2 * range.c: implementation of the Nikoli game 'Kurodoko' / 'Kuromasu'.
6 * Puzzle rules: the player is given a WxH grid of white squares, some
7 * of which contain numbers. The goal is to paint some of the squares
10 * - no cell (err, cell = square) with a number is painted black
11 * - no black cells have an adjacent (horz/vert) black cell
12 * - the white cells are all connected (through other white cells)
13 * - if a cell contains a number n, let h and v be the lengths of the
14 * maximal horizontal and vertical white sequences containing that
15 * cell. Then n must equal h + v - 1.
18 /* example instance with its encoding:
20 * +--+--+--+--+--+--+--+
22 * +--+--+--+--+--+--+--+
24 * +--+--+--+--+--+--+--+
26 * +--+--+--+--+--+--+--+
28 * +--+--+--+--+--+--+--+
30 * +--+--+--+--+--+--+--+
32 * +--+--+--+--+--+--+--+
34 * +--+--+--+--+--+--+--+
36 * 7x7:d7b3e8e5c7a7c13e4d8b4d
50 #define setmember(obj, field) ( (obj) . field = field )
52 char *nfmtstr(int n, char *fmt, ...) {
54 char *ret = snewn(n+1, char);
56 vsprintf(ret, fmt, va);
61 #define SWAP(type, lvar1, lvar2) do { \
67 /* ----------------------------------------------------------------------
68 * Game parameters, presets, states
71 typedef signed char puzzle_size;
79 struct game_params params;
80 unsigned int has_cheated: 1;
81 unsigned int was_solved: 1;
85 #define DEFAULT_PRESET 0
86 static struct game_params presets[] = {{9, 6}, {12, 8}, {13, 9}, {16, 11}};
87 /* rationale: I want all four combinations of {odd/even, odd/even}, as
88 * they play out differently with respect to two-way symmetry. I also
89 * want them to be generated relatively fast yet still be large enough
90 * to be entertaining for a decent amount of time, and I want them to
91 * make good use of monitor real estate (the typical screen resolution
92 * is why I do 13x9 and not 9x13).
95 static game_params *default_params(void)
97 game_params *ret = snew(game_params);
98 *ret = presets[DEFAULT_PRESET]; /* structure copy */
102 static game_params *dup_params(game_params *params)
104 game_params *ret = snew(game_params);
105 *ret = *params; /* structure copy */
109 static int game_fetch_preset(int i, char **name, game_params **params)
111 if (i < 0 || i >= lenof(presets)) return FALSE;
113 *name = nfmtstr(40, "%d x %d", presets[i].w, presets[i].h);
114 *params = dup_params(&presets[i]);
119 static void free_params(game_params *params)
124 static void decode_params(game_params *params, char const *string)
126 /* FIXME check for puzzle_size overflow and decoding issues */
127 params->w = params->h = atoi(string);
128 while (*string && isdigit((unsigned char) *string)) ++string;
129 if (*string == 'x') {
131 params->h = atoi(string);
132 while (*string && isdigit((unsigned char)*string)) string++;
136 static char *encode_params(game_params *params, int full)
139 sprintf(str, "%dx%d", params->w, params->h);
143 static config_item *game_configure(game_params *params)
147 ret = snewn(3, config_item);
149 ret[0].name = "Width";
150 ret[0].type = C_STRING;
151 ret[0].sval = nfmtstr(10, "%d", params->w);
154 ret[1].name = "Height";
155 ret[1].type = C_STRING;
156 ret[1].sval = nfmtstr(10, "%d", params->h);
167 static game_params *custom_params(config_item *configuration)
169 game_params *ret = snew(game_params);
170 ret->w = atoi(configuration[0].sval);
171 ret->h = atoi(configuration[1].sval);
175 #define memdup(dst, src, n, type) do { \
176 dst = snewn(n, type); \
177 memcpy(dst, src, n * sizeof (type)); \
180 static game_state *dup_game(game_state *state)
182 game_state *ret = snew(game_state);
183 int const n = state->params.w * state->params.h;
185 *ret = *state; /* structure copy */
187 /* copy the poin_tee_, set a new value of the poin_ter_ */
188 memdup(ret->grid, state->grid, n, puzzle_size);
193 static void free_game(game_state *state)
200 /* ----------------------------------------------------------------------
201 * The solver subsystem.
203 * The solver is used for two purposes:
204 * - To solve puzzles when the user selects `Solve'.
205 * - To test solubility of a grid as clues are being removed from it
206 * during the puzzle generation.
208 * It supports the following ways of reasoning:
210 * - A cell adjacent to a black cell must be white.
212 * - If painting a square black would bisect the white regions, that
213 * square is white (by finding biconnected components' cut points)
215 * - A cell with number n, covering at most k white squares in three
216 * directions must white-cover n-k squares in the last direction.
218 * - A cell with number n known to cover k squares, if extending the
219 * cover by one square in a given direction causes the cell to
220 * cover _more_ than n squares, that extension cell must be black.
222 * (either if the square already covers n, or if it extends into a
223 * chunk of size > n - k)
225 * - Recursion. Pick any cell and see if this leads to either a
226 * contradiction or a solution (and then act appropriately).
231 * (propagation upper limit)
232 * - If one has two numbers on the same line, the smaller limits the
233 * larger. Example: in |b|_|_|8|4|_|_|b|, only two _'s can be both
234 * white and connected to the "8" cell; so that cell will propagate
235 * at least four cells orthogonally to the displayed line (which is
236 * better than the current "at least 2").
238 * (propagation upper limit)
239 * - cells can't propagate into other cells if doing so exceeds that
240 * number. Example: in |b|4|.|.|2|b|, at most one _ can be white;
241 * otherwise, the |2| would have too many reaching white cells.
243 * (propagation lower and upper limit)
244 * - `Full Combo': in each four directions d_1 ... d_4, find a set of
245 * possible propagation distances S_1 ... S_4. For each i=1..4,
246 * for each x in S_i: if not exists (y, z, w) in the other sets
247 * such that (x+y+z+w+1 == clue value): then remove x from S_i.
248 * Repeat until this stabilizes. If any cell would contradict
251 #define idx(i, j, w) ((i)*(w) + (j))
252 #define out_of_bounds(r, c, w, h) \
253 ((r) < 0 || (r) >= h || (c) < 0 || (c) >= w)
255 typedef struct square {
259 enum {BLACK = -2, WHITE, EMPTY};
260 /* white is for pencil marks, empty is undecided */
262 static int const dr[4] = {+1, 0, -1, 0};
263 static int const dc[4] = { 0, +1, 0, -1};
264 static int const cursors[4] = /* must match dr and dc */
265 {CURSOR_DOWN, CURSOR_RIGHT, CURSOR_UP, CURSOR_LEFT};
267 typedef struct move {
269 unsigned int colour: 1;
271 enum {M_BLACK = 0, M_WHITE = 1};
273 typedef move *(reasoning)(game_state *state,
278 static reasoning solver_reasoning_not_too_big;
279 static reasoning solver_reasoning_adjacency;
280 static reasoning solver_reasoning_connectedness;
281 static reasoning solver_reasoning_recursion;
290 static move *solve_internal(game_state *state, move *base, int diff);
292 static char *solve_game(game_state *orig, game_state *curpos,
293 char *aux, char **error)
295 int const n = orig->params.w * orig->params.h;
296 move *const base = snewn(n, move);
297 move *moves = solve_internal(orig, base, DIFF_RECURSION);
302 int const k = moves - base;
303 char *str = ret = snewn(15*k + 2, char);
304 char colour[2] = "BW";
308 for (it = base; it < moves; ++it)
309 str += sprintf(str, "%c,%d,%d", colour[it->colour],
310 it->square.r, it->square.c);
311 } else *error = "This puzzle instance contains a contradiction";
317 static square *find_clues(game_state *state, int *ret_nclues);
318 static move *do_solve(game_state *state,
324 /* new_game_desc entry point in the solver subsystem */
325 static move *solve_internal(game_state *state, move *base, int diff)
328 square *const clues = find_clues(state, &nclues);
329 game_state *dup = dup_game(state);
330 move *const moves = do_solve(dup, nclues, clues, base, diff);
336 static move *do_solve(game_state *state,
342 reasoning *reasonings[] = {
343 solver_reasoning_not_too_big,
344 solver_reasoning_adjacency,
345 solver_reasoning_connectedness,
346 solver_reasoning_recursion
349 struct move *buf = move_buffer, *oldbuf;
354 for (i = 0; i < lenof(reasonings) && i <= difficulty; ++i) {
355 /* only recurse if all else fails */
356 if (i == DIFF_RECURSION && buf > oldbuf) continue;
357 buf = (*reasonings[i])(state, nclues, clues, buf);
358 if (buf == NULL) return NULL;
360 } while (buf > oldbuf);
365 #define MASK(n) (1 << ((n) + 2))
367 static int runlength(puzzle_size r, puzzle_size c,
368 puzzle_size dr, puzzle_size dc,
369 game_state *state, int colourmask)
371 int const w = state->params.w, h = state->params.h;
374 int cell = idx(r, c, w);
375 if (out_of_bounds(r, c, w, h)) break;
376 if (state->grid[cell] > 0) {
377 if (!(colourmask & ~(MASK(BLACK) | MASK(WHITE) | MASK(EMPTY))))
379 } else if (!(MASK(state->grid[cell]) & colourmask)) break;
387 static void solver_makemove(puzzle_size r, puzzle_size c, int colour,
388 game_state *state, move **buffer_ptr)
390 int const cell = idx(r, c, state->params.w);
391 if (out_of_bounds(r, c, state->params.w, state->params.h)) return;
392 if (state->grid[cell] != EMPTY) return;
393 setmember((*buffer_ptr)->square, r);
394 setmember((*buffer_ptr)->square, c);
395 setmember(**buffer_ptr, colour);
397 state->grid[cell] = (colour == M_BLACK ? BLACK : WHITE);
400 static move *solver_reasoning_adjacency(game_state *state,
406 for (r = 0; r < state->params.h; ++r)
407 for (c = 0; c < state->params.w; ++c) {
408 int const cell = idx(r, c, state->params.w);
409 if (state->grid[cell] != BLACK) continue;
410 for (i = 0; i < 4; ++i)
411 solver_makemove(r + dr[i], c + dc[i], M_WHITE, state, &buf);
416 enum {NOT_VISITED = -1};
418 static int dfs_biconnect_visit(puzzle_size r, puzzle_size c,
420 square *dfs_parent, int *dfs_depth,
423 static move *solver_reasoning_connectedness(game_state *state,
428 int const w = state->params.w, h = state->params.h, n = w * h;
430 square *const dfs_parent = snewn(n, square);
431 int *const dfs_depth = snewn(n, int);
434 for (i = 0; i < n; ++i) {
435 dfs_parent[i].r = NOT_VISITED;
439 for (i = 0; i < n && state->grid[i] == BLACK; ++i);
441 dfs_parent[i].r = i / w;
442 dfs_parent[i].c = i % w; /* `dfs root`.parent == `dfs root` */
445 dfs_biconnect_visit(i / w, i % w, state, dfs_parent, dfs_depth, &buf);
453 /* returns the `lowpoint` of (r, c) */
454 static int dfs_biconnect_visit(puzzle_size r, puzzle_size c,
456 square *dfs_parent, int *dfs_depth,
459 const puzzle_size w = state->params.w, h = state->params.h;
460 int const i = idx(r, c, w), mydepth = dfs_depth[i];
461 int lowpoint = mydepth, j, nchildren = 0;
463 for (j = 0; j < 4; ++j) {
464 const puzzle_size rr = r + dr[j], cc = c + dc[j];
465 int const cell = idx(rr, cc, w);
467 if (out_of_bounds(rr, cc, w, h)) continue;
468 if (state->grid[cell] == BLACK) continue;
470 if (dfs_parent[cell].r == NOT_VISITED) {
472 dfs_parent[cell].r = r;
473 dfs_parent[cell].c = c;
474 dfs_depth[cell] = mydepth + 1;
475 child_lowpoint = dfs_biconnect_visit(rr, cc, state, dfs_parent,
478 if (child_lowpoint >= mydepth && mydepth > 0)
479 solver_makemove(r, c, M_WHITE, state, buf);
481 lowpoint = min(lowpoint, child_lowpoint);
483 } else if (rr != dfs_parent[i].r || cc != dfs_parent[i].c) {
484 lowpoint = min(lowpoint, dfs_depth[cell]);
488 if (mydepth == 0 && nchildren >= 2)
489 solver_makemove(r, c, M_WHITE, state, buf);
494 static move *solver_reasoning_not_too_big(game_state *state,
499 int const w = state->params.w, runmasks[4] = {
500 ~(MASK(BLACK) | MASK(EMPTY)),
502 ~(MASK(BLACK) | MASK(EMPTY)),
505 enum {RUN_WHITE, RUN_EMPTY, RUN_BEYOND, RUN_SPACE};
507 int i, runlengths[4][4];
509 for (i = 0; i < nclues; ++i) {
510 int j, k, whites, space;
512 const puzzle_size row = clues[i].r, col = clues[i].c;
513 int const clue = state->grid[idx(row, col, w)];
515 for (j = 0; j < 4; ++j) {
516 puzzle_size r = row + dr[j], c = col + dc[j];
517 runlengths[RUN_SPACE][j] = 0;
518 for (k = 0; k <= RUN_SPACE; ++k) {
519 int l = runlength(r, c, dr[j], dc[j], state, runmasks[k]);
521 runlengths[k][j] = l;
525 runlengths[RUN_SPACE][j] += l;
530 for (j = 0; j < 4; ++j) whites += runlengths[RUN_WHITE][j];
532 for (j = 0; j < 4; ++j) {
533 int const delta = 1 + runlengths[RUN_WHITE][j];
534 const puzzle_size r = row + delta * dr[j];
535 const puzzle_size c = col + delta * dc[j];
537 if (whites == clue) {
538 solver_makemove(r, c, M_BLACK, state, &buf);
542 if (runlengths[RUN_EMPTY][j] == 1 &&
544 + runlengths[RUN_EMPTY][j]
545 + runlengths[RUN_BEYOND][j]
547 solver_makemove(r, c, M_BLACK, state, &buf);
552 + runlengths[RUN_EMPTY][j]
553 + runlengths[RUN_BEYOND][j]
555 runlengths[RUN_SPACE][j] =
556 runlengths[RUN_WHITE][j] +
557 runlengths[RUN_EMPTY][j] - 1;
559 if (runlengths[RUN_EMPTY][j] == 1)
560 solver_makemove(r, c, M_BLACK, state, &buf);
565 for (j = 0; j < 4; ++j) space += runlengths[RUN_SPACE][j];
566 for (j = 0; j < 4; ++j) {
567 puzzle_size r = row + dr[j], c = col + dc[j];
569 int k = space - runlengths[RUN_SPACE][j];
570 if (k >= clue) continue;
572 for (; k < clue; ++k, r += dr[j], c += dc[j])
573 solver_makemove(r, c, M_WHITE, state, &buf);
579 static move *solver_reasoning_recursion(game_state *state,
584 int const w = state->params.w, n = w * state->params.h;
587 for (cell = 0; cell < n; ++cell) {
588 int const r = cell / w, c = cell % w;
590 game_state *newstate;
591 move *recursive_result;
593 if (state->grid[cell] != EMPTY) continue;
595 /* FIXME: add enum alias for smallest and largest (or N) */
596 for (colour = M_BLACK; colour <= M_WHITE; ++colour) {
597 newstate = dup_game(state);
598 newstate->grid[cell] = colour;
599 recursive_result = do_solve(newstate, nclues, clues, buf,
602 if (recursive_result == NULL) {
603 solver_makemove(r, c, M_BLACK + M_WHITE - colour, state, &buf);
606 for (i = 0; i < n && newstate->grid[i] != EMPTY; ++i);
607 if (i == n) return buf;
613 static square *find_clues(game_state *state, int *ret_nclues)
615 int r, c, i, nclues = 0;
616 square *ret = snewn(state->params.w * state->params.h, struct square);
618 for (i = r = 0; r < state->params.h; ++r)
619 for (c = 0; c < state->params.w; ++c, ++i)
620 if (state->grid[i] > 0) {
626 *ret_nclues = nclues;
627 return sresize(ret, nclues + (nclues == 0), square);
630 /* ----------------------------------------------------------------------
633 * Generating kurodoko instances is rather straightforward:
635 * - Start with a white grid and add black squares at randomly chosen
636 * locations, unless colouring that square black would violate
637 * either the adjacency or connectedness constraints.
639 * - For each white square, compute the number it would contain if it
640 * were given as a clue.
642 * - From a starting point of "give _every_ white square as a clue",
643 * for each white square (in a random order), see if the board is
644 * solvable when that square is not given as a clue. If not, don't
645 * give it as a clue, otherwise do.
647 * This never fails, but it's only _almost_ what I do. The real final
650 * - From a starting point of "give _every_ white square as a clue",
651 * first remove all clues that are two-way rotationally symmetric
652 * to a black square. If this leaves the puzzle unsolvable, throw
653 * it out and try again. Otherwise, remove all _pairs_ of clues
654 * (that are rotationally symmetric) which can be removed without
655 * rendering the puzzle unsolvable.
657 * This can fail even if one only removes the black and symmetric
658 * clues; indeed it happens often (avg. once or twice per puzzle) when
659 * generating 1xN instances. (If you add black cells they must be in
660 * the end, and if you only add one, it's ambiguous where).
663 /* forward declarations of internal calls */
664 static void newdesc_choose_black_squares(game_state *state,
665 const int *shuffle_1toN);
666 static void newdesc_compute_clues(game_state *state);
667 static int newdesc_strip_clues(game_state *state, int *shuffle_1toN);
668 static char *newdesc_encode_game_description(int n, puzzle_size *grid);
670 static char *new_game_desc(game_params *params, random_state *rs,
671 char **aux, int interactive)
673 int const w = params->w, h = params->h, n = w * h;
675 puzzle_size *const grid = snewn(n, puzzle_size);
676 int *const shuffle_1toN = snewn(n, int);
678 int i, clues_removed;
683 state.params = *params;
686 interactive = 0; /* I don't need it, I shouldn't use it*/
688 for (i = 0; i < n; ++i) shuffle_1toN[i] = i;
691 shuffle(shuffle_1toN, n, sizeof (int), rs);
692 newdesc_choose_black_squares(&state, shuffle_1toN);
694 newdesc_compute_clues(&state);
696 shuffle(shuffle_1toN, n, sizeof (int), rs);
697 clues_removed = newdesc_strip_clues(&state, shuffle_1toN);
699 if (clues_removed < 0) continue; else break;
702 encoding = newdesc_encode_game_description(n, grid);
710 static int dfs_count_white(game_state *state, int cell);
712 static void newdesc_choose_black_squares(game_state *state,
713 const int *shuffle_1toN)
715 int const w = state->params.w, h = state->params.h, n = w * h;
717 int k, any_white_cell, n_black_cells;
719 for (k = 0; k < n; ++k) state->grid[k] = WHITE;
721 any_white_cell = shuffle_1toN[n - 1];
724 /* I like the puzzles that result from n / 3, but maybe this
725 * could be made a (generation, i.e. non-full) parameter? */
726 for (k = 0; k < n / 3; ++k) {
727 int const i = shuffle_1toN[k], c = i % w, r = i / w;
730 for (j = 0; j < 4; ++j) {
731 int const rr = r + dr[j], cc = c + dc[j], cell = idx(rr, cc, w);
732 /* if you're out of bounds, we skip you */
733 if (out_of_bounds(rr, cc, w, h)) continue;
734 if (state->grid[cell] == BLACK) break; /* I can't be black */
735 } if (j < 4) continue; /* I have black neighbour: I'm white */
737 state->grid[i] = BLACK;
740 j = dfs_count_white(state, any_white_cell);
741 if (j + n_black_cells < n) {
742 state->grid[i] = WHITE;
748 static void newdesc_compute_clues(game_state *state)
750 int const w = state->params.w, h = state->params.h;
753 for (r = 0; r < h; ++r) {
754 int run_size = 0, c, cc;
755 for (c = 0; c <= w; ++c) {
756 if (c == w || state->grid[idx(r, c, w)] == BLACK) {
757 for (cc = c - run_size; cc < c; ++cc)
758 state->grid[idx(r, cc, w)] += run_size;
764 for (c = 0; c < w; ++c) {
765 int run_size = 0, r, rr;
766 for (r = 0; r <= h; ++r) {
767 if (r == h || state->grid[idx(r, c, w)] == BLACK) {
768 for (rr = r - run_size; rr < r; ++rr)
769 state->grid[idx(rr, c, w)] += run_size;
776 #define rotate(x) (n - 1 - (x))
778 static int newdesc_strip_clues(game_state *state, int *shuffle_1toN)
780 int const w = state->params.w, n = w * state->params.h;
782 move *const move_buffer = snewn(n, move);
784 game_state *dupstate;
787 * do a partition/pivot of shuffle_1toN into three groups:
788 * (1) squares rotationally-symmetric to (3)
789 * (2) squares not in (1) or (3)
792 * They go from [0, left), [left, right) and [right, n) in
793 * shuffle_1toN (and from there into state->grid[ ])
795 * Then, remove clues from the grid one by one in shuffle_1toN
796 * order, until the solver becomes unhappy. If we didn't remove
797 * all of (1), return (-1). Else, we're happy.
800 /* do the partition */
801 int clues_removed, k = 0, left = 0, right = n;
804 while (k < right && state->grid[shuffle_1toN[k]] == BLACK) {
806 SWAP(int, shuffle_1toN[right], shuffle_1toN[k]);
807 assert(state->grid[shuffle_1toN[right]] == BLACK);
809 if (k >= right) break;
811 if (state->grid[rotate(shuffle_1toN[k])] == BLACK) {
812 SWAP(int, shuffle_1toN[k], shuffle_1toN[left]);
815 assert (state->grid[rotate(shuffle_1toN[k])] != BLACK
819 for (k = 0; k < left; ++k) {
820 assert (state->grid[rotate(shuffle_1toN[k])] == BLACK);
821 state->grid[shuffle_1toN[k]] = EMPTY;
823 for (k = left; k < right; ++k) {
824 assert (state->grid[rotate(shuffle_1toN[k])] != BLACK);
825 assert (state->grid[shuffle_1toN[k]] != BLACK);
827 for (k = right; k < n; ++k) {
828 assert (state->grid[shuffle_1toN[k]] == BLACK);
829 state->grid[shuffle_1toN[k]] = EMPTY;
832 clues_removed = (left - 0) + (n - right);
834 dupstate = dup_game(state);
835 buf = solve_internal(dupstate, move_buffer, DIFF_RECURSION - 1);
837 if (buf - move_buffer < clues_removed) {
838 /* branch prediction: I don't think I'll go here */
843 for (k = left; k < right; ++k) {
844 const int i = shuffle_1toN[k], j = rotate(i);
845 int const clue = state->grid[i], clue_rot = state->grid[j];
846 if (clue == BLACK) continue;
847 state->grid[i] = state->grid[j] = EMPTY;
848 dupstate = dup_game(state);
849 buf = solve_internal(dupstate, move_buffer, DIFF_RECURSION - 1);
851 clues_removed += 2 - (i == j);
852 /* if i is the center square, then i == (j = rotate(i))
853 * when i and j are one, removing i and j removes only one */
854 if (buf - move_buffer == clues_removed) continue;
855 /* if the solver is sound, refilling all removed clues means
856 * we have filled all squares, i.e. solved the puzzle. */
857 state->grid[i] = clue;
858 state->grid[j] = clue_rot;
859 clues_removed -= 2 - (i == j);
864 return clues_removed;
867 static int dfs_count_rec(puzzle_size *grid, int r, int c, int w, int h)
869 int const cell = idx(r, c, w);
870 if (out_of_bounds(r, c, w, h)) return 0;
871 if (grid[cell] != WHITE) return 0;
874 dfs_count_rec(grid, r + 0, c + 1, w, h) +
875 dfs_count_rec(grid, r + 0, c - 1, w, h) +
876 dfs_count_rec(grid, r + 1, c + 0, w, h) +
877 dfs_count_rec(grid, r - 1, c + 0, w, h);
880 static int dfs_count_white(game_state *state, int cell)
882 int const w = state->params.w, h = state->params.h, n = w * h;
883 int const r = cell / w, c = cell % w;
884 int i, k = dfs_count_rec(state->grid, r, c, w, h);
885 for (i = 0; i < n; ++i)
886 if (state->grid[i] == EMPTY)
887 state->grid[i] = WHITE;
891 static char *validate_params(game_params *params, int full)
893 int const w = params->w, h = params->h;
894 if (w < 1) return "Error: width is less than 1";
895 if (h < 1) return "Error: height is less than 1";
896 if (w * h < 1) return "Error: size is less than 1";
897 if (w + h - 1 > SCHAR_MAX) return "Error: w + h is too big";
898 /* I might be unable to store clues in my puzzle_size *grid; */
900 if (w == 2 && h == 2) return "Error: can't create 2x2 puzzles";
901 if (w == 1 && h == 2) return "Error: can't create 1x2 puzzles";
902 if (w == 2 && h == 1) return "Error: can't create 2x1 puzzles";
903 if (w == 1 && h == 1) return "Error: can't create 1x1 puzzles";
908 /* Definition: a puzzle instance is _good_ if:
909 * - it has a unique solution
910 * - the solver can find this solution without using recursion
911 * - the solution contains at least one black square
912 * - the clues are 2-way rotationally symmetric
914 * (the idea being: the generator can not output any _bad_ puzzles)
916 * Theorem: validate_params, when full != 0, discards exactly the set
917 * of parameters for which there are _no_ good puzzle instances.
919 * Proof: it's an immediate consequence of the five lemmas below.
921 * Observation: not only do puzzles on non-tiny grids exist, the
922 * generator is pretty fast about coming up with them. On my pre-2004
923 * desktop box, it generates 100 puzzles on the highest preset (16x11)
924 * in 8.383 seconds, or <= 0.1 second per puzzle.
926 * ----------------------------------------------------------------------
928 * Lemma: On a 1x1 grid, there are no good puzzles.
930 * Proof: the one square can't be a clue because at least one square
931 * is black. But both a white square and a black square satisfy the
932 * solution criteria, so the puzzle is ambiguous (and hence bad).
934 * Lemma: On a 1x2 grid, there are no good puzzles.
936 * Proof: let's name the squares l and r. Note that there can be at
937 * most one black square, or adjacency is violated. By assumption at
938 * least one square is black, so let's call that one l. By clue
939 * symmetry, neither l nor r can be given as a clue, so the puzzle
940 * instance is blank and thus ambiguous.
942 * Corollary: On a 2x1 grid, there are no good puzzles.
943 * Proof: rotate the above proof 90 degrees ;-)
945 * ----------------------------------------------------------------------
947 * Lemma: On a 2x2 grid, there are no soluble puzzles with 2-way
948 * rotational symmetric clues and at least one black square.
950 * Proof: Let's name the squares a, b, c, and d, with a and b on the
951 * top row, a and c in the left column. Let's consider the case where
952 * a is black. Then no other square can be black: b and c would both
953 * violate the adjacency constraint; d would disconnect b from c.
955 * So exactly one square is black (and by 4-way rotation symmetry of
956 * the 2x2 square, it doesn't matter which one, so let's stick to a).
957 * By 2-way rotational symmetry of the clues and the rule about not
958 * painting numbers black, neither a nor d can be clues. A blank
959 * puzzle would be ambiguous, so one of {b, c} is a clue; by symmetry,
960 * so is the other one.
962 * It is readily seen that their clue value is 2. But "a is black"
963 * and "d is black" are both valid solutions in this case, so the
964 * puzzle is ambiguous (and hence bad).
966 * ----------------------------------------------------------------------
968 * Lemma: On a wxh grid with w, h >= 1 and (w > 2 or h > 2), there is
969 * at least one good puzzle.
971 * Proof: assume that w > h (otherwise rotate the proof again). Paint
972 * the top left and bottom right corners black, and fill a clue into
973 * all the other squares. Present this board to the solver code (or
974 * player, hypothetically), except with the two black squares as blank
977 * For an Nx1 puzzle, observe that every clue is N - 2, and there are
978 * N - 2 of them in one connected sequence, so the remaining two
979 * squares can be deduced to be black, which solves the puzzle.
981 * For any other puzzle, let j be a cell in the same row as a black
982 * cell, but not in the same column (such a cell doesn't exist in 2x3
983 * puzzles, but we assume w > h and such cells exist in 3x2 puzzles).
985 * Note that the number of cells in axis parallel `rays' going out
986 * from j exceeds j's clue value by one. Only one such cell is a
987 * non-clue, so it must be black. Similarly for the other corner (let
988 * j' be a cell in the same row as the _other_ black cell, but not in
989 * the same column as _any_ black cell; repeat this argument at j').
991 * This fills the grid and satisfies all clues and the adjacency
992 * constraint and doesn't paint on top of any clues. All that is left
993 * to see is connectedness.
995 * Observe that the white cells in each column form a single connected
996 * `run', and each column contains a white cell adjacent to a white
997 * cell in the column to the right, if that column exists.
999 * Thus, any cell in the left-most column can reach any other cell:
1000 * first go to the target column (by repeatedly going to the cell in
1001 * your current column that lets you go right, then going right), then
1002 * go up or down to the desired cell.
1004 * As reachability is symmetric (in undirected graphs) and transitive,
1005 * any cell can reach any left-column cell, and from there any other
1009 /* ----------------------------------------------------------------------
1010 * Game encoding and decoding
1013 #define NDIGITS_BASE '!'
1015 static char *newdesc_encode_game_description(int area, puzzle_size *grid)
1018 int desclen = 0, descsize = 0;
1022 for (i = 0; i <= area; i++) {
1023 int n = (i < area ? grid[i] : -1);
1028 if (descsize < desclen + 40) {
1029 descsize = desclen * 3 / 2 + 40;
1030 desc = sresize(desc, descsize, char);
1034 int c = 'a' - 1 + run;
1037 desc[desclen++] = c;
1038 run -= c - ('a' - 1);
1042 * If there's a number in the very top left or
1043 * bottom right, there's no point putting an
1044 * unnecessary _ before or after it.
1046 if (desclen > 0 && n > 0)
1047 desc[desclen++] = '_';
1050 desclen += sprintf(desc+desclen, "%d", n);
1054 desc[desclen] = '\0';
1058 static char *validate_desc(game_params *params, char *desc)
1060 int const n = params->w * params->h;
1062 int range = params->w + params->h - 1; /* maximum cell value */
1064 while (*desc && *desc != ',') {
1066 if (c >= 'a' && c <= 'z') {
1067 squares += c - 'a' + 1;
1068 } else if (c == '_') {
1070 } else if (c > '0' && c <= '9') {
1071 int val = atoi(desc-1);
1072 if (val < 1 || val > range)
1073 return "Out-of-range number in game description";
1075 while (*desc >= '0' && *desc <= '9')
1078 return "Invalid character in game description";
1082 return "Not enough data to fill grid";
1085 return "Too much data to fit in grid";
1090 static game_state *new_game(midend *me, game_params *params, char *desc)
1095 int const n = params->w * params->h;
1096 game_state *state = snew(game_state);
1098 me = NULL; /* I don't need it, I shouldn't use it */
1100 state->params = *params; /* structure copy */
1101 state->grid = snewn(n, puzzle_size);
1105 while (i < n && *p) {
1107 if (c >= 'a' && c <= 'z') {
1108 int squares = c - 'a' + 1;
1110 state->grid[i++] = 0;
1111 } else if (c == '_') {
1113 } else if (c > '0' && c <= '9') {
1114 int val = atoi(p-1);
1115 assert(val >= 1 && val <= params->w+params->h-1);
1116 state->grid[i++] = val;
1117 while (*p >= '0' && *p <= '9')
1122 state->has_cheated = FALSE;
1123 state->was_solved = FALSE;
1128 /* ----------------------------------------------------------------------
1129 * User interface: ascii
1132 static int game_can_format_as_text_now(game_params *params)
1137 static char *game_text_format(game_state *state)
1139 int cellsize, r, c, i, w_string, h_string, n_string;
1140 char *ret, *buf, *gridline;
1142 int const w = state->params.w, h = state->params.h;
1144 cellsize = 0; /* or may be used uninitialized */
1146 for (c = 0; c < w; ++c) {
1147 for (r = 1; r < h; ++r) {
1148 puzzle_size k = state->grid[idx(r, c, w)];
1150 for (d = 0; k; k /= 10, ++d);
1151 cellsize = max(cellsize, d);
1157 w_string = w * cellsize + 2; /* "|%d|%d|...|\n" */
1158 h_string = 2 * h + 1; /* "+--+--+...+\n%s\n+--+--+...+\n" */
1159 n_string = w_string * h_string;
1161 gridline = snewn(w_string + 1, char); /* +1: NUL terminator */
1162 memset(gridline, '-', w_string);
1163 for (c = 0; c <= w; ++c) gridline[c * cellsize] = '+';
1164 gridline[w_string - 1] = '\n';
1165 gridline[w_string - 0] = '\0';
1167 buf = ret = snewn(n_string + 1, char); /* +1: NUL terminator */
1168 for (i = r = 0; r < h; ++r) {
1169 memcpy(buf, gridline, w_string);
1171 for (c = 0; c < w; ++c, ++i) {
1173 switch (state->grid[i]) {
1174 case BLACK: ch = '#'; break;
1175 case WHITE: ch = '.'; break;
1176 case EMPTY: ch = ' '; break;
1178 buf += sprintf(buf, "|%*d", cellsize - 1, state->grid[i]);
1182 memset(buf, ch, cellsize - 1);
1183 buf += cellsize - 1;
1185 buf += sprintf(buf, "|\n");
1187 memcpy(buf, gridline, w_string);
1189 assert (buf - ret == n_string);
1197 /* ----------------------------------------------------------------------
1198 * User interfaces: interactive
1202 puzzle_size r, c; /* cursor position */
1203 unsigned int cursor_show: 1;
1204 unsigned int cheated: 1;
1207 static game_ui *new_ui(game_state *state)
1209 struct game_ui *ui = snew(game_ui);
1211 ui->cursor_show = ui->cheated = FALSE;
1215 static void free_ui(game_ui *ui)
1220 static char *encode_ui(game_ui *ui)
1222 return dupstr(ui->cheated ? "1" : "0");
1225 static void decode_ui(game_ui *ui, char *encoding)
1227 ui->cheated = (*encoding == '1');
1230 typedef struct drawcell {
1232 unsigned int error: 1;
1233 unsigned int cursor: 1;
1234 unsigned int flash: 1;
1237 struct game_drawstate {
1240 unsigned int started: 1;
1243 #define TILESIZE (ds->tilesize)
1244 #define BORDER (TILESIZE / 2)
1245 #define COORD(x) ((x) * TILESIZE + BORDER)
1246 #define FROMCOORD(x) (((x) - BORDER) / TILESIZE)
1248 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
1249 int x, int y, int button)
1251 enum {none, forwards, backwards, hint};
1252 int const w = state->params.w, h = state->params.h;
1253 int r = ui->r, c = ui->c, action = none, cell;
1255 if (IS_CURSOR_SELECT(button) && !ui->cursor_show) return NULL;
1257 if (IS_MOUSE_DOWN(button)) {
1258 r = FROMCOORD(y + TILESIZE) - 1; /* or (x, y) < TILESIZE) */
1259 c = FROMCOORD(x + TILESIZE) - 1; /* are considered inside */
1260 if (out_of_bounds(r, c, w, h)) return NULL;
1263 ui->cursor_show = FALSE;
1266 if (button == LEFT_BUTTON || button == RIGHT_BUTTON) {
1268 * Utterly awful hack, exactly analogous to the one in Slant,
1269 * to configure the left and right mouse buttons the opposite
1272 * The original puzzle submitter thought it would be more
1273 * useful to have the left button turn an empty square into a
1274 * dotted one, on the grounds that that was what you did most
1275 * often; I (SGT) felt instinctively that the left button
1276 * ought to place black squares and the right button place
1277 * dots, on the grounds that that was consistent with many
1278 * other puzzles in which the left button fills in the data
1279 * used by the solution checker while the right button places
1280 * pencil marks for the user's convenience.
1282 * My first beta-player wasn't sure either, so I thought I'd
1283 * pre-emptively put in a 'configuration' mechanism just in
1287 static int swap_buttons = -1;
1288 if (swap_buttons < 0) {
1289 char *env = getenv("RANGE_SWAP_BUTTONS");
1290 swap_buttons = (env && (env[0] == 'y' || env[0] == 'Y'));
1293 if (button == LEFT_BUTTON)
1294 button = RIGHT_BUTTON;
1296 button = LEFT_BUTTON;
1302 case CURSOR_SELECT : case LEFT_BUTTON: action = backwards; break;
1303 case CURSOR_SELECT2: case RIGHT_BUTTON: action = forwards; break;
1304 case 'h': case 'H' : action = hint; break;
1305 case CURSOR_UP: case CURSOR_DOWN:
1306 case CURSOR_LEFT: case CURSOR_RIGHT:
1307 if (ui->cursor_show) {
1309 for (i = 0; i < 4 && cursors[i] != button; ++i);
1311 if (!out_of_bounds(ui->r + dr[i], ui->c + dc[i], w, h)) {
1315 } else ui->cursor_show = TRUE;
1319 if (action == hint) {
1320 move *end, *buf = snewn(state->params.w * state->params.h,
1323 end = solve_internal(state, buf, DIFF_RECURSION);
1324 if (end != NULL && end > buf) {
1325 ret = nfmtstr(40, "%c,%d,%d",
1326 buf->colour == M_BLACK ? 'B' : 'W',
1327 buf->square.r, buf->square.c);
1328 ui->cheated = TRUE; /* you are being naughty ;-) */
1334 cell = state->grid[idx(r, c, state->params.w)];
1335 if (cell > 0) return NULL;
1337 if (action == forwards) switch (cell) {
1338 case EMPTY: return nfmtstr(40, "W,%d,%d", r, c);
1339 case WHITE: return nfmtstr(40, "B,%d,%d", r, c);
1340 case BLACK: return nfmtstr(40, "E,%d,%d", r, c);
1343 else if (action == backwards) switch (cell) {
1344 case BLACK: return nfmtstr(40, "W,%d,%d", r, c);
1345 case WHITE: return nfmtstr(40, "E,%d,%d", r, c);
1346 case EMPTY: return nfmtstr(40, "B,%d,%d", r, c);
1352 static int find_errors(game_state *state, int *report)
1354 int const w = state->params.w, h = state->params.h, n = w * h;
1358 int nblack = 0, any_white_cell = -1;
1359 game_state *dup = dup_game(state);
1361 for (i = r = 0; r < h; ++r)
1362 for (c = 0; c < w; ++c, ++i) {
1363 switch (state->grid[i]) {
1369 for (j = 0; j < 4; ++j) {
1370 int const rr = r + dr[j], cc = c + dc[j];
1371 if (out_of_bounds(rr, cc, w, h)) continue;
1372 if (state->grid[idx(rr, cc, w)] != BLACK) continue;
1373 if (!report) goto found_error;
1382 for (runs = 1, j = 0; j < 4; ++j) {
1383 int const rr = r + dr[j], cc = c + dc[j];
1384 runs += runlength(rr, cc, dr[j], dc[j], state,
1388 if (runs != state->grid[i]) goto found_error;
1389 } else if (runs < state->grid[i]) report[i] = TRUE;
1391 for (runs = 1, j = 0; j < 4; ++j) {
1392 int const rr = r + dr[j], cc = c + dc[j];
1393 runs += runlength(rr, cc, dr[j], dc[j], state,
1394 ~(MASK(BLACK) | MASK(EMPTY)));
1396 if (runs > state->grid[i]) report[i] = TRUE;
1400 /* note: fallthrough _into_ these cases */
1402 case WHITE: any_white_cell = i;
1406 for (i = 0; i < n; ++i) if (dup->grid[i] != BLACK) dup->grid[i] = WHITE;
1407 if (nblack + dfs_count_white(dup, any_white_cell) < n) {
1409 printf("dfs fail at %d\n", any_white_cell);
1412 for (i = 0; i < n; ++i) if (state->grid[i] != BLACK) report[i] = TRUE;
1416 return FALSE; /* if report != NULL, this is ignored */
1423 static game_state *execute_move(game_state *state, char *move)
1425 signed int r, c, value, nchars, ntok;
1426 signed char what_to_do;
1431 ret = dup_game(state);
1435 ret->has_cheated = ret->was_solved = TRUE;
1438 for (; *move; move += nchars) {
1439 ntok = sscanf(move, "%c,%d,%d%n", &what_to_do, &r, &c, &nchars);
1440 if (ntok < 3) goto failure;
1441 switch (what_to_do) {
1442 case 'W': value = WHITE; break;
1443 case 'E': value = EMPTY; break;
1444 case 'B': value = BLACK; break;
1445 default: goto failure;
1447 if (out_of_bounds(r, c, ret->params.w, ret->params.h)) goto failure;
1448 ret->grid[idx(r, c, ret->params.w)] = value;
1451 if (ret->was_solved == FALSE)
1452 ret->was_solved = !find_errors(ret, NULL);
1461 static void game_changed_state(game_ui *ui, game_state *oldstate,
1462 game_state *newstate)
1464 if (newstate->has_cheated) ui->cheated = TRUE;
1467 static float game_anim_length(game_state *oldstate, game_state *newstate,
1468 int dir, game_ui *ui)
1473 #define FLASH_TIME 0.7F
1475 static float game_flash_length(game_state *from, game_state *to,
1476 int dir, game_ui *ui)
1478 if (!from->was_solved && to->was_solved && !ui->cheated)
1483 /* ----------------------------------------------------------------------
1487 #define PREFERRED_TILE_SIZE 32
1492 COL_BLACK = COL_GRID,
1493 COL_TEXT = COL_GRID,
1494 COL_USER = COL_GRID,
1497 COL_HIGHLIGHT = COL_ERROR, /* mkhighlight needs it, I don't */
1498 COL_CURSOR = COL_LOWLIGHT,
1502 static void game_compute_size(game_params *params, int tilesize,
1505 *x = (1 + params->w) * tilesize;
1506 *y = (1 + params->h) * tilesize;
1509 static void game_set_size(drawing *dr, game_drawstate *ds,
1510 game_params *params, int tilesize)
1512 ds->tilesize = tilesize;
1515 #define COLOUR(ret, i, r, g, b) \
1516 ((ret[3*(i)+0] = (r)), (ret[3*(i)+1] = (g)), (ret[3*(i)+2] = (b)))
1518 static float *game_colours(frontend *fe, int *ncolours)
1520 float *ret = snewn(3 * NCOLOURS, float);
1522 game_mkhighlight(fe, ret, COL_BACKGROUND, COL_HIGHLIGHT, COL_LOWLIGHT);
1523 COLOUR(ret, COL_GRID, 0.0F, 0.0F, 0.0F);
1524 COLOUR(ret, COL_ERROR, 1.0F, 0.0F, 0.0F);
1526 *ncolours = NCOLOURS;
1530 static drawcell makecell(puzzle_size value, int error, int cursor, int flash)
1533 setmember(ret, value);
1534 setmember(ret, error);
1535 setmember(ret, cursor);
1536 setmember(ret, flash);
1540 static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
1542 int const w = state->params.w, h = state->params.h, n = w * h;
1543 struct game_drawstate *ds = snew(struct game_drawstate);
1547 ds->started = FALSE;
1549 ds->grid = snewn(n, drawcell);
1550 for (i = 0; i < n; ++i)
1551 ds->grid[i] = makecell(w + h, FALSE, FALSE, FALSE);
1556 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
1562 #define cmpmember(a, b, field) ((a) . field == (b) . field)
1564 static int cell_eq(drawcell a, drawcell b)
1567 cmpmember(a, b, value) &&
1568 cmpmember(a, b, error) &&
1569 cmpmember(a, b, cursor) &&
1570 cmpmember(a, b, flash);
1573 static void draw_cell(drawing *dr, game_drawstate *ds, int r, int c,
1576 static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
1577 game_state *state, int dir, game_ui *ui,
1578 float animtime, float flashtime)
1580 int const w = state->params.w, h = state->params.h, n = w * h;
1581 int const wpx = (w+1) * ds->tilesize, hpx = (h+1) * ds->tilesize;
1582 int const flash = ((int) (flashtime * 5 / FLASH_TIME)) % 2;
1586 int *errors = snewn(n, int);
1587 memset(errors, FALSE, n * sizeof (int));
1588 find_errors(state, errors);
1590 assert (oldstate == NULL); /* only happens if animating moves */
1594 draw_rect(dr, 0, 0, wpx, hpx, COL_BACKGROUND);
1595 draw_rect(dr, BORDER-1, BORDER-1,
1596 ds->tilesize*w+2, ds->tilesize*h+2, COL_GRID);
1597 draw_update(dr, 0, 0, wpx, hpx);
1600 for (i = r = 0; r < h; ++r) {
1601 for (c = 0; c < w; ++c, ++i) {
1602 drawcell cell = makecell(state->grid[i], errors[i], FALSE, flash);
1603 if (r == ui->r && c == ui->c && ui->cursor_show)
1605 if (!cell_eq(cell, ds->grid[i])) {
1606 draw_cell(dr, ds, r, c, cell);
1615 static void draw_cell(drawing *draw, game_drawstate *ds, int r, int c,
1618 int const ts = ds->tilesize;
1619 int const y = BORDER + ts * r, x = BORDER + ts * c;
1620 int const tx = x + (ts / 2), ty = y + (ts / 2);
1621 int const dotsz = (ds->tilesize + 9) / 10;
1623 int const colour = (cell.value == BLACK ?
1624 cell.error ? COL_ERROR : COL_BLACK :
1625 cell.flash || cell.cursor ?
1626 COL_LOWLIGHT : COL_BACKGROUND);
1628 draw_rect (draw, x, y, ts, ts, colour);
1629 draw_rect_outline(draw, x, y, ts, ts, COL_GRID);
1631 switch (cell.value) {
1632 case WHITE: draw_rect(draw, tx - dotsz / 2, ty - dotsz / 2, dotsz, dotsz,
1633 cell.error ? COL_ERROR : COL_USER);
1637 draw_circle(draw, tx, ty, dotsz / 2, COL_ERROR, COL_GRID);
1641 int const colour = (cell.error ? COL_ERROR : COL_GRID);
1642 char *msg = nfmtstr(10, "%d", cell.value);
1643 draw_text(draw, tx, ty, FONT_VARIABLE, ts * 3 / 5,
1644 ALIGN_VCENTRE | ALIGN_HCENTRE, colour, msg);
1649 draw_update(draw, x, y, ts, ts);
1652 static int game_timing_state(game_state *state, game_ui *ui)
1654 puts("warning: game_timing_state was called (this shouldn't happen)");
1655 return FALSE; /* the (non-existing) timer should not be running */
1658 /* ----------------------------------------------------------------------
1659 * User interface: print
1662 static void game_print_size(game_params *params, float *x, float *y)
1664 int print_width, print_height;
1665 game_compute_size(params, 800, &print_width, &print_height);
1666 *x = print_width / 100.0F;
1667 *y = print_height / 100.0F;
1670 static void game_print(drawing *dr, game_state *state, int tilesize)
1672 int const w = state->params.w, h = state->params.h;
1673 game_drawstate ds_obj, *ds = &ds_obj;
1674 int r, c, i, colour;
1676 ds->tilesize = tilesize;
1678 colour = print_mono_colour(dr, 1); assert(colour == COL_BACKGROUND);
1679 colour = print_mono_colour(dr, 0); assert(colour == COL_GRID);
1680 colour = print_mono_colour(dr, 1); assert(colour == COL_ERROR);
1681 colour = print_mono_colour(dr, 0); assert(colour == COL_LOWLIGHT);
1682 colour = print_mono_colour(dr, 0); assert(colour == NCOLOURS);
1684 for (i = r = 0; r < h; ++r)
1685 for (c = 0; c < w; ++c, ++i)
1686 draw_cell(dr, ds, r, c,
1687 makecell(state->grid[i], FALSE, FALSE, FALSE));
1689 print_line_width(dr, 3 * tilesize / 40);
1690 draw_rect_outline(dr, BORDER, BORDER, w*TILESIZE, h*TILESIZE, COL_GRID);
1693 /* And that's about it ;-) **************************************************/
1696 #define thegame range
1699 struct game const thegame = {
1700 "Range", "games.range", "range",
1707 TRUE, game_configure, custom_params,
1715 TRUE, game_can_format_as_text_now, game_text_format,
1723 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
1726 game_free_drawstate,
1730 TRUE, FALSE, game_print_size, game_print,
1731 FALSE, /* wants_statusbar */
1732 FALSE, game_timing_state,