7e83fc4dccbd82e4171555d573f8a5fe155a8b3b
2 * This program implements a breadth-first search which
3 * exhaustively solves the Countdown numbers game, and related
4 * games with slightly different rule sets such as `Flippo'.
6 * Currently it is simply a standalone command-line utility to
7 * which you provide a set of numbers and it tells you everything
8 * it can make together with how many different ways it can be
9 * made. I would like ultimately to turn it into the generator for
10 * a Puzzles puzzle, but I haven't even started on writing a
11 * Puzzles user interface yet.
17 * - start thinking about difficulty ratings
18 * + anything involving associative operations will be flagged
19 * as many-paths because of the associative options (e.g.
20 * 2*3*4 can be (2*3)*4 or 2*(3*4), or indeed (2*4)*3). This
21 * is probably a _good_ thing, since those are unusually
23 * + tree-structured calculations ((a*b)/(c+d)) have multiple
24 * paths because the independent branches of the tree can be
25 * evaluated in either order, whereas straight-line
26 * calculations with no branches will be considered easier.
27 * Can we do anything about this? It's certainly not clear to
28 * me that tree-structure calculations are _easier_, although
29 * I'm also not convinced they're harder.
30 * + I think for a realistic difficulty assessment we must also
31 * consider the `obviousness' of the arithmetic operations in
32 * some heuristic sense, and also (in Countdown) how many
33 * numbers ended up being used.
34 * - actually try some generations
35 * - at this point we're probably ready to start on the Puzzles
49 * To search for numbers we can make, we employ a breadth-first
50 * search across the space of sets of input numbers. That is, for
51 * example, we start with the set (3,6,25,50,75,100); we apply
52 * moves which involve combining two numbers (e.g. adding the 50
53 * and the 75 takes us to the set (3,6,25,100,125); and then we see
54 * if we ever end up with a set containing (say) 952.
56 * If the rules are changed so that all the numbers must be used,
57 * this is easy to adjust to: we simply see if we end up with a set
58 * containing _only_ (say) 952.
60 * Obviously, we can vary the rules about permitted arithmetic
61 * operations simply by altering the set of valid moves in the bfs.
62 * However, there's one common rule in this sort of puzzle which
63 * takes a little more thought, and that's _concatenation_. For
64 * example, if you are given (say) four 4s and required to make 10,
65 * you are permitted to combine two of the 4s into a 44 to begin
66 * with, making (44-4)/4 = 10. However, you are generally not
67 * allowed to concatenate two numbers that _weren't_ both in the
68 * original input set (you couldn't multiply two 4s to get 16 and
69 * then concatenate a 4 on to it to make 164), so concatenation is
70 * not an operation which is valid in all situations.
72 * We could enforce this restriction by storing a flag alongside
73 * each number indicating whether or not it's an original number;
74 * the rules being that concatenation of two numbers is only valid
75 * if they both have the original flag, and that its output _also_
76 * has the original flag (so that you can concatenate three 4s into
77 * a 444), but that applying any other arithmetic operation clears
78 * the original flag on the output. However, we can get marginally
79 * simpler than that by observing that since concatenation has to
80 * happen to a number before any other operation, we can simply
81 * place all the concatenations at the start of the search. In
82 * other words, we have a global flag on an entire number _set_
83 * which indicates whether we are still permitted to perform
84 * concatenations; if so, we can concatenate any of the numbers in
85 * that set. Performing any other operation clears the flag.
88 #define SETFLAG_CONCAT 1 /* we can do concatenation */
93 struct set
*prev
; /* index of ancestor set in set list */
94 unsigned char pa
, pb
, po
, pr
; /* operation that got here from prev */
98 int *numbers
; /* rationals stored as n,d pairs */
99 short nnumbers
; /* # of rationals, so half # of ints */
100 short flags
; /* SETFLAG_CONCAT only, at present */
101 int npaths
; /* number of ways to reach this set */
102 struct ancestor a
; /* primary ancestor */
103 struct ancestor
*as
; /* further ancestors, if we care */
110 int index
; /* which number in the set is it? */
111 int npaths
; /* number of ways to reach this */
114 #define SETLISTLEN 1024
115 #define NUMBERLISTLEN 32768
116 #define OUTPUTLISTLEN 1024
119 struct set
**setlists
;
120 int nsets
, nsetlists
, setlistsize
;
123 int nnumbers
, nnumberlists
, numberlistsize
;
124 struct output
**outputlists
;
125 int noutputs
, noutputlists
, outputlistsize
;
127 const struct operation
*const *ops
;
130 #define OPFLAG_NEEDS_CONCAT 1
131 #define OPFLAG_KEEPS_CONCAT 2
132 #define OPFLAG_UNARY 4
133 #define OPFLAG_UNARYPFX 8
137 * Most operations should be shown in the output working, but
138 * concatenation should not; we just take the result of the
139 * concatenation and assume that it's obvious how it was
145 * Text display of the operator.
150 * Flags dictating when the operator can be applied.
155 * Priority of the operator (for avoiding unnecessary
156 * parentheses when formatting it into a string).
161 * Associativity of the operator. Bit 0 means we need parens
162 * when the left operand of one of these operators is another
163 * instance of it, e.g. (2^3)^4. Bit 1 means we need parens
164 * when the right operand is another instance of the same
165 * operator, e.g. 2-(3-4). Thus:
167 * - this field is 0 for a fully associative operator, since
168 * we never need parens.
169 * - it's 1 for a right-associative operator.
170 * - it's 2 for a left-associative operator.
171 * - it's 3 for a _non_-associative operator (which always
172 * uses parens just to be sure).
177 * Whether the operator is commutative. Saves time in the
178 * search if we don't have to try it both ways round.
183 * Function which implements the operator. Returns TRUE on
184 * success, FALSE on failure. Takes two rationals and writes
187 int (*perform
)(int *a
, int *b
, int *output
);
191 const struct operation
*const *ops
;
195 #define MUL(r, a, b) do { \
197 if ((b) && (a) && (r) / (b) != (a)) return FALSE; \
200 #define ADD(r, a, b) do { \
202 if ((a) > 0 && (b) > 0 && (r) < 0) return FALSE; \
203 if ((a) < 0 && (b) < 0 && (r) > 0) return FALSE; \
206 #define OUT(output, n, d) do { \
207 int g = gcd((n),(d)); \
209 if ((d) < 0) g = -g; \
210 if (g == -1 && (n) < -INT_MAX) return FALSE; \
211 if (g == -1 && (d) < -INT_MAX) return FALSE; \
212 (output)[0] = (n)/g; \
213 (output)[1] = (d)/g; \
214 assert((output)[1] > 0); \
217 static int gcd(int x
, int y
)
219 while (x
!= 0 && y
!= 0) {
225 return abs(x
+ y
); /* i.e. whichever one isn't zero */
228 static int perform_add(int *a
, int *b
, int *output
)
232 * a0/a1 + b0/b1 = (a0*b1 + b0*a1) / (a1*b1)
242 static int perform_sub(int *a
, int *b
, int *output
)
246 * a0/a1 - b0/b1 = (a0*b1 - b0*a1) / (a1*b1)
256 static int perform_mul(int *a
, int *b
, int *output
)
260 * a0/a1 * b0/b1 = (a0*b0) / (a1*b1)
268 static int perform_div(int *a
, int *b
, int *output
)
273 * Division by zero is outlawed.
279 * a0/a1 / b0/b1 = (a0*b1) / (a1*b0)
287 static int perform_exact_div(int *a
, int *b
, int *output
)
292 * Division by zero is outlawed.
298 * a0/a1 / b0/b1 = (a0*b1) / (a1*b0)
305 * Exact division means we require the result to be an integer.
307 return (output
[1] == 1);
310 static int perform_concat(int *a
, int *b
, int *output
)
315 * We can't concatenate anything which isn't a non-negative
318 if (a
[1] != 1 || b
[1] != 1 || a
[0] < 0 || b
[0] < 0)
322 * For concatenation, we can safely assume leading zeroes
323 * aren't an issue. It isn't clear whether they `should' be
324 * allowed, but it turns out not to matter: concatenating a
325 * leading zero on to a number in order to harmlessly get rid
326 * of the zero is never necessary because unwanted zeroes can
327 * be disposed of by adding them to something instead. So we
328 * disallow them always.
330 * The only other possibility is that you might want to
331 * concatenate a leading zero on to something and then
332 * concatenate another non-zero digit on to _that_ (to make,
333 * for example, 106); but that's also unnecessary, because you
334 * can make 106 just as easily by concatenating the 0 on to the
335 * _end_ of the 1 first.
341 * Find the smallest power of ten strictly greater than b. This
342 * is the power of ten by which we'll multiply a.
344 * Special case: we must multiply a by at least 10, even if b
348 while (p10
<= (INT_MAX
/10) && p10
<= b
[0])
350 if (p10
> INT_MAX
/10)
351 return FALSE
; /* integer overflow */
358 #define IPOW(ret, x, y) do { \
359 int ipow_limit = (y); \
360 if ((x) == 1 || (x) == 0) ipow_limit = 1; \
361 else if ((x) == -1) ipow_limit &= 1; \
363 while (ipow_limit-- > 0) { \
370 static int perform_exp(int *a
, int *b
, int *output
)
372 int an
, ad
, xn
, xd
, limit
, t
, i
;
375 * Exponentiation is permitted if the result is rational. This
378 * - first we see whether we can take the (denominator-of-b)th
379 * root of a and get a rational; if not, we give up.
381 * - then we do take that root of a
383 * - then we multiply by itself (numerator-of-b) times.
386 an
= 0.5 + pow(a
[0], 1.0/b
[1]);
387 ad
= 0.5 + pow(a
[1], 1.0/b
[1]);
390 if (xn
!= a
[0] || xd
!= a
[1])
410 static int perform_factorial(int *a
, int *b
, int *output
)
415 * Factorials of non-negative integers are permitted.
417 if (a
[1] != 1 || a
[0] < 0)
421 for (i
= 1; i
<= a
[0]; i
++) {
430 const static struct operation op_add
= {
431 TRUE
, "+", 0, 10, 0, TRUE
, perform_add
433 const static struct operation op_sub
= {
434 TRUE
, "-", 0, 10, 2, FALSE
, perform_sub
436 const static struct operation op_mul
= {
437 TRUE
, "*", 0, 20, 0, TRUE
, perform_mul
439 const static struct operation op_div
= {
440 TRUE
, "/", 0, 20, 2, FALSE
, perform_div
442 const static struct operation op_xdiv
= {
443 TRUE
, "/", 0, 20, 2, FALSE
, perform_exact_div
445 const static struct operation op_concat
= {
446 FALSE
, "", OPFLAG_NEEDS_CONCAT
| OPFLAG_KEEPS_CONCAT
,
447 1000, 0, FALSE
, perform_concat
449 const static struct operation op_exp
= {
450 TRUE
, "^", 0, 30, 1, FALSE
, perform_exp
452 const static struct operation op_factorial
= {
453 TRUE
, "!", OPFLAG_UNARY
, 40, 0, FALSE
, perform_factorial
457 * In Countdown, divisions resulting in fractions are disallowed.
458 * http://www.askoxford.com/wordgames/countdown/rules/
460 const static struct operation
*const ops_countdown
[] = {
461 &op_add
, &op_mul
, &op_sub
, &op_xdiv
, NULL
463 const static struct rules rules_countdown
= {
468 * A slightly different rule set which handles the reasonably well
469 * known puzzle of making 24 using two 3s and two 8s. For this we
470 * need rational rather than integer division.
472 const static struct operation
*const ops_3388
[] = {
473 &op_add
, &op_mul
, &op_sub
, &op_div
, NULL
475 const static struct rules rules_3388
= {
480 * A still more permissive rule set usable for the four-4s problem
481 * and similar things. Permits concatenation.
483 const static struct operation
*const ops_four4s
[] = {
484 &op_add
, &op_mul
, &op_sub
, &op_div
, &op_concat
, NULL
486 const static struct rules rules_four4s
= {
491 * The most permissive ruleset I can think of. Permits
492 * exponentiation, and also silly unary operators like factorials.
494 const static struct operation
*const ops_anythinggoes
[] = {
495 &op_add
, &op_mul
, &op_sub
, &op_div
, &op_concat
, &op_exp
, &op_factorial
, NULL
497 const static struct rules rules_anythinggoes
= {
498 ops_anythinggoes
, TRUE
501 #define ratcmp(a,op,b) ( (long long)(a)[0] * (b)[1] op \
502 (long long)(b)[0] * (a)[1] )
504 static int addtoset(struct set
*set
, int newnumber
[2])
508 /* Find where we want to insert the new number */
509 for (i
= 0; i
< set
->nnumbers
&&
510 ratcmp(set
->numbers
+2*i
, <, newnumber
); i
++);
512 /* Move everything else up */
513 for (j
= set
->nnumbers
; j
> i
; j
--) {
514 set
->numbers
[2*j
] = set
->numbers
[2*j
-2];
515 set
->numbers
[2*j
+1] = set
->numbers
[2*j
-1];
518 /* Insert the new number */
519 set
->numbers
[2*i
] = newnumber
[0];
520 set
->numbers
[2*i
+1] = newnumber
[1];
527 #define ensure(array, size, newlen, type) do { \
528 if ((newlen) > (size)) { \
529 (size) = (newlen) + 512; \
530 (array) = sresize((array), (size), type); \
534 static int setcmp(void *av
, void *bv
)
536 struct set
*a
= (struct set
*)av
;
537 struct set
*b
= (struct set
*)bv
;
540 if (a
->nnumbers
< b
->nnumbers
)
542 else if (a
->nnumbers
> b
->nnumbers
)
545 if (a
->flags
< b
->flags
)
547 else if (a
->flags
> b
->flags
)
550 for (i
= 0; i
< a
->nnumbers
; i
++) {
551 if (ratcmp(a
->numbers
+2*i
, <, b
->numbers
+2*i
))
553 else if (ratcmp(a
->numbers
+2*i
, >, b
->numbers
+2*i
))
560 static int outputcmp(void *av
, void *bv
)
562 struct output
*a
= (struct output
*)av
;
563 struct output
*b
= (struct output
*)bv
;
565 if (a
->number
< b
->number
)
567 else if (a
->number
> b
->number
)
573 static int outputfindcmp(void *av
, void *bv
)
576 struct output
*b
= (struct output
*)bv
;
580 else if (*a
> b
->number
)
586 static void addset(struct sets
*s
, struct set
*set
, int multiple
,
587 struct set
*prev
, int pa
, int po
, int pb
, int pr
)
590 int npaths
= (prev ? prev
->npaths
: 1);
592 assert(set
== s
->setlists
[s
->nsets
/ SETLISTLEN
] + s
->nsets
% SETLISTLEN
);
593 s2
= add234(s
->settree
, set
);
596 * New set added to the tree.
603 set
->npaths
= npaths
;
605 s
->nnumbers
+= 2 * set
->nnumbers
;
607 set
->nas
= set
->assize
= 0;
610 * Rediscovered an existing set. Update its npaths.
612 s2
->npaths
+= npaths
;
614 * And optionally enter it as an additional ancestor.
617 if (s2
->nas
>= s2
->assize
) {
618 s2
->assize
= s2
->nas
* 3 / 2 + 4;
619 s2
->as
= sresize(s2
->as
, s2
->assize
, struct ancestor
);
621 s2
->as
[s2
->nas
].prev
= prev
;
622 s2
->as
[s2
->nas
].pa
= pa
;
623 s2
->as
[s2
->nas
].po
= po
;
624 s2
->as
[s2
->nas
].pb
= pb
;
625 s2
->as
[s2
->nas
].pr
= pr
;
631 static struct set
*newset(struct sets
*s
, int nnumbers
, int flags
)
635 ensure(s
->setlists
, s
->setlistsize
, s
->nsets
/SETLISTLEN
+1, struct set
*);
636 while (s
->nsetlists
<= s
->nsets
/ SETLISTLEN
)
637 s
->setlists
[s
->nsetlists
++] = snewn(SETLISTLEN
, struct set
);
638 sn
= s
->setlists
[s
->nsets
/ SETLISTLEN
] + s
->nsets
% SETLISTLEN
;
640 if (s
->nnumbers
+ nnumbers
* 2 > s
->nnumberlists
* NUMBERLISTLEN
)
641 s
->nnumbers
= s
->nnumberlists
* NUMBERLISTLEN
;
642 ensure(s
->numberlists
, s
->numberlistsize
,
643 s
->nnumbers
/NUMBERLISTLEN
+1, int *);
644 while (s
->nnumberlists
<= s
->nnumbers
/ NUMBERLISTLEN
)
645 s
->numberlists
[s
->nnumberlists
++] = snewn(NUMBERLISTLEN
, int);
646 sn
->numbers
= s
->numberlists
[s
->nnumbers
/ NUMBERLISTLEN
] +
647 s
->nnumbers
% NUMBERLISTLEN
;
650 * Start the set off empty.
659 static int addoutput(struct sets
*s
, struct set
*ss
, int index
, int *n
)
661 struct output
*o
, *o2
;
664 * Target numbers are always integers.
666 if (ss
->numbers
[2*index
+1] != 1)
669 ensure(s
->outputlists
, s
->outputlistsize
, s
->noutputs
/OUTPUTLISTLEN
+1,
671 while (s
->noutputlists
<= s
->noutputs
/ OUTPUTLISTLEN
)
672 s
->outputlists
[s
->noutputlists
++] = snewn(OUTPUTLISTLEN
,
674 o
= s
->outputlists
[s
->noutputs
/ OUTPUTLISTLEN
] +
675 s
->noutputs
% OUTPUTLISTLEN
;
677 o
->number
= ss
->numbers
[2*index
];
680 o
->npaths
= ss
->npaths
;
681 o2
= add234(s
->outputtree
, o
);
683 o2
->npaths
+= o
->npaths
;
691 static struct sets
*do_search(int ninputs
, int *inputs
,
692 const struct rules
*rules
, int *target
,
698 const struct operation
*const *ops
= rules
->ops
;
700 s
= snew(struct sets
);
702 s
->nsets
= s
->nsetlists
= s
->setlistsize
= 0;
703 s
->numberlists
= NULL
;
704 s
->nnumbers
= s
->nnumberlists
= s
->numberlistsize
= 0;
705 s
->outputlists
= NULL
;
706 s
->noutputs
= s
->noutputlists
= s
->outputlistsize
= 0;
707 s
->settree
= newtree234(setcmp
);
708 s
->outputtree
= newtree234(outputcmp
);
712 * Start with the input set.
714 sn
= newset(s
, ninputs
, SETFLAG_CONCAT
);
715 for (i
= 0; i
< ninputs
; i
++) {
717 newnumber
[0] = inputs
[i
];
719 addtoset(sn
, newnumber
);
721 addset(s
, sn
, multiple
, NULL
, 0, 0, 0, 0);
724 * Now perform the breadth-first search: keep looping over sets
725 * until we run out of steam.
728 while (qpos
< s
->nsets
) {
729 struct set
*ss
= s
->setlists
[qpos
/ SETLISTLEN
] + qpos
% SETLISTLEN
;
734 * Record all the valid output numbers in this state. We
735 * can always do this if there's only one number in the
736 * state; otherwise, we can only do it if we aren't
737 * required to use all the numbers in coming to our answer.
739 if (ss
->nnumbers
== 1 || !rules
->use_all
) {
740 for (i
= 0; i
< ss
->nnumbers
; i
++) {
743 if (addoutput(s
, ss
, i
, &n
) && target
&& n
== *target
)
749 * Try every possible operation from this state.
751 for (k
= 0; ops
[k
] && ops
[k
]->perform
; k
++) {
752 if ((ops
[k
]->flags
& OPFLAG_NEEDS_CONCAT
) &&
753 !(ss
->flags
& SETFLAG_CONCAT
))
754 continue; /* can't use this operation here */
755 for (i
= 0; i
< ss
->nnumbers
; i
++) {
756 int jlimit
= (ops
[k
]->flags
& OPFLAG_UNARY ?
1 : ss
->nnumbers
);
757 for (j
= 0; j
< jlimit
; j
++) {
761 if (!(ops
[k
]->flags
& OPFLAG_UNARY
)) {
763 continue; /* can't combine a number with itself */
764 if (i
> j
&& ops
[k
]->commutes
)
765 continue; /* no need to do this both ways round */
767 if (!ops
[k
]->perform(ss
->numbers
+2*i
, ss
->numbers
+2*j
, n
))
768 continue; /* operation failed */
770 sn
= newset(s
, ss
->nnumbers
-1, ss
->flags
);
772 if (!(ops
[k
]->flags
& OPFLAG_KEEPS_CONCAT
))
773 sn
->flags
&= ~SETFLAG_CONCAT
;
775 for (m
= 0; m
< ss
->nnumbers
; m
++) {
776 if (m
== i
|| (!(ops
[k
]->flags
& OPFLAG_UNARY
) &&
779 sn
->numbers
[2*sn
->nnumbers
] = ss
->numbers
[2*m
];
780 sn
->numbers
[2*sn
->nnumbers
+ 1] = ss
->numbers
[2*m
+ 1];
784 if (ops
[k
]->flags
& OPFLAG_UNARY
)
785 pb
= sn
->nnumbers
+10;
789 pr
= addtoset(sn
, n
);
790 addset(s
, sn
, multiple
, ss
, pa
, po
, pb
, pr
);
801 static void free_sets(struct sets
*s
)
805 freetree234(s
->settree
);
806 freetree234(s
->outputtree
);
807 for (i
= 0; i
< s
->nsetlists
; i
++)
808 sfree(s
->setlists
[i
]);
810 for (i
= 0; i
< s
->nnumberlists
; i
++)
811 sfree(s
->numberlists
[i
]);
812 sfree(s
->numberlists
);
813 for (i
= 0; i
< s
->noutputlists
; i
++)
814 sfree(s
->outputlists
[i
]);
815 sfree(s
->outputlists
);
820 * Print a text formula for producing a given output.
822 void print_recurse(struct sets
*s
, struct set
*ss
, int pathindex
, int index
,
823 int priority
, int assoc
, int child
);
824 void print_recurse_inner(struct sets
*s
, struct set
*ss
,
825 struct ancestor
*a
, int pathindex
, int index
,
826 int priority
, int assoc
, int child
)
828 if (a
->prev
&& index
!= a
->pr
) {
832 * This number was passed straight down from this set's
833 * predecessor. Find its index in the previous set and
840 if (pi
>= min(a
->pa
, a
->pb
)) {
842 if (pi
>= max(a
->pa
, a
->pb
))
845 print_recurse(s
, a
->prev
, pathindex
, pi
, priority
, assoc
, child
);
846 } else if (a
->prev
&& index
== a
->pr
&&
847 s
->ops
[a
->po
]->display
) {
849 * This number was created by a displayed operator in the
850 * transition from this set to its predecessor. Hence we
851 * write an open paren, then recurse into the first
852 * operand, then write the operator, then the second
853 * operand, and finally close the paren.
856 int parens
, thispri
, thisassoc
;
859 * Determine whether we need parentheses.
861 thispri
= s
->ops
[a
->po
]->priority
;
862 thisassoc
= s
->ops
[a
->po
]->assoc
;
863 parens
= (thispri
< priority
||
864 (thispri
== priority
&& (assoc
& child
)));
869 if (s
->ops
[a
->po
]->flags
& OPFLAG_UNARYPFX
)
870 for (op
= s
->ops
[a
->po
]->text
; *op
; op
++)
873 print_recurse(s
, a
->prev
, pathindex
, a
->pa
, thispri
, thisassoc
, 1);
875 if (!(s
->ops
[a
->po
]->flags
& OPFLAG_UNARYPFX
))
876 for (op
= s
->ops
[a
->po
]->text
; *op
; op
++)
879 if (!(s
->ops
[a
->po
]->flags
& OPFLAG_UNARY
))
880 print_recurse(s
, a
->prev
, pathindex
, a
->pb
, thispri
, thisassoc
, 2);
886 * This number is either an original, or something formed
887 * by a non-displayed operator (concatenation). Either way,
888 * we display it as is.
890 printf("%d", ss
->numbers
[2*index
]);
891 if (ss
->numbers
[2*index
+1] != 1)
892 printf("/%d", ss
->numbers
[2*index
+1]);
895 void print_recurse(struct sets
*s
, struct set
*ss
, int pathindex
, int index
,
896 int priority
, int assoc
, int child
)
898 if (!ss
->a
.prev
|| pathindex
< ss
->a
.prev
->npaths
) {
899 print_recurse_inner(s
, ss
, &ss
->a
, pathindex
,
900 index
, priority
, assoc
, child
);
903 pathindex
-= ss
->a
.prev
->npaths
;
904 for (i
= 0; i
< ss
->nas
; i
++) {
905 if (pathindex
< ss
->as
[i
].prev
->npaths
) {
906 print_recurse_inner(s
, ss
, &ss
->as
[i
], pathindex
,
907 index
, priority
, assoc
, child
);
910 pathindex
-= ss
->as
[i
].prev
->npaths
;
914 void print(int pathindex
, struct sets
*s
, struct output
*o
)
916 print_recurse(s
, o
->set
, pathindex
, o
->index
, 0, 0, 0);
920 * gcc -g -O0 -o numgame numgame.c -I.. ../{malloc,tree234,nullfe}.c -lm
922 int main(int argc
, char **argv
)
924 int doing_opts
= TRUE
;
925 const struct rules
*rules
= NULL
;
926 char *pname
= argv
[0];
927 int got_target
= FALSE
, target
= 0;
928 int numbers
[10], nnumbers
= 0;
930 int pathcounts
= FALSE
;
931 int multiple
= FALSE
;
941 if (doing_opts
&& *p
== '-') {
944 if (!strcmp(p
, "-")) {
947 } else while (*p
) switch (c
= *p
++) {
949 rules
= &rules_countdown
;
955 rules
= &rules_four4s
;
958 rules
= &rules_anythinggoes
;
978 fprintf(stderr
, "%s: option '-%c' expects an"
979 " argument\n", pname
, c
);
991 fprintf(stderr
, "%s: option '-%c' not"
992 " recognised\n", pname
, c
);
996 if (nnumbers
>= lenof(numbers
)) {
997 fprintf(stderr
, "%s: internal limit of %d numbers exceeded\n",
998 pname
, lenof(numbers
));
1001 numbers
[nnumbers
++] = atoi(p
);
1007 fprintf(stderr
, "%s: no rule set specified; use -C,-B,-D,-A\n", pname
);
1012 fprintf(stderr
, "%s: no input numbers specified\n", pname
);
1016 s
= do_search(nnumbers
, numbers
, rules
, (got_target ?
&target
: NULL
),
1020 o
= findrelpos234(s
->outputtree
, &target
, outputfindcmp
,
1024 o
= findrelpos234(s
->outputtree
, &target
, outputfindcmp
,
1028 assert(start
!= -1 || limit
!= -1);
1031 else if (limit
== -1)
1036 limit
= count234(s
->outputtree
);
1039 for (i
= start
; i
< limit
; i
++) {
1042 o
= index234(s
->outputtree
, i
);
1044 sprintf(buf
, "%d", o
->number
);
1047 sprintf(buf
+ strlen(buf
), " [%d]", o
->npaths
);
1049 if (got_target
|| verbose
) {
1057 for (j
= 0; j
< npaths
; j
++) {
1058 printf("%s = ", buf
);
1063 printf("%s\n", buf
);