chiark / gitweb /
Fix completion checking in Killer Solo.
[sgt-puzzles.git] / loopy.c
diff --git a/loopy.c b/loopy.c
index 16d23cf40440054f28cd0bc7d6dfbd16877ebb6d..44d51eeacaf42f58bdd47335e3e3ba585943e8ce 100644 (file)
--- a/loopy.c
+++ b/loopy.c
  */
 
 /*
- *
- *  - There's an interesting deductive technique which makes use of topology
- *    rather than just graph theory. Each _square_ in the grid is either inside
- *    or outside the loop; you can tell that two squares are on the same side
- *    of the loop if they're separated by an x (or, more generally, by a path
- *    crossing no LINE_UNKNOWNs and an even number of LINE_YESes), and on the
- *    opposite side of the loop if they're separated by a line (or an odd
- *    number of LINE_YESes and no LINE_UNKNOWNs). Oh, and any square separated
- *    from the outside of the grid by a LINE_YES or a LINE_NO is on the inside
- *    or outside respectively. So if you can track this for all squares, you
- *    figure out the state of the line between a pair once their relative
- *    insideness is known.
+ * Possible future solver enhancements:
+ * 
+ *  - There's an interesting deductive technique which makes use
+ *    of topology rather than just graph theory. Each _face_ in
+ *    the grid is either inside or outside the loop; you can tell
+ *    that two faces are on the same side of the loop if they're
+ *    separated by a LINE_NO (or, more generally, by a path
+ *    crossing no LINE_UNKNOWNs and an even number of LINE_YESes),
+ *    and on the opposite side of the loop if they're separated by
+ *    a LINE_YES (or an odd number of LINE_YESes and no
+ *    LINE_UNKNOWNs). Oh, and any face separated from the outside
+ *    of the grid by a LINE_YES or a LINE_NO is on the inside or
+ *    outside respectively. So if you can track this for all
+ *    faces, you figure out the state of the line between a pair
+ *    once their relative insideness is known.
+ *     + The way I envisage this working is simply to keep an edsf
+ *      of all _faces_, which indicates whether they're on
+ *      opposite sides of the loop from one another. We also
+ *      include a special entry in the edsf for the infinite
+ *      exterior "face".
+ *     + So, the simple way to do this is to just go through the
+ *      edges: every time we see an edge in a state other than
+ *      LINE_UNKNOWN which separates two faces that aren't in the
+ *      same edsf class, we can rectify that by merging the
+ *      classes. Then, conversely, an edge in LINE_UNKNOWN state
+ *      which separates two faces that _are_ in the same edsf
+ *      class can immediately have its state determined.
+ *     + But you can go one better, if you're prepared to loop
+ *      over all _pairs_ of edges. Suppose we have edges A and B,
+ *      which respectively separate faces A1,A2 and B1,B2.
+ *      Suppose that A,B are in the same edge-edsf class and that
+ *      A1,B1 (wlog) are in the same face-edsf class; then we can
+ *      immediately place A2,B2 into the same face-edsf class (as
+ *      each other, not as A1 and A2) one way round or the other.
+ *      And conversely again, if A1,B1 are in the same face-edsf
+ *      class and so are A2,B2, then we can put A,B into the same
+ *      face-edsf class.
+ *       * Of course, this deduction requires a quadratic-time
+ *         loop over all pairs of edges in the grid, so it should
+ *         be reserved until there's nothing easier left to be
+ *         done.
+ * 
+ *  - The generalised grid support has made me (SGT) notice a
+ *    possible extension to the loop-avoidance code. When you have
+ *    a path of connected edges such that no other edges at all
+ *    are incident on any vertex in the middle of the path - or,
+ *    alternatively, such that any such edges are already known to
+ *    be LINE_NO - then you know those edges are either all
+ *    LINE_YES or all LINE_NO. Hence you can mentally merge the
+ *    entire path into a single long curly edge for the purposes
+ *    of loop avoidance, and look directly at whether or not the
+ *    extreme endpoints of the path are connected by some other
+ *    route. I find this coming up fairly often when I play on the
+ *    octagonal grid setting, so it might be worth implementing in
+ *    the solver.
  *
  *  - (Just a speed optimisation.)  Consider some todo list queue where every
  *    time we modify something we mark it for consideration by other bits of
@@ -30,6 +73,7 @@
 
 #include <stdio.h>
 #include <stdlib.h>
+#include <stddef.h>
 #include <string.h>
 #include <assert.h>
 #include <ctype.h>
@@ -38,6 +82,7 @@
 #include "puzzles.h"
 #include "tree234.h"
 #include "grid.h"
+#include "loopgen.h"
 
 /* Debugging options */
 
@@ -58,11 +103,12 @@ enum {
     COL_HIGHLIGHT,
     COL_MISTAKE,
     COL_SATISFIED,
+    COL_FAINT,
     NCOLOURS
 };
 
 struct game_state {
-    grid *game_grid;
+    grid *game_grid; /* ref-counted (internally) */
 
     /* Put -1 in a face that doesn't get a clue */
     signed char *clues;
@@ -71,6 +117,9 @@ struct game_state {
      * YES, NO or UNKNOWN */
     char *lines;
 
+    unsigned char *line_errors;
+    int exactly_one_loop;
+
     int solved;
     int cheated;
 
@@ -87,17 +136,6 @@ enum solver_status {
 };
 
 /* ------ Solver state ------ */
-typedef struct normal {
-    /* For each dline, store a bitmask for whether we know:
-     * (bit 0) at least one is YES
-     * (bit 1) at most one is YES */
-    char *dlines;
-} normal_mode_state;
-
-typedef struct hard {
-    int *linedsf;
-} hard_mode_state;
-
 typedef struct solver_state {
     game_state *state;
     enum solver_status solver_status;
@@ -105,6 +143,10 @@ typedef struct solver_state {
      * looplen of 1 means there are no lines to a particular dot */
     int *looplen;
 
+    /* Difficulty level of solver.  Used by solver functions that want to
+     * vary their behaviour depending on the requested difficulty level. */
+    int diff;
+
     /* caches */
     char *dot_yes_count;
     char *dot_no_count;
@@ -113,8 +155,14 @@ typedef struct solver_state {
     char *dot_solved, *face_solved;
     int *dotdsf;
 
-    normal_mode_state *normal;
-    hard_mode_state *hard;
+    /* Information for Normal level deductions:
+     * For each dline, store a bitmask for whether we know:
+     * (bit 0) at least one is YES
+     * (bit 1) at most one is YES */
+    char *dlines;
+
+    /* Hard level information */
+    int *linedsf;
 } solver_state;
 
 /*
@@ -123,33 +171,52 @@ typedef struct solver_state {
  */
 
 #define DIFFLIST(A) \
-    A(EASY,Easy,e,easy_mode_deductions) \
-    A(NORMAL,Normal,n,normal_mode_deductions) \
-    A(HARD,Hard,h,hard_mode_deductions)
-#define ENUM(upper,title,lower,fn) DIFF_ ## upper,
-#define TITLE(upper,title,lower,fn) #title,
-#define ENCODE(upper,title,lower,fn) #lower
-#define CONFIG(upper,title,lower,fn) ":" #title
-#define SOLVER_FN_DECL(upper,title,lower,fn) static int fn(solver_state *);
-#define SOLVER_FN(upper,title,lower,fn) &fn,
+    A(EASY,Easy,e) \
+    A(NORMAL,Normal,n) \
+    A(TRICKY,Tricky,t) \
+    A(HARD,Hard,h)
+#define ENUM(upper,title,lower) DIFF_ ## upper,
+#define TITLE(upper,title,lower) #title,
+#define ENCODE(upper,title,lower) #lower
+#define CONFIG(upper,title,lower) ":" #title
 enum { DIFFLIST(ENUM) DIFF_MAX };
 static char const *const diffnames[] = { DIFFLIST(TITLE) };
 static char const diffchars[] = DIFFLIST(ENCODE);
 #define DIFFCONFIG DIFFLIST(CONFIG)
-DIFFLIST(SOLVER_FN_DECL);
-static int (*(solver_fns[]))(solver_state *) = { DIFFLIST(SOLVER_FN) };
+
+/*
+ * Solver routines, sorted roughly in order of computational cost.
+ * The solver will run the faster deductions first, and slower deductions are
+ * only invoked when the faster deductions are unable to make progress.
+ * Each function is associated with a difficulty level, so that the generated
+ * puzzles are solvable by applying only the functions with the chosen
+ * difficulty level or lower.
+ */
+#define SOLVERLIST(A) \
+    A(trivial_deductions, DIFF_EASY) \
+    A(dline_deductions, DIFF_NORMAL) \
+    A(linedsf_deductions, DIFF_HARD) \
+    A(loop_deductions, DIFF_EASY)
+#define SOLVER_FN_DECL(fn,diff) static int fn(solver_state *);
+#define SOLVER_FN(fn,diff) &fn,
+#define SOLVER_DIFF(fn,diff) diff,
+SOLVERLIST(SOLVER_FN_DECL)
+static int (*(solver_fns[]))(solver_state *) = { SOLVERLIST(SOLVER_FN) };
+static int const solver_diffs[] = { SOLVERLIST(SOLVER_DIFF) };
+static const int NUM_SOLVERS = sizeof(solver_diffs)/sizeof(*solver_diffs);
 
 struct game_params {
     int w, h;
     int diff;
     int type;
-
-    /* Grid generation is expensive, so keep a (ref-counted) reference to the
-     * grid for these parameters, and only generate when required. */
-    grid *game_grid;
 };
 
+/* line_drawstate is the same as line_state, but with the extra ERROR
+ * possibility.  The drawing code copies line_state to line_drawstate,
+ * except in the case that the line is an error. */
 enum line_state { LINE_YES, LINE_UNKNOWN, LINE_NO };
+enum line_drawstate { DS_LINE_YES, DS_LINE_UNKNOWN,
+                      DS_LINE_NO, DS_LINE_ERROR };
 
 #define OPP(line_state) \
     (2 - line_state)
@@ -159,16 +226,16 @@ struct game_drawstate {
     int started;
     int tilesize;
     int flashing;
+    int *textx, *texty;
     char *lines;
     char *clue_error;
     char *clue_satisfied;
 };
 
-static char *validate_desc(game_params *params, char *desc);
+static char *validate_desc(const game_params *params, const char *desc);
 static int dot_order(const game_state* state, int i, char line_type);
 static int face_order(const game_state* state, int i, char line_type);
-static solver_state *solve_game_rec(const solver_state *sstate,
-                                    int diff);
+static solver_state *solve_game_rec(const solver_state *sstate);
 
 #ifdef DEBUG_CACHES
 static void check_caches(const solver_state* sstate);
@@ -178,32 +245,43 @@ static void check_caches(const solver_state* sstate);
 
 /* ------- List of grid generators ------- */
 #define GRIDLIST(A) \
-    A(Squares,grid_new_square) \
-    A(Triangular,grid_new_triangular) \
-    A(Honeycomb,grid_new_honeycomb) \
-    A(Snub-Square,grid_new_snubsquare) \
-    A(Cairo,grid_new_cairo) \
-    A(Great-Hexagonal,grid_new_greathexagonal) \
-    A(Octagonal,grid_new_octagonal) \
-    A(Kites,grid_new_kites)
-
-#define GRID_NAME(title,fn) #title,
-#define GRID_CONFIG(title,fn) ":" #title
-#define GRID_FN(title,fn) &fn,
+    A(Squares,GRID_SQUARE,3,3) \
+    A(Triangular,GRID_TRIANGULAR,3,3) \
+    A(Honeycomb,GRID_HONEYCOMB,3,3) \
+    A(Snub-Square,GRID_SNUBSQUARE,3,3) \
+    A(Cairo,GRID_CAIRO,3,4) \
+    A(Great-Hexagonal,GRID_GREATHEXAGONAL,3,3) \
+    A(Octagonal,GRID_OCTAGONAL,3,3) \
+    A(Kites,GRID_KITE,3,3) \
+    A(Floret,GRID_FLORET,1,2) \
+    A(Dodecagonal,GRID_DODECAGONAL,2,2) \
+    A(Great-Dodecagonal,GRID_GREATDODECAGONAL,2,2) \
+    A(Penrose (kite/dart),GRID_PENROSE_P2,3,3) \
+    A(Penrose (rhombs),GRID_PENROSE_P3,3,3)
+
+#define GRID_NAME(title,type,amin,omin) #title,
+#define GRID_CONFIG(title,type,amin,omin) ":" #title
+#define GRID_TYPE(title,type,amin,omin) type,
+#define GRID_SIZES(title,type,amin,omin) \
+    {amin, omin, \
+     "Width and height for this grid type must both be at least " #amin, \
+     "At least one of width and height for this grid type must be at least " #omin,},
 static char const *const gridnames[] = { GRIDLIST(GRID_NAME) };
 #define GRID_CONFIGS GRIDLIST(GRID_CONFIG)
-static grid * (*(grid_fns[]))(int w, int h) = { GRIDLIST(GRID_FN) };
-static const int NUM_GRID_TYPES = sizeof(grid_fns) / sizeof(grid_fns[0]);
+static grid_type grid_types[] = { GRIDLIST(GRID_TYPE) };
+#define NUM_GRID_TYPES (sizeof(grid_types) / sizeof(grid_types[0]))
+static const struct {
+    int amin, omin;
+    char *aerr, *oerr;
+} grid_size_limits[] = { GRIDLIST(GRID_SIZES) };
 
 /* Generates a (dynamically allocated) new grid, according to the
  * type and size requested in params.  Does nothing if the grid is already
- * generated.  The allocated grid is owned by the params object, and will be
- * freed in free_params(). */
-static void params_generate_grid(game_params *params)
+ * generated. */
+static grid *loopy_generate_grid(const game_params *params,
+                                 const char *grid_desc)
 {
-    if (!params->game_grid) {
-        params->game_grid = grid_fns[params->type](params->w, params->h);
-    }
+    return grid_new(grid_types[params->type], params->w, params->h, grid_desc);
 }
 
 /* ----------------------------------------------------------------------
@@ -224,13 +302,13 @@ static void params_generate_grid(game_params *params)
                                ((field) &= ~(1<<(bit)), TRUE) : FALSE)
 
 #define CLUE2CHAR(c) \
-    ((c < 0) ? ' ' : c + '0')
+    ((c < 0) ? ' ' : c < 10 ? c + '0' : c - 10 + 'A')
 
 /* ----------------------------------------------------------------------
  * General struct manipulation and other straightforward code
  */
 
-static game_state *dup_game(game_state *state)
+static game_state *dup_game(const game_state *state)
 {
     game_state *ret = snew(game_state);
 
@@ -246,6 +324,10 @@ static game_state *dup_game(game_state *state)
     ret->lines = snewn(state->game_grid->num_edges, char);
     memcpy(ret->lines, state->lines, state->game_grid->num_edges);
 
+    ret->line_errors = snewn(state->game_grid->num_edges, unsigned char);
+    memcpy(ret->line_errors, state->line_errors, state->game_grid->num_edges);
+    ret->exactly_one_loop = state->exactly_one_loop;
+
     ret->grid_type = state->grid_type;
     return ret;
 }
@@ -256,11 +338,12 @@ static void free_game(game_state *state)
         grid_free(state->game_grid);
         sfree(state->clues);
         sfree(state->lines);
+        sfree(state->line_errors);
         sfree(state);
     }
 }
 
-static solver_state *new_solver_state(game_state *state, int diff) {
+static solver_state *new_solver_state(const game_state *state, int diff) {
     int i;
     int num_dots = state->game_grid->num_dots;
     int num_faces = state->game_grid->num_faces;
@@ -270,6 +353,7 @@ static solver_state *new_solver_state(game_state *state, int diff) {
     ret->state = dup_game(state);
 
     ret->solver_status = SOLVER_INCOMPLETE;
+    ret->diff = diff;
 
     ret->dotdsf = snew_dsf(num_dots);
     ret->looplen = snewn(num_dots, int);
@@ -293,18 +377,16 @@ static solver_state *new_solver_state(game_state *state, int diff) {
     memset(ret->face_no_count, 0, num_faces);
 
     if (diff < DIFF_NORMAL) {
-        ret->normal = NULL;
+        ret->dlines = NULL;
     } else {
-        ret->normal = snew(normal_mode_state);
-        ret->normal->dlines = snewn(2*num_edges, char);
-        memset(ret->normal->dlines, 0, 2*num_edges);
+        ret->dlines = snewn(2*num_edges, char);
+        memset(ret->dlines, 0, 2*num_edges);
     }
 
     if (diff < DIFF_HARD) {
-        ret->hard = NULL;
+        ret->linedsf = NULL;
     } else {
-        ret->hard = snew(hard_mode_state);
-        ret->hard->linedsf = snew_dsf(state->game_grid->num_edges);
+        ret->linedsf = snew_dsf(state->game_grid->num_edges);
     }
 
     return ret;
@@ -322,15 +404,9 @@ static void free_solver_state(solver_state *sstate) {
         sfree(sstate->face_yes_count);
         sfree(sstate->face_no_count);
 
-        if (sstate->normal) {
-            sfree(sstate->normal->dlines);
-            sfree(sstate->normal);
-        }
-
-        if (sstate->hard) {
-            sfree(sstate->hard->linedsf);
-            sfree(sstate->hard);
-        }
+        /* OK, because sfree(NULL) is a no-op */
+        sfree(sstate->dlines);
+        sfree(sstate->linedsf);
 
         sfree(sstate);
     }
@@ -346,6 +422,7 @@ static solver_state *dup_solver_state(const solver_state *sstate) {
     ret->state = state = dup_game(sstate->state);
 
     ret->solver_status = sstate->solver_status;
+    ret->diff = sstate->diff;
 
     ret->dotdsf = snewn(num_dots, int);
     ret->looplen = snewn(num_dots, int);
@@ -369,22 +446,20 @@ static solver_state *dup_solver_state(const solver_state *sstate) {
     ret->face_no_count = snewn(num_faces, char);
     memcpy(ret->face_no_count, sstate->face_no_count, num_faces);
 
-    if (sstate->normal) {
-        ret->normal = snew(normal_mode_state);
-        ret->normal->dlines = snewn(2*num_edges, char);
-        memcpy(ret->normal->dlines, sstate->normal->dlines,
+    if (sstate->dlines) {
+        ret->dlines = snewn(2*num_edges, char);
+        memcpy(ret->dlines, sstate->dlines,
                2*num_edges);
     } else {
-        ret->normal = NULL;
+        ret->dlines = NULL;
     }
 
-    if (sstate->hard) {
-        ret->hard = snew(hard_mode_state);
-        ret->hard->linedsf = snewn(num_edges, int);
-        memcpy(ret->hard->linedsf, sstate->hard->linedsf,
+    if (sstate->linedsf) {
+        ret->linedsf = snewn(num_edges, int);
+        memcpy(ret->linedsf, sstate->linedsf,
                num_edges * sizeof(int));
     } else {
-        ret->hard = NULL;
+        ret->linedsf = NULL;
     }
 
     return ret;
@@ -404,36 +479,54 @@ static game_params *default_params(void)
     ret->diff = DIFF_EASY;
     ret->type = 0;
 
-    ret->game_grid = NULL;
-
     return ret;
 }
 
-static game_params *dup_params(game_params *params)
+static game_params *dup_params(const game_params *params)
 {
     game_params *ret = snew(game_params);
 
     *ret = *params;                       /* structure copy */
-    if (ret->game_grid) {
-        ret->game_grid->refcount++;
-    }
     return ret;
 }
 
 static const game_params presets[] = {
-    {  7,  7, DIFF_EASY, 0, NULL },
-    {  10,  10, DIFF_EASY, 0, NULL },
-    {  7,  7, DIFF_NORMAL, 0, NULL },
-    {  10,  10, DIFF_NORMAL, 0, NULL },
-    {  7,  7, DIFF_HARD, 0, NULL },
-    {  10,  10, DIFF_HARD, 0, NULL },
-    {  10,  10, DIFF_HARD, 1, NULL },
-    {  12,  10, DIFF_HARD, 2, NULL },
-    {  7,  7, DIFF_HARD, 3, NULL },
-    {  9,  9, DIFF_HARD, 4, NULL },
-    {  5,  4, DIFF_HARD, 5, NULL },
-    {  7,  7, DIFF_HARD, 6, NULL },
-    {  5,  5, DIFF_HARD, 7, NULL },
+#ifdef SMALL_SCREEN
+    {  7,  7, DIFF_EASY, 0 },
+    {  7,  7, DIFF_NORMAL, 0 },
+    {  7,  7, DIFF_HARD, 0 },
+    {  7,  7, DIFF_HARD, 1 },
+    {  7,  7, DIFF_HARD, 2 },
+    {  5,  5, DIFF_HARD, 3 },
+    {  7,  7, DIFF_HARD, 4 },
+    {  5,  4, DIFF_HARD, 5 },
+    {  5,  5, DIFF_HARD, 6 },
+    {  5,  5, DIFF_HARD, 7 },
+    {  3,  3, DIFF_HARD, 8 },
+    {  3,  3, DIFF_HARD, 9 },
+    {  3,  3, DIFF_HARD, 10 },
+    {  6,  6, DIFF_HARD, 11 },
+    {  6,  6, DIFF_HARD, 12 },
+#else
+    {  7,  7, DIFF_EASY, 0 },
+    {  10,  10, DIFF_EASY, 0 },
+    {  7,  7, DIFF_NORMAL, 0 },
+    {  10,  10, DIFF_NORMAL, 0 },
+    {  7,  7, DIFF_HARD, 0 },
+    {  10,  10, DIFF_HARD, 0 },
+    {  10,  10, DIFF_HARD, 1 },
+    {  12,  10, DIFF_HARD, 2 },
+    {  7,  7, DIFF_HARD, 3 },
+    {  9,  9, DIFF_HARD, 4 },
+    {  5,  4, DIFF_HARD, 5 },
+    {  7,  7, DIFF_HARD, 6 },
+    {  5,  5, DIFF_HARD, 7 },
+    {  5,  5, DIFF_HARD, 8 },
+    {  5,  4, DIFF_HARD, 9 },
+    {  5,  4, DIFF_HARD, 10 },
+    {  10, 10, DIFF_HARD, 11 },
+    {  10, 10, DIFF_HARD, 12 }
+#endif
 };
 
 static int game_fetch_preset(int i, char **name, game_params **params)
@@ -456,18 +549,11 @@ static int game_fetch_preset(int i, char **name, game_params **params)
 
 static void free_params(game_params *params)
 {
-    if (params->game_grid) {
-        grid_free(params->game_grid);
-    }
     sfree(params);
 }
 
 static void decode_params(game_params *params, char const *string)
 {
-    if (params->game_grid) {
-        grid_free(params->game_grid);
-        params->game_grid = NULL;
-    }
     params->h = params->w = atoi(string);
     params->diff = DIFF_EASY;
     while (*string && isdigit((unsigned char)*string)) string++;
@@ -491,7 +577,7 @@ static void decode_params(game_params *params, char const *string)
     }
 }
 
-static char *encode_params(game_params *params, int full)
+static char *encode_params(const game_params *params, int full)
 {
     char str[80];
     sprintf(str, "%dx%dt%d", params->w, params->h, params->type);
@@ -500,7 +586,7 @@ static char *encode_params(game_params *params, int full)
     return dupstr(str);
 }
 
-static config_item *game_configure(game_params *params)
+static config_item *game_configure(const game_params *params)
 {
     config_item *ret;
     char buf[80];
@@ -537,7 +623,7 @@ static config_item *game_configure(game_params *params)
     return ret;
 }
 
-static game_params *custom_params(config_item *cfg)
+static game_params *custom_params(const config_item *cfg)
 {
     game_params *ret = snew(game_params);
 
@@ -546,16 +632,19 @@ static game_params *custom_params(config_item *cfg)
     ret->type = cfg[2].ival;
     ret->diff = cfg[3].ival;
 
-    ret->game_grid = NULL;
     return ret;
 }
 
-static char *validate_params(game_params *params, int full)
+static char *validate_params(const game_params *params, int full)
 {
-    if (params->w < 3 || params->h < 3)
-        return "Width and height must both be at least 3";
     if (params->type < 0 || params->type >= NUM_GRID_TYPES)
         return "Illegal grid type";
+    if (params->w < grid_size_limits[params->type].amin ||
+       params->h < grid_size_limits[params->type].amin)
+        return grid_size_limits[params->type].aerr;
+    if (params->w < grid_size_limits[params->type].omin &&
+       params->h < grid_size_limits[params->type].omin)
+        return grid_size_limits[params->type].oerr;
 
     /*
      * This shouldn't be able to happen at all, since decode_params
@@ -603,17 +692,47 @@ static char *state_to_text(const game_state *state)
     return retval;
 }
 
+#define GRID_DESC_SEP '_'
+
+/* Splits up a (optional) grid_desc from the game desc. Returns the
+ * grid_desc (which needs freeing) and updates the desc pointer to
+ * start of real desc, or returns NULL if no desc. */
+static char *extract_grid_desc(const char **desc)
+{
+    char *sep = strchr(*desc, GRID_DESC_SEP), *gd;
+    int gd_len;
+
+    if (!sep) return NULL;
+
+    gd_len = sep - (*desc);
+    gd = snewn(gd_len+1, char);
+    memcpy(gd, *desc, gd_len);
+    gd[gd_len] = '\0';
+
+    *desc = sep+1;
+
+    return gd;
+}
+
 /* We require that the params pass the test in validate_params and that the
  * description fills the entire game area */
-static char *validate_desc(game_params *params, char *desc)
+static char *validate_desc(const game_params *params, const char *desc)
 {
     int count = 0;
     grid *g;
-    params_generate_grid(params);
-    g = params->game_grid;
+    char *grid_desc, *ret;
+
+    /* It's pretty inefficient to do this just for validation. All we need to
+     * know is the precise number of faces. */
+    grid_desc = extract_grid_desc(&desc);
+    ret = grid_validate_desc(grid_types[params->type], params->w, params->h, grid_desc);
+    if (ret) return ret;
+
+    g = loopy_generate_grid(params, grid_desc);
+    if (grid_desc) sfree(grid_desc);
 
     for (; *desc; ++desc) {
-        if (*desc >= '0' && *desc <= '9') {
+        if ((*desc >= '0' && *desc <= '9') || (*desc >= 'A' && *desc <= 'Z')) {
             count++;
             continue;
         }
@@ -629,6 +748,8 @@ static char *validate_desc(game_params *params, char *desc)
     if (count > g->num_faces)
         return "Description too long for board size";
 
+    grid_free(g);
+
     return NULL;
 }
 
@@ -684,7 +805,7 @@ static char *encode_solve_move(const game_state *state)
     return ret;
 }
 
-static game_ui *new_ui(game_state *state)
+static game_ui *new_ui(const game_state *state)
 {
     return NULL;
 }
@@ -693,44 +814,45 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static char *encode_ui(game_ui *ui)
+static char *encode_ui(const game_ui *ui)
 {
     return NULL;
 }
 
-static void decode_ui(game_ui *ui, char *encoding)
+static void decode_ui(game_ui *ui, const char *encoding)
 {
 }
 
-static void game_changed_state(game_ui *ui, game_state *oldstate,
-                               game_state *newstate)
+static void game_changed_state(game_ui *ui, const game_state *oldstate,
+                               const game_state *newstate)
 {
 }
 
-static void game_compute_size(game_params *params, int tilesize,
+static void game_compute_size(const game_params *params, int tilesize,
                               int *x, int *y)
 {
-    grid *g;
-    params_generate_grid(params);
-    g = params->game_grid;
-    int grid_width = g->highest_x - g->lowest_x;
-    int grid_height = g->highest_y - g->lowest_y;
+    int grid_width, grid_height, rendered_width, rendered_height;
+    int g_tilesize;
+
+    grid_compute_size(grid_types[params->type], params->w, params->h,
+                      &g_tilesize, &grid_width, &grid_height);
+
     /* multiply first to minimise rounding error on integer division */
-    int rendered_width = grid_width * tilesize / g->tilesize;
-    int rendered_height = grid_height * tilesize / g->tilesize;
+    rendered_width = grid_width * tilesize / g_tilesize;
+    rendered_height = grid_height * tilesize / g_tilesize;
     *x = rendered_width + 2 * BORDER(tilesize) + 1;
     *y = rendered_height + 2 * BORDER(tilesize) + 1;
 }
 
 static void game_set_size(drawing *dr, game_drawstate *ds,
-                         game_params *params, int tilesize)
+                          const game_params *params, int tilesize)
 {
     ds->tilesize = tilesize;
 }
 
 static float *game_colours(frontend *fe, int *ncolours)
 {
-    float *ret = snewn(4 * NCOLOURS, float);
+    float *ret = snewn(3 * NCOLOURS, float);
 
     frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
 
@@ -738,8 +860,14 @@ static float *game_colours(frontend *fe, int *ncolours)
     ret[COL_FOREGROUND * 3 + 1] = 0.0F;
     ret[COL_FOREGROUND * 3 + 2] = 0.0F;
 
-    ret[COL_LINEUNKNOWN * 3 + 0] = 0.8F;
-    ret[COL_LINEUNKNOWN * 3 + 1] = 0.8F;
+    /*
+     * We want COL_LINEUNKNOWN to be a yellow which is a bit darker
+     * than the background. (I previously set it to 0.8,0.8,0, but
+     * found that this went badly with the 0.8,0.8,0.8 favoured as a
+     * background by the Java frontend.)
+     */
+    ret[COL_LINEUNKNOWN * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
+    ret[COL_LINEUNKNOWN * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
     ret[COL_LINEUNKNOWN * 3 + 2] = 0.0F;
 
     ret[COL_HIGHLIGHT * 3 + 0] = 1.0F;
@@ -754,57 +882,72 @@ static float *game_colours(frontend *fe, int *ncolours)
     ret[COL_SATISFIED * 3 + 1] = 0.0F;
     ret[COL_SATISFIED * 3 + 2] = 0.0F;
 
+    /* We want the faint lines to be a bit darker than the background.
+     * Except if the background is pretty dark already; then it ought to be a
+     * bit lighter.  Oy vey.
+     */
+    ret[COL_FAINT * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
+    ret[COL_FAINT * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
+    ret[COL_FAINT * 3 + 2] = ret[COL_BACKGROUND * 3 + 2] * 0.9F;
+
     *ncolours = NCOLOURS;
     return ret;
 }
 
-static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
+static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
 {
     struct game_drawstate *ds = snew(struct game_drawstate);
     int num_faces = state->game_grid->num_faces;
     int num_edges = state->game_grid->num_edges;
+    int i;
 
     ds->tilesize = 0;
     ds->started = 0;
     ds->lines = snewn(num_edges, char);
     ds->clue_error = snewn(num_faces, char);
     ds->clue_satisfied = snewn(num_faces, char);
+    ds->textx = snewn(num_faces, int);
+    ds->texty = snewn(num_faces, int);
     ds->flashing = 0;
 
     memset(ds->lines, LINE_UNKNOWN, num_edges);
     memset(ds->clue_error, 0, num_faces);
     memset(ds->clue_satisfied, 0, num_faces);
+    for (i = 0; i < num_faces; i++)
+        ds->textx[i] = ds->texty[i] = -1;
 
     return ds;
 }
 
 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
 {
+    sfree(ds->textx);
+    sfree(ds->texty);
     sfree(ds->clue_error);
     sfree(ds->clue_satisfied);
     sfree(ds->lines);
     sfree(ds);
 }
 
-static int game_timing_state(game_state *state, game_ui *ui)
+static int game_timing_state(const game_state *state, game_ui *ui)
 {
     return TRUE;
 }
 
-static float game_anim_length(game_state *oldstate, game_state *newstate,
-                              int dir, game_ui *ui)
+static float game_anim_length(const game_state *oldstate,
+                              const game_state *newstate, int dir, game_ui *ui)
 {
     return 0.0F;
 }
 
-static int game_can_format_as_text_now(game_params *params)
+static int game_can_format_as_text_now(const game_params *params)
 {
     if (params->type != 0)
         return FALSE;
     return TRUE;
 }
 
-static char *game_text_format(game_state *state)
+static char *game_text_format(const game_state *state)
 {
     int w, h, W, H;
     int x, y, i;
@@ -865,13 +1008,15 @@ static char *game_text_format(game_state *state)
 
     /* Fill in clues */
     for (i = 0; i < g->num_faces; i++) {
+       int x1, x2, y1, y2;
+
         f = g->faces + i;
         assert(f->order == 4);
         /* Cell coordinates, from (0,0) to (w-1,h-1) */
-        int x1 = (f->dots[0]->x - g->lowest_x) / cell_size;
-        int x2 = (f->dots[2]->x - g->lowest_x) / cell_size;
-        int y1 = (f->dots[0]->y - g->lowest_y) / cell_size;
-        int y2 = (f->dots[2]->y - g->lowest_y) / cell_size;
+       x1 = (f->dots[0]->x - g->lowest_x) / cell_size;
+       x2 = (f->dots[2]->x - g->lowest_x) / cell_size;
+       y1 = (f->dots[0]->y - g->lowest_y) / cell_size;
+       y2 = (f->dots[2]->y - g->lowest_y) / cell_size;
         /* Midpoint, in canvas coordinates */
         x = x1 + x2;
         y = y1 + y2;
@@ -1021,12 +1166,12 @@ static int merge_lines(solver_state *sstate, int i, int j, int inverse
     assert(i < sstate->state->game_grid->num_edges);
     assert(j < sstate->state->game_grid->num_edges);
 
-    i = edsf_canonify(sstate->hard->linedsf, i, &inv_tmp);
+    i = edsf_canonify(sstate->linedsf, i, &inv_tmp);
     inverse ^= inv_tmp;
-    j = edsf_canonify(sstate->hard->linedsf, j, &inv_tmp);
+    j = edsf_canonify(sstate->linedsf, j, &inv_tmp);
     inverse ^= inv_tmp;
 
-    edsf_merge(sstate->hard->linedsf, i, j, inverse);
+    edsf_merge(sstate->linedsf, i, j, inverse);
 
 #ifdef SHOW_WORKING
     if (i != j) {
@@ -1136,345 +1281,33 @@ static int face_setall(solver_state *sstate, int face,
  * Loop generation and clue removal
  */
 
-/* We're going to store a list of current candidate faces for lighting.
- * Each face gets a 'score', which tells us how adding that face right
- * now would affect the length of the solution loop.  We're trying to
- * maximise that quantity so will bias our random selection of faces to
- * light towards those with high scores */
-struct face {
-    int score;
-    unsigned long random;
-    grid_face *f;
-};
-
-static int get_face_cmpfn(void *v1, void *v2)
-{
-    struct face *f1 = v1;
-    struct face *f2 = v2;
-    /* These grid_face pointers always point into the same list of
-     * 'grid_face's, so it's valid to subtract them. */
-    return f1->f - f2->f;
-}
-
-static int face_sort_cmpfn(void *v1, void *v2)
-{
-    struct face *f1 = v1;
-    struct face *f2 = v2;
-    int r;
-
-    r = f2->score - f1->score;
-    if (r) {
-        return r;
-    }
-
-    if (f1->random < f2->random)
-        return -1;
-    else if (f1->random > f2->random)
-        return 1;
-
-    /*
-     * It's _just_ possible that two faces might have been given
-     * the same random value. In that situation, fall back to
-     * comparing based on the positions within the grid's face-list.
-     * This introduces a tiny directional bias, but not a significant one.
-     */
-    return get_face_cmpfn(f1, f2);
-}
-
-enum { FACE_LIT, FACE_UNLIT };
-
-/* face should be of type grid_face* here. */
-#define FACE_LIT_STATE(face) \
-    ( (face) == NULL ? FACE_UNLIT : \
-         board[(face) - g->faces] )
-
-/* 'board' is an array of these enums, indicating which faces are
- * currently lit.  Returns whether it's legal to light up the
- * given face. */
-static int can_light_face(grid *g, char* board, int face_index)
-{
-    int i, j;
-    grid_face *test_face = g->faces + face_index;
-    grid_face *starting_face, *current_face;
-    int transitions;
-    int current_state, s;
-    int found_lit_neighbour = FALSE;
-    assert(board[face_index] == FACE_UNLIT);
-
-    /* Can only consider a face for lighting if it's adjacent to an
-     * already lit face. */
-    for (i = 0; i < test_face->order; i++) {
-        grid_edge *e = test_face->edges[i];
-        grid_face *f = (e->face1 == test_face) ? e->face2 : e->face1;
-        if (FACE_LIT_STATE(f) == FACE_LIT) {
-            found_lit_neighbour = TRUE;
-            break;
-        }
-    }
-    if (!found_lit_neighbour)
-        return FALSE;
-
-    /* Need to avoid creating a loop of lit faces around some unlit faces.
-     * Also need to avoid meeting another lit face at a corner, with
-     * unlit faces in between.  Here's a simple test that (I believe) takes
-     * care of both these conditions:
-     *
-     * Take the circular path formed by this face's edges, and inflate it
-     * slightly outwards.  Imagine walking around this path and consider
-     * the faces that you visit in sequence.  This will include all faces
-     * touching the given face, either along an edge or just at a corner.
-     * Count the number of LIT/UNLIT transitions you encounter, as you walk
-     * along the complete loop.  This will obviously turn out to be an even
-     * number.
-     * If 0, we're either in a completely unlit zone, or this face is a hole
-     * in a completely lit zone.  If the former, we would create a brand new
-     * island by lighting this face.  And the latter ought to be impossible -
-     * it would mean there's already a lit loop, so something went wrong
-     * earlier.
-     * If 4 or greater, there are too many separate lit regions touching this
-     * face, and lighting it up would create a loop or a corner-violation.
-     * The only allowed case is when the count is exactly 2. */
-
-    /* i points to a dot around the test face.
-     * j points to a face around the i^th dot.
-     * The current face will always be:
-     *     test_face->dots[i]->faces[j]
-     * We assume dots go clockwise around the test face,
-     * and faces go clockwise around dots. */
-    i = j = 0;
-    starting_face = test_face->dots[0]->faces[0];
-    if (starting_face == test_face) {
-        j = 1;
-        starting_face = test_face->dots[0]->faces[1];
-    }
-    current_face = starting_face;
-    transitions = 0;
-    current_state = FACE_LIT_STATE(current_face);
-
-    do {
-        /* Advance to next face.
-         * Need to loop here because it might take several goes to
-         * find it. */
-        while (TRUE) {
-            j++;
-            if (j == test_face->dots[i]->order)
-                j = 0;
-
-            if (test_face->dots[i]->faces[j] == test_face) {
-                /* Advance to next dot round test_face, then
-                 * find current_face around new dot
-                 * and advance to the next face clockwise */
-                i++;
-                if (i == test_face->order)
-                    i = 0;
-                for (j = 0; j < test_face->dots[i]->order; j++) {
-                    if (test_face->dots[i]->faces[j] == current_face)
-                        break;
-                }
-                /* Must actually find current_face around new dot,
-                 * or else something's wrong with the grid. */
-                assert(j != test_face->dots[i]->order);
-                /* Found, so advance to next face and try again */
-            } else {
-                break;
-            }
-        }
-        /* (i,j) are now advanced to next face */
-        current_face = test_face->dots[i]->faces[j];
-        s = FACE_LIT_STATE(current_face);
-        if (s != current_state) {
-            ++transitions;
-            current_state = s;
-            if (transitions > 2)
-                return FALSE; /* no point in continuing */
-        }
-    } while (current_face != starting_face);
-
-    return (transitions == 2) ? TRUE : FALSE;
-}
-
-/* The 'score' of a face reflects its current desirability for selection
- * as the next face to light.  We want to encourage moving into uncharted
- * areas so we give scores according to how many of the face's neighbours
- * are currently unlit. */
-static int face_score(grid *g, char *board, grid_face *face)
-{
-    /* Simple formula: score = neighbours unlit - neighbours lit */
-    int lit_count = 0, unlit_count = 0;
-    int i;
-    grid_face *f;
-    grid_edge *e;
-    for (i = 0; i < face->order; i++) {
-        e = face->edges[i];
-        f = (e->face1 == face) ? e->face2 : e->face1;
-        if (FACE_LIT_STATE(f) == FACE_LIT)
-            ++lit_count;
-        else
-            ++unlit_count;
-    }
-    return unlit_count - lit_count;
-}
-
-/* Generate a new complete set of clues for the given game_state. */
 static void add_full_clues(game_state *state, random_state *rs)
 {
     signed char *clues = state->clues;
-    char *board;
     grid *g = state->game_grid;
-    int i, j, c;
-    int num_faces = g->num_faces;
-    int first_time = TRUE;
-
-    struct face *face, *tmpface;
-    struct face face_pos;
-
-    /* These will contain exactly the same information, sorted into different
-     * orders */
-    tree234 *lightable_faces_sorted, *lightable_faces_gettable;
-
-#define IS_LIGHTING_CANDIDATE(i) \
-    (board[i] == FACE_UNLIT && \
-        can_light_face(g, board, i))
-
-    board = snewn(num_faces, char);
-
-    /* Make a board */
-    memset(board, FACE_UNLIT, num_faces);
-
-    /* We need a way of favouring faces that will increase our loopiness.
-     * We do this by maintaining a list of all candidate faces sorted by
-     * their score and choose randomly from that with appropriate skew.
-     * In order to avoid consistently biasing towards particular faces, we
-     * need the sort order _within_ each group of scores to be completely
-     * random.  But it would be abusing the hospitality of the tree234 data
-     * structure if our comparison function were nondeterministic :-).  So with
-     * each face we associate a random number that does not change during a
-     * particular run of the generator, and use that as a secondary sort key.
-     * Yes, this means we will be biased towards particular random faces in
-     * any one run but that doesn't actually matter. */
-
-    lightable_faces_sorted   = newtree234(face_sort_cmpfn);
-    lightable_faces_gettable = newtree234(get_face_cmpfn);
-#define ADD_FACE(f) \
-    do { \
-        struct face *x = add234(lightable_faces_sorted, f); \
-        assert(x == f); \
-        x = add234(lightable_faces_gettable, f); \
-        assert(x == f); \
-    } while (0)
-
-#define REMOVE_FACE(f) \
-    do { \
-        struct face *x = del234(lightable_faces_sorted, f); \
-        assert(x); \
-        x = del234(lightable_faces_gettable, f); \
-        assert(x); \
-    } while (0)
-
-    /* Light faces one at a time until the board is interesting enough */
-    while (TRUE)
-    {
-        if (first_time) {
-            first_time = FALSE;
-            /* lightable_faces_xxx are empty, so start the process by
-             * lighting up the middle face.  These tree234s should
-             * remain empty, consistent with what would happen if
-             * first_time were FALSE. */
-            board[g->middle_face - g->faces] = FACE_LIT;
-            face = snew(struct face);
-            face->f = g->middle_face;
-            /* No need to initialise any more of 'face' here, no other fields
-             * are used in this case. */
-        } else {
-            /* We have count234(lightable_faces_gettable) possibilities, and in
-             * lightable_faces_sorted they are sorted with the most desirable
-             * first. */
-            c = count234(lightable_faces_sorted);
-            if (c == 0)
-                break;
-            assert(c == count234(lightable_faces_gettable));
-
-            /* Check that the best face available is any good */
-            face = (struct face *)index234(lightable_faces_sorted, 0);
-            assert(face);
-
-            /*
-             * The situation for a general grid is slightly different from
-             * a square grid.  Decreasing the perimeter should be allowed
-             * sometimes (think about creating a hexagon of lit triangles,
-             * for example).  For if it were _never_ done, then the user would
-             * be able to illicitly deduce certain things.  So we do it
-             * sometimes but not always.
-             */
-            if (face->score <= 0 && random_upto(rs, 2) == 0) {
-                break;
-            }
-
-            assert(face->f); /* not the infinite face */
-            assert(FACE_LIT_STATE(face->f) == FACE_UNLIT);
-
-            /* Update data structures */
-            /* Light up the face and remove it from the lists */
-            board[face->f - g->faces] = FACE_LIT;
-            REMOVE_FACE(face);
-        }
-
-        /* The face we've just lit up potentially affects the lightability
-         * of any neighbouring faces (touching at a corner or edge).  So the
-         * search needs to be conducted around all faces touching the one
-         * we've just lit.  Iterate over its corners, then over each corner's
-         * faces. */
-        for (i = 0; i < face->f->order; i++) {
-            grid_dot *d = face->f->dots[i];
-            for (j = 0; j < d->order; j++) {
-                grid_face *f2 = d->faces[j];
-                if (f2 == NULL)
-                    continue;
-                if (f2 == face->f)
-                    continue;
-                face_pos.f = f2;
-                tmpface = find234(lightable_faces_gettable, &face_pos, NULL);
-                if (tmpface) {
-                    assert(tmpface->f == face_pos.f);
-                    assert(FACE_LIT_STATE(tmpface->f) == FACE_UNLIT);
-                    REMOVE_FACE(tmpface);
-                } else {
-                    tmpface = snew(struct face);
-                    tmpface->f = face_pos.f;
-                    tmpface->random = random_bits(rs, 31);
-                }
-                tmpface->score = face_score(g, board, tmpface->f);
-
-                if (IS_LIGHTING_CANDIDATE(tmpface->f - g->faces)) {
-                    ADD_FACE(tmpface);
-                } else {
-                    sfree(tmpface);
-                }
-            }
-        }
-        sfree(face);
-    }
+    char *board = snewn(g->num_faces, char);
+    int i;
 
-    /* Clean up */
-    while ((face = delpos234(lightable_faces_gettable, 0)) != NULL)
-        sfree(face);
-    freetree234(lightable_faces_gettable);
-    freetree234(lightable_faces_sorted);
+    generate_loop(g, board, rs, NULL, NULL);
 
     /* Fill out all the clues by initialising to 0, then iterating over
      * all edges and incrementing each clue as we find edges that border
-     * between LIT/UNLIT faces */
-    memset(clues, 0, num_faces);
+     * between BLACK/WHITE faces.  While we're at it, we verify that the
+     * algorithm does work, and there aren't any GREY faces still there. */
+    memset(clues, 0, g->num_faces);
     for (i = 0; i < g->num_edges; i++) {
         grid_edge *e = g->edges + i;
         grid_face *f1 = e->face1;
         grid_face *f2 = e->face2;
-        if (FACE_LIT_STATE(f1) != FACE_LIT_STATE(f2)) {
+        enum face_colour c1 = FACE_COLOUR(f1);
+        enum face_colour c2 = FACE_COLOUR(f2);
+        assert(c1 != FACE_GREY);
+        assert(c2 != FACE_GREY);
+        if (c1 != c2) {
             if (f1) clues[f1 - g->faces]++;
             if (f2) clues[f2 - g->faces]++;
         }
     }
-
     sfree(board);
 }
 
@@ -1485,7 +1318,7 @@ static int game_has_unique_soln(const game_state *state, int diff)
     solver_state *sstate_new;
     solver_state *sstate = new_solver_state((game_state *)state, diff);
 
-    sstate_new = solve_game_rec(sstate, diff);
+    sstate_new = solve_game_rec(sstate);
 
     assert(sstate_new->solver_status != SOLVER_MISTAKE);
     ret = (sstate_new->solver_status == SOLVER_SOLVED);
@@ -1534,25 +1367,29 @@ static game_state *remove_clues(game_state *state, random_state *rs,
 }
 
 
-static char *new_game_desc(game_params *params, random_state *rs,
+static char *new_game_desc(const game_params *params, random_state *rs,
                            char **aux, int interactive)
 {
     /* solution and description both use run-length encoding in obvious ways */
-    char *retval;
+    char *retval, *game_desc, *grid_desc;
     grid *g;
     game_state *state = snew(game_state);
     game_state *state_new;
-    params_generate_grid(params);
-    state->game_grid = g = params->game_grid;
-    g->refcount++;
+
+    grid_desc = grid_new_desc(grid_types[params->type], params->w, params->h, rs);
+    state->game_grid = g = loopy_generate_grid(params, grid_desc);
+
     state->clues = snewn(g->num_faces, signed char);
     state->lines = snewn(g->num_edges, char);
+    state->line_errors = snewn(g->num_edges, unsigned char);
+    state->exactly_one_loop = FALSE;
 
     state->grid_type = params->type;
 
     newboard_please:
 
     memset(state->lines, LINE_UNKNOWN, g->num_edges);
+    memset(state->line_errors, 0, g->num_edges);
 
     state->solved = state->cheated = FALSE;
 
@@ -1575,31 +1412,49 @@ static char *new_game_desc(game_params *params, random_state *rs,
         goto newboard_please;
     }
 
-    retval = state_to_text(state);
+    game_desc = state_to_text(state);
 
     free_game(state);
 
+    if (grid_desc) {
+        retval = snewn(strlen(grid_desc) + 1 + strlen(game_desc) + 1, char);
+        sprintf(retval, "%s%c%s", grid_desc, (int)GRID_DESC_SEP, game_desc);
+        sfree(grid_desc);
+        sfree(game_desc);
+    } else {
+        retval = game_desc;
+    }
+
     assert(!validate_desc(params, retval));
 
     return retval;
 }
 
-static game_state *new_game(midend *me, game_params *params, char *desc)
+static game_state *new_game(midend *me, const game_params *params,
+                            const char *desc)
 {
     int i;
     game_state *state = snew(game_state);
     int empties_to_make = 0;
-    int n;
-    const char *dp = desc;
+    int n,n2;
+    const char *dp;
+    char *grid_desc;
     grid *g;
-    params_generate_grid(params);
-    state->game_grid = g = params->game_grid;
-    g->refcount++;
-    int num_faces = g->num_faces;
-    int num_edges = g->num_edges;
+    int num_faces, num_edges;
+
+    grid_desc = extract_grid_desc(&desc);
+    state->game_grid = g = loopy_generate_grid(params, grid_desc);
+    if (grid_desc) sfree(grid_desc);
+
+    dp = desc;
+
+    num_faces = g->num_faces;
+    num_edges = g->num_edges;
 
     state->clues = snewn(num_faces, signed char);
     state->lines = snewn(num_edges, char);
+    state->line_errors = snewn(num_edges, unsigned char);
+    state->exactly_one_loop = FALSE;
 
     state->solved = state->cheated = FALSE;
 
@@ -1614,8 +1469,11 @@ static game_state *new_game(midend *me, game_params *params, char *desc)
 
         assert(*dp);
         n = *dp - '0';
+        n2 = *dp - 'A' + 10;
         if (n >= 0 && n < 10) {
             state->clues[i] = n;
+       } else if (n2 >= 10 && n2 < 36) {
+            state->clues[i] = n2;
         } else {
             n = *dp - 'a' + 1;
             assert(n > 0);
@@ -1626,11 +1484,242 @@ static game_state *new_game(midend *me, game_params *params, char *desc)
     }
 
     memset(state->lines, LINE_UNKNOWN, num_edges);
-
+    memset(state->line_errors, 0, num_edges);
     return state;
 }
 
-enum { LOOP_NONE=0, LOOP_SOLN, LOOP_NOT_SOLN };
+/* Calculates the line_errors data, and checks if the current state is a
+ * solution */
+static int check_completion(game_state *state)
+{
+    grid *g = state->game_grid;
+    int i, ret;
+    int *dsf, *component_state;
+    int nsilly, nloop, npath, largest_comp, largest_size, total_pathsize;
+    enum { COMP_NONE, COMP_LOOP, COMP_PATH, COMP_SILLY, COMP_EMPTY };
+
+    memset(state->line_errors, 0, g->num_edges);
+
+    /*
+     * Find loops in the grid, and determine whether the puzzle is
+     * solved.
+     *
+     * Loopy is a bit more complicated than most puzzles that care
+     * about loop detection. In most of them, loops are simply
+     * _forbidden_; so the obviously right way to do
+     * error-highlighting during play is to light up a graph edge red
+     * iff it is part of a loop, which is exactly what the centralised
+     * findloop.c makes easy.
+     *
+     * But Loopy is unusual in that you're _supposed_ to be making a
+     * loop - and yet _some_ loops are not the right loop. So we need
+     * to be more discriminating, by identifying loops one by one and
+     * then thinking about which ones to highlight, and so findloop.c
+     * isn't quite the right tool for the job in this case.
+     *
+     * Worse still, consider situations in which the grid contains a
+     * loop and also some non-loop edges: there are some cases like
+     * this in which the user's intuitive expectation would be to
+     * highlight the loop (if you're only about half way through the
+     * puzzle and have accidentally made a little loop in some corner
+     * of the grid), and others in which they'd be more likely to
+     * expect you to highlight the non-loop edges (if you've just
+     * closed off a whole loop that you thought was the entire
+     * solution, but forgot some disconnected edges in a corner
+     * somewhere). So while it's easy enough to check whether the
+     * solution is _right_, highlighting the wrong parts is a tricky
+     * problem for this puzzle!
+     *
+     * I'd quite like, in some situations, to identify the largest
+     * loop among the player's YES edges, and then light up everything
+     * other than that. But finding the longest cycle in a graph is an
+     * NP-complete problem (because, in particular, it must return a
+     * Hamilton cycle if one exists).
+     *
+     * However, I think we can make the problem tractable by
+     * exercising the Puzzles principle that it isn't absolutely
+     * necessary to highlight _all_ errors: the key point is that by
+     * the time the user has filled in the whole grid, they should
+     * either have seen a completion flash, or have _some_ error
+     * highlight showing them why the solution isn't right. So in
+     * principle it would be *just about* good enough to highlight
+     * just one error in the whole grid, if there was really no better
+     * way. But we'd like to highlight as many errors as possible.
+     *
+     * In this case, I think the simple approach is to make use of the
+     * fact that no vertex may have degree > 2, and that's really
+     * simple to detect. So the plan goes like this:
+     *
+     *  - Form the dsf of connected components of the graph vertices.
+     *
+     *  - Highlight an error at any vertex with degree > 2. (It so
+     *    happens that we do this by lighting up all the edges
+     *    incident to that vertex, but that's an output detail.)
+     *
+     *  - Any component that contains such a vertex is now excluded
+     *    from further consideration, because it already has a
+     *    highlight.
+     *
+     *  - The remaining components have no vertex with degree > 2, and
+     *    hence they all consist of either a simple loop, or a simple
+     *    path with two endpoints.
+     *
+     *  - For these purposes, group together all the paths and imagine
+     *    them to be a single component (because in most normal
+     *    situations the player will gradually build up the solution
+     *    _not_ all in one connected segment, but as lots of separate
+     *    little path pieces that gradually connect to each other).
+     *
+     *  - After doing that, if there is exactly one (sensible)
+     *    component - be it a collection of paths or a loop - then
+     *    highlight no further edge errors. (The former case is normal
+     *    during play, and the latter is a potentially solved puzzle.)
+     *
+     *  - Otherwise, find the largest of the sensible components,
+     *    leave that one unhighlighted, and light the rest up in red.
+     */
+
+    dsf = snew_dsf(g->num_dots);
+
+    /* Build the dsf. */
+    for (i = 0; i < g->num_edges; i++) {
+        if (state->lines[i] == LINE_YES) {
+            grid_edge *e = g->edges + i;
+            int d1 = e->dot1 - g->dots, d2 = e->dot2 - g->dots;
+            dsf_merge(dsf, d1, d2);
+        }
+    }
+
+    /* Initialise a state variable for each connected component. */
+    component_state = snewn(g->num_dots, int);
+    for (i = 0; i < g->num_dots; i++) {
+        if (dsf_canonify(dsf, i) == i)
+            component_state[i] = COMP_LOOP;
+        else
+            component_state[i] = COMP_NONE;
+    }
+
+    /* Check for dots with degree > 3. Here we also spot dots of
+     * degree 1 in which the user has marked all the non-edges as
+     * LINE_NO, because those are also clear vertex-level errors, so
+     * we give them the same treatment of excluding their connected
+     * component from the subsequent loop analysis. */
+    for (i = 0; i < g->num_dots; i++) {
+        int comp = dsf_canonify(dsf, i);
+        int yes = dot_order(state, i, LINE_YES);
+        int unknown = dot_order(state, i, LINE_UNKNOWN);
+        if ((yes == 1 && unknown == 0) || (yes >= 3)) {
+            /* violation, so mark all YES edges as errors */
+            grid_dot *d = g->dots + i;
+            int j;
+            for (j = 0; j < d->order; j++) {
+                int e = d->edges[j] - g->edges;
+                if (state->lines[e] == LINE_YES)
+                    state->line_errors[e] = TRUE;
+            }
+            /* And mark this component as not worthy of further
+             * consideration. */
+            component_state[comp] = COMP_SILLY;
+
+        } else if (yes == 0) {
+            /* A completely isolated dot must also be excluded it from
+             * the subsequent loop highlighting pass, but we tag it
+             * with a different enum value to avoid it counting
+             * towards the components that inhibit returning a win
+             * status. */
+            component_state[comp] = COMP_EMPTY;
+        } else if (yes == 1) {
+            /* A dot with degree 1 that didn't fall into the 'clearly
+             * erroneous' case above indicates that this connected
+             * component will be a path rather than a loop - unless
+             * something worse elsewhere in the component has
+             * classified it as silly. */
+            if (component_state[comp] != COMP_SILLY)
+                component_state[comp] = COMP_PATH;
+        }
+    }
+
+    /* Count up the components. Also, find the largest sensible
+     * component. (Tie-breaking condition is derived from the order of
+     * vertices in the grid data structure, which is fairly arbitrary
+     * but at least stays stable throughout the game.) */
+    nsilly = nloop = npath = 0;
+    total_pathsize = 0;
+    largest_comp = largest_size = -1;
+    for (i = 0; i < g->num_dots; i++) {
+        if (component_state[i] == COMP_SILLY) {
+            nsilly++;
+        } else if (component_state[i] == COMP_PATH) {
+            total_pathsize += dsf_size(dsf, i);
+            npath = 1;
+        } else if (component_state[i] == COMP_LOOP) {
+            int this_size;
+
+            nloop++;
+
+            if ((this_size = dsf_size(dsf, i)) > largest_size) {
+                largest_comp = i;
+                largest_size = this_size;
+            }
+        }
+    }
+    if (largest_size < total_pathsize) {
+        largest_comp = -1;             /* means the paths */
+        largest_size = total_pathsize;
+    }
+
+    if (nloop > 0 && nloop + npath > 1) {
+        /*
+         * If there are at least two sensible components including at
+         * least one loop, highlight all edges in every sensible
+         * component that is not the largest one.
+         */
+        for (i = 0; i < g->num_edges; i++) {
+            if (state->lines[i] == LINE_YES) {
+                grid_edge *e = g->edges + i;
+                int d1 = e->dot1 - g->dots; /* either endpoint is good enough */
+                int comp = dsf_canonify(dsf, d1);
+                if ((component_state[comp] == COMP_PATH &&
+                     -1 != largest_comp) ||
+                    (component_state[comp] == COMP_LOOP &&
+                     comp != largest_comp))
+                    state->line_errors[i] = TRUE;
+            }
+        }
+    }
+
+    if (nloop == 1 && npath == 0 && nsilly == 0) {
+        /*
+         * If there is exactly one component and it is a loop, then
+         * the puzzle is potentially complete, so check the clues.
+         */
+        ret = TRUE;
+
+        for (i = 0; i < g->num_faces; i++) {
+            int c = state->clues[i];
+            if (c >= 0 && face_order(state, i, LINE_YES) != c) {
+                ret = FALSE;
+                break;
+            }
+        }
+
+        /*
+         * Also, whether or not the puzzle is actually complete, set
+         * the flag that says this game_state has exactly one loop and
+         * nothing else, which will be used to vary the semantics of
+         * clue highlighting at display time.
+         */
+        state->exactly_one_loop = TRUE;
+    } else {
+        ret = FALSE;
+        state->exactly_one_loop = FALSE;
+    }
+
+    sfree(component_state);
+    sfree(dsf);
+
+    return ret;
+}
 
 /* ----------------------------------------------------------------------
  * Solver logic
@@ -1640,7 +1729,7 @@ enum { LOOP_NONE=0, LOOP_SOLN, LOOP_NOT_SOLN };
  *   Easy Mode
  *   Just implement the rules of the game.
  *
- *   Normal Mode
+ *   Normal and Tricky Modes
  *   For each (adjacent) pair of lines through each dot we store a bit for
  *   whether at least one of them is on and whether at most one is on.  (If we
  *   know both or neither is on that's already stored more directly.)
@@ -1777,7 +1866,7 @@ static int dline_set_opp_atleastone(solver_state *sstate,
             continue;
         /* Found opposite UNKNOWNS and they're next to each other */
         opp_dline_index = dline_index_from_dot(g, d, opp);
-        return set_atleastone(sstate->normal->dlines, opp_dline_index);
+        return set_atleastone(sstate->dlines, opp_dline_index);
     }
     return FALSE;
 }
@@ -1810,8 +1899,8 @@ static int face_setall_identical(solver_state *sstate, int face_index,
                 continue;
 
             /* Found two UNKNOWNS */
-            can1 = edsf_canonify(sstate->hard->linedsf, line1_index, &inv1);
-            can2 = edsf_canonify(sstate->hard->linedsf, line2_index, &inv2);
+            can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
+            can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
             if (can1 == can2 && inv1 == inv2) {
                 solver_set_line(sstate, line1_index, line_new);
                 solver_set_line(sstate, line2_index, line_new);
@@ -1852,7 +1941,7 @@ static int parity_deductions(solver_state *sstate,
 {
     game_state *state = sstate->state;
     int diff = DIFF_MAX;
-    int *linedsf = sstate->hard->linedsf;
+    int *linedsf = sstate->linedsf;
 
     if (unknown_count == 2) {
         /* Lines are known alike/opposite, depending on inv. */
@@ -1951,7 +2040,7 @@ static int parity_deductions(solver_state *sstate,
  *      Answer: first all squares then all dots.
  */
 
-static int easy_mode_deductions(solver_state *sstate)
+static int trivial_deductions(solver_state *sstate)
 {
     int i, current_yes, current_no;
     game_state *state = sstate->state;
@@ -1976,6 +2065,13 @@ static int easy_mode_deductions(solver_state *sstate)
         if (state->clues[i] < 0)
             continue;
 
+        /*
+         * This code checks whether the numeric clue on a face is so
+         * large as to permit all its remaining LINE_UNKNOWNs to be
+         * filled in as LINE_YES, or alternatively so small as to
+         * permit them all to be filled in as LINE_NO.
+         */
+
         if (state->clues[i] < current_yes) {
             sstate->solver_status = SOLVER_MISTAKE;
             return DIFF_EASY;
@@ -1997,6 +2093,57 @@ static int easy_mode_deductions(solver_state *sstate)
             sstate->face_solved[i] = TRUE;
             continue;
         }
+
+        if (f->order - state->clues[i] == current_no + 1 &&
+            f->order - current_yes - current_no > 2) {
+            /*
+             * One small refinement to the above: we also look for any
+             * adjacent pair of LINE_UNKNOWNs around the face with
+             * some LINE_YES incident on it from elsewhere. If we find
+             * one, then we know that pair of LINE_UNKNOWNs can't
+             * _both_ be LINE_YES, and hence that pushes us one line
+             * closer to being able to determine all the rest.
+             */
+            int j, k, e1, e2, e, d;
+
+            for (j = 0; j < f->order; j++) {
+                e1 = f->edges[j] - g->edges;
+                e2 = f->edges[j+1 < f->order ? j+1 : 0] - g->edges;
+
+                if (g->edges[e1].dot1 == g->edges[e2].dot1 ||
+                    g->edges[e1].dot1 == g->edges[e2].dot2) {
+                    d = g->edges[e1].dot1 - g->dots;
+                } else {
+                    assert(g->edges[e1].dot2 == g->edges[e2].dot1 ||
+                           g->edges[e1].dot2 == g->edges[e2].dot2);
+                    d = g->edges[e1].dot2 - g->dots;
+                }
+
+                if (state->lines[e1] == LINE_UNKNOWN &&
+                    state->lines[e2] == LINE_UNKNOWN) {
+                    for (k = 0; k < g->dots[d].order; k++) {
+                        int e = g->dots[d].edges[k] - g->edges;
+                        if (state->lines[e] == LINE_YES)
+                            goto found;    /* multi-level break */
+                    }
+                }
+            }
+            continue;
+
+          found:
+            /*
+             * If we get here, we've found such a pair of edges, and
+             * they're e1 and e2.
+             */
+            for (j = 0; j < f->order; j++) {
+                e = f->edges[j] - g->edges;
+                if (state->lines[e] == LINE_UNKNOWN && e != e1 && e != e2) {
+                    int r = solver_set_line(sstate, e, LINE_YES);
+                    assert(r);
+                    diff = min(diff, DIFF_EASY);
+                }
+            }
+        }
     }
 
     check_caches(sstate);
@@ -2046,11 +2193,11 @@ static int easy_mode_deductions(solver_state *sstate)
     return diff;
 }
 
-static int normal_mode_deductions(solver_state *sstate)
+static int dline_deductions(solver_state *sstate)
 {
     game_state *state = sstate->state;
     grid *g = state->game_grid;
-    char *dlines = sstate->normal->dlines;
+    char *dlines = sstate->dlines;
     int i;
     int diff = DIFF_MAX;
 
@@ -2095,7 +2242,7 @@ static int normal_mode_deductions(solver_state *sstate)
      * on that.  We check this with an assertion, in case someone decides to
      * make a grid which has larger faces than this.  Note, this algorithm
      * could get quite expensive if there are many large faces. */
-#define MAX_FACE_SIZE 8
+#define MAX_FACE_SIZE 12
 
     for (i = 0; i < g->num_faces; i++) {
         int maxs[MAX_FACE_SIZE][MAX_FACE_SIZE];
@@ -2196,29 +2343,34 @@ static int normal_mode_deductions(solver_state *sstate)
                 diff = min(diff, DIFF_EASY);
             }
 
-            /* Now see if we can make dline deduction for edges{j,j+1} */
-            e = f->edges[k];
-            if (state->lines[e - g->edges] != LINE_UNKNOWN)
-                /* Only worth doing this for an UNKNOWN,UNKNOWN pair.
-                 * Dlines where one of the edges is known, are handled in the
-                 * dot-deductions */
-                continue;
-
-            dline_index = dline_index_from_face(g, f, k);
-            k++;
-            if (k >= N) k = 0;
-
-            /* minimum YESs in the complement of this dline */
-            if (mins[k][j] > clue - 2) {
-                /* Adding 2 YESs would break the clue */
-                if (set_atmostone(dlines, dline_index))
-                    diff = min(diff, DIFF_NORMAL);
-            }
-            /* maximum YESs in the complement of this dline */
-            if (maxs[k][j] < clue) {
-                /* Adding 2 NOs would mean not enough YESs */
-                if (set_atleastone(dlines, dline_index))
-                    diff = min(diff, DIFF_NORMAL);
+            /* More advanced deduction that allows propagation along diagonal
+             * chains of faces connected by dots, for example, 3-2-...-2-3
+             * in square grids. */
+            if (sstate->diff >= DIFF_TRICKY) {
+                /* Now see if we can make dline deduction for edges{j,j+1} */
+                e = f->edges[k];
+                if (state->lines[e - g->edges] != LINE_UNKNOWN)
+                    /* Only worth doing this for an UNKNOWN,UNKNOWN pair.
+                     * Dlines where one of the edges is known, are handled in the
+                     * dot-deductions */
+                    continue;
+    
+                dline_index = dline_index_from_face(g, f, k);
+                k++;
+                if (k >= N) k = 0;
+    
+                /* minimum YESs in the complement of this dline */
+                if (mins[k][j] > clue - 2) {
+                    /* Adding 2 YESs would break the clue */
+                    if (set_atmostone(dlines, dline_index))
+                        diff = min(diff, DIFF_NORMAL);
+                }
+                /* maximum YESs in the complement of this dline */
+                if (maxs[k][j] < clue) {
+                    /* Adding 2 NOs would mean not enough YESs */
+                    if (set_atleastone(dlines, dline_index))
+                        diff = min(diff, DIFF_NORMAL);
+                }
             }
         }
     }
@@ -2312,48 +2464,54 @@ static int normal_mode_deductions(solver_state *sstate)
                 }
             }
 
-            /* If we have atleastone set for this dline, infer
-             * atmostone for each "opposite" dline (that is, each
-             * dline without edges in common with this one).
-             * Again, this test is only worth doing if both these
-             * lines are UNKNOWN.  For if one of these lines were YES,
-             * the (yes == 1) test above would kick in instead. */
-            if (is_atleastone(dlines, dline_index)) {
-                int opp;
-                for (opp = 0; opp < N; opp++) {
-                    int opp_dline_index;
-                    if (opp == j || opp == j+1 || opp == j-1)
-                        continue;
-                    if (j == 0 && opp == N-1)
-                        continue;
-                    if (j == N-1 && opp == 0)
-                        continue;
-                    opp_dline_index = dline_index_from_dot(g, d, opp);
-                    if (set_atmostone(dlines, opp_dline_index))
-                        diff = min(diff, DIFF_NORMAL);
-                }
-
-                if (yes == 0 && is_atmostone(dlines, dline_index)) {
-                    /* This dline has *exactly* one YES and there are no
-                     * other YESs.  This allows more deductions. */
-                    if (unknown == 3) {
-                        /* Third unknown must be YES */
-                        for (opp = 0; opp < N; opp++) {
-                            int opp_index;
-                            if (opp == j || opp == k)
-                                continue;
-                            opp_index = d->edges[opp] - g->edges;
-                            if (state->lines[opp_index] == LINE_UNKNOWN) {
-                                solver_set_line(sstate, opp_index, LINE_YES);
-                                diff = min(diff, DIFF_EASY);
+            /* More advanced deduction that allows propagation along diagonal
+             * chains of faces connected by dots, for example: 3-2-...-2-3
+             * in square grids. */
+            if (sstate->diff >= DIFF_TRICKY) {
+                /* If we have atleastone set for this dline, infer
+                 * atmostone for each "opposite" dline (that is, each
+                 * dline without edges in common with this one).
+                 * Again, this test is only worth doing if both these
+                 * lines are UNKNOWN.  For if one of these lines were YES,
+                 * the (yes == 1) test above would kick in instead. */
+                if (is_atleastone(dlines, dline_index)) {
+                    int opp;
+                    for (opp = 0; opp < N; opp++) {
+                        int opp_dline_index;
+                        if (opp == j || opp == j+1 || opp == j-1)
+                            continue;
+                        if (j == 0 && opp == N-1)
+                            continue;
+                        if (j == N-1 && opp == 0)
+                            continue;
+                        opp_dline_index = dline_index_from_dot(g, d, opp);
+                        if (set_atmostone(dlines, opp_dline_index))
+                            diff = min(diff, DIFF_NORMAL);
+                    }
+                    if (yes == 0 && is_atmostone(dlines, dline_index)) {
+                        /* This dline has *exactly* one YES and there are no
+                         * other YESs.  This allows more deductions. */
+                        if (unknown == 3) {
+                            /* Third unknown must be YES */
+                            for (opp = 0; opp < N; opp++) {
+                                int opp_index;
+                                if (opp == j || opp == k)
+                                    continue;
+                                opp_index = d->edges[opp] - g->edges;
+                                if (state->lines[opp_index] == LINE_UNKNOWN) {
+                                    solver_set_line(sstate, opp_index,
+                                                    LINE_YES);
+                                    diff = min(diff, DIFF_EASY);
+                                }
                             }
+                        } else if (unknown == 4) {
+                            /* Exactly one of opposite UNKNOWNS is YES.  We've
+                             * already set atmostone, so set atleastone as
+                             * well.
+                             */
+                            if (dline_set_opp_atleastone(sstate, d, j))
+                                diff = min(diff, DIFF_NORMAL);
                         }
-                    } else if (unknown == 4) {
-                        /* Exactly one of opposite UNKNOWNS is YES.  We've
-                         * already set atmostone, so set atleastone as well.
-                         */
-                        if (dline_set_opp_atleastone(sstate, d, j))
-                            diff = min(diff, DIFF_NORMAL);
                     }
                 }
             }
@@ -2362,11 +2520,11 @@ static int normal_mode_deductions(solver_state *sstate)
     return diff;
 }
 
-static int hard_mode_deductions(solver_state *sstate)
+static int linedsf_deductions(solver_state *sstate)
 {
     game_state *state = sstate->state;
     grid *g = state->game_grid;
-    char *dlines = sstate->normal->dlines;
+    char *dlines = sstate->dlines;
     int i;
     int diff = DIFF_MAX;
     int diff_tmp;
@@ -2436,8 +2594,8 @@ static int hard_mode_deductions(solver_state *sstate)
             if (state->lines[line2_index] != LINE_UNKNOWN)
                 continue;
             /* Infer dline flags from linedsf */
-            can1 = edsf_canonify(sstate->hard->linedsf, line1_index, &inv1);
-            can2 = edsf_canonify(sstate->hard->linedsf, line2_index, &inv2);
+            can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
+            can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
             if (can1 == can2 && inv1 != inv2) {
                 /* These are opposites, so set dline atmostone/atleastone */
                 if (set_atmostone(dlines, dline_index))
@@ -2471,7 +2629,7 @@ static int hard_mode_deductions(solver_state *sstate)
     for (i = 0; i < g->num_edges; i++) {
         int can, inv;
         enum line_state s;
-        can = edsf_canonify(sstate->hard->linedsf, i, &inv);
+        can = edsf_canonify(sstate->linedsf, i, &inv);
         if (can == i)
             continue;
         s = sstate->state->lines[can];
@@ -2644,52 +2802,59 @@ static int loop_deductions(solver_state *sstate)
 
 /* This will return a dynamically allocated solver_state containing the (more)
  * solved grid */
-static solver_state *solve_game_rec(const solver_state *sstate_start,
-                                    int diff)
-{
-    solver_state *sstate, *sstate_saved;
-    int solver_progress;
-    game_state *state;
-
-    /* Indicates which solver we should call next.  This is a sensible starting
-     * point */
-    int current_solver = DIFF_EASY, next_solver;
+static solver_state *solve_game_rec(const solver_state *sstate_start)
+{
+    solver_state *sstate;
+
+    /* Index of the solver we should call next. */
+    int i = 0;
+    
+    /* As a speed-optimisation, we avoid re-running solvers that we know
+     * won't make any progress.  This happens when a high-difficulty
+     * solver makes a deduction that can only help other high-difficulty
+     * solvers.
+     * For example: if a new 'dline' flag is set by dline_deductions, the
+     * trivial_deductions solver cannot do anything with this information.
+     * If we've already run the trivial_deductions solver (because it's
+     * earlier in the list), there's no point running it again.
+     *
+     * Therefore: if a solver is earlier in the list than "threshold_index",
+     * we don't bother running it if it's difficulty level is less than
+     * "threshold_diff".
+     */
+    int threshold_diff = 0;
+    int threshold_index = 0;
+    
     sstate = dup_solver_state(sstate_start);
 
-    /* Cache the values of some variables for readability */
-    state = sstate->state;
-
-    sstate_saved = NULL;
-
-    solver_progress = FALSE;
-
     check_caches(sstate);
 
-    do {
+    while (i < NUM_SOLVERS) {
         if (sstate->solver_status == SOLVER_MISTAKE)
             return sstate;
-
-        next_solver = solver_fns[current_solver](sstate);
-
-        if (next_solver == DIFF_MAX) {
-            if (current_solver < diff && current_solver + 1 < DIFF_MAX) {
-                /* Try next beefier solver */
-                next_solver = current_solver + 1;
-            } else {
-                next_solver = loop_deductions(sstate);
-            }
-        }
-
         if (sstate->solver_status == SOLVER_SOLVED ||
             sstate->solver_status == SOLVER_AMBIGUOUS) {
-/*            fprintf(stderr, "Solver completed\n"); */
+            /* solver finished */
             break;
         }
 
-        /* Once we've looped over all permitted solvers then the loop
-         * deductions without making any progress, we'll exit this while loop */
-        current_solver = next_solver;
-    } while (current_solver < DIFF_MAX);
+        if ((solver_diffs[i] >= threshold_diff || i >= threshold_index)
+            && solver_diffs[i] <= sstate->diff) {
+            /* current_solver is eligible, so use it */
+            int next_diff = solver_fns[i](sstate);
+            if (next_diff != DIFF_MAX) {
+                /* solver made progress, so use new thresholds and
+                * start again at top of list. */
+                threshold_diff = next_diff;
+                threshold_index = i;
+                i = 0;
+                continue;
+            }
+        }
+        /* current_solver is ineligible, or failed to make progress, so
+         * go to the next solver in the list */
+        i++;
+    }
 
     if (sstate->solver_status == SOLVER_SOLVED ||
         sstate->solver_status == SOLVER_AMBIGUOUS) {
@@ -2702,14 +2867,14 @@ static solver_state *solve_game_rec(const solver_state *sstate_start,
     return sstate;
 }
 
-static char *solve_game(game_state *state, game_state *currstate,
-                        char *aux, char **error)
+static char *solve_game(const game_state *state, const game_state *currstate,
+                        const char *aux, char **error)
 {
     char *soln = NULL;
     solver_state *sstate, *new_sstate;
 
     sstate = new_solver_state(state, DIFF_MAX);
-    new_sstate = solve_game_rec(sstate, DIFF_MAX);
+    new_sstate = solve_game_rec(sstate);
 
     if (new_sstate->solver_status == SOLVER_SOLVED) {
         soln = encode_solve_move(new_sstate->state);
@@ -2731,7 +2896,8 @@ static char *solve_game(game_state *state, game_state *currstate,
  * Drawing and mouse-handling
  */
 
-static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
+static char *interpret_move(const game_state *state, game_ui *ui,
+                            const game_drawstate *ds,
                             int x, int y, int button)
 {
     grid *g = state->game_grid;
@@ -2768,6 +2934,10 @@ static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
            button_char = 'y';
            break;
          case LINE_YES:
+#ifdef STYLUS_BASED
+           button_char = 'n';
+           break;
+#endif
          case LINE_NO:
            button_char = 'u';
            break;
@@ -2782,6 +2952,10 @@ static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
            button_char = 'n';
            break;
          case LINE_NO:
+#ifdef STYLUS_BASED
+           button_char = 'y';
+           break;
+#endif
          case LINE_YES:
            button_char = 'u';
            break;
@@ -2798,11 +2972,10 @@ static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
     return ret;
 }
 
-static game_state *execute_move(game_state *state, char *move)
+static game_state *execute_move(const game_state *state, const char *move)
 {
     int i;
     game_state *newstate = dup_game(state);
-    grid *g = state->game_grid;
 
     if (move[0] == 'S') {
         move++;
@@ -2811,6 +2984,8 @@ static game_state *execute_move(game_state *state, char *move)
 
     while (*move) {
         i = atoi(move);
+        if (i < 0 || i >= newstate->game_grid->num_edges)
+            goto fail;
         move += strspn(move, "1234567890");
         switch (*(move++)) {
          case 'y':
@@ -2830,77 +3005,9 @@ static game_state *execute_move(game_state *state, char *move)
     /*
      * Check for completion.
      */
-    for (i = 0; i < g->num_edges; i++) {
-        if (newstate->lines[i] == LINE_YES)
-            break;
-    }
-    if (i < g->num_edges) {
-        int looplen, count;
-        grid_edge *start_edge = g->edges + i;
-        grid_edge *e = start_edge;
-        grid_dot *d = e->dot1;
-        /*
-         * We've found an edge i. Follow it round
-         * to see if it's part of a loop.
-         */
-        looplen = 0;
-        while (1) {
-            int j;
-            int order = dot_order(newstate, d - g->dots, LINE_YES);
-            if (order != 2)
-                goto completion_check_done;
-
-            /* Find other edge around this dot */
-            for (j = 0; j < d->order; j++) {
-                grid_edge *e2 = d->edges[j];
-                if (e2 != e && newstate->lines[e2 - g->edges] == LINE_YES)
-                    break;
-            }
-            assert(j != d->order); /* dot_order guarantees success */
-
-            e = d->edges[j];
-            d = (e->dot1 == d) ? e->dot2 : e->dot1;
-            looplen++;
-
-            if (e == start_edge)
-                break;
-        }
-
-        /*
-         * We've traced our way round a loop, and we know how many
-         * line segments were involved. Count _all_ the line
-         * segments in the grid, to see if the loop includes them
-         * all.
-         */
-        count = 0;
-        for (i = 0; i < g->num_edges; i++) {
-            if (newstate->lines[i] == LINE_YES)
-                count++;
-        }
-        assert(count >= looplen);
-        if (count != looplen)
-            goto completion_check_done;
-
-        /*
-         * The grid contains one closed loop and nothing else.
-         * Check that all the clues are satisfied.
-         */
-        for (i = 0; i < g->num_faces; i++) {
-            int c = newstate->clues[i];
-            if (c >= 0) {
-                if (face_order(newstate, i, LINE_YES) != c) {
-                    goto completion_check_done;
-                }
-            }
-        }
-
-        /*
-         * Completed!
-         */
+    if (check_completion(newstate))
         newstate->solved = TRUE;
-    }
 
-    completion_check_done:
     return newstate;
 
     fail:
@@ -2927,69 +3034,318 @@ static void grid_to_screen(const game_drawstate *ds, const grid *g,
 /* Returns (into x,y) position of centre of face for rendering the text clue.
  */
 static void face_text_pos(const game_drawstate *ds, const grid *g,
-                          const grid_face *f, int *x, int *y)
+                          grid_face *f, int *xret, int *yret)
 {
-    int i;
+    int faceindex = f - g->faces;
+
+    /*
+     * Return the cached position for this face, if we've already
+     * worked it out.
+     */
+    if (ds->textx[faceindex] >= 0) {
+        *xret = ds->textx[faceindex];
+        *yret = ds->texty[faceindex];
+        return;
+    }
 
-    /* Simplest solution is the centroid. Might not work in some cases. */
+    /*
+     * Otherwise, use the incentre computed by grid.c and convert it
+     * to screen coordinates.
+     */
+    grid_find_incentre(f);
+    grid_to_screen(ds, g, f->ix, f->iy,
+                   &ds->textx[faceindex], &ds->texty[faceindex]);
+
+    *xret = ds->textx[faceindex];
+    *yret = ds->texty[faceindex];
+}
 
-    /* Another algorithm to look into:
-     * Find the midpoints of the sides, find the bounding-box,
-     * then take the centre of that. */
+static void face_text_bbox(game_drawstate *ds, grid *g, grid_face *f,
+                           int *x, int *y, int *w, int *h)
+{
+    int xx, yy;
+    face_text_pos(ds, g, f, &xx, &yy);
 
-    /* Best solution probably involves incentres (inscribed circles) */
+    /* There seems to be a certain amount of trial-and-error involved
+     * in working out the correct bounding-box for the text. */
 
-    int sx = 0, sy = 0; /* sums */
-    for (i = 0; i < f->order; i++) {
-        grid_dot *d = f->dots[i];
-        sx += d->x;
-        sy += d->y;
+    *x = xx - ds->tilesize/4 - 1;
+    *y = yy - ds->tilesize/4 - 3;
+    *w = ds->tilesize/2 + 2;
+    *h = ds->tilesize/2 + 5;
+}
+
+static void game_redraw_clue(drawing *dr, game_drawstate *ds,
+                            const game_state *state, int i)
+{
+    grid *g = state->game_grid;
+    grid_face *f = g->faces + i;
+    int x, y;
+    char c[20];
+
+    sprintf(c, "%d", state->clues[i]);
+
+    face_text_pos(ds, g, f, &x, &y);
+    draw_text(dr, x, y,
+             FONT_VARIABLE, ds->tilesize/2,
+             ALIGN_VCENTRE | ALIGN_HCENTRE,
+             ds->clue_error[i] ? COL_MISTAKE :
+             ds->clue_satisfied[i] ? COL_SATISFIED : COL_FOREGROUND, c);
+}
+
+static void edge_bbox(game_drawstate *ds, grid *g, grid_edge *e,
+                      int *x, int *y, int *w, int *h)
+{
+    int x1 = e->dot1->x;
+    int y1 = e->dot1->y;
+    int x2 = e->dot2->x;
+    int y2 = e->dot2->y;
+    int xmin, xmax, ymin, ymax;
+
+    grid_to_screen(ds, g, x1, y1, &x1, &y1);
+    grid_to_screen(ds, g, x2, y2, &x2, &y2);
+    /* Allow extra margin for dots, and thickness of lines */
+    xmin = min(x1, x2) - 2;
+    xmax = max(x1, x2) + 2;
+    ymin = min(y1, y2) - 2;
+    ymax = max(y1, y2) + 2;
+
+    *x = xmin;
+    *y = ymin;
+    *w = xmax - xmin + 1;
+    *h = ymax - ymin + 1;
+}
+
+static void dot_bbox(game_drawstate *ds, grid *g, grid_dot *d,
+                     int *x, int *y, int *w, int *h)
+{
+    int x1, y1;
+
+    grid_to_screen(ds, g, d->x, d->y, &x1, &y1);
+
+    *x = x1 - 2;
+    *y = y1 - 2;
+    *w = 5;
+    *h = 5;
+}
+
+static const int loopy_line_redraw_phases[] = {
+    COL_FAINT, COL_LINEUNKNOWN, COL_FOREGROUND, COL_HIGHLIGHT, COL_MISTAKE
+};
+#define NPHASES lenof(loopy_line_redraw_phases)
+
+static void game_redraw_line(drawing *dr, game_drawstate *ds,
+                            const game_state *state, int i, int phase)
+{
+    grid *g = state->game_grid;
+    grid_edge *e = g->edges + i;
+    int x1, x2, y1, y2;
+    int line_colour;
+
+    if (state->line_errors[i])
+       line_colour = COL_MISTAKE;
+    else if (state->lines[i] == LINE_UNKNOWN)
+       line_colour = COL_LINEUNKNOWN;
+    else if (state->lines[i] == LINE_NO)
+       line_colour = COL_FAINT;
+    else if (ds->flashing)
+       line_colour = COL_HIGHLIGHT;
+    else
+       line_colour = COL_FOREGROUND;
+    if (line_colour != loopy_line_redraw_phases[phase])
+        return;
+
+    /* Convert from grid to screen coordinates */
+    grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
+    grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
+
+    if (line_colour == COL_FAINT) {
+       static int draw_faint_lines = -1;
+       if (draw_faint_lines < 0) {
+           char *env = getenv("LOOPY_FAINT_LINES");
+           draw_faint_lines = (!env || (env[0] == 'y' ||
+                                        env[0] == 'Y'));
+       }
+       if (draw_faint_lines)
+           draw_line(dr, x1, y1, x2, y2, line_colour);
+    } else {
+       draw_thick_line(dr, 3.0,
+                       x1 + 0.5, y1 + 0.5,
+                       x2 + 0.5, y2 + 0.5,
+                       line_colour);
+    }
+}
+
+static void game_redraw_dot(drawing *dr, game_drawstate *ds,
+                           const game_state *state, int i)
+{
+    grid *g = state->game_grid;
+    grid_dot *d = g->dots + i;
+    int x, y;
+
+    grid_to_screen(ds, g, d->x, d->y, &x, &y);
+    draw_circle(dr, x, y, 2, COL_FOREGROUND, COL_FOREGROUND);
+}
+
+static int boxes_intersect(int x0, int y0, int w0, int h0,
+                           int x1, int y1, int w1, int h1)
+{
+    /*
+     * Two intervals intersect iff neither is wholly on one side of
+     * the other. Two boxes intersect iff their horizontal and
+     * vertical intervals both intersect.
+     */
+    return (x0 < x1+w1 && x1 < x0+w0 && y0 < y1+h1 && y1 < y0+h0);
+}
+
+static void game_redraw_in_rect(drawing *dr, game_drawstate *ds,
+                                const game_state *state,
+                                int x, int y, int w, int h)
+{
+    grid *g = state->game_grid;
+    int i, phase;
+    int bx, by, bw, bh;
+
+    clip(dr, x, y, w, h);
+    draw_rect(dr, x, y, w, h, COL_BACKGROUND);
+
+    for (i = 0; i < g->num_faces; i++) {
+        if (state->clues[i] >= 0) {
+            face_text_bbox(ds, g, &g->faces[i], &bx, &by, &bw, &bh);
+            if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
+                game_redraw_clue(dr, ds, state, i);
+        }
+    }
+    for (phase = 0; phase < NPHASES; phase++) {
+        for (i = 0; i < g->num_edges; i++) {
+            edge_bbox(ds, g, &g->edges[i], &bx, &by, &bw, &bh);
+            if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
+                game_redraw_line(dr, ds, state, i, phase);
+        }
+    }
+    for (i = 0; i < g->num_dots; i++) {
+        dot_bbox(ds, g, &g->dots[i], &bx, &by, &bw, &bh);
+        if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
+            game_redraw_dot(dr, ds, state, i);
     }
-    sx /= f->order;
-    sy /= f->order;
 
-    /* convert to screen coordinates */
-    grid_to_screen(ds, g, sx, sy, x, y);
+    unclip(dr);
+    draw_update(dr, x, y, w, h);
 }
 
-static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
-                        game_state *state, int dir, game_ui *ui,
+static void game_redraw(drawing *dr, game_drawstate *ds,
+                        const game_state *oldstate, const game_state *state,
+                        int dir, const game_ui *ui,
                         float animtime, float flashtime)
 {
+#define REDRAW_OBJECTS_LIMIT 16                /* Somewhat arbitrary tradeoff */
+
     grid *g = state->game_grid;
     int border = BORDER(ds->tilesize);
-    int i, n;
-    char c[2];
-    int line_colour, flash_changed;
-    int clue_mistake;
-    int clue_satisfied;
+    int i;
+    int flash_changed;
+    int redraw_everything = FALSE;
+
+    int edges[REDRAW_OBJECTS_LIMIT], nedges = 0;
+    int faces[REDRAW_OBJECTS_LIMIT], nfaces = 0;
+
+    /* Redrawing is somewhat involved.
+     *
+     * An update can theoretically affect an arbitrary number of edges
+     * (consider, for example, completing or breaking a cycle which doesn't
+     * satisfy all the clues -- we'll switch many edges between error and
+     * normal states).  On the other hand, redrawing the whole grid takes a
+     * while, making the game feel sluggish, and many updates are actually
+     * quite well localized.
+     *
+     * This redraw algorithm attempts to cope with both situations gracefully
+     * and correctly.  For localized changes, we set a clip rectangle, fill
+     * it with background, and then redraw (a plausible but conservative
+     * guess at) the objects which intersect the rectangle; if several
+     * objects need redrawing, we'll do them individually.  However, if lots
+     * of objects are affected, we'll just redraw everything.
+     *
+     * The reason for all of this is that it's just not safe to do the redraw
+     * piecemeal.  If you try to draw an antialiased diagonal line over
+     * itself, you get a slightly thicker antialiased diagonal line, which
+     * looks rather ugly after a while.
+     *
+     * So, we take two passes over the grid.  The first attempts to work out
+     * what needs doing, and the second actually does it.
+     */
 
     if (!ds->started) {
+       redraw_everything = TRUE;
         /*
-         * The initial contents of the window are not guaranteed and
-         * can vary with front ends. To be on the safe side, all games
-         * should start by drawing a big background-colour rectangle
-         * covering the whole window.
+         * But we must still go through the upcoming loops, so that we
+         * set up stuff in ds correctly for the initial redraw.
          */
-        int grid_width = g->highest_x - g->lowest_x;
-        int grid_height = g->highest_y - g->lowest_y;
-        int w = grid_width * ds->tilesize / g->tilesize;
-        int h = grid_height * ds->tilesize / g->tilesize;
-        draw_rect(dr, 0, 0, w + 2 * border, h + 2 * border, COL_BACKGROUND);
+    }
 
-        /* Draw clues */
-        for (i = 0; i < g->num_faces; i++) {
-            c[0] = CLUE2CHAR(state->clues[i]);
-            c[1] = '\0';
-            int x, y;
-            grid_face *f = g->faces + i;
-            face_text_pos(ds, g, f, &x, &y);
-            draw_text(dr, x, y, FONT_VARIABLE, ds->tilesize/2,
-                      ALIGN_VCENTRE | ALIGN_HCENTRE, COL_FOREGROUND, c);
+    /* First, trundle through the faces. */
+    for (i = 0; i < g->num_faces; i++) {
+        grid_face *f = g->faces + i;
+        int sides = f->order;
+        int yes_order, no_order;
+        int clue_mistake;
+        int clue_satisfied;
+        int n = state->clues[i];
+        if (n < 0)
+            continue;
+
+        yes_order = face_order(state, i, LINE_YES);
+        if (state->exactly_one_loop) {
+            /*
+             * Special case: if the set of LINE_YES edges in the grid
+             * consists of exactly one loop and nothing else, then we
+             * switch to treating LINE_UNKNOWN the same as LINE_NO for
+             * purposes of clue checking.
+             *
+             * This is because some people like to play Loopy without
+             * using the right-click, i.e. never setting anything to
+             * LINE_NO. Without this special case, if a person playing
+             * in that style fills in what they think is a correct
+             * solution loop but in fact it has an underfilled clue,
+             * then we will display no victory flash and also no error
+             * highlight explaining why not. With this special case,
+             * we light up underfilled clues at the instant the loop
+             * is closed. (Of course, *overfilled* clues are fine
+             * either way.)
+             *
+             * (It might still be considered unfortunate that we can't
+             * warn this style of player any earlier, if they make a
+             * mistake very near the beginning which doesn't show up
+             * until they close the last edge of the loop. One other
+             * thing we _could_ do here is to treat any LINE_UNKNOWN
+             * as LINE_NO if either of its endpoints has yes-degree 2,
+             * reflecting the fact that setting that line to YES would
+             * be an obvious error. But I don't think even that could
+             * catch _all_ clue errors in a timely manner; I think
+             * there are some that won't be displayed until the loop
+             * is filled in, even so, and there's no way to avoid that
+             * with complete reliability except to switch to being a
+             * player who sets things to LINE_NO.)
+             */
+            no_order = sides - yes_order;
+        } else {
+            no_order = face_order(state, i, LINE_NO);
+        }
+
+        clue_mistake = (yes_order > n || no_order > (sides-n));
+        clue_satisfied = (yes_order == n && no_order == (sides-n));
+
+        if (clue_mistake != ds->clue_error[i] ||
+            clue_satisfied != ds->clue_satisfied[i]) {
+            ds->clue_error[i] = clue_mistake;
+            ds->clue_satisfied[i] = clue_satisfied;
+            if (nfaces == REDRAW_OBJECTS_LIMIT)
+                redraw_everything = TRUE;
+            else
+                faces[nfaces++] = i;
         }
-        draw_update(dr, 0, 0, w + 2 * border, h + 2 * border);
     }
 
+    /* Work out what the flash state needs to be. */
     if (flashtime > 0 &&
         (flashtime <= FLASH_TIME/3 ||
          flashtime >= FLASH_TIME*2/3)) {
@@ -3000,171 +3356,55 @@ static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
         ds->flashing = FALSE;
     }
 
-    /* Some platforms may perform anti-aliasing, which may prevent clean
-     * repainting of lines when the colour is changed.
-     * If a line needs to be over-drawn in a different colour, erase a
-     * bounding-box around the line, then flag all nearby objects for redraw.
-     */
-    if (ds->started) {
-        const char redraw_flag = 1<<7;
-        for (i = 0; i < g->num_edges; i++) {
-            /* If we're changing state, AND
-             * the previous state was a coloured line */
-            if ((state->lines[i] != (ds->lines[i] & ~redraw_flag)) &&
-               ((ds->lines[i] & ~redraw_flag) != LINE_NO)) {
-                grid_edge *e = g->edges + i;
-                int x1 = e->dot1->x;
-                int y1 = e->dot1->y;
-                int x2 = e->dot2->x;
-                int y2 = e->dot2->y;
-                int xmin, xmax, ymin, ymax;
-                int j;
-                grid_to_screen(ds, g, x1, y1, &x1, &y1);
-                grid_to_screen(ds, g, x2, y2, &x2, &y2);
-                /* Allow extra margin for dots, and thickness of lines */
-                xmin = min(x1, x2) - 2;
-                xmax = max(x1, x2) + 2;
-                ymin = min(y1, y2) - 2;
-                ymax = max(y1, y2) + 2;
-                /* For testing, I find it helpful to change COL_BACKGROUND
-                 * to COL_SATISFIED here. */
-                draw_rect(dr, xmin, ymin, xmax - xmin + 1, ymax - ymin + 1,
-                          COL_BACKGROUND);
-                draw_update(dr, xmin, ymin, xmax - xmin + 1, ymax - ymin + 1);
-
-                /* Mark nearby lines for redraw */
-                for (j = 0; j < e->dot1->order; j++)
-                    ds->lines[e->dot1->edges[j] - g->edges] |= redraw_flag;
-                for (j = 0; j < e->dot2->order; j++)
-                    ds->lines[e->dot2->edges[j] - g->edges] |= redraw_flag;
-                /* Mark nearby clues for redraw.  Use a value that is
-                 * neither TRUE nor FALSE for this. */
-                if (e->face1)
-                    ds->clue_error[e->face1 - g->faces] = 2;
-                if (e->face2)
-                    ds->clue_error[e->face2 - g->faces] = 2;
-            }
+    /* Now, trundle through the edges. */
+    for (i = 0; i < g->num_edges; i++) {
+        char new_ds =
+            state->line_errors[i] ? DS_LINE_ERROR : state->lines[i];
+        if (new_ds != ds->lines[i] ||
+            (flash_changed && state->lines[i] == LINE_YES)) {
+            ds->lines[i] = new_ds;
+            if (nedges == REDRAW_OBJECTS_LIMIT)
+                redraw_everything = TRUE;
+            else
+                edges[nedges++] = i;
         }
     }
 
-    /* Redraw clue colours if necessary */
-    for (i = 0; i < g->num_faces; i++) {
-        grid_face *f = g->faces + i;
-        int sides = f->order;
-        int j;
-        n = state->clues[i];
-        if (n < 0)
-            continue;
-
-        c[0] = CLUE2CHAR(n);
-        c[1] = '\0';
-
-        clue_mistake = (face_order(state, i, LINE_YES) > n ||
-                        face_order(state, i, LINE_NO ) > (sides-n));
-
-        clue_satisfied = (face_order(state, i, LINE_YES) == n &&
-                          face_order(state, i, LINE_NO ) == (sides-n));
-
-        if (clue_mistake != ds->clue_error[i]
-           || clue_satisfied != ds->clue_satisfied[i]) {
-            int x, y;
-            face_text_pos(ds, g, f, &x, &y);
-            /* There seems to be a certain amount of trial-and-error
-             * involved in working out the correct bounding-box for
-             * the text. */
-            draw_rect(dr, x - ds->tilesize/4 - 1, y - ds->tilesize/4 - 3,
-                      ds->tilesize/2 + 2, ds->tilesize/2 + 5,
-                      COL_BACKGROUND);
-            draw_text(dr, x, y,
-                      FONT_VARIABLE, ds->tilesize/2,
-                      ALIGN_VCENTRE | ALIGN_HCENTRE,
-                      clue_mistake ? COL_MISTAKE :
-                      clue_satisfied ? COL_SATISFIED : COL_FOREGROUND, c);
-            draw_update(dr, x - ds->tilesize/4 - 1, y - ds->tilesize/4 - 3,
-                        ds->tilesize/2 + 2, ds->tilesize/2 + 5);
-
-            ds->clue_error[i] = clue_mistake;
-            ds->clue_satisfied[i] = clue_satisfied;
+    /* Pass one is now done.  Now we do the actual drawing. */
+    if (redraw_everything) {
+        int grid_width = g->highest_x - g->lowest_x;
+        int grid_height = g->highest_y - g->lowest_y;
+        int w = grid_width * ds->tilesize / g->tilesize;
+        int h = grid_height * ds->tilesize / g->tilesize;
 
-            /* Sometimes, the bounding-box encroaches into the surrounding
-             * lines (particularly if the window is resized fairly small).
-             * So redraw them. */
-            for (j = 0; j < f->order; j++)
-                ds->lines[f->edges[j] - g->edges] = -1;
-        }
-    }
+        game_redraw_in_rect(dr, ds, state,
+                            0, 0, w + 2*border + 1, h + 2*border + 1);
+    } else {
 
-    /* I've also had a request to colour lines red if they make a non-solution
-     * loop, or if more than two lines go into any point.  I think that would
-     * be good some time. */
+       /* Right.  Now we roll up our sleeves. */
 
-    /* Lines */
-    for (i = 0; i < g->num_edges; i++) {
-        grid_edge *e = g->edges + i;
-        int x1, x2, y1, y2;
-        int xmin, ymin, xmax, ymax;
-        int need_draw = (state->lines[i] != ds->lines[i]) ? TRUE : FALSE;
-        if (flash_changed && (state->lines[i] == LINE_YES))
-            need_draw = TRUE;
-        if (!ds->started)
-            need_draw = TRUE; /* draw everything at the start */
-        ds->lines[i] = state->lines[i];
-        if (!need_draw)
-            continue;
-        if (state->lines[i] == LINE_UNKNOWN)
-            line_colour = COL_LINEUNKNOWN;
-        else if (state->lines[i] == LINE_NO)
-            line_colour = COL_BACKGROUND;
-        else if (ds->flashing)
-            line_colour = COL_HIGHLIGHT;
-        else
-            line_colour = COL_FOREGROUND;
+       for (i = 0; i < nfaces; i++) {
+           grid_face *f = g->faces + faces[i];
+           int x, y, w, h;
 
-        /* Convert from grid to screen coordinates */
-        grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
-        grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
+            face_text_bbox(ds, g, f, &x, &y, &w, &h);
+            game_redraw_in_rect(dr, ds, state, x, y, w, h);
+       }
 
-        xmin = min(x1, x2);
-        xmax = max(x1, x2);
-        ymin = min(y1, y2);
-        ymax = max(y1, y2);
+       for (i = 0; i < nedges; i++) {
+           grid_edge *e = g->edges + edges[i];
+            int x, y, w, h;
 
-        if (line_colour != COL_BACKGROUND) {
-            /* (dx, dy) points roughly from (x1, y1) to (x2, y2).
-             * The line is then "fattened" in a (roughly) perpendicular
-             * direction to create a thin rectangle. */
-            int dx = (x1 > x2) ? -1 : ((x1 < x2) ? 1 : 0);
-            int dy = (y1 > y2) ? -1 : ((y1 < y2) ? 1 : 0);
-            int points[] = {
-                x1 + dy, y1 - dx,
-                x1 - dy, y1 + dx,
-                x2 - dy, y2 + dx,
-                x2 + dy, y2 - dx
-            };
-            draw_polygon(dr, points, 4, line_colour, line_colour);
-        }
-        if (ds->started) {
-            /* Draw dots at ends of the line */
-            draw_circle(dr, x1, y1, 2, COL_FOREGROUND, COL_FOREGROUND);
-            draw_circle(dr, x2, y2, 2, COL_FOREGROUND, COL_FOREGROUND);
-        }
-        draw_update(dr, xmin-2, ymin-2, xmax - xmin + 4, ymax - ymin + 4);
+            edge_bbox(ds, g, e, &x, &y, &w, &h);
+            game_redraw_in_rect(dr, ds, state, x, y, w, h);
+       }
     }
 
-    /* Draw dots */
-    if (!ds->started) {
-        for (i = 0; i < g->num_dots; i++) {
-            grid_dot *d = g->dots + i;
-            int x, y;
-            grid_to_screen(ds, g, d->x, d->y, &x, &y);
-            draw_circle(dr, x, y, 2, COL_FOREGROUND, COL_FOREGROUND);
-        }
-    }
     ds->started = TRUE;
 }
 
-static float game_flash_length(game_state *oldstate, game_state *newstate,
-                               int dir, game_ui *ui)
+static float game_flash_length(const game_state *oldstate,
+                               const game_state *newstate, int dir, game_ui *ui)
 {
     if (!oldstate->solved  &&  newstate->solved &&
         !oldstate->cheated && !newstate->cheated) {
@@ -3174,7 +3414,12 @@ static float game_flash_length(game_state *oldstate, game_state *newstate,
     return 0.0F;
 }
 
-static void game_print_size(game_params *params, float *x, float *y)
+static int game_status(const game_state *state)
+{
+    return state->solved ? +1 : 0;
+}
+
+static void game_print_size(const game_params *params, float *x, float *y)
 {
     int pw, ph;
 
@@ -3186,14 +3431,18 @@ static void game_print_size(game_params *params, float *x, float *y)
     *y = ph / 100.0F;
 }
 
-static void game_print(drawing *dr, game_state *state, int tilesize)
+static void game_print(drawing *dr, const game_state *state, int tilesize)
 {
     int ink = print_mono_colour(dr, 0);
     int i;
     game_drawstate ads, *ds = &ads;
     grid *g = state->game_grid;
 
-    game_set_size(dr, ds, NULL, tilesize);
+    ds->tilesize = tilesize;
+    ds->textx = snewn(g->num_faces, int);
+    ds->texty = snewn(g->num_faces, int);
+    for (i = 0; i < g->num_faces; i++)
+        ds->textx[i] = ds->texty[i] = -1;
 
     for (i = 0; i < g->num_dots; i++) {
         int x, y;
@@ -3208,10 +3457,9 @@ static void game_print(drawing *dr, game_state *state, int tilesize)
         grid_face *f = g->faces + i;
         int clue = state->clues[i];
         if (clue >= 0) {
-            char c[2];
+            char c[20];
             int x, y;
-            c[0] = CLUE2CHAR(clue);
-            c[1] = '\0';
+            sprintf(c, "%d", state->clues[i]);
             face_text_pos(ds, g, f, &x, &y);
             draw_text(dr, x, y,
                       FONT_VARIABLE, ds->tilesize / 2,
@@ -3236,14 +3484,18 @@ static void game_print(drawing *dr, game_state *state, int tilesize)
             double d = sqrt(SQ((double)x1 - x2) + SQ((double)y1 - y2));
             double dx = (x2 - x1) / d;
             double dy = (y2 - y1) / d;
+           int points[8];
+
             dx = (dx * ds->tilesize) / thickness;
             dy = (dy * ds->tilesize) / thickness;
-            int points[] = {
-                x1 + dy, y1 - dx,
-                x1 - dy, y1 + dx,
-                x2 - dy, y2 + dx,
-                x2 + dy, y2 - dx
-            };
+           points[0] = x1 + (int)dy;
+           points[1] = y1 - (int)dx;
+           points[2] = x1 - (int)dy;
+           points[3] = y1 + (int)dx;
+           points[4] = x2 - (int)dy;
+           points[5] = y2 + (int)dx;
+           points[6] = x2 + (int)dy;
+           points[7] = y2 - (int)dx;
             draw_polygon(dr, points, 4, ink, ink);
         }
         else
@@ -3259,6 +3511,9 @@ static void game_print(drawing *dr, game_state *state, int tilesize)
             }
         }
     }
+
+    sfree(ds->textx);
+    sfree(ds->texty);
 }
 
 #ifdef COMBINED
@@ -3296,8 +3551,138 @@ const struct game thegame = {
     game_redraw,
     game_anim_length,
     game_flash_length,
+    game_status,
     TRUE, FALSE, game_print_size, game_print,
     FALSE /* wants_statusbar */,
     FALSE, game_timing_state,
     0,                                       /* mouse_priorities */
 };
+
+#ifdef STANDALONE_SOLVER
+
+/*
+ * Half-hearted standalone solver. It can't output the solution to
+ * anything but a square puzzle, and it can't log the deductions
+ * it makes either. But it can solve square puzzles, and more
+ * importantly it can use its solver to grade the difficulty of
+ * any puzzle you give it.
+ */
+
+#include <stdarg.h>
+
+int main(int argc, char **argv)
+{
+    game_params *p;
+    game_state *s;
+    char *id = NULL, *desc, *err;
+    int grade = FALSE;
+    int ret, diff;
+#if 0 /* verbose solver not supported here (yet) */
+    int really_verbose = FALSE;
+#endif
+
+    while (--argc > 0) {
+        char *p = *++argv;
+#if 0 /* verbose solver not supported here (yet) */
+        if (!strcmp(p, "-v")) {
+            really_verbose = TRUE;
+        } else
+#endif
+       if (!strcmp(p, "-g")) {
+            grade = TRUE;
+        } else if (*p == '-') {
+            fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
+            return 1;
+        } else {
+            id = p;
+        }
+    }
+
+    if (!id) {
+        fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
+        return 1;
+    }
+
+    desc = strchr(id, ':');
+    if (!desc) {
+        fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
+        return 1;
+    }
+    *desc++ = '\0';
+
+    p = default_params();
+    decode_params(p, id);
+    err = validate_desc(p, desc);
+    if (err) {
+        fprintf(stderr, "%s: %s\n", argv[0], err);
+        return 1;
+    }
+    s = new_game(NULL, p, desc);
+
+    /*
+     * When solving an Easy puzzle, we don't want to bother the
+     * user with Hard-level deductions. For this reason, we grade
+     * the puzzle internally before doing anything else.
+     */
+    ret = -1;                         /* placate optimiser */
+    for (diff = 0; diff < DIFF_MAX; diff++) {
+       solver_state *sstate_new;
+       solver_state *sstate = new_solver_state((game_state *)s, diff);
+
+       sstate_new = solve_game_rec(sstate);
+
+       if (sstate_new->solver_status == SOLVER_MISTAKE)
+           ret = 0;
+       else if (sstate_new->solver_status == SOLVER_SOLVED)
+           ret = 1;
+       else
+           ret = 2;
+
+       free_solver_state(sstate_new);
+       free_solver_state(sstate);
+
+       if (ret < 2)
+           break;
+    }
+
+    if (diff == DIFF_MAX) {
+       if (grade)
+           printf("Difficulty rating: harder than Hard, or ambiguous\n");
+       else
+           printf("Unable to find a unique solution\n");
+    } else {
+       if (grade) {
+           if (ret == 0)
+               printf("Difficulty rating: impossible (no solution exists)\n");
+           else if (ret == 1)
+               printf("Difficulty rating: %s\n", diffnames[diff]);
+       } else {
+           solver_state *sstate_new;
+           solver_state *sstate = new_solver_state((game_state *)s, diff);
+
+           /* If we supported a verbose solver, we'd set verbosity here */
+
+           sstate_new = solve_game_rec(sstate);
+
+           if (sstate_new->solver_status == SOLVER_MISTAKE)
+               printf("Puzzle is inconsistent\n");
+           else {
+               assert(sstate_new->solver_status == SOLVER_SOLVED);
+               if (s->grid_type == 0) {
+                   fputs(game_text_format(sstate_new->state), stdout);
+               } else {
+                   printf("Unable to output non-square grids\n");
+               }
+           }
+
+           free_solver_state(sstate_new);
+           free_solver_state(sstate);
+       }
+    }
+
+    return 0;
+}
+
+#endif
+
+/* vim: set shiftwidth=4 tabstop=8: */