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 static 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 range_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 = range_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)
113 if (i < 0 || i >= lenof(range_presets)) return FALSE;
115 ret = default_params();
116 *ret = range_presets[i]; /* struct copy */
119 *name = nfmtstr(40, "%d x %d", range_presets[i].w, range_presets[i].h);
124 static void free_params(game_params *params)
129 static void decode_params(game_params *params, char const *string)
131 /* FIXME check for puzzle_size overflow and decoding issues */
132 params->w = params->h = atoi(string);
133 while (*string && isdigit((unsigned char) *string)) ++string;
134 if (*string == 'x') {
136 params->h = atoi(string);
137 while (*string && isdigit((unsigned char)*string)) string++;
141 static char *encode_params(game_params *params, int full)
144 sprintf(str, "%dx%d", params->w, params->h);
148 static config_item *game_configure(game_params *params)
152 ret = snewn(3, config_item);
154 ret[0].name = "Width";
155 ret[0].type = C_STRING;
156 ret[0].sval = nfmtstr(10, "%d", params->w);
159 ret[1].name = "Height";
160 ret[1].type = C_STRING;
161 ret[1].sval = nfmtstr(10, "%d", params->h);
172 static game_params *custom_params(config_item *configuration)
174 game_params *ret = snew(game_params);
175 ret->w = atoi(configuration[0].sval);
176 ret->h = atoi(configuration[1].sval);
180 #define memdup(dst, src, n, type) do { \
181 dst = snewn(n, type); \
182 memcpy(dst, src, n * sizeof (type)); \
185 static game_state *dup_game(game_state *state)
187 game_state *ret = snew(game_state);
188 int const n = state->params.w * state->params.h;
190 *ret = *state; /* structure copy */
192 /* copy the poin_tee_, set a new value of the poin_ter_ */
193 memdup(ret->grid, state->grid, n, puzzle_size);
198 static void free_game(game_state *state)
205 /* ----------------------------------------------------------------------
206 * The solver subsystem.
208 * The solver is used for two purposes:
209 * - To solve puzzles when the user selects `Solve'.
210 * - To test solubility of a grid as clues are being removed from it
211 * during the puzzle generation.
213 * It supports the following ways of reasoning:
215 * - A cell adjacent to a black cell must be white.
217 * - If painting a square black would bisect the white regions, that
218 * square is white (by finding biconnected components' cut points)
220 * - A cell with number n, covering at most k white squares in three
221 * directions must white-cover n-k squares in the last direction.
223 * - A cell with number n known to cover k squares, if extending the
224 * cover by one square in a given direction causes the cell to
225 * cover _more_ than n squares, that extension cell must be black.
227 * (either if the square already covers n, or if it extends into a
228 * chunk of size > n - k)
230 * - Recursion. Pick any cell and see if this leads to either a
231 * contradiction or a solution (and then act appropriately).
236 * (propagation upper limit)
237 * - If one has two numbers on the same line, the smaller limits the
238 * larger. Example: in |b|_|_|8|4|_|_|b|, only two _'s can be both
239 * white and connected to the "8" cell; so that cell will propagate
240 * at least four cells orthogonally to the displayed line (which is
241 * better than the current "at least 2").
243 * (propagation upper limit)
244 * - cells can't propagate into other cells if doing so exceeds that
245 * number. Example: in |b|4|.|.|2|b|, at most one _ can be white;
246 * otherwise, the |2| would have too many reaching white cells.
248 * (propagation lower and upper limit)
249 * - `Full Combo': in each four directions d_1 ... d_4, find a set of
250 * possible propagation distances S_1 ... S_4. For each i=1..4,
251 * for each x in S_i: if not exists (y, z, w) in the other sets
252 * such that (x+y+z+w+1 == clue value): then remove x from S_i.
253 * Repeat until this stabilizes. If any cell would contradict
256 #define idx(i, j, w) ((i)*(w) + (j))
257 #define out_of_bounds(r, c, w, h) \
258 ((r) < 0 || (r) >= h || (c) < 0 || (c) >= w)
260 typedef struct square {
264 enum {BLACK = -2, WHITE, EMPTY};
265 /* white is for pencil marks, empty is undecided */
267 static int const dr[4] = {+1, 0, -1, 0};
268 static int const dc[4] = { 0, +1, 0, -1};
269 static int const cursors[4] = /* must match dr and dc */
270 {CURSOR_DOWN, CURSOR_RIGHT, CURSOR_UP, CURSOR_LEFT};
272 typedef struct move {
274 unsigned int colour: 1;
276 enum {M_BLACK = 0, M_WHITE = 1};
278 typedef move *(reasoning)(game_state *state,
283 static reasoning solver_reasoning_not_too_big;
284 static reasoning solver_reasoning_adjacency;
285 static reasoning solver_reasoning_connectedness;
286 static reasoning solver_reasoning_recursion;
295 static move *solve_internal(game_state *state, move *base, int diff);
297 static char *solve_game(game_state *orig, game_state *curpos,
298 char *aux, char **error)
300 int const n = orig->params.w * orig->params.h;
301 move *const base = snewn(n, move);
302 move *moves = solve_internal(orig, base, DIFF_RECURSION);
307 int const k = moves - base;
308 char *str = ret = snewn(15*k + 2, char);
309 char colour[2] = "BW";
313 for (it = base; it < moves; ++it)
314 str += sprintf(str, "%c,%d,%d", colour[it->colour],
315 it->square.r, it->square.c);
316 } else *error = "This puzzle instance contains a contradiction";
322 static square *find_clues(game_state *state, int *ret_nclues);
323 static move *do_solve(game_state *state,
329 /* new_game_desc entry point in the solver subsystem */
330 static move *solve_internal(game_state *state, move *base, int diff)
333 square *const clues = find_clues(state, &nclues);
334 game_state *dup = dup_game(state);
335 move *const moves = do_solve(dup, nclues, clues, base, diff);
341 static reasoning *const reasonings[] = {
342 solver_reasoning_not_too_big,
343 solver_reasoning_adjacency,
344 solver_reasoning_connectedness,
345 solver_reasoning_recursion
348 static move *do_solve(game_state *state,
354 struct move *buf = move_buffer, *oldbuf;
359 for (i = 0; i < lenof(reasonings) && i <= difficulty; ++i) {
360 /* only recurse if all else fails */
361 if (i == DIFF_RECURSION && buf > oldbuf) continue;
362 buf = (*reasonings[i])(state, nclues, clues, buf);
363 if (buf == NULL) return NULL;
365 } while (buf > oldbuf);
370 #define MASK(n) (1 << ((n) + 2))
372 static int runlength(puzzle_size r, puzzle_size c,
373 puzzle_size dr, puzzle_size dc,
374 game_state *state, int colourmask)
376 int const w = state->params.w, h = state->params.h;
379 int cell = idx(r, c, w);
380 if (out_of_bounds(r, c, w, h)) break;
381 if (state->grid[cell] > 0) {
382 if (!(colourmask & ~(MASK(BLACK) | MASK(WHITE) | MASK(EMPTY))))
384 } else if (!(MASK(state->grid[cell]) & colourmask)) break;
392 static void solver_makemove(puzzle_size r, puzzle_size c, int colour,
393 game_state *state, move **buffer_ptr)
395 int const cell = idx(r, c, state->params.w);
396 if (out_of_bounds(r, c, state->params.w, state->params.h)) return;
397 if (state->grid[cell] != EMPTY) return;
398 setmember((*buffer_ptr)->square, r);
399 setmember((*buffer_ptr)->square, c);
400 setmember(**buffer_ptr, colour);
402 state->grid[cell] = (colour == M_BLACK ? BLACK : WHITE);
405 static move *solver_reasoning_adjacency(game_state *state,
411 for (r = 0; r < state->params.h; ++r)
412 for (c = 0; c < state->params.w; ++c) {
413 int const cell = idx(r, c, state->params.w);
414 if (state->grid[cell] != BLACK) continue;
415 for (i = 0; i < 4; ++i)
416 solver_makemove(r + dr[i], c + dc[i], M_WHITE, state, &buf);
421 enum {NOT_VISITED = -1};
423 static int dfs_biconnect_visit(puzzle_size r, puzzle_size c,
425 square *dfs_parent, int *dfs_depth,
428 static move *solver_reasoning_connectedness(game_state *state,
433 int const w = state->params.w, h = state->params.h, n = w * h;
435 square *const dfs_parent = snewn(n, square);
436 int *const dfs_depth = snewn(n, int);
439 for (i = 0; i < n; ++i) {
440 dfs_parent[i].r = NOT_VISITED;
444 for (i = 0; i < n && state->grid[i] == BLACK; ++i);
446 dfs_parent[i].r = i / w;
447 dfs_parent[i].c = i % w; /* `dfs root`.parent == `dfs root` */
450 dfs_biconnect_visit(i / w, i % w, state, dfs_parent, dfs_depth, &buf);
458 /* returns the `lowpoint` of (r, c) */
459 static int dfs_biconnect_visit(puzzle_size r, puzzle_size c,
461 square *dfs_parent, int *dfs_depth,
464 const puzzle_size w = state->params.w, h = state->params.h;
465 int const i = idx(r, c, w), mydepth = dfs_depth[i];
466 int lowpoint = mydepth, j, nchildren = 0;
468 for (j = 0; j < 4; ++j) {
469 const puzzle_size rr = r + dr[j], cc = c + dc[j];
470 int const cell = idx(rr, cc, w);
472 if (out_of_bounds(rr, cc, w, h)) continue;
473 if (state->grid[cell] == BLACK) continue;
475 if (dfs_parent[cell].r == NOT_VISITED) {
477 dfs_parent[cell].r = r;
478 dfs_parent[cell].c = c;
479 dfs_depth[cell] = mydepth + 1;
480 child_lowpoint = dfs_biconnect_visit(rr, cc, state, dfs_parent,
483 if (child_lowpoint >= mydepth && mydepth > 0)
484 solver_makemove(r, c, M_WHITE, state, buf);
486 lowpoint = min(lowpoint, child_lowpoint);
488 } else if (rr != dfs_parent[i].r || cc != dfs_parent[i].c) {
489 lowpoint = min(lowpoint, dfs_depth[cell]);
493 if (mydepth == 0 && nchildren >= 2)
494 solver_makemove(r, c, M_WHITE, state, buf);
499 static move *solver_reasoning_not_too_big(game_state *state,
504 int const w = state->params.w, runmasks[4] = {
505 ~(MASK(BLACK) | MASK(EMPTY)),
507 ~(MASK(BLACK) | MASK(EMPTY)),
510 enum {RUN_WHITE, RUN_EMPTY, RUN_BEYOND, RUN_SPACE};
512 int i, runlengths[4][4];
514 for (i = 0; i < nclues; ++i) {
515 int j, k, whites, space;
517 const puzzle_size row = clues[i].r, col = clues[i].c;
518 int const clue = state->grid[idx(row, col, w)];
520 for (j = 0; j < 4; ++j) {
521 puzzle_size r = row + dr[j], c = col + dc[j];
522 runlengths[RUN_SPACE][j] = 0;
523 for (k = 0; k <= RUN_SPACE; ++k) {
524 int l = runlength(r, c, dr[j], dc[j], state, runmasks[k]);
526 runlengths[k][j] = l;
530 runlengths[RUN_SPACE][j] += l;
535 for (j = 0; j < 4; ++j) whites += runlengths[RUN_WHITE][j];
537 for (j = 0; j < 4; ++j) {
538 int const delta = 1 + runlengths[RUN_WHITE][j];
539 const puzzle_size r = row + delta * dr[j];
540 const puzzle_size c = col + delta * dc[j];
542 if (whites == clue) {
543 solver_makemove(r, c, M_BLACK, state, &buf);
547 if (runlengths[RUN_EMPTY][j] == 1 &&
549 + runlengths[RUN_EMPTY][j]
550 + runlengths[RUN_BEYOND][j]
552 solver_makemove(r, c, M_BLACK, state, &buf);
557 + runlengths[RUN_EMPTY][j]
558 + runlengths[RUN_BEYOND][j]
560 runlengths[RUN_SPACE][j] =
561 runlengths[RUN_WHITE][j] +
562 runlengths[RUN_EMPTY][j] - 1;
564 if (runlengths[RUN_EMPTY][j] == 1)
565 solver_makemove(r, c, M_BLACK, state, &buf);
570 for (j = 0; j < 4; ++j) space += runlengths[RUN_SPACE][j];
571 for (j = 0; j < 4; ++j) {
572 puzzle_size r = row + dr[j], c = col + dc[j];
574 int k = space - runlengths[RUN_SPACE][j];
575 if (k >= clue) continue;
577 for (; k < clue; ++k, r += dr[j], c += dc[j])
578 solver_makemove(r, c, M_WHITE, state, &buf);
584 static move *solver_reasoning_recursion(game_state *state,
589 int const w = state->params.w, n = w * state->params.h;
592 for (cell = 0; cell < n; ++cell) {
593 int const r = cell / w, c = cell % w;
595 game_state *newstate;
596 move *recursive_result;
598 if (state->grid[cell] != EMPTY) continue;
600 /* FIXME: add enum alias for smallest and largest (or N) */
601 for (colour = M_BLACK; colour <= M_WHITE; ++colour) {
602 newstate = dup_game(state);
603 newstate->grid[cell] = colour;
604 recursive_result = do_solve(newstate, nclues, clues, buf,
607 if (recursive_result == NULL) {
608 solver_makemove(r, c, M_BLACK + M_WHITE - colour, state, &buf);
611 for (i = 0; i < n && newstate->grid[i] != EMPTY; ++i);
612 if (i == n) return buf;
618 static square *find_clues(game_state *state, int *ret_nclues)
620 int r, c, i, nclues = 0;
621 square *ret = snewn(state->params.w * state->params.h, struct square);
623 for (i = r = 0; r < state->params.h; ++r)
624 for (c = 0; c < state->params.w; ++c, ++i)
625 if (state->grid[i] > 0) {
631 *ret_nclues = nclues;
632 return sresize(ret, nclues + (nclues == 0), square);
635 /* ----------------------------------------------------------------------
638 * Generating kurodoko instances is rather straightforward:
640 * - Start with a white grid and add black squares at randomly chosen
641 * locations, unless colouring that square black would violate
642 * either the adjacency or connectedness constraints.
644 * - For each white square, compute the number it would contain if it
645 * were given as a clue.
647 * - From a starting point of "give _every_ white square as a clue",
648 * for each white square (in a random order), see if the board is
649 * solvable when that square is not given as a clue. If not, don't
650 * give it as a clue, otherwise do.
652 * This never fails, but it's only _almost_ what I do. The real final
655 * - From a starting point of "give _every_ white square as a clue",
656 * first remove all clues that are two-way rotationally symmetric
657 * to a black square. If this leaves the puzzle unsolvable, throw
658 * it out and try again. Otherwise, remove all _pairs_ of clues
659 * (that are rotationally symmetric) which can be removed without
660 * rendering the puzzle unsolvable.
662 * This can fail even if one only removes the black and symmetric
663 * clues; indeed it happens often (avg. once or twice per puzzle) when
664 * generating 1xN instances. (If you add black cells they must be in
665 * the end, and if you only add one, it's ambiguous where).
668 /* forward declarations of internal calls */
669 static void newdesc_choose_black_squares(game_state *state,
670 const int *shuffle_1toN);
671 static void newdesc_compute_clues(game_state *state);
672 static int newdesc_strip_clues(game_state *state, int *shuffle_1toN);
673 static char *newdesc_encode_game_description(int n, puzzle_size *grid);
675 static char *new_game_desc(game_params *params, random_state *rs,
676 char **aux, int interactive)
678 int const w = params->w, h = params->h, n = w * h;
680 puzzle_size *const grid = snewn(n, puzzle_size);
681 int *const shuffle_1toN = snewn(n, int);
683 int i, clues_removed;
688 state.params = *params;
691 interactive = 0; /* I don't need it, I shouldn't use it*/
693 for (i = 0; i < n; ++i) shuffle_1toN[i] = i;
696 shuffle(shuffle_1toN, n, sizeof (int), rs);
697 newdesc_choose_black_squares(&state, shuffle_1toN);
699 newdesc_compute_clues(&state);
701 shuffle(shuffle_1toN, n, sizeof (int), rs);
702 clues_removed = newdesc_strip_clues(&state, shuffle_1toN);
704 if (clues_removed < 0) continue; else break;
707 encoding = newdesc_encode_game_description(n, grid);
715 static int dfs_count_white(game_state *state, int cell);
717 static void newdesc_choose_black_squares(game_state *state,
718 const int *shuffle_1toN)
720 int const w = state->params.w, h = state->params.h, n = w * h;
722 int k, any_white_cell, n_black_cells;
724 for (k = 0; k < n; ++k) state->grid[k] = WHITE;
726 any_white_cell = shuffle_1toN[n - 1];
729 /* I like the puzzles that result from n / 3, but maybe this
730 * could be made a (generation, i.e. non-full) parameter? */
731 for (k = 0; k < n / 3; ++k) {
732 int const i = shuffle_1toN[k], c = i % w, r = i / w;
735 for (j = 0; j < 4; ++j) {
736 int const rr = r + dr[j], cc = c + dc[j], cell = idx(rr, cc, w);
737 /* if you're out of bounds, we skip you */
738 if (out_of_bounds(rr, cc, w, h)) continue;
739 if (state->grid[cell] == BLACK) break; /* I can't be black */
740 } if (j < 4) continue; /* I have black neighbour: I'm white */
742 state->grid[i] = BLACK;
745 j = dfs_count_white(state, any_white_cell);
746 if (j + n_black_cells < n) {
747 state->grid[i] = WHITE;
753 static void newdesc_compute_clues(game_state *state)
755 int const w = state->params.w, h = state->params.h;
758 for (r = 0; r < h; ++r) {
759 int run_size = 0, c, cc;
760 for (c = 0; c <= w; ++c) {
761 if (c == w || state->grid[idx(r, c, w)] == BLACK) {
762 for (cc = c - run_size; cc < c; ++cc)
763 state->grid[idx(r, cc, w)] += run_size;
769 for (c = 0; c < w; ++c) {
770 int run_size = 0, r, rr;
771 for (r = 0; r <= h; ++r) {
772 if (r == h || state->grid[idx(r, c, w)] == BLACK) {
773 for (rr = r - run_size; rr < r; ++rr)
774 state->grid[idx(rr, c, w)] += run_size;
781 #define rotate(x) (n - 1 - (x))
783 static int newdesc_strip_clues(game_state *state, int *shuffle_1toN)
785 int const w = state->params.w, n = w * state->params.h;
787 move *const move_buffer = snewn(n, move);
789 game_state *dupstate;
792 * do a partition/pivot of shuffle_1toN into three groups:
793 * (1) squares rotationally-symmetric to (3)
794 * (2) squares not in (1) or (3)
797 * They go from [0, left), [left, right) and [right, n) in
798 * shuffle_1toN (and from there into state->grid[ ])
800 * Then, remove clues from the grid one by one in shuffle_1toN
801 * order, until the solver becomes unhappy. If we didn't remove
802 * all of (1), return (-1). Else, we're happy.
805 /* do the partition */
806 int clues_removed, k = 0, left = 0, right = n;
809 while (k < right && state->grid[shuffle_1toN[k]] == BLACK) {
811 SWAP(int, shuffle_1toN[right], shuffle_1toN[k]);
812 assert(state->grid[shuffle_1toN[right]] == BLACK);
814 if (k >= right) break;
816 if (state->grid[rotate(shuffle_1toN[k])] == BLACK) {
817 SWAP(int, shuffle_1toN[k], shuffle_1toN[left]);
820 assert (state->grid[rotate(shuffle_1toN[k])] != BLACK
824 for (k = 0; k < left; ++k) {
825 assert (state->grid[rotate(shuffle_1toN[k])] == BLACK);
826 state->grid[shuffle_1toN[k]] = EMPTY;
828 for (k = left; k < right; ++k) {
829 assert (state->grid[rotate(shuffle_1toN[k])] != BLACK);
830 assert (state->grid[shuffle_1toN[k]] != BLACK);
832 for (k = right; k < n; ++k) {
833 assert (state->grid[shuffle_1toN[k]] == BLACK);
834 state->grid[shuffle_1toN[k]] = EMPTY;
837 clues_removed = (left - 0) + (n - right);
839 dupstate = dup_game(state);
840 buf = solve_internal(dupstate, move_buffer, DIFF_RECURSION - 1);
842 if (buf - move_buffer < clues_removed) {
843 /* branch prediction: I don't think I'll go here */
848 for (k = left; k < right; ++k) {
849 const int i = shuffle_1toN[k], j = rotate(i);
850 int const clue = state->grid[i], clue_rot = state->grid[j];
851 if (clue == BLACK) continue;
852 state->grid[i] = state->grid[j] = EMPTY;
853 dupstate = dup_game(state);
854 buf = solve_internal(dupstate, move_buffer, DIFF_RECURSION - 1);
856 clues_removed += 2 - (i == j);
857 /* if i is the center square, then i == (j = rotate(i))
858 * when i and j are one, removing i and j removes only one */
859 if (buf - move_buffer == clues_removed) continue;
860 /* if the solver is sound, refilling all removed clues means
861 * we have filled all squares, i.e. solved the puzzle. */
862 state->grid[i] = clue;
863 state->grid[j] = clue_rot;
864 clues_removed -= 2 - (i == j);
869 return clues_removed;
872 static int dfs_count_rec(puzzle_size *grid, int r, int c, int w, int h)
874 int const cell = idx(r, c, w);
875 if (out_of_bounds(r, c, w, h)) return 0;
876 if (grid[cell] != WHITE) return 0;
879 dfs_count_rec(grid, r + 0, c + 1, w, h) +
880 dfs_count_rec(grid, r + 0, c - 1, w, h) +
881 dfs_count_rec(grid, r + 1, c + 0, w, h) +
882 dfs_count_rec(grid, r - 1, c + 0, w, h);
885 static int dfs_count_white(game_state *state, int cell)
887 int const w = state->params.w, h = state->params.h, n = w * h;
888 int const r = cell / w, c = cell % w;
889 int i, k = dfs_count_rec(state->grid, r, c, w, h);
890 for (i = 0; i < n; ++i)
891 if (state->grid[i] == EMPTY)
892 state->grid[i] = WHITE;
896 static char *validate_params(game_params *params, int full)
898 int const w = params->w, h = params->h;
899 if (w < 1) return "Error: width is less than 1";
900 if (h < 1) return "Error: height is less than 1";
901 if (w * h < 1) return "Error: size is less than 1";
902 if (w + h - 1 > SCHAR_MAX) return "Error: w + h is too big";
903 /* I might be unable to store clues in my puzzle_size *grid; */
905 if (w == 2 && h == 2) return "Error: can't create 2x2 puzzles";
906 if (w == 1 && h == 2) return "Error: can't create 1x2 puzzles";
907 if (w == 2 && h == 1) return "Error: can't create 2x1 puzzles";
908 if (w == 1 && h == 1) return "Error: can't create 1x1 puzzles";
913 /* Definition: a puzzle instance is _good_ if:
914 * - it has a unique solution
915 * - the solver can find this solution without using recursion
916 * - the solution contains at least one black square
917 * - the clues are 2-way rotationally symmetric
919 * (the idea being: the generator can not output any _bad_ puzzles)
921 * Theorem: validate_params, when full != 0, discards exactly the set
922 * of parameters for which there are _no_ good puzzle instances.
924 * Proof: it's an immediate consequence of the five lemmas below.
926 * Observation: not only do puzzles on non-tiny grids exist, the
927 * generator is pretty fast about coming up with them. On my pre-2004
928 * desktop box, it generates 100 puzzles on the highest preset (16x11)
929 * in 8.383 seconds, or <= 0.1 second per puzzle.
931 * ----------------------------------------------------------------------
933 * Lemma: On a 1x1 grid, there are no good puzzles.
935 * Proof: the one square can't be a clue because at least one square
936 * is black. But both a white square and a black square satisfy the
937 * solution criteria, so the puzzle is ambiguous (and hence bad).
939 * Lemma: On a 1x2 grid, there are no good puzzles.
941 * Proof: let's name the squares l and r. Note that there can be at
942 * most one black square, or adjacency is violated. By assumption at
943 * least one square is black, so let's call that one l. By clue
944 * symmetry, neither l nor r can be given as a clue, so the puzzle
945 * instance is blank and thus ambiguous.
947 * Corollary: On a 2x1 grid, there are no good puzzles.
948 * Proof: rotate the above proof 90 degrees ;-)
950 * ----------------------------------------------------------------------
952 * Lemma: On a 2x2 grid, there are no soluble puzzles with 2-way
953 * rotational symmetric clues and at least one black square.
955 * Proof: Let's name the squares a, b, c, and d, with a and b on the
956 * top row, a and c in the left column. Let's consider the case where
957 * a is black. Then no other square can be black: b and c would both
958 * violate the adjacency constraint; d would disconnect b from c.
960 * So exactly one square is black (and by 4-way rotation symmetry of
961 * the 2x2 square, it doesn't matter which one, so let's stick to a).
962 * By 2-way rotational symmetry of the clues and the rule about not
963 * painting numbers black, neither a nor d can be clues. A blank
964 * puzzle would be ambiguous, so one of {b, c} is a clue; by symmetry,
965 * so is the other one.
967 * It is readily seen that their clue value is 2. But "a is black"
968 * and "d is black" are both valid solutions in this case, so the
969 * puzzle is ambiguous (and hence bad).
971 * ----------------------------------------------------------------------
973 * Lemma: On a wxh grid with w, h >= 1 and (w > 2 or h > 2), there is
974 * at least one good puzzle.
976 * Proof: assume that w > h (otherwise rotate the proof again). Paint
977 * the top left and bottom right corners black, and fill a clue into
978 * all the other squares. Present this board to the solver code (or
979 * player, hypothetically), except with the two black squares as blank
982 * For an Nx1 puzzle, observe that every clue is N - 2, and there are
983 * N - 2 of them in one connected sequence, so the remaining two
984 * squares can be deduced to be black, which solves the puzzle.
986 * For any other puzzle, let j be a cell in the same row as a black
987 * cell, but not in the same column (such a cell doesn't exist in 2x3
988 * puzzles, but we assume w > h and such cells exist in 3x2 puzzles).
990 * Note that the number of cells in axis parallel `rays' going out
991 * from j exceeds j's clue value by one. Only one such cell is a
992 * non-clue, so it must be black. Similarly for the other corner (let
993 * j' be a cell in the same row as the _other_ black cell, but not in
994 * the same column as _any_ black cell; repeat this argument at j').
996 * This fills the grid and satisfies all clues and the adjacency
997 * constraint and doesn't paint on top of any clues. All that is left
998 * to see is connectedness.
1000 * Observe that the white cells in each column form a single connected
1001 * `run', and each column contains a white cell adjacent to a white
1002 * cell in the column to the right, if that column exists.
1004 * Thus, any cell in the left-most column can reach any other cell:
1005 * first go to the target column (by repeatedly going to the cell in
1006 * your current column that lets you go right, then going right), then
1007 * go up or down to the desired cell.
1009 * As reachability is symmetric (in undirected graphs) and transitive,
1010 * any cell can reach any left-column cell, and from there any other
1014 /* ----------------------------------------------------------------------
1015 * Game encoding and decoding
1018 #define NDIGITS_BASE '!'
1020 static char *newdesc_encode_game_description(int area, puzzle_size *grid)
1023 int desclen = 0, descsize = 0;
1027 for (i = 0; i <= area; i++) {
1028 int n = (i < area ? grid[i] : -1);
1033 if (descsize < desclen + 40) {
1034 descsize = desclen * 3 / 2 + 40;
1035 desc = sresize(desc, descsize, char);
1039 int c = 'a' - 1 + run;
1042 desc[desclen++] = c;
1043 run -= c - ('a' - 1);
1047 * If there's a number in the very top left or
1048 * bottom right, there's no point putting an
1049 * unnecessary _ before or after it.
1051 if (desclen > 0 && n > 0)
1052 desc[desclen++] = '_';
1055 desclen += sprintf(desc+desclen, "%d", n);
1059 desc[desclen] = '\0';
1063 static char *validate_desc(game_params *params, char *desc)
1065 int const n = params->w * params->h;
1067 int range = params->w + params->h - 1; /* maximum cell value */
1069 while (*desc && *desc != ',') {
1071 if (c >= 'a' && c <= 'z') {
1072 squares += c - 'a' + 1;
1073 } else if (c == '_') {
1075 } else if (c > '0' && c <= '9') {
1076 int val = atoi(desc-1);
1077 if (val < 1 || val > range)
1078 return "Out-of-range number in game description";
1080 while (*desc >= '0' && *desc <= '9')
1083 return "Invalid character in game description";
1087 return "Not enough data to fill grid";
1090 return "Too much data to fit in grid";
1095 static game_state *new_game(midend *me, game_params *params, char *desc)
1100 int const n = params->w * params->h;
1101 game_state *state = snew(game_state);
1103 me = NULL; /* I don't need it, I shouldn't use it */
1105 state->params = *params; /* structure copy */
1106 state->grid = snewn(n, puzzle_size);
1110 while (i < n && *p) {
1112 if (c >= 'a' && c <= 'z') {
1113 int squares = c - 'a' + 1;
1115 state->grid[i++] = 0;
1116 } else if (c == '_') {
1118 } else if (c > '0' && c <= '9') {
1119 int val = atoi(p-1);
1120 assert(val >= 1 && val <= params->w+params->h-1);
1121 state->grid[i++] = val;
1122 while (*p >= '0' && *p <= '9')
1127 state->has_cheated = FALSE;
1128 state->was_solved = FALSE;
1133 /* ----------------------------------------------------------------------
1134 * User interface: ascii
1137 static int game_can_format_as_text_now(game_params *params)
1142 static char *game_text_format(game_state *state)
1144 int cellsize, r, c, i, w_string, h_string, n_string;
1145 char *ret, *buf, *gridline;
1147 int const w = state->params.w, h = state->params.h;
1149 cellsize = 0; /* or may be used uninitialized */
1151 for (c = 0; c < w; ++c) {
1152 for (r = 1; r < h; ++r) {
1153 puzzle_size k = state->grid[idx(r, c, w)];
1155 for (d = 0; k; k /= 10, ++d);
1156 cellsize = max(cellsize, d);
1162 w_string = w * cellsize + 2; /* "|%d|%d|...|\n" */
1163 h_string = 2 * h + 1; /* "+--+--+...+\n%s\n+--+--+...+\n" */
1164 n_string = w_string * h_string;
1166 gridline = snewn(w_string + 1, char); /* +1: NUL terminator */
1167 memset(gridline, '-', w_string);
1168 for (c = 0; c <= w; ++c) gridline[c * cellsize] = '+';
1169 gridline[w_string - 1] = '\n';
1170 gridline[w_string - 0] = '\0';
1172 buf = ret = snewn(n_string + 1, char); /* +1: NUL terminator */
1173 for (i = r = 0; r < h; ++r) {
1174 memcpy(buf, gridline, w_string);
1176 for (c = 0; c < w; ++c, ++i) {
1178 switch (state->grid[i]) {
1179 case BLACK: ch = '#'; break;
1180 case WHITE: ch = '.'; break;
1181 case EMPTY: ch = ' '; break;
1183 buf += sprintf(buf, "|%*d", cellsize - 1, state->grid[i]);
1187 memset(buf, ch, cellsize - 1);
1188 buf += cellsize - 1;
1190 buf += sprintf(buf, "|\n");
1192 memcpy(buf, gridline, w_string);
1194 assert (buf - ret == n_string);
1202 /* ----------------------------------------------------------------------
1203 * User interfaces: interactive
1207 puzzle_size r, c; /* cursor position */
1208 unsigned int cursor_show: 1;
1211 static game_ui *new_ui(game_state *state)
1213 struct game_ui *ui = snew(game_ui);
1215 ui->cursor_show = FALSE;
1219 static void free_ui(game_ui *ui)
1224 static char *encode_ui(game_ui *ui)
1229 static void decode_ui(game_ui *ui, char *encoding)
1233 typedef struct drawcell {
1235 unsigned int error: 1;
1236 unsigned int cursor: 1;
1237 unsigned int flash: 1;
1240 struct game_drawstate {
1243 unsigned int started: 1;
1246 #define TILESIZE (ds->tilesize)
1247 #define BORDER (TILESIZE / 2)
1248 #define COORD(x) ((x) * TILESIZE + BORDER)
1249 #define FROMCOORD(x) (((x) - BORDER) / TILESIZE)
1251 static char *interpret_move(game_state *state, game_ui *ui, const game_drawstate *ds,
1252 int x, int y, int button)
1254 enum {none, forwards, backwards, hint};
1255 int const w = state->params.w, h = state->params.h;
1256 int r = ui->r, c = ui->c, action = none, cell;
1258 if (IS_CURSOR_SELECT(button) && !ui->cursor_show) return NULL;
1260 if (IS_MOUSE_DOWN(button)) {
1261 r = FROMCOORD(y + TILESIZE) - 1; /* or (x, y) < TILESIZE) */
1262 c = FROMCOORD(x + TILESIZE) - 1; /* are considered inside */
1263 if (out_of_bounds(r, c, w, h)) return NULL;
1266 ui->cursor_show = FALSE;
1269 if (button == LEFT_BUTTON || button == RIGHT_BUTTON) {
1271 * Utterly awful hack, exactly analogous to the one in Slant,
1272 * to configure the left and right mouse buttons the opposite
1275 * The original puzzle submitter thought it would be more
1276 * useful to have the left button turn an empty square into a
1277 * dotted one, on the grounds that that was what you did most
1278 * often; I (SGT) felt instinctively that the left button
1279 * ought to place black squares and the right button place
1280 * dots, on the grounds that that was consistent with many
1281 * other puzzles in which the left button fills in the data
1282 * used by the solution checker while the right button places
1283 * pencil marks for the user's convenience.
1285 * My first beta-player wasn't sure either, so I thought I'd
1286 * pre-emptively put in a 'configuration' mechanism just in
1290 static int swap_buttons = -1;
1291 if (swap_buttons < 0) {
1292 char *env = getenv("RANGE_SWAP_BUTTONS");
1293 swap_buttons = (env && (env[0] == 'y' || env[0] == 'Y'));
1296 if (button == LEFT_BUTTON)
1297 button = RIGHT_BUTTON;
1299 button = LEFT_BUTTON;
1305 case CURSOR_SELECT : case LEFT_BUTTON: action = backwards; break;
1306 case CURSOR_SELECT2: case RIGHT_BUTTON: action = forwards; break;
1307 case 'h': case 'H' : action = hint; break;
1308 case CURSOR_UP: case CURSOR_DOWN:
1309 case CURSOR_LEFT: case CURSOR_RIGHT:
1310 if (ui->cursor_show) {
1312 for (i = 0; i < 4 && cursors[i] != button; ++i);
1314 if (!out_of_bounds(ui->r + dr[i], ui->c + dc[i], w, h)) {
1318 } else ui->cursor_show = TRUE;
1322 if (action == hint) {
1323 move *end, *buf = snewn(state->params.w * state->params.h,
1326 end = solve_internal(state, buf, DIFF_RECURSION);
1327 if (end != NULL && end > buf) {
1328 ret = nfmtstr(40, "%c,%d,%d",
1329 buf->colour == M_BLACK ? 'B' : 'W',
1330 buf->square.r, buf->square.c);
1331 /* We used to set a flag here in the game_ui indicating
1332 * that the player had used the hint function. I (SGT)
1333 * retired it, on grounds of consistency with other games
1334 * (most of these games will still flash to indicate
1335 * completion if you solved and undid it, so why not if
1336 * you got a hint?) and because the flash is as much about
1337 * checking you got it all right than about congratulating
1338 * you on a job well done. */
1344 cell = state->grid[idx(r, c, state->params.w)];
1345 if (cell > 0) return NULL;
1347 if (action == forwards) switch (cell) {
1348 case EMPTY: return nfmtstr(40, "W,%d,%d", r, c);
1349 case WHITE: return nfmtstr(40, "B,%d,%d", r, c);
1350 case BLACK: return nfmtstr(40, "E,%d,%d", r, c);
1353 else if (action == backwards) switch (cell) {
1354 case BLACK: return nfmtstr(40, "W,%d,%d", r, c);
1355 case WHITE: return nfmtstr(40, "E,%d,%d", r, c);
1356 case EMPTY: return nfmtstr(40, "B,%d,%d", r, c);
1362 static int find_errors(game_state *state, int *report)
1364 int const w = state->params.w, h = state->params.h, n = w * h;
1368 int nblack = 0, any_white_cell = -1;
1369 game_state *dup = dup_game(state);
1371 for (i = r = 0; r < h; ++r)
1372 for (c = 0; c < w; ++c, ++i) {
1373 switch (state->grid[i]) {
1379 for (j = 0; j < 4; ++j) {
1380 int const rr = r + dr[j], cc = c + dc[j];
1381 if (out_of_bounds(rr, cc, w, h)) continue;
1382 if (state->grid[idx(rr, cc, w)] != BLACK) continue;
1383 if (!report) goto found_error;
1392 for (runs = 1, j = 0; j < 4; ++j) {
1393 int const rr = r + dr[j], cc = c + dc[j];
1394 runs += runlength(rr, cc, dr[j], dc[j], state,
1398 if (runs != state->grid[i]) goto found_error;
1399 } else if (runs < state->grid[i]) report[i] = TRUE;
1401 for (runs = 1, j = 0; j < 4; ++j) {
1402 int const rr = r + dr[j], cc = c + dc[j];
1403 runs += runlength(rr, cc, dr[j], dc[j], state,
1404 ~(MASK(BLACK) | MASK(EMPTY)));
1406 if (runs > state->grid[i]) report[i] = TRUE;
1410 /* note: fallthrough _into_ these cases */
1412 case WHITE: any_white_cell = i;
1416 for (i = 0; i < n; ++i) if (dup->grid[i] != BLACK) dup->grid[i] = WHITE;
1417 if (nblack + dfs_count_white(dup, any_white_cell) < n) {
1419 printf("dfs fail at %d\n", any_white_cell);
1422 for (i = 0; i < n; ++i) if (state->grid[i] != BLACK) report[i] = TRUE;
1426 return FALSE; /* if report != NULL, this is ignored */
1433 static game_state *execute_move(game_state *state, char *move)
1435 signed int r, c, value, nchars, ntok;
1436 signed char what_to_do;
1441 ret = dup_game(state);
1445 ret->has_cheated = ret->was_solved = TRUE;
1448 for (; *move; move += nchars) {
1449 ntok = sscanf(move, "%c,%d,%d%n", &what_to_do, &r, &c, &nchars);
1450 if (ntok < 3) goto failure;
1451 switch (what_to_do) {
1452 case 'W': value = WHITE; break;
1453 case 'E': value = EMPTY; break;
1454 case 'B': value = BLACK; break;
1455 default: goto failure;
1457 if (out_of_bounds(r, c, ret->params.w, ret->params.h)) goto failure;
1458 ret->grid[idx(r, c, ret->params.w)] = value;
1461 if (ret->was_solved == FALSE)
1462 ret->was_solved = !find_errors(ret, NULL);
1471 static void game_changed_state(game_ui *ui, game_state *oldstate,
1472 game_state *newstate)
1476 static float game_anim_length(game_state *oldstate, game_state *newstate,
1477 int dir, game_ui *ui)
1482 #define FLASH_TIME 0.7F
1484 static float game_flash_length(game_state *from, game_state *to,
1485 int dir, game_ui *ui)
1487 if (!from->was_solved && to->was_solved && !to->has_cheated)
1492 static int game_status(game_state *state)
1494 return state->was_solved ? +1 : 0;
1497 /* ----------------------------------------------------------------------
1501 #define PREFERRED_TILE_SIZE 32
1506 COL_BLACK = COL_GRID,
1507 COL_TEXT = COL_GRID,
1508 COL_USER = COL_GRID,
1511 COL_HIGHLIGHT = COL_ERROR, /* mkhighlight needs it, I don't */
1512 COL_CURSOR = COL_LOWLIGHT,
1516 static void game_compute_size(game_params *params, int tilesize,
1519 *x = (1 + params->w) * tilesize;
1520 *y = (1 + params->h) * tilesize;
1523 static void game_set_size(drawing *dr, game_drawstate *ds,
1524 game_params *params, int tilesize)
1526 ds->tilesize = tilesize;
1529 #define COLOUR(ret, i, r, g, b) \
1530 ((ret[3*(i)+0] = (r)), (ret[3*(i)+1] = (g)), (ret[3*(i)+2] = (b)))
1532 static float *game_colours(frontend *fe, int *ncolours)
1534 float *ret = snewn(3 * NCOLOURS, float);
1536 game_mkhighlight(fe, ret, COL_BACKGROUND, COL_HIGHLIGHT, COL_LOWLIGHT);
1537 COLOUR(ret, COL_GRID, 0.0F, 0.0F, 0.0F);
1538 COLOUR(ret, COL_ERROR, 1.0F, 0.0F, 0.0F);
1540 *ncolours = NCOLOURS;
1544 static drawcell makecell(puzzle_size value, int error, int cursor, int flash)
1547 setmember(ret, value);
1548 setmember(ret, error);
1549 setmember(ret, cursor);
1550 setmember(ret, flash);
1554 static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
1556 int const w = state->params.w, h = state->params.h, n = w * h;
1557 struct game_drawstate *ds = snew(struct game_drawstate);
1561 ds->started = FALSE;
1563 ds->grid = snewn(n, drawcell);
1564 for (i = 0; i < n; ++i)
1565 ds->grid[i] = makecell(w + h, FALSE, FALSE, FALSE);
1570 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
1576 #define cmpmember(a, b, field) ((a) . field == (b) . field)
1578 static int cell_eq(drawcell a, drawcell b)
1581 cmpmember(a, b, value) &&
1582 cmpmember(a, b, error) &&
1583 cmpmember(a, b, cursor) &&
1584 cmpmember(a, b, flash);
1587 static void draw_cell(drawing *dr, game_drawstate *ds, int r, int c,
1590 static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
1591 game_state *state, int dir, game_ui *ui,
1592 float animtime, float flashtime)
1594 int const w = state->params.w, h = state->params.h, n = w * h;
1595 int const wpx = (w+1) * ds->tilesize, hpx = (h+1) * ds->tilesize;
1596 int const flash = ((int) (flashtime * 5 / FLASH_TIME)) % 2;
1600 int *errors = snewn(n, int);
1601 memset(errors, FALSE, n * sizeof (int));
1602 find_errors(state, errors);
1604 assert (oldstate == NULL); /* only happens if animating moves */
1608 draw_rect(dr, 0, 0, wpx, hpx, COL_BACKGROUND);
1609 draw_rect(dr, BORDER-1, BORDER-1,
1610 ds->tilesize*w+2, ds->tilesize*h+2, COL_GRID);
1611 draw_update(dr, 0, 0, wpx, hpx);
1614 for (i = r = 0; r < h; ++r) {
1615 for (c = 0; c < w; ++c, ++i) {
1616 drawcell cell = makecell(state->grid[i], errors[i], FALSE, flash);
1617 if (r == ui->r && c == ui->c && ui->cursor_show)
1619 if (!cell_eq(cell, ds->grid[i])) {
1620 draw_cell(dr, ds, r, c, cell);
1629 static void draw_cell(drawing *draw, game_drawstate *ds, int r, int c,
1632 int const ts = ds->tilesize;
1633 int const y = BORDER + ts * r, x = BORDER + ts * c;
1634 int const tx = x + (ts / 2), ty = y + (ts / 2);
1635 int const dotsz = (ds->tilesize + 9) / 10;
1637 int const colour = (cell.value == BLACK ?
1638 cell.error ? COL_ERROR : COL_BLACK :
1639 cell.flash || cell.cursor ?
1640 COL_LOWLIGHT : COL_BACKGROUND);
1642 draw_rect (draw, x, y, ts, ts, colour);
1643 draw_rect_outline(draw, x, y, ts, ts, COL_GRID);
1645 switch (cell.value) {
1646 case WHITE: draw_rect(draw, tx - dotsz / 2, ty - dotsz / 2, dotsz, dotsz,
1647 cell.error ? COL_ERROR : COL_USER);
1651 draw_circle(draw, tx, ty, dotsz / 2, COL_ERROR, COL_GRID);
1655 int const colour = (cell.error ? COL_ERROR : COL_GRID);
1656 char *msg = nfmtstr(10, "%d", cell.value);
1657 draw_text(draw, tx, ty, FONT_VARIABLE, ts * 3 / 5,
1658 ALIGN_VCENTRE | ALIGN_HCENTRE, colour, msg);
1663 draw_update(draw, x, y, ts, ts);
1666 static int game_timing_state(game_state *state, game_ui *ui)
1668 puts("warning: game_timing_state was called (this shouldn't happen)");
1669 return FALSE; /* the (non-existing) timer should not be running */
1672 /* ----------------------------------------------------------------------
1673 * User interface: print
1676 static void game_print_size(game_params *params, float *x, float *y)
1678 int print_width, print_height;
1679 game_compute_size(params, 800, &print_width, &print_height);
1680 *x = print_width / 100.0F;
1681 *y = print_height / 100.0F;
1684 static void game_print(drawing *dr, game_state *state, int tilesize)
1686 int const w = state->params.w, h = state->params.h;
1687 game_drawstate ds_obj, *ds = &ds_obj;
1688 int r, c, i, colour;
1690 ds->tilesize = tilesize;
1692 colour = print_mono_colour(dr, 1); assert(colour == COL_BACKGROUND);
1693 colour = print_mono_colour(dr, 0); assert(colour == COL_GRID);
1694 colour = print_mono_colour(dr, 1); assert(colour == COL_ERROR);
1695 colour = print_mono_colour(dr, 0); assert(colour == COL_LOWLIGHT);
1696 colour = print_mono_colour(dr, 0); assert(colour == NCOLOURS);
1698 for (i = r = 0; r < h; ++r)
1699 for (c = 0; c < w; ++c, ++i)
1700 draw_cell(dr, ds, r, c,
1701 makecell(state->grid[i], FALSE, FALSE, FALSE));
1703 print_line_width(dr, 3 * tilesize / 40);
1704 draw_rect_outline(dr, BORDER, BORDER, w*TILESIZE, h*TILESIZE, COL_GRID);
1707 /* And that's about it ;-) **************************************************/
1710 #define thegame range
1713 struct game const thegame = {
1714 "Range", "games.range", "range",
1721 TRUE, game_configure, custom_params,
1729 TRUE, game_can_format_as_text_now, game_text_format,
1737 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
1740 game_free_drawstate,
1745 TRUE, FALSE, game_print_size, game_print,
1746 FALSE, /* wants_statusbar */
1747 FALSE, game_timing_state,