ref: c91471e6c155853377d0ac9b5a9a4219c214674e
parent: b629e34beb60fcf2e880012e00cca52d0cf2fe39
author: Simon Tatham <anakin@pobox.com>
date: Wed Dec 30 11:53:36 EST 2009
New puzzle in 'unfinished'. Essentially, Sudoku for group theorists: you are given a partially specified Cayley table of a small finite group, and must fill in all the missing entries using both Sudoku- style deductions (minus the square block constraint) and the group axioms. I've just thrown it together in about five hours by cloning- and-hacking from Keen, as much as anything else to demonstrate that the new latin.c interface really does make it extremely easy to write new Latin square puzzles. It's not really _unfinished_, as such, but it is just too esoteric (not to mention difficult) for me to feel entirely comfortable with adding it to the main puzzle collection. I can't bring myself to throw it away, though, and who knows - perhaps a university maths department might find it a useful teaching tool :-) [originally from svn r8800]
--- /dev/null
+++ b/unfinished/group.R
@@ -1,0 +1,25 @@
+# -*- makefile -*-
+
+GROUP_LATIN_EXTRA = tree234 maxflow
+GROUP_EXTRA = latin GROUP_LATIN_EXTRA
+
+group : [X] GTK COMMON group GROUP_EXTRA group-icon|no-icon
+
+group : [G] WINDOWS COMMON group GROUP_EXTRA group.res|noicon.res
+
+groupsolver : [U] group[STANDALONE_SOLVER] latin[STANDALONE_SOLVER] GROUP_LATIN_EXTRA STANDALONE
+groupsolver : [C] group[STANDALONE_SOLVER] latin[STANDALONE_SOLVER] GROUP_LATIN_EXTRA STANDALONE
+
+ALL += group[COMBINED] GROUP_EXTRA
+
+!begin gtk
+GAMES += group
+!end
+
+!begin >list.c
+ A(group) \
+!end
+
+!begin >wingames.lst
+group.exe:Group
+!end
--- /dev/null
+++ b/unfinished/group.c
@@ -1,0 +1,1761 @@
+/*
+ * group.c: a Latin-square puzzle, but played with groups' Cayley
+ * tables. That is, you are given a Cayley table of a group with
+ * most elements blank and a few clues, and you must fill it in
+ * so as to preserve the group axioms.
+ *
+ * This is a perfectly playable and fully working puzzle, but I'm
+ * leaving it for the moment in the 'unfinished' directory because
+ * it's just too esoteric (not to mention _hard_) for me to be
+ * comfortable presenting it to the general public as something they
+ * might (implicitly) actually want to play.
+ *
+ * TODO:
+ *
+ * - more solver techniques?
+ * * Inverses: once we know that gh = e, we can immediately
+ * deduce hg = e as well; then for any gx=y we can deduce
+ * hy=x, and for any xg=y we have yh=x.
+ * * Hard-mode associativity: we currently deduce based on
+ * definite numbers in the grid, but we could also winnow
+ * based on _possible_ numbers.
+ * * My overambitious original thoughts included wondering if we
+ * could infer that there must be elements of certain orders
+ * (e.g. a group of order divisible by 5 must contain an
+ * element of order 5), but I think in fact this is probably
+ * silly.
+ *
+ * - a mode which shuffles the identity element into the mix
+ * instead of keeping it clearly shown for you?
+ * * shuffle more fully during table generation
+ * * start clue removal by clearing the identity row and column
+ * completely, or else it'll be totally obvious where it is
+ * * have to print the group elements outside the grid
+ * * new_ui should start the cursor at 0,0 not 1,1, and cursor
+ * should not be constrained to x,y >= 1
+ * * get rid of the COL_IDENTITY highlights
+ * * will we need more checks in check_errors?
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include <ctype.h>
+#include <math.h>
+
+#include "puzzles.h"
+#include "latin.h"
+
+/*
+ * Difficulty levels. I do some macro ickery here to ensure that my
+ * enum and the various forms of my name list always match up.
+ */
+#define DIFFLIST(A) \
+ A(TRIVIAL,Trivial,NULL,t) \
+ A(NORMAL,Normal,solver_normal,n) \
+ A(HARD,Hard,NULL,h) \
+ A(EXTREME,Extreme,NULL,x) \
+ A(UNREASONABLE,Unreasonable,NULL,u)
+#define ENUM(upper,title,func,lower) DIFF_ ## upper,
+#define TITLE(upper,title,func,lower) #title,
+#define ENCODE(upper,title,func,lower) #lower
+#define CONFIG(upper,title,func,lower) ":" #title
+enum { DIFFLIST(ENUM) DIFFCOUNT };+static char const *const group_diffnames[] = { DIFFLIST(TITLE) };+static char const group_diffchars[] = DIFFLIST(ENCODE);
+#define DIFFCONFIG DIFFLIST(CONFIG)
+
+enum {+ COL_BACKGROUND,
+ COL_IDENTITY,
+ COL_GRID,
+ COL_USER,
+ COL_HIGHLIGHT,
+ COL_ERROR,
+ COL_PENCIL,
+ NCOLOURS
+};
+
+#define FROMCHAR(c) ((c)>='0'&&(c)<='9' ? (c)-'0' : \
+ (c)>='A'&&(c)<='Z' ? (c)-'A'+10 : (c)-'a'+10)
+#define ISCHAR(c) (((c)>='0'&&(c)<='9') || \
+ ((c)>='A'&&(c)<='Z') || ((c)>='a'&&(c)<='z'))
+#define TOCHAR(c) ((c)>=10 ? (c)-10+'a' : (c)+'0')
+
+struct game_params {+ int w, diff;
+};
+
+struct game_state {+ game_params par;
+ digit *grid;
+ unsigned char *immutable;
+ int *pencil; /* bitmaps using bits 1<<1..1<<n */
+ int completed, cheated;
+};
+
+static game_params *default_params(void)
+{+ game_params *ret = snew(game_params);
+
+ ret->w = 6;
+ ret->diff = DIFF_NORMAL;
+
+ return ret;
+}
+
+const static struct game_params group_presets[] = {+ { 4, DIFF_NORMAL },+ { 6, DIFF_NORMAL },+};
+
+static int game_fetch_preset(int i, char **name, game_params **params)
+{+ game_params *ret;
+ char buf[80];
+
+ if (i < 0 || i >= lenof(group_presets))
+ return FALSE;
+
+ ret = snew(game_params);
+ *ret = group_presets[i]; /* structure copy */
+
+ sprintf(buf, "%dx%d %s", ret->w, ret->w, group_diffnames[ret->diff]);
+
+ *name = dupstr(buf);
+ *params = ret;
+ return TRUE;
+}
+
+static void free_params(game_params *params)
+{+ sfree(params);
+}
+
+static game_params *dup_params(game_params *params)
+{+ game_params *ret = snew(game_params);
+ *ret = *params; /* structure copy */
+ return ret;
+}
+
+static void decode_params(game_params *params, char const *string)
+{+ char const *p = string;
+
+ params->w = atoi(p);
+ while (*p && isdigit((unsigned char)*p)) p++;
+
+ if (*p == 'd') {+ int i;
+ p++;
+ params->diff = DIFFCOUNT+1; /* ...which is invalid */
+ if (*p) {+ for (i = 0; i < DIFFCOUNT; i++) {+ if (*p == group_diffchars[i])
+ params->diff = i;
+ }
+ p++;
+ }
+ }
+}
+
+static char *encode_params(game_params *params, int full)
+{+ char ret[80];
+
+ sprintf(ret, "%d", params->w);
+ if (full)
+ sprintf(ret + strlen(ret), "d%c", group_diffchars[params->diff]);
+
+ return dupstr(ret);
+}
+
+static config_item *game_configure(game_params *params)
+{+ config_item *ret;
+ char buf[80];
+
+ ret = snewn(3, config_item);
+
+ ret[0].name = "Grid size";
+ ret[0].type = C_STRING;
+ sprintf(buf, "%d", params->w);
+ ret[0].sval = dupstr(buf);
+ ret[0].ival = 0;
+
+ ret[1].name = "Difficulty";
+ ret[1].type = C_CHOICES;
+ ret[1].sval = DIFFCONFIG;
+ ret[1].ival = params->diff;
+
+ ret[2].name = NULL;
+ ret[2].type = C_END;
+ ret[2].sval = NULL;
+ ret[2].ival = 0;
+
+ return ret;
+}
+
+static game_params *custom_params(config_item *cfg)
+{+ game_params *ret = snew(game_params);
+
+ ret->w = atoi(cfg[0].sval);
+ ret->diff = cfg[1].ival;
+
+ return ret;
+}
+
+static char *validate_params(game_params *params, int full)
+{+ if (params->w < 3 || params->w > 31)
+ return "Grid size must be between 3 and 31";
+ if (params->diff >= DIFFCOUNT)
+ return "Unknown difficulty rating";
+ return NULL;
+}
+
+/* ----------------------------------------------------------------------
+ * Solver.
+ */
+
+static int solver_normal(struct latin_solver *solver, void *vctx)
+{+ int w = solver->o;
+ digit *grid = solver->grid;
+ int i, j, k;
+
+ /*
+ * Deduce using associativity: (ab)c = a(bc).
+ *
+ * So we pick any a,b,c we like; then if we know ab, bc, and
+ * (ab)c we can fill in a(bc).
+ */
+ for (i = 1; i < w; i++)
+ for (j = 1; j < w; j++)
+ for (k = 1; k < w; k++) {+ if (!grid[i*w+j] || !grid[j*w+k])
+ continue;
+ if (grid[(grid[i*w+j]-1)*w+k] &&
+ !grid[i*w+(grid[j*w+k]-1)]) {+ int x = grid[j*w+k]-1, y = i;
+ int n = grid[(grid[i*w+j]-1)*w+k];
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {+ printf("%*sassociativity on %d,%d,%d: %d*%d = %d*%d\n",+ solver_recurse_depth*4, "",
+ i+1, j+1, k+1,
+ grid[i*w+j], k+1, i+1, grid[j*w+k]);
+ printf("%*s placing %d at (%d,%d)\n",+ solver_recurse_depth*4, "",
+ n, x+1, y+1);
+ }
+#endif
+ if (solver->cube[(x*w+y)*w+n-1]) {+ latin_solver_place(solver, x, y, n);
+ return 1;
+ } else {+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*s contradiction!\n",+ solver_recurse_depth*4, "");
+ return -1;
+#endif
+ }
+ }
+ if (!grid[(grid[i*w+j]-1)*w+k] &&
+ grid[i*w+(grid[j*w+k]-1)]) {+ int x = k, y = grid[i*w+j]-1;
+ int n = grid[i*w+(grid[j*w+k]-1)];
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {+ printf("%*sassociativity on %d,%d,%d: %d*%d = %d*%d\n",+ solver_recurse_depth*4, "",
+ i+1, j+1, k+1,
+ grid[i*w+j], k+1, i+1, grid[j*w+k]);
+ printf("%*s placing %d at (%d,%d)\n",+ solver_recurse_depth*4, "",
+ n, x+1, y+1);
+ }
+#endif
+ if (solver->cube[(x*w+y)*w+n-1]) {+ latin_solver_place(solver, x, y, n);
+ return 1;
+ } else {+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*s contradiction!\n",+ solver_recurse_depth*4, "");
+ return -1;
+#endif
+ }
+ }
+ }
+
+ return 0;
+}
+
+#define SOLVER(upper,title,func,lower) func,
+static usersolver_t const group_solvers[] = { DIFFLIST(SOLVER) };+
+static int solver(int w, digit *grid, int maxdiff)
+{+ int ret;
+
+ ret = latin_solver(grid, w, maxdiff,
+ DIFF_TRIVIAL, DIFF_HARD, DIFF_EXTREME,
+ DIFF_EXTREME, DIFF_UNREASONABLE,
+ group_solvers, NULL, NULL, NULL);
+
+ return ret;
+}
+
+/* ----------------------------------------------------------------------
+ * Grid generation.
+ */
+
+static char *encode_grid(char *desc, digit *grid, int area)
+{+ int run, i;
+ char *p = desc;
+
+ run = 0;
+ for (i = 0; i <= area; i++) {+ int n = (i < area ? grid[i] : -1);
+
+ if (!n)
+ run++;
+ else {+ if (run) {+ while (run > 0) {+ int c = 'a' - 1 + run;
+ if (run > 26)
+ c = 'z';
+ *p++ = c;
+ run -= c - ('a' - 1);+ }
+ } else {+ /*
+ * If there's a number in the very top left or
+ * bottom right, there's no point putting an
+ * unnecessary _ before or after it.
+ */
+ if (p > desc && n > 0)
+ *p++ = '_';
+ }
+ if (n > 0)
+ p += sprintf(p, "%d", n);
+ run = 0;
+ }
+ }
+ return p;
+}
+
+/* ----- data generated by group.gap begins ----- */
+
+struct group {+ unsigned long autosize;
+ int order, ngens;
+ const char *gens;
+};
+struct groups {+ int ngroups;
+ const struct group *groups;
+};
+
+static const struct group groupdata[] = {+ /* order 2 */
+ {1L, 2, 1, "21"},+ /* order 3 */
+ {2L, 3, 1, "231"},+ /* order 4 */
+ {2L, 4, 1, "2341"},+ {6L, 4, 2, "2143" "3412"},+ /* order 5 */
+ {4L, 5, 1, "23451"},+ /* order 6 */
+ {6L, 6, 2, "365214" "214365"},+ {2L, 6, 1, "436521"},+ /* order 7 */
+ {6L, 7, 1, "2345671"},+ /* order 8 */
+ {4L, 8, 1, "23564781"},+ {8L, 8, 2, "24567183" "57284361"},+ {8L, 8, 2, "57284361" "21563487"},+ {24L, 8, 2, "24567183" "38472516"},+ {168L, 8, 3, "21563487" "35172846" "46718235"},+ /* order 9 */
+ {6L, 9, 1, "245378691"},+ {48L, 9, 2, "245178396" "356781924"},+ /* order 10 */
+ {20L, 10, 2, "3A52749618" "21436587A9"},+ {4L, 10, 1, "436587A921"},+ /* order 11 */
+ {10L, 11, 1, "23456789AB1"},+ /* order 12 */
+ {12L, 12, 2, "7C4BA5832916" "2356179A4BC8"},+ {4L, 12, 1, "589AB32C4761"},+ {24L, 12, 2, "256719AB34C8" "6A2B8C574391"},+ {12L, 12, 2, "7C4BA5832916" "2156349A78CB"},+ {12L, 12, 2, "649A78C2B153" "794B6C83A512"},+ /* order 13 */
+ {12L, 13, 1, "23456789ABCD1"},+ /* order 14 */
+ {42L, 14, 2, "5C7E92B4D6183A" "21436587A9CBED"},+ {6L, 14, 1, "6587A9CBED2143"},+ /* order 15 */
+ {8L, 15, 1, "5783AB6DE9F2C41"},+ /* order 16 */
+ {8L, 16, 1, "DBEG6F1427C3958A"},+ {96L, 16, 2, "9CB3FE6G54A87D12" "2467891BCDE3F5GA"},+ {32L, 16, 2, "D98G643FE2C1BA75" "25678AB1CDEF34G9"},+ {32L, 16, 2, "9613F7CD45A2EGB8" "25678AB1CDEF34G9"},+ {16L, 16, 2, "DF8G6B39E2C14A75" "2467895BCDEAF1G3"},+ {16L, 16, 2, "D98G64AFE2C5B371" "2467895BCDEAF1G3"},+ {32L, 16, 2, "DF8G6439E2C5BA71" "21678345CDE9ABGF"},+ {16L, 16, 2, "D98G6BAFE2C14375" "74G8EF5B6C2391DA"},+ {32L, 16, 2, "D92G64AF78C5B3E1" "3C59A7DGB1F8E642"},+ {192L, 16, 3,+ "D38G619AE2C45F7B" "25678AB1CDEF34G9" "7BC2EF546G8A91D3"},
+ {64L, 16, 3, "D38G619AE2C45F7B" "CF76GBA92ED54381" "3D19A8G645FE2CB7"},+ {192L, 16, 3,+ "9GB3F7DC54A2E618" "25678AB1CDEF34G9" "3D59A2G6B1F78C4E"},
+ {48L, 16, 3, "9G4AFE6C5B327D18" "6A2CD5F378GB19E4" "4795BC8EAF1DG236"},+ {20160L, 16, 4,+ "58AB1DE2F34G679C" "21678345CDE9ABGF" "3619A2CD45F78GBE"
+ "4791BC2E3F56G8AD"},
+ /* order 17 */
+ {16L, 17, 1, "56789ABCDEFGH1234"},+ /* order 18 */
+ {54L, 18, 2, "DB9HFGE17CI5342A86" "215634ABC789FGDEIH"},+ {6L, 18, 1, "53AB786FG4DECI9H21"},+ {12L, 18, 2, "53AB782FG1DE6I4HC9" "BEFGH36I5978CA1D24"},+ {432L, 18, 3,+ "96E1BCH34FG278I5DA" "EFH36I978BCA1DG245" "215634ABC789FGDEIH"},
+ {48L, 18, 2, "53AB782FG1DE6I4HC9" "64BC89FG2DE1I5H3A7"},+ /* order 19 */
+ {18L, 19, 1, "56789ABCDEFGHIJ1234"},+ /* order 20 */
+ {40L, 20, 2, "7K4BI58F29CJ6DG3AH1E" "5129346D78AHBCEKFGIJ"},+ {8L, 20, 1, "589AC3DEG7HIJB2K4F61"},+ {20L, 20, 2, "4AJ8HE3CKI7G52B196FD" "5129346D78AHBCEKFGIJ"},+ {40L, 20, 2, "7K4BI58F29CJ6DG3AH1E" "5329176D4BAH8FEKCJIG"},+ {24L, 20, 2, "976D4BAH8FEKCJI5G321" "649A78DEBCHIFGK2J153"},+ /* order 21 */
+ {42L, 21, 2, "9KCJ2FL5I4817B3AE6DHG" "5A8CDBFGEIJH1LK342679"},+ {12L, 21, 1, "5783AB6DE9GHCJKFL2I41"},+ /* order 22 */
+ {110L, 22, 2, "5K7M92B4D6F8HAJCLE1G3I" "21436587A9CBEDGFIHKJML"},+ {10L, 22, 1, "6587A9CBEDGFIHKJML2143"},+ /* order 23 */
+ {22L, 23, 1, "56789ABCDEFGHIJKLMN1234"},+ /* order 24 */
+ {24L, 24, 2, "HO5ANGLDBCI9M26KJ1378E4F" "8IEFGJN3KLM2C49AO671BHD5"},+ {8L, 24, 1, "DH2KL4IN678OA5C9EFGBJ1M3"},+ {24L, 24, 2, "9FHI25LM6N78BC1ODEGJ34KA" "EAOFM74BJDK69GH5C3LI2N18"},+ {48L, 24, 2, "HL5ANMO6BCI9G7DEJ132FK48" "8JEFGNC4KLM2I91BO673H5DA"},+ {24L, 24, 2, "HO5ANGLDBCI9M26KJ1378E4F" "KN8EOCI9FGLDJ13HM2645A7B"},+ {48L, 24, 2, "HL5ANMO6BCI9G7DEJ132FK48" "21678345DEFG9ABCKLMHIJON"},+ {48L, 24, 3,+ "HOBANMLD5JI9G76KC432FE18" "AL5HIGO6BCN3M2DEJ1978K4F"
+ "8JEFGNC4KLM2I91BO673H5DA"},
+ {24L, 24, 3,+ "HLBANGO65JI9M2DEC4378K1F" "AO5HIMLDBCN3G76KJ192FE48"
+ "KIFEOCN38MLDJ19AG7645H2B"},
+ {16L, 24, 2, "DI7KLCN9FG6OJ4AH2ME5B381" "MBO8FH1JEKG23N45L679ACDI"},+ {16L, 24, 2, "DI7KLCN9FG6OJ4AH2ME5B381" "IDCN97KLJ4AHFG6O5B32ME18"},+ {48L, 24, 2, "9LCHI7ODJ43NFGEK5BA2M618" "7CDFGIJ4KL2MN95B6O8AH1E3"},+ {24L, 24, 2, "LAGODI3JE87KCN9B6M254HF1" "EIL6MCN9GODFA54H87K3J12B"},+ {24L, 24, 2, "D92KL1HI678O345NEFGABCMJ" "FBOM6NJ37LKE4IHA2GD1C985"},+ {144L, 24, 3,+ "HOBANMLD5JI9G76KC432FE18" "AL5HIGO6BCN3M2DEJ1978K4F"
+ "21678345DEFG9ABCKLMHIJON"},
+ {336L, 24, 3,+ "HKBANFEO5JI98MLDC43G7612" "AE5HI8KLBCN3FGO6J19M2D47"
+ "85EFGABCKLM2HIJ1O67N34D9"},
+ /* order 25 */
+ {20L, 25, 1, "589CDEGHIJ6KLM2ANO4FP71B3"},+ {480L, 25, 2, "589CDEGHIJ3KLM26NO4AP7FB1" "245789BCDE1GHIJ3KLM6NOAPF"},+ /* order 26 */
+ {156L, 26, 2,+ "5O7Q92B4D6F8HAJCLENGPI1K3M" "21436587A9CBEDGFIHKJMLONQP"},
+ {12L, 26, 1, "6587A9CBEDGFIHKJMLONQP2143"},+ /* order 27 */
+ {18L, 27, 1, "53BC689IJKDE4GHOP7LMANRFQ12"},+ {108L, 27, 2,+ "54BC79AIJKEFGH1OPLM2N3RQ68D" "DI2LG5O67Q4NBCREF9A8JKMH1P3"},
+ {432L, 27, 2,+ "51BC234IJK6789AOPDEFGHRLMNQ" "3E89PLM1GHRB7Q64NKIJFDA5O2C"},
+ {54L, 27, 2,+ "54BC79AIJKEFGH1OPLM2N3RQ68D" "DR2LNKI67QA8P5OEFH1GBCM34J9"},
+ {11232L, 27, 3,+ "51BC234IJK6789AOPDEFGHRLMNQ" "3689BDE1GHIJ2LM4N5OP7QACRFK"
+ "479ACEFGH1JKLM2N3OP5Q68RBDI"},
+ /* order 28 */
+ {84L, 28, 2,+ "7S4BQ58F29CJ6DGNAHKRELO3IP1M" "5129346D78AHBCELFGIPJKMSNOQR"},
+ {12L, 28, 1, "589AC3DEG7HIKBLMOFPQRJ2S4N61"},+ {84L, 28, 2,+ "7S4BQ58F29CJ6DGNAHKRELO3IP1M" "5329176D4BAH8FELCJIPGNMSKRQO"},
+ {36L, 28, 2,+ "976D4BAH8FELCJIPGNMSKRQ5O321" "649A78DEBCHIFGLMJKPQNOS2R153"},
+ /* order 29 */
+ {28L, 29, 1, "56789ABCDEFGHIJKLMNOPQRST1234"},+ /* order 30 */
+ {24L, 30, 2,+ "LHQ7NOTDERSA9JK6UGF1PBCM34I285" "BFHIL3NO5Q78RSATDE6UG9JKCM1P24"},
+ {40L, 30, 2,+ "DU4JOA89PS2GEFT56MKL7BCRQ1HI3N" "BQGHT36MNL78CRS1DEIU54JKOA9P2F"},
+ {120L, 30, 2,+ "DS4JU589POABEFT2GHKL76MNQ1CR3I" "215634ABC789GHIDEFMNOJKLRSPQUT"},
+ {8L, 30, 1, "HEMNJKCRS9PQIU5FT3OABL782G1D64"},+ /* order 31 */
+ {30L, 31, 1, "56789ABCDEFGHIJKLMNOPQRSTUV1234"},+};
+
+static const struct groups groups[] = {+ {0, NULL}, /* trivial case: 0 */+ {0, NULL}, /* trivial case: 1 */+ {1, groupdata + 0}, /* 2 */+ {1, groupdata + 1}, /* 3 */+ {2, groupdata + 2}, /* 4 */+ {1, groupdata + 4}, /* 5 */+ {2, groupdata + 5}, /* 6 */+ {1, groupdata + 7}, /* 7 */+ {5, groupdata + 8}, /* 8 */+ {2, groupdata + 13}, /* 9 */+ {2, groupdata + 15}, /* 10 */+ {1, groupdata + 17}, /* 11 */+ {5, groupdata + 18}, /* 12 */+ {1, groupdata + 23}, /* 13 */+ {2, groupdata + 24}, /* 14 */+ {1, groupdata + 26}, /* 15 */+ {14, groupdata + 27}, /* 16 */+ {1, groupdata + 41}, /* 17 */+ {5, groupdata + 42}, /* 18 */+ {1, groupdata + 47}, /* 19 */+ {5, groupdata + 48}, /* 20 */+ {2, groupdata + 53}, /* 21 */+ {2, groupdata + 55}, /* 22 */+ {1, groupdata + 57}, /* 23 */+ {15, groupdata + 58}, /* 24 */+ {2, groupdata + 73}, /* 25 */+ {2, groupdata + 75}, /* 26 */+ {5, groupdata + 77}, /* 27 */+ {4, groupdata + 82}, /* 28 */+ {1, groupdata + 86}, /* 29 */+ {4, groupdata + 87}, /* 30 */+ {1, groupdata + 91}, /* 31 */+};
+
+/* ----- data generated by group.gap ends ----- */
+
+static char *new_game_desc(game_params *params, random_state *rs,
+ char **aux, int interactive)
+{+ int w = params->w, a = w*w;
+ digit *grid, *soln, *soln2;
+ int *indices;
+ int i, j, k, qh, qt;
+ int diff = params->diff;
+ const struct group *group;
+ char *desc, *p;
+
+ /*
+ * Difficulty exceptions: some combinations of size and
+ * difficulty cannot be satisfied, because all puzzles of at
+ * most that difficulty are actually even easier.
+ *
+ * Remember to re-test this whenever a change is made to the
+ * solver logic!
+ *
+ * I tested it using the following shell command:
+
+for d in t n h x u; do
+ for i in {3..9}; do+ echo ./group --generate 1 ${i}d${d}+ perl -e 'alarm 30; exec @ARGV' ./group --generate 5 ${i}d${d} >/dev/null \+ || echo broken
+ done
+done
+
+ * Of course, it's better to do that after taking the exceptions
+ * _out_, so as to detect exceptions that should be removed as
+ * well as those which should be added.
+ */
+ if (w <= 9 && diff == DIFF_EXTREME)
+ diff--;
+ if (w <= 6 && diff == DIFF_HARD)
+ diff--;
+ if (w <= 4 && diff > DIFF_TRIVIAL)
+ diff = DIFF_TRIVIAL;
+
+ grid = snewn(a, digit);
+ soln = snewn(a, digit);
+ soln2 = snewn(a, digit);
+ indices = snewn(a, int);
+
+ while (1) {+ /*
+ * Construct a valid group table, by picking a group from
+ * the above data table, decompressing it into a full
+ * representation by BFS, and then randomly permuting its
+ * non-identity elements.
+ *
+ * We build the canonical table in 'soln' (and use 'grid' as
+ * our BFS queue), then transfer the table into 'grid'
+ * having shuffled the rows.
+ */
+ assert(w >= 2);
+ assert(w < lenof(groups));
+ group = groups[w].groups + random_upto(rs, groups[w].ngroups);
+ assert(group->order == w);
+ memset(soln, 0, a);
+ for (i = 0; i < w; i++)
+ soln[i] = i+1;
+ qh = qt = 0;
+ grid[qt++] = 1;
+ while (qh < qt) {+ digit *row, *newrow;
+
+ i = grid[qh++];
+ row = soln + (i-1)*w;
+
+ for (j = 0; j < group->ngens; j++) {+ int nri;
+ const char *gen = group->gens + j*w;
+
+ /*
+ * Apply each group generator to row, constructing a
+ * new row.
+ */
+ nri = FROMCHAR(gen[row[0]-1]); /* which row is it? */
+ newrow = soln + (nri-1)*w;
+ if (!newrow[0]) { /* not done yet */+ for (k = 0; k < w; k++)
+ newrow[k] = FROMCHAR(gen[row[k]-1]);
+ grid[qt++] = nri;
+ }
+ }
+ }
+ /* That's got the canonical table. Now shuffle it. */
+ for (i = 0; i < w; i++)
+ grid[i] = i+1;
+ shuffle(grid+1, w-1, sizeof(*grid), rs);
+ for (i = 1; i < w; i++)
+ for (j = 0; j < w; j++)
+ grid[(grid[i]-1)*w+(grid[j]-1)] = grid[soln[i*w+j]-1];
+ for (i = 0; i < w; i++)
+ grid[i] = i+1;
+
+ /*
+ * Remove entries one by one while the puzzle is still
+ * soluble at the appropriate difficulty level.
+ */
+ memcpy(soln, grid, a);
+
+ k = 0;
+ for (i = 1; i < w; i++)
+ for (j = 1; j < w; j++)
+ indices[k++] = i*w+j;
+ shuffle(indices, k, sizeof(indices), rs);
+
+ for (i = 0; i < k; i++) {+ memcpy(soln2, grid, a);
+ soln2[indices[i]] = 0;
+ if (solver(w, soln2, diff) <= diff)
+ grid[indices[i]] = 0;
+ }
+
+ /*
+ * Make sure the puzzle isn't too easy.
+ */
+ if (diff > 0) {+ memcpy(soln2, grid, a);
+ if (solver(w, soln2, diff-1) < diff)
+ continue; /* go round and try again */
+ }
+
+ /*
+ * Done.
+ */
+ break;
+ }
+
+ /*
+ * Encode the puzzle description.
+ */
+ desc = snewn(a*20, char);
+ p = encode_grid(desc, grid, a);
+ *p++ = '\0';
+ desc = sresize(desc, p - desc, char);
+
+ /*
+ * Encode the solution.
+ */
+ *aux = snewn(a+2, char);
+ (*aux)[0] = 'S';
+ for (i = 0; i < a; i++)
+ (*aux)[i+1] = TOCHAR(soln[i]);
+ (*aux)[a+1] = '\0';
+
+ sfree(grid);
+ sfree(soln);
+ sfree(soln2);
+ sfree(indices);
+
+ return desc;
+}
+
+/* ----------------------------------------------------------------------
+ * Gameplay.
+ */
+
+static char *validate_grid_desc(const char **pdesc, int range, int area)
+{+ const char *desc = *pdesc;
+ int squares = 0;
+ while (*desc && *desc != ',') {+ int n = *desc++;
+ if (n >= 'a' && n <= 'z') {+ squares += n - 'a' + 1;
+ } else if (n == '_') {+ /* do nothing */;
+ } else if (n > '0' && n <= '9') {+ int val = atoi(desc-1);
+ if (val < 1 || val > range)
+ return "Out-of-range number in game description";
+ squares++;
+ while (*desc >= '0' && *desc <= '9')
+ desc++;
+ } else
+ return "Invalid character in game description";
+ }
+
+ if (squares < area)
+ return "Not enough data to fill grid";
+
+ if (squares > area)
+ return "Too much data to fit in grid";
+ *pdesc = desc;
+ return NULL;
+}
+
+static char *validate_desc(game_params *params, char *desc)
+{+ int w = params->w, a = w*w;
+ const char *p = desc;
+
+ return validate_grid_desc(&p, w, a);
+}
+
+static char *spec_to_grid(char *desc, digit *grid, int area)
+{+ int i = 0;
+ while (*desc && *desc != ',') {+ int n = *desc++;
+ if (n >= 'a' && n <= 'z') {+ int run = n - 'a' + 1;
+ assert(i + run <= area);
+ while (run-- > 0)
+ grid[i++] = 0;
+ } else if (n == '_') {+ /* do nothing */;
+ } else if (n > '0' && n <= '9') {+ assert(i < area);
+ grid[i++] = atoi(desc-1);
+ while (*desc >= '0' && *desc <= '9')
+ desc++;
+ } else {+ assert(!"We can't get here");
+ }
+ }
+ assert(i == area);
+ return desc;
+}
+
+static game_state *new_game(midend *me, game_params *params, char *desc)
+{+ int w = params->w, a = w*w;
+ game_state *state = snew(game_state);
+ int i;
+
+ state->par = *params; /* structure copy */
+ state->grid = snewn(a, digit);
+ state->immutable = snewn(a, unsigned char);
+ state->pencil = snewn(a, int);
+ for (i = 0; i < a; i++) {+ state->grid[i] = 0;
+ state->immutable[i] = 0;
+ state->pencil[i] = 0;
+ }
+
+ desc = spec_to_grid(desc, state->grid, a);
+ for (i = 0; i < a; i++)
+ if (state->grid[i] != 0)
+ state->immutable[i] = TRUE;
+
+ state->completed = state->cheated = FALSE;
+
+ return state;
+}
+
+static game_state *dup_game(game_state *state)
+{+ int w = state->par.w, a = w*w;
+ game_state *ret = snew(game_state);
+
+ ret->par = state->par; /* structure copy */
+
+ ret->grid = snewn(a, digit);
+ ret->immutable = snewn(a, unsigned char);
+ ret->pencil = snewn(a, int);
+ memcpy(ret->grid, state->grid, a*sizeof(digit));
+ memcpy(ret->immutable, state->immutable, a*sizeof(unsigned char));
+ memcpy(ret->pencil, state->pencil, a*sizeof(int));
+
+ ret->completed = state->completed;
+ ret->cheated = state->cheated;
+
+ return ret;
+}
+
+static void free_game(game_state *state)
+{+ sfree(state->grid);
+ sfree(state->immutable);
+ sfree(state->pencil);
+ sfree(state);
+}
+
+static char *solve_game(game_state *state, game_state *currstate,
+ char *aux, char **error)
+{+ int w = state->par.w, a = w*w;
+ int i, ret;
+ digit *soln;
+ char *out;
+
+ if (aux)
+ return dupstr(aux);
+
+ soln = snewn(a, digit);
+ memcpy(soln, state->grid, a*sizeof(digit));
+
+ ret = solver(w, soln, DIFFCOUNT-1);
+
+ if (ret == diff_impossible) {+ *error = "No solution exists for this puzzle";
+ out = NULL;
+ } else if (ret == diff_ambiguous) {+ *error = "Multiple solutions exist for this puzzle";
+ out = NULL;
+ } else {+ out = snewn(a+2, char);
+ out[0] = 'S';
+ for (i = 0; i < a; i++)
+ out[i+1] = TOCHAR(soln[i]);
+ out[a+1] = '\0';
+ }
+
+ sfree(soln);
+ return out;
+}
+
+static int game_can_format_as_text_now(game_params *params)
+{+ return TRUE;
+}
+
+static char *game_text_format(game_state *state)
+{+ int w = state->par.w;
+ int x, y;
+ char *ret, *p, ch;
+
+ ret = snewn(2*w*w+1, char); /* leave room for terminating NUL */
+
+ p = ret;
+ for (y = 0; y < w; y++) {+ for (x = 0; x < w; x++) {+ digit d = state->grid[y*w+x];
+
+ if (d == 0) {+ ch = '.';
+ } else {+ ch = TOCHAR(d);
+ }
+
+ *p++ = ch;
+ if (x == w-1) {+ *p++ = '\n';
+ } else {+ *p++ = ' ';
+ }
+ }
+ }
+
+ assert(p - ret == 2*w*w);
+ *p = '\0';
+ return ret;
+}
+
+struct game_ui {+ /*
+ * These are the coordinates of the currently highlighted
+ * square on the grid, if hshow = 1.
+ */
+ int hx, hy;
+ /*
+ * This indicates whether the current highlight is a
+ * pencil-mark one or a real one.
+ */
+ int hpencil;
+ /*
+ * This indicates whether or not we're showing the highlight
+ * (used to be hx = hy = -1); important so that when we're
+ * using the cursor keys it doesn't keep coming back at a
+ * fixed position. When hshow = 1, pressing a valid number
+ * or letter key or Space will enter that number or letter in the grid.
+ */
+ int hshow;
+ /*
+ * This indicates whether we're using the highlight as a cursor;
+ * it means that it doesn't vanish on a keypress, and that it is
+ * allowed on immutable squares.
+ */
+ int hcursor;
+};
+
+static game_ui *new_ui(game_state *state)
+{+ game_ui *ui = snew(game_ui);
+
+ ui->hx = ui->hy = 1;
+ ui->hpencil = ui->hshow = ui->hcursor = 0;
+
+ return ui;
+}
+
+static void free_ui(game_ui *ui)
+{+ sfree(ui);
+}
+
+static char *encode_ui(game_ui *ui)
+{+ return NULL;
+}
+
+static void decode_ui(game_ui *ui, char *encoding)
+{+}
+
+static void game_changed_state(game_ui *ui, game_state *oldstate,
+ game_state *newstate)
+{+ int w = newstate->par.w;
+ /*
+ * We prevent pencil-mode highlighting of a filled square, unless
+ * we're using the cursor keys. So if the user has just filled in
+ * a square which we had a pencil-mode highlight in (by Undo, or
+ * by Redo, or by Solve), then we cancel the highlight.
+ */
+ if (ui->hshow && ui->hpencil && !ui->hcursor &&
+ newstate->grid[ui->hy * w + ui->hx] != 0) {+ ui->hshow = 0;
+ }
+}
+
+#define PREFERRED_TILESIZE 48
+#define TILESIZE (ds->tilesize)
+#define BORDER (TILESIZE / 2)
+#define GRIDEXTRA max((TILESIZE / 32),1)
+#define COORD(x) ((x)*TILESIZE + BORDER)
+#define FROMCOORD(x) (((x)+(TILESIZE-BORDER)) / TILESIZE - 1)
+
+#define FLASH_TIME 0.4F
+
+#define DF_HIGHLIGHT 0x0400
+#define DF_HIGHLIGHT_PENCIL 0x0200
+#define DF_IMMUTABLE 0x0100
+#define DF_DIGIT_MASK 0x001F
+
+#define EF_DIGIT_SHIFT 5
+#define EF_DIGIT_MASK ((1 << EF_DIGIT_SHIFT) - 1)
+#define EF_LEFT_SHIFT 0
+#define EF_RIGHT_SHIFT (3*EF_DIGIT_SHIFT)
+#define EF_LEFT_MASK ((1UL << (3*EF_DIGIT_SHIFT)) - 1UL)
+#define EF_RIGHT_MASK (EF_LEFT_MASK << EF_RIGHT_SHIFT)
+#define EF_LATIN (1UL << (6*EF_DIGIT_SHIFT))
+
+struct game_drawstate {+ int w, tilesize;
+ int started;
+ long *tiles, *pencil, *errors;
+ long *errtmp;
+};
+
+static int check_errors(game_state *state, long *errors)
+{+ int w = state->par.w, a = w*w;
+ digit *grid = state->grid;
+ int i, j, k, x, y, errs = FALSE;
+
+ if (errors)
+ for (i = 0; i < a; i++)
+ errors[i] = 0;
+
+ for (y = 0; y < w; y++) {+ unsigned long mask = 0, errmask = 0;
+ for (x = 0; x < w; x++) {+ unsigned long bit = 1UL << grid[y*w+x];
+ errmask |= (mask & bit);
+ mask |= bit;
+ }
+
+ if (mask != (1 << (w+1)) - (1 << 1)) {+ errs = TRUE;
+ errmask &= ~1UL;
+ if (errors) {+ for (x = 0; x < w; x++)
+ if (errmask & (1UL << grid[y*w+x]))
+ errors[y*w+x] |= EF_LATIN;
+ }
+ }
+ }
+
+ for (x = 0; x < w; x++) {+ unsigned long mask = 0, errmask = 0;
+ for (y = 0; y < w; y++) {+ unsigned long bit = 1UL << grid[y*w+x];
+ errmask |= (mask & bit);
+ mask |= bit;
+ }
+
+ if (mask != (1 << (w+1)) - (1 << 1)) {+ errs = TRUE;
+ errmask &= ~1UL;
+ if (errors) {+ for (y = 0; y < w; y++)
+ if (errmask & (1UL << grid[y*w+x]))
+ errors[y*w+x] |= EF_LATIN;
+ }
+ }
+ }
+
+ for (i = 1; i < w; i++)
+ for (j = 1; j < w; j++)
+ for (k = 1; k < w; k++)
+ if (grid[i*w+j] && grid[j*w+k] &&
+ grid[(grid[i*w+j]-1)*w+k] &&
+ grid[i*w+(grid[j*w+k]-1)] &&
+ grid[(grid[i*w+j]-1)*w+k] != grid[i*w+(grid[j*w+k]-1)]) {+ if (errors) {+ int a = i+1, b = j+1, c = k+1;
+ int ab = grid[i*w+j], bc = grid[j*w+k];
+ int left = (ab-1)*w+(c-1), right = (a-1)*w+(bc-1);
+ /*
+ * If the appropriate error slot is already
+ * used for one of the squares, we don't
+ * fill either of them.
+ */
+ if (!(errors[left] & EF_LEFT_MASK) &&
+ !(errors[right] & EF_RIGHT_MASK)) {+ long err;
+ err = a;
+ err = (err << EF_DIGIT_SHIFT) | b;
+ err = (err << EF_DIGIT_SHIFT) | c;
+ errors[left] |= err << EF_LEFT_SHIFT;
+ errors[right] |= err << EF_RIGHT_SHIFT;
+ }
+ }
+ errs = TRUE;
+ }
+
+ return errs;
+}
+
+static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
+ int x, int y, int button)
+{+ int w = state->par.w;
+ int tx, ty;
+ char buf[80];
+
+ button &= ~MOD_MASK;
+
+ tx = FROMCOORD(x);
+ ty = FROMCOORD(y);
+
+ if (tx > 0 && tx < w && ty > 0 && ty < w) {+ if (button == LEFT_BUTTON) {+ if (tx == ui->hx && ty == ui->hy &&
+ ui->hshow && ui->hpencil == 0) {+ ui->hshow = 0;
+ } else {+ ui->hx = tx;
+ ui->hy = ty;
+ ui->hshow = !state->immutable[ty*w+tx];
+ ui->hpencil = 0;
+ }
+ ui->hcursor = 0;
+ return ""; /* UI activity occurred */
+ }
+ if (button == RIGHT_BUTTON) {+ /*
+ * Pencil-mode highlighting for non filled squares.
+ */
+ if (state->grid[ty*w+tx] == 0) {+ if (tx == ui->hx && ty == ui->hy &&
+ ui->hshow && ui->hpencil) {+ ui->hshow = 0;
+ } else {+ ui->hpencil = 1;
+ ui->hx = tx;
+ ui->hy = ty;
+ ui->hshow = 1;
+ }
+ } else {+ ui->hshow = 0;
+ }
+ ui->hcursor = 0;
+ return ""; /* UI activity occurred */
+ }
+ }
+ if (IS_CURSOR_MOVE(button)) {+ ui->hx--; ui->hy--;
+ move_cursor(button, &ui->hx, &ui->hy, w-1, w-1, 0);
+ ui->hx++; ui->hy++;
+ ui->hshow = ui->hcursor = 1;
+ return "";
+ }
+ if (ui->hshow &&
+ (button == CURSOR_SELECT)) {+ ui->hpencil = 1 - ui->hpencil;
+ ui->hcursor = 1;
+ return "";
+ }
+
+ if (ui->hshow &&
+ ((ISCHAR(button) && FROMCHAR(button) <= w) ||
+ button == CURSOR_SELECT2 || button == '\b')) {+ int n = FROMCHAR(button);
+ if (button == CURSOR_SELECT2 || button == '\b')
+ n = 0;
+
+ /*
+ * Can't make pencil marks in a filled square. This can only
+ * become highlighted if we're using cursor keys.
+ */
+ if (ui->hpencil && state->grid[ui->hy*w+ui->hx])
+ return NULL;
+
+ /*
+ * Can't do anything to an immutable square.
+ */
+ if (state->immutable[ui->hy*w+ui->hx])
+ return NULL;
+
+ sprintf(buf, "%c%d,%d,%d",
+ (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
+
+ if (!ui->hcursor) ui->hshow = 0;
+
+ return dupstr(buf);
+ }
+
+ if (button == 'M' || button == 'm')
+ return dupstr("M");+
+ return NULL;
+}
+
+static game_state *execute_move(game_state *from, char *move)
+{+ int w = from->par.w, a = w*w;
+ game_state *ret;
+ int x, y, i, n;
+
+ if (move[0] == 'S') {+ ret = dup_game(from);
+ ret->completed = ret->cheated = TRUE;
+
+ for (i = 0; i < a; i++) {+ if (!ISCHAR(move[i+1]) || FROMCHAR(move[i+1]) > w) {+ free_game(ret);
+ return NULL;
+ }
+ ret->grid[i] = FROMCHAR(move[i+1]);
+ ret->pencil[i] = 0;
+ }
+
+ if (move[a+1] != '\0') {+ free_game(ret);
+ return NULL;
+ }
+
+ return ret;
+ } else if ((move[0] == 'P' || move[0] == 'R') &&
+ sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
+ x >= 0 && x < w && y >= 0 && y < w && n >= 0 && n <= w) {+ if (from->immutable[y*w+x])
+ return NULL;
+
+ ret = dup_game(from);
+ if (move[0] == 'P' && n > 0) {+ ret->pencil[y*w+x] ^= 1 << n;
+ } else {+ ret->grid[y*w+x] = n;
+ ret->pencil[y*w+x] = 0;
+
+ if (!ret->completed && !check_errors(ret, NULL))
+ ret->completed = TRUE;
+ }
+ return ret;
+ } else if (move[0] == 'M') {+ /*
+ * Fill in absolutely all pencil marks everywhere. (I
+ * wouldn't use this for actual play, but it's a handy
+ * starting point when following through a set of
+ * diagnostics output by the standalone solver.)
+ */
+ ret = dup_game(from);
+ for (i = 0; i < a; i++) {+ if (!ret->grid[i])
+ ret->pencil[i] = (1 << (w+1)) - (1 << 1);
+ }
+ return ret;
+ } else
+ return NULL; /* couldn't parse move string */
+}
+
+/* ----------------------------------------------------------------------
+ * Drawing routines.
+ */
+
+#define SIZE(w) ((w) * TILESIZE + 2*BORDER)
+
+static void game_compute_size(game_params *params, int tilesize,
+ int *x, int *y)
+{+ /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+ struct { int tilesize; } ads, *ds = &ads;+ ads.tilesize = tilesize;
+
+ *x = *y = SIZE(params->w);
+}
+
+static void game_set_size(drawing *dr, game_drawstate *ds,
+ game_params *params, int tilesize)
+{+ ds->tilesize = tilesize;
+}
+
+static float *game_colours(frontend *fe, int *ncolours)
+{+ float *ret = snewn(3 * NCOLOURS, float);
+
+ frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
+
+ ret[COL_GRID * 3 + 0] = 0.0F;
+ ret[COL_GRID * 3 + 1] = 0.0F;
+ ret[COL_GRID * 3 + 2] = 0.0F;
+
+ ret[COL_IDENTITY * 3 + 0] = 0.89F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_IDENTITY * 3 + 1] = 0.89F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_IDENTITY * 3 + 2] = 0.89F * ret[COL_BACKGROUND * 3 + 2];
+
+ ret[COL_USER * 3 + 0] = 0.0F;
+ ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_USER * 3 + 2] = 0.0F;
+
+ ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
+
+ ret[COL_ERROR * 3 + 0] = 1.0F;
+ ret[COL_ERROR * 3 + 1] = 0.0F;
+ ret[COL_ERROR * 3 + 2] = 0.0F;
+
+ ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
+
+ *ncolours = NCOLOURS;
+ return ret;
+}
+
+static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
+{+ int w = state->par.w, a = w*w;
+ struct game_drawstate *ds = snew(struct game_drawstate);
+ int i;
+
+ ds->w = w;
+ ds->tilesize = 0;
+ ds->started = FALSE;
+ ds->tiles = snewn(a, long);
+ ds->pencil = snewn(a, long);
+ ds->errors = snewn(a, long);
+ for (i = 0; i < a; i++)
+ ds->tiles[i] = ds->pencil[i] = -1;
+ ds->errtmp = snewn(a, long);
+
+ return ds;
+}
+
+static void game_free_drawstate(drawing *dr, game_drawstate *ds)
+{+ sfree(ds->tiles);
+ sfree(ds->pencil);
+ sfree(ds->errors);
+ sfree(ds->errtmp);
+ sfree(ds);
+}
+
+void draw_tile(drawing *dr, game_drawstate *ds, int x, int y, long tile,
+ long pencil, long error)
+{+ int w = ds->w /* , a = w*w */;
+ int tx, ty, tw, th;
+ int cx, cy, cw, ch;
+ char str[64];
+
+ tx = BORDER + x * TILESIZE + 1;
+ ty = BORDER + y * TILESIZE + 1;
+
+ cx = tx;
+ cy = ty;
+ cw = tw = TILESIZE-1;
+ ch = th = TILESIZE-1;
+
+ clip(dr, cx, cy, cw, ch);
+
+ /* background needs erasing */
+ draw_rect(dr, cx, cy, cw, ch,
+ (tile & DF_HIGHLIGHT) ? COL_HIGHLIGHT :
+ (x == 0 || y == 0) ? COL_IDENTITY : COL_BACKGROUND);
+
+ /* pencil-mode highlight */
+ if (tile & DF_HIGHLIGHT_PENCIL) {+ int coords[6];
+ coords[0] = cx;
+ coords[1] = cy;
+ coords[2] = cx+cw/2;
+ coords[3] = cy;
+ coords[4] = cx;
+ coords[5] = cy+ch/2;
+ draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
+ }
+
+ /* new number needs drawing? */
+ if (tile & DF_DIGIT_MASK) {+ str[1] = '\0';
+ str[0] = TOCHAR(tile & DF_DIGIT_MASK);
+ draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/2,
+ FONT_VARIABLE, TILESIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
+ (error & EF_LATIN) ? COL_ERROR :
+ (tile & DF_IMMUTABLE) ? COL_GRID : COL_USER, str);
+
+ if (error & EF_LEFT_MASK) {+ int a = (error >> (EF_LEFT_SHIFT+2*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+ int b = (error >> (EF_LEFT_SHIFT+1*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+ int c = (error >> (EF_LEFT_SHIFT ))&EF_DIGIT_MASK;
+ char buf[10];
+ sprintf(buf, "(%c%c)%c", TOCHAR(a), TOCHAR(b), TOCHAR(c));
+ draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/6,
+ FONT_VARIABLE, TILESIZE/6, ALIGN_VCENTRE | ALIGN_HCENTRE,
+ COL_ERROR, buf);
+ }
+ if (error & EF_RIGHT_MASK) {+ int a = (error >> (EF_RIGHT_SHIFT+2*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+ int b = (error >> (EF_RIGHT_SHIFT+1*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+ int c = (error >> (EF_RIGHT_SHIFT ))&EF_DIGIT_MASK;
+ char buf[10];
+ sprintf(buf, "%c(%c%c)", TOCHAR(a), TOCHAR(b), TOCHAR(c));
+ draw_text(dr, tx + TILESIZE/2, ty + TILESIZE - TILESIZE/6,
+ FONT_VARIABLE, TILESIZE/6, ALIGN_VCENTRE | ALIGN_HCENTRE,
+ COL_ERROR, buf);
+ }
+ } else {+ int i, j, npencil;
+ int pl, pr, pt, pb;
+ float bestsize;
+ int pw, ph, minph, pbest, fontsize;
+
+ /* Count the pencil marks required. */
+ for (i = 1, npencil = 0; i <= w; i++)
+ if (pencil & (1 << i))
+ npencil++;
+ if (npencil) {+
+ minph = 2;
+
+ /*
+ * Determine the bounding rectangle within which we're going
+ * to put the pencil marks.
+ */
+ /* Start with the whole square */
+ pl = tx + GRIDEXTRA;
+ pr = pl + TILESIZE - GRIDEXTRA;
+ pt = ty + GRIDEXTRA;
+ pb = pt + TILESIZE - GRIDEXTRA;
+
+ /*
+ * We arrange our pencil marks in a grid layout, with
+ * the number of rows and columns adjusted to allow the
+ * maximum font size.
+ *
+ * So now we work out what the grid size ought to be.
+ */
+ bestsize = 0.0;
+ pbest = 0;
+ /* Minimum */
+ for (pw = 3; pw < max(npencil,4); pw++) {+ float fw, fh, fs;
+
+ ph = (npencil + pw - 1) / pw;
+ ph = max(ph, minph);
+ fw = (pr - pl) / (float)pw;
+ fh = (pb - pt) / (float)ph;
+ fs = min(fw, fh);
+ if (fs > bestsize) {+ bestsize = fs;
+ pbest = pw;
+ }
+ }
+ assert(pbest > 0);
+ pw = pbest;
+ ph = (npencil + pw - 1) / pw;
+ ph = max(ph, minph);
+
+ /*
+ * Now we've got our grid dimensions, work out the pixel
+ * size of a grid element, and round it to the nearest
+ * pixel. (We don't want rounding errors to make the
+ * grid look uneven at low pixel sizes.)
+ */
+ fontsize = min((pr - pl) / pw, (pb - pt) / ph);
+
+ /*
+ * Centre the resulting figure in the square.
+ */
+ pl = tx + (TILESIZE - fontsize * pw) / 2;
+ pt = ty + (TILESIZE - fontsize * ph) / 2;
+
+ /*
+ * Now actually draw the pencil marks.
+ */
+ for (i = 1, j = 0; i <= w; i++)
+ if (pencil & (1 << i)) {+ int dx = j % pw, dy = j / pw;
+
+ str[1] = '\0';
+ str[0] = TOCHAR(i);
+ draw_text(dr, pl + fontsize * (2*dx+1) / 2,
+ pt + fontsize * (2*dy+1) / 2,
+ FONT_VARIABLE, fontsize,
+ ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
+ j++;
+ }
+ }
+ }
+
+ unclip(dr);
+
+ draw_update(dr, cx, cy, cw, ch);
+}
+
+static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
+ game_state *state, int dir, game_ui *ui,
+ float animtime, float flashtime)
+{+ int w = state->par.w /*, a = w*w */;
+ int x, y;
+
+ if (!ds->started) {+ /*
+ * 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.
+ */
+ draw_rect(dr, 0, 0, SIZE(w), SIZE(w), COL_BACKGROUND);
+
+ /*
+ * Big containing rectangle.
+ */
+ draw_rect(dr, COORD(0) - GRIDEXTRA, COORD(0) - GRIDEXTRA,
+ w*TILESIZE+1+GRIDEXTRA*2, w*TILESIZE+1+GRIDEXTRA*2,
+ COL_GRID);
+
+ draw_update(dr, 0, 0, SIZE(w), SIZE(w));
+
+ ds->started = TRUE;
+ }
+
+ check_errors(state, ds->errtmp);
+
+ for (y = 0; y < w; y++) {+ for (x = 0; x < w; x++) {+ long tile = 0L, pencil = 0L, error;
+
+ if (state->grid[y*w+x])
+ tile = state->grid[y*w+x];
+ else
+ pencil = (long)state->pencil[y*w+x];
+
+ if (state->immutable[y*w+x])
+ tile |= DF_IMMUTABLE;
+
+ if (ui->hshow && ui->hx == x && ui->hy == y)
+ tile |= (ui->hpencil ? DF_HIGHLIGHT_PENCIL : DF_HIGHLIGHT);
+
+ if (flashtime > 0 &&
+ (flashtime <= FLASH_TIME/3 ||
+ flashtime >= FLASH_TIME*2/3))
+ tile |= DF_HIGHLIGHT; /* completion flash */
+
+ error = ds->errtmp[y*w+x];
+
+ if (ds->tiles[y*w+x] != tile ||
+ ds->pencil[y*w+x] != pencil ||
+ ds->errors[y*w+x] != error) {+ ds->tiles[y*w+x] = tile;
+ ds->pencil[y*w+x] = pencil;
+ ds->errors[y*w+x] = error;
+ draw_tile(dr, ds, x, y, tile, pencil, error);
+ }
+ }
+ }
+}
+
+static float game_anim_length(game_state *oldstate, game_state *newstate,
+ int dir, game_ui *ui)
+{+ return 0.0F;
+}
+
+static float game_flash_length(game_state *oldstate, game_state *newstate,
+ int dir, game_ui *ui)
+{+ if (!oldstate->completed && newstate->completed &&
+ !oldstate->cheated && !newstate->cheated)
+ return FLASH_TIME;
+ return 0.0F;
+}
+
+static int game_timing_state(game_state *state, game_ui *ui)
+{+ if (state->completed)
+ return FALSE;
+ return TRUE;
+}
+
+static void game_print_size(game_params *params, float *x, float *y)
+{+ int pw, ph;
+
+ /*
+ * We use 9mm squares by default, like Solo.
+ */
+ game_compute_size(params, 900, &pw, &ph);
+ *x = pw / 100.0F;
+ *y = ph / 100.0F;
+}
+
+static void game_print(drawing *dr, game_state *state, int tilesize)
+{+ int w = state->par.w;
+ int ink = print_mono_colour(dr, 0);
+ int ehighlight = print_grey_colour(dr, 0.90F);
+ int x, y;
+
+ /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+ game_drawstate ads, *ds = &ads;
+ game_set_size(dr, ds, NULL, tilesize);
+
+ /*
+ * Highlight the identity row and column.
+ */
+ for (x = 1; x < w; x++)
+ draw_rect(dr, BORDER + x*TILESIZE, BORDER,
+ TILESIZE, TILESIZE, ehighlight);
+ for (y = 0; y < w; y++)
+ draw_rect(dr, BORDER, BORDER + y*TILESIZE,
+ TILESIZE, TILESIZE, ehighlight);
+
+ /*
+ * Border.
+ */
+ print_line_width(dr, 3 * TILESIZE / 40);
+ draw_rect_outline(dr, BORDER, BORDER, w*TILESIZE, w*TILESIZE, ink);
+
+ /*
+ * Main grid.
+ */
+ for (x = 1; x < w; x++) {+ print_line_width(dr, TILESIZE / 40);
+ draw_line(dr, BORDER+x*TILESIZE, BORDER,
+ BORDER+x*TILESIZE, BORDER+w*TILESIZE, ink);
+ }
+ for (y = 1; y < w; y++) {+ print_line_width(dr, TILESIZE / 40);
+ draw_line(dr, BORDER, BORDER+y*TILESIZE,
+ BORDER+w*TILESIZE, BORDER+y*TILESIZE, ink);
+ }
+
+ /*
+ * Numbers.
+ */
+ for (y = 0; y < w; y++)
+ for (x = 0; x < w; x++)
+ if (state->grid[y*w+x]) {+ char str[2];
+ str[1] = '\0';
+ str[0] = TOCHAR(state->grid[y*w+x]);
+ draw_text(dr, BORDER + x*TILESIZE + TILESIZE/2,
+ BORDER + y*TILESIZE + TILESIZE/2,
+ FONT_VARIABLE, TILESIZE/2,
+ ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+ }
+}
+
+#ifdef COMBINED
+#define thegame group
+#endif
+
+const struct game thegame = {+ "Group", NULL, NULL,
+ default_params,
+ game_fetch_preset,
+ decode_params,
+ encode_params,
+ free_params,
+ dup_params,
+ TRUE, game_configure, custom_params,
+ validate_params,
+ new_game_desc,
+ validate_desc,
+ new_game,
+ dup_game,
+ free_game,
+ TRUE, solve_game,
+ TRUE, game_can_format_as_text_now, game_text_format,
+ new_ui,
+ free_ui,
+ encode_ui,
+ decode_ui,
+ game_changed_state,
+ interpret_move,
+ execute_move,
+ PREFERRED_TILESIZE, game_compute_size, game_set_size,
+ game_colours,
+ game_new_drawstate,
+ game_free_drawstate,
+ game_redraw,
+ game_anim_length,
+ game_flash_length,
+ TRUE, FALSE, game_print_size, game_print,
+ FALSE, /* wants_statusbar */
+ FALSE, game_timing_state,
+ REQUIRE_RBUTTON | REQUIRE_NUMPAD, /* flags */
+};
+
+#ifdef STANDALONE_SOLVER
+
+#include <stdarg.h>
+
+int main(int argc, char **argv)
+{+ game_params *p;
+ game_state *s;
+ char *id = NULL, *desc, *err;
+ digit *grid;
+ int grade = FALSE;
+ int ret, diff, really_show_working = FALSE;
+
+ while (--argc > 0) {+ char *p = *++argv;
+ if (!strcmp(p, "-v")) {+ really_show_working = TRUE;
+ } else 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);
+
+ grid = snewn(p->w * p->w, digit);
+
+ /*
+ * When solving a Normal 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 */
+ solver_show_working = FALSE;
+ for (diff = 0; diff < DIFFCOUNT; diff++) {+ memcpy(grid, s->grid, p->w * p->w);
+ ret = solver(p->w, grid, diff);
+ if (ret <= diff)
+ break;
+ }
+
+ if (diff == DIFFCOUNT) {+ if (grade)
+ printf("Difficulty rating: ambiguous\n");+ else
+ printf("Unable to find a unique solution\n");+ } else {+ if (grade) {+ if (ret == diff_impossible)
+ printf("Difficulty rating: impossible (no solution exists)\n");+ else
+ printf("Difficulty rating: %s\n", group_diffnames[ret]);+ } else {+ solver_show_working = really_show_working;
+ memcpy(grid, s->grid, p->w * p->w);
+ ret = solver(p->w, grid, diff);
+ if (ret != diff)
+ printf("Puzzle is inconsistent\n");+ else {+ memcpy(s->grid, grid, p->w * p->w);
+ fputs(game_text_format(s), stdout);
+ }
+ }
+ }
+
+ return 0;
+}
+
+#endif
+
+/* vim: set shiftwidth=4 tabstop=8: */
--- /dev/null
+++ b/unfinished/group.gap
@@ -1,0 +1,97 @@
+# run this file with
+# gap -b -q < /dev/null group.gap | perl -pe 's/\\\n//s' | indent -kr
+
+Print("/* ----- data generated by group.gap begins ----- */\n\n");+Print("struct group {\n unsigned long autosize;\n");+Print(" int order, ngens;\n const char *gens;\n};\n");+Print("struct groups {\n int ngroups;\n");+Print(" const struct group *groups;\n};\n\n");+Print("static const struct group groupdata[] = {\n");+offsets := [0];
+offset := 0;
+for n in [2..31] do
+ Print(" /* order ", n, " */\n");+ for G in AllSmallGroups(n) do
+
+ # Construct a representation of the group G as a subgroup
+ # of a permutation group, and find its generators in that
+ # group.
+
+ # GAP has the 'IsomorphismPermGroup' function, but I don't want
+ # to use it because it doesn't guarantee that the permutation
+ # representation of the group forms a Cayley table. For example,
+ # C_4 could be represented as a subgroup of S_4 in many ways,
+ # and not all of them work: the group generated by (12) and (34)
+ # is clearly isomorphic to C_4 but its four elements do not form
+ # a Cayley table. The group generated by (12)(34) and (13)(24)
+ # is OK, though.
+ #
+ # Hence I construct the permutation representation _as_ the
+ # Cayley table, and then pick generators of that. This
+ # guarantees that when we rebuild the full group by BFS in
+ # group.c, we will end up with the right thing.
+
+ ge := Elements(G);
+ gi := [];
+ for g in ge do
+ gr := [];
+ for h in ge do
+ k := g*h;
+ for i in [1..n] do
+ if k = ge[i] then
+ Add(gr, i);
+ fi;
+ od;
+ od;
+ Add(gi, PermList(gr));
+ od;
+
+ # GAP has the 'GeneratorsOfGroup' function, but we don't want to
+ # use it because it's bad at picking generators - it thinks the
+ # generators of C_4 are [ (1,2)(3,4), (1,3,2,4) ] and that those
+ # of C_6 are [ (1,2,3)(4,5,6), (1,4)(2,5)(3,6) ] !
+
+ gl := ShallowCopy(Elements(gi));
+ Sort(gl, function(v,w) return Order(v) > Order(w); end);
+
+ gens := [];
+ for x in gl do
+ if gens = [] or not (x in gp) then
+ Add(gens, x);
+ gp := GroupWithGenerators(gens);
+ fi;
+ od;
+
+ # Construct the C representation of the group generators.
+ s := [];
+ for x in gens do
+ if Size(s) > 0 then
+ Add(s, '"');
+ Add(s, ' ');
+ Add(s, '"');
+ fi;
+ sep := "\\0";
+ for i in ListPerm(x) do
+ chars := "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+ Add(s, chars[i]);
+ od;
+ od;
+ s := JoinStringsWithSeparator([" {", String(Size(AutomorphismGroup(G))),+ "L, ", String(Size(G)),
+ ", ", String(Size(gens)),
+ ", \"", s, "\"},\n"],"");
+ Print(s);
+ offset := offset + 1;
+ od;
+ Add(offsets, offset);
+od;
+Print("};\n\nstatic const struct groups groups[] = {\n");+Print(" {0, NULL}, /* trivial case: 0 */\n");+Print(" {0, NULL}, /* trivial case: 1 */\n");+n := 2;
+for i in [1..Size(offsets)-1] do
+ Print(" {", offsets[i+1] - offsets[i], ", groupdata+",+ offsets[i], "}, /* ", i+1, " */\n");
+od;
+Print("};\n\n/* ----- data generated by group.gap ends ----- */\n");+quit;