From: simon Date: Wed, 30 Dec 2009 16:53:36 +0000 (+0000) Subject: New puzzle in 'unfinished'. Essentially, Sudoku for group theorists: X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/commitdiff_plain/d8fa223c0f1a18e94c8d1fbb1f87cfd6f933504b 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 :-) git-svn-id: svn://svn.tartarus.org/sgt/puzzles@8800 cda61777-01e9-0310-a592-d414129be87e --- diff --git a/unfinished/group.R b/unfinished/group.R new file mode 100644 index 0000000..16cb41b --- /dev/null +++ b/unfinished/group.R @@ -0,0 +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 diff --git a/unfinished/group.c b/unfinished/group.c new file mode 100644 index 0000000..142654c --- /dev/null +++ b/unfinished/group.c @@ -0,0 +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 +#include +#include +#include +#include +#include + +#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<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 + +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] \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: */ diff --git a/unfinished/group.gap b/unfinished/group.gap new file mode 100644 index 0000000..de916ba --- /dev/null +++ b/unfinished/group.gap @@ -0,0 +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;