[1] > 0); \ assert((output)[1] > 0); \
@ -299,9 +312,10 @@ static int perform_concat(int *a, int *b, int *output)
int t1, t2, p10; 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; return FALSE;
/* /*
@ -341,6 +355,78 @@ static int perform_concat(int *a, int *b, int *output)
return TRUE; 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 = { const static struct operation op_add = {
TRUE, "+", 0, 10, 0, TRUE, perform_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, FALSE, "", OPFLAG_NEEDS_CONCAT | OPFLAG_KEEPS_CONCAT,
1000, 0, FALSE, perform_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. * In Countdown, divisions resulting in fractions are disallowed.
@ -395,6 +487,17 @@ const static struct rules rules_four4s = {
ops_four4s, TRUE 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 \ #define ratcmp(a,op,b) ( (long long)(a)[0] * (b)[1] op \
(long long)(b)[0] * (a)[1] ) (long long)(b)[0] * (a)[1] )
@ -480,7 +583,8 @@ static int outputfindcmp(void *av, void *bv)
return 0; 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; struct set *s2;
int npaths = (prev ? prev->npaths : 1); 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. * 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; set->npaths = npaths;
s->nsets++; s->nsets++;
s->nnumbers += 2 * set->nnumbers; s->nnumbers += 2 * set->nnumbers;
set->as = NULL;
set->nas = set->assize = 0;
} else { } else {
/* /*
* Rediscovered an existing set. Update its npaths only. * Rediscovered an existing set. Update its npaths.
*/ */
s2->npaths += 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, 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 sets *s;
struct set *sn; struct set *sn;
@ -592,7 +718,7 @@ static struct sets *do_search(int ninputs, int *inputs,
newnumber[1] = 1; newnumber[1] = 1;
addtoset(sn, newnumber); 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 * 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)) !(ss->flags & SETFLAG_CONCAT))
continue; /* can't use this operation here */ continue; /* can't use this operation here */
for (i = 0; i < ss->nnumbers; i++) { 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 n[2];
int pa, po, pb, pr;
if (!(ops[k]->flags & OPFLAG_UNARY)) {
if (i == j) if (i == j)
continue; /* can't combine a number with itself */ continue; /* can't combine a number with itself */
if (i > j && ops[k]->commutes) if (i > j && ops[k]->commutes)
continue; /* no need to do this both ways round */ continue; /* no need to do this both ways round */
}
if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n)) if (!ops[k]->perform(ss->numbers+2*i, ss->numbers+2*j, n))
continue; /* operation failed */ continue; /* operation failed */
@ -643,17 +773,21 @@ static struct sets *do_search(int ninputs, int *inputs,
sn->flags &= ~SETFLAG_CONCAT; sn->flags &= ~SETFLAG_CONCAT;
for (m = 0; m < ss->nnumbers; m++) { for (m = 0; m < ss->nnumbers; m++) {
if (m == i || m == j) if (m == i || (!(ops[k]->flags & OPFLAG_UNARY) &&
m == j))
continue; continue;
sn->numbers[2*sn->nnumbers] = ss->numbers[2*m]; sn->numbers[2*sn->nnumbers] = ss->numbers[2*m];
sn->numbers[2*sn->nnumbers + 1] = ss->numbers[2*m + 1]; sn->numbers[2*sn->nnumbers + 1] = ss->numbers[2*m + 1];
sn->nnumbers++; sn->nnumbers++;
} }
sn->pa = i; pa = i;
sn->pb = j; if (ops[k]->flags & OPFLAG_UNARY)
sn->po = k; pb = sn->nnumbers+10;
sn->pr = addtoset(sn, n); else
addset(s, sn, ss); 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, void print_recurse(struct sets *s, struct set *ss, int pathindex, int index,
struct sets *s, struct set *ss, 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) int priority, int assoc, int child)
{ {
if (ss->prev && index != ss->pr) { if (a->prev && index != a->pr) {
int pi; int pi;
/* /*
@ -698,17 +834,17 @@ void mkstring_recurse(char **str, int *len,
* recurse to there. * recurse to there.
*/ */
pi = index; pi = index;
assert(pi != ss->pr); assert(pi != a->pr);
if (pi > ss->pr) if (pi > a->pr)
pi--; pi--;
if (pi >= min(ss->pa, ss->pb)) { if (pi >= min(a->pa, a->pb)) {
pi++; pi++;
if (pi >= max(ss->pa, ss->pb)) if (pi >= max(a->pa, a->pb))
pi++; pi++;
} }
mkstring_recurse(str, len, s, ss->prev, pi, priority, assoc, child); print_recurse(s, a->prev, pathindex, pi, priority, assoc, child);
} else if (ss->prev && index == ss->pr && } else if (a->prev && index == a->pr &&
s->ops[ss->po]->display) { s->ops[a->po]->display) {
/* /*
* This number was created by a displayed operator in the * This number was created by a displayed operator in the
* transition from this set to its predecessor. Hence we * 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. * Determine whether we need parentheses.
*/ */
thispri = s->ops[ss->po]->priority; thispri = s->ops[a->po]->priority;
thisassoc = s->ops[ss->po]->assoc; thisassoc = s->ops[a->po]->assoc;
parens = (thispri < priority || parens = (thispri < priority ||
(thispri == priority && (assoc & child))); (thispri == priority && (assoc & child)));
if (parens) { if (parens)
if (str) putchar('(');
*(*str)++ = '(';
if (len) if (s->ops[a->po]->flags & OPFLAG_UNARYPFX)
(*len)++; for (op = s->ops[a->po]->text; *op; op++)
} putchar(*op);
mkstring_recurse(str, len, s, ss->prev, ss->pa, thispri, thisassoc, 1);
for (op = s->ops[ss->po]->text; *op; op++) { print_recurse(s, a->prev, pathindex, a->pa, thispri, thisassoc, 1);
if (str)
*(*str)++ = *op; if (!(s->ops[a->po]->flags & OPFLAG_UNARYPFX))
if (len) for (op = s->ops[a->po]->text; *op; op++)
(*len)++; putchar(*op);
}
mkstring_recurse(str, len, s, ss->prev, ss->pb, thispri, thisassoc, 2); if (!(s->ops[a->po]->flags & OPFLAG_UNARY))
if (parens) { print_recurse(s, a->prev, pathindex, a->pb, thispri, thisassoc, 2);
if (str)
*(*str)++ = ')'; if (parens)
if (len) putchar(')');
(*len)++;
}
} else { } else {
/* /*
* This number is either an original, or something formed * This number is either an original, or something formed
* by a non-displayed operator (concatenation). Either way, * by a non-displayed operator (concatenation). Either way,
* we display it as is. * we display it as is.
*/ */
char buf[80], *p; printf("%d", ss->numbers[2*index]);
int blen;
blen = sprintf(buf, "%d", ss->numbers[2*index]);
if (ss->numbers[2*index+1] != 1) if (ss->numbers[2*index+1] != 1)
blen += sprintf(buf+blen, "/%d", ss->numbers[2*index+1]); printf("/%d", ss->numbers[2*index+1]);
assert(blen < lenof(buf));
for (p = buf; *p; p++) {
if (str)
*(*str)++ = *p;
if (len)
(*len)++;
} }
} }
} void print_recurse(struct sets *s, struct set *ss, int pathindex, int index,
char *mkstring(struct sets *s, struct output *o) int priority, int assoc, int child)
{ {
int len; if (!ss->a.prev || pathindex < ss->a.prev->npaths) {
char *str, *p; print_recurse_inner(s, ss, &ss->a, pathindex,
index, priority, assoc, child);
len = 0; } else {
mkstring_recurse(NULL, &len, s, o->set, o->index, 0, 0, 0); int i;
str = snewn(len+1, char); pathindex -= ss->a.prev->npaths;
p = str; for (i = 0; i < ss->nas; i++) {
mkstring_recurse(&p, NULL, s, o->set, o->index, 0, 0, 0); if (pathindex < ss->as[i].prev->npaths) {
assert(p - str <= len); print_recurse_inner(s, ss, &ss->as[i], pathindex,
*p = '\0'; index, priority, assoc, child);
return str; break;
}
pathindex -= ss->as[i].prev->npaths;
}
}
}
void print(int pathindex, struct sets *s, struct output *o)
{
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 main(int argc, char **argv)
{ {
int doing_opts = TRUE; int doing_opts = TRUE;
@ -791,6 +928,7 @@ int main(int argc, char **argv)
int numbers[10], nnumbers = 0; int numbers[10], nnumbers = 0;
int verbose = FALSE; int verbose = FALSE;
int pathcounts = FALSE; int pathcounts = FALSE;
int multiple = FALSE;
struct output *o; struct output *o;
struct sets *s; struct sets *s;
@ -816,12 +954,18 @@ int main(int argc, char **argv)
case 'D': case 'D':
rules = &rules_four4s; rules = &rules_four4s;
break; break;
case 'A':
rules = &rules_anythinggoes;
break;
case 'v': case 'v':
verbose = TRUE; verbose = TRUE;
break; break;
case 'p': case 'p':
pathcounts = TRUE; pathcounts = TRUE;
break; break;
case 'm':
multiple = TRUE;
break;
case 't': case 't':
{ {
char *v; char *v;
@ -860,7 +1004,7 @@ int main(int argc, char **argv)
} }
if (!rules) { 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; return 1;
} }
@ -869,7 +1013,8 @@ int main(int argc, char **argv)
return 1; 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) { if (got_target) {
o = findrelpos234(s->outputtree, &target, outputfindcmp, o = findrelpos234(s->outputtree, &target, outputfindcmp,
@ -892,20 +1037,31 @@ int main(int argc, char **argv)
} }
for (i = start; i < limit; i++) { for (i = start; i < limit; i++) {
char buf[256];
o = index234(s->outputtree, i); o = index234(s->outputtree, i);
printf("%d", o->number); sprintf(buf, "%d", o->number);
if (pathcounts) if (pathcounts)
printf(" [%d]", o->npaths); sprintf(buf + strlen(buf), " [%d]", o->npaths);
if (got_target || verbose) { if (got_target || verbose) {
char *p = mkstring(s, o); int j, npaths;
printf(" = %s", p);
sfree(p);
}
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); free_sets(s);