ref: 7ada9a5742dd4766cc42909ac01bbb2505f74e47
dir: /solo.c/
/*
* solo.c: the number-placing puzzle most popularly known as `Sudoku'.
*
* TODO:
*
* - reports from users are that `Trivial'-mode puzzles are still
* rather hard compared to newspapers' easy ones, so some better
* low-end difficulty grading would be nice
* + it's possible that really easy puzzles always have
* _several_ things you can do, so don't make you hunt too
* hard for the one deduction you can currently make
* + it's also possible that easy puzzles require fewer
* cross-eliminations: perhaps there's a higher incidence of
* things you can deduce by looking only at (say) rows,
* rather than things you have to check both rows and columns
* for
* + but really, what I need to do is find some really easy
* puzzles and _play_ them, to see what's actually easy about
* them
* + while I'm revamping this area, filling in the _last_
* number in a nearly-full row or column should certainly be
* permitted even at the lowest difficulty level.
* + also Alex noticed that `Basic' grids requiring numeric
* elimination are actually very hard, so I wonder if a
* difficulty gradation between that and positional-
* elimination-only might be in order
* + but it's not good to have _too_ many difficulty levels, or
* it'll take too long to randomly generate a given level.
*
* - it might still be nice to do some prioritisation on the
* removal of numbers from the grid
* + one possibility is to try to minimise the maximum number
* of filled squares in any block, which in particular ought
* to enforce never leaving a completely filled block in the
* puzzle as presented.
*
* - alternative interface modes
* + sudoku.com's Windows program has a palette of possible
* entries; you select a palette entry first and then click
* on the square you want it to go in, thus enabling
* mouse-only play. Useful for PDAs! I don't think it's
* actually incompatible with the current highlight-then-type
* approach: you _either_ highlight a palette entry and then
* click, _or_ you highlight a square and then type. At most
* one thing is ever highlighted at a time, so there's no way
* to confuse the two.
* + then again, I don't actually like sudoku.com's interface;
* it's too much like a paint package whereas I prefer to
* think of Solo as a text editor.
* + another PDA-friendly possibility is a drag interface:
* _drag_ numbers from the palette into the grid squares.
* Thought experiments suggest I'd prefer that to the
* sudoku.com approach, but I haven't actually tried it.
*/
/*
* Solo puzzles need to be square overall (since each row and each
* column must contain one of every digit), but they need not be
* subdivided the same way internally. I am going to adopt a
* convention whereby I _always_ refer to `r' as the number of rows
* of _big_ divisions, and `c' as the number of columns of _big_
* divisions. Thus, a 2c by 3r puzzle looks something like this:
*
* 4 5 1 | 2 6 3
* 6 3 2 | 5 4 1
* ------+------ (Of course, you can't subdivide it the other way
* 1 4 5 | 6 3 2 or you'll get clashes; observe that the 4 in the
* 3 2 6 | 4 1 5 top left would conflict with the 4 in the second
* ------+------ box down on the left-hand side.)
* 5 1 4 | 3 2 6
* 2 6 3 | 1 5 4
*
* The need for a strong naming convention should now be clear:
* each small box is two rows of digits by three columns, while the
* overall puzzle has three rows of small boxes by two columns. So
* I will (hopefully) consistently use `r' to denote the number of
* rows _of small boxes_ (here 3), which is also the number of
* columns of digits in each small box; and `c' vice versa (here
* 2).
*
* I'm also going to choose arbitrarily to list c first wherever
* possible: the above is a 2x3 puzzle, not a 3x2 one.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#ifdef NO_TGMATH_H
# include <math.h>
#else
# include <tgmath.h>
#endif
#ifdef STANDALONE_SOLVER
#include <stdarg.h>
static int solver_show_working, solver_recurse_depth;
#endif
#include "puzzles.h"
/*
* To save space, I store digits internally as unsigned char. This
* imposes a hard limit of 255 on the order of the puzzle. Since
* even a 5x5 takes unacceptably long to generate, I don't see this
* as a serious limitation unless something _really_ impressive
* happens in computing technology; but here's a typedef anyway for
* general good practice.
*/
typedef unsigned char digit;
#define ORDER_MAX 255
#define PREFERRED_TILE_SIZE 48
#define TILE_SIZE (ds->tilesize)
#define BORDER (TILE_SIZE / 2)
#define GRIDEXTRA max((TILE_SIZE / 32),1)
#define FLASH_TIME 0.4F
enum { SYMM_NONE, SYMM_ROT2, SYMM_ROT4, SYMM_REF2, SYMM_REF2D, SYMM_REF4,
SYMM_REF4D, SYMM_REF8 };
enum { DIFF_BLOCK,
DIFF_SIMPLE, DIFF_INTERSECT, DIFF_SET, DIFF_EXTREME, DIFF_RECURSIVE,
DIFF_AMBIGUOUS, DIFF_IMPOSSIBLE };
enum { DIFF_KSINGLE, DIFF_KMINMAX, DIFF_KSUMS, DIFF_KINTERSECT };
enum {
COL_BACKGROUND,
COL_XDIAGONALS,
COL_GRID,
COL_CLUE,
COL_USER,
COL_HIGHLIGHT,
COL_ERROR,
COL_PENCIL,
COL_KILLER,
NCOLOURS
};
/*
* To determine all possible ways to reach a given sum by adding two or
* three numbers from 1..9, each of which occurs exactly once in the sum,
* these arrays contain a list of bitmasks for each sum value, where if
* bit N is set, it means that N occurs in the sum. Each list is
* terminated by a zero if it is shorter than the size of the array.
*/
#define MAX_2SUMS 5
#define MAX_3SUMS 8
#define MAX_4SUMS 12
static unsigned long sum_bits2[18][MAX_2SUMS];
static unsigned long sum_bits3[25][MAX_3SUMS];
static unsigned long sum_bits4[31][MAX_4SUMS];
static int find_sum_bits(unsigned long *array, int idx, int value_left,
int addends_left, int min_addend,
unsigned long bitmask_so_far)
{
int i;
assert(addends_left >= 2);
for (i = min_addend; i < value_left; i++) {
unsigned long new_bitmask = bitmask_so_far | (1L << i);
assert(bitmask_so_far != new_bitmask);
if (addends_left == 2) {
int j = value_left - i;
if (j <= i)
break;
if (j > 9)
continue;
array[idx++] = new_bitmask | (1L << j);
} else
idx = find_sum_bits(array, idx, value_left - i,
addends_left - 1, i + 1,
new_bitmask);
}
return idx;
}
static void precompute_sum_bits(void)
{
int i;
for (i = 3; i < 31; i++) {
int j;
if (i < 18) {
j = find_sum_bits(sum_bits2[i], 0, i, 2, 1, 0);
assert (j <= MAX_2SUMS);
if (j < MAX_2SUMS)
sum_bits2[i][j] = 0;
}
if (i < 25) {
j = find_sum_bits(sum_bits3[i], 0, i, 3, 1, 0);
assert (j <= MAX_3SUMS);
if (j < MAX_3SUMS)
sum_bits3[i][j] = 0;
}
j = find_sum_bits(sum_bits4[i], 0, i, 4, 1, 0);
assert (j <= MAX_4SUMS);
if (j < MAX_4SUMS)
sum_bits4[i][j] = 0;
}
}
struct game_params {
/*
* For a square puzzle, `c' and `r' indicate the puzzle
* parameters as described above.
*
* A jigsaw-style puzzle is indicated by r==1, in which case c
* can be whatever it likes (there is no constraint on
* compositeness - a 7x7 jigsaw sudoku makes perfect sense).
*/
int c, r, symm, diff, kdiff;
bool xtype; /* require all digits in X-diagonals */
bool killer;
};
struct block_structure {
int refcount;
/*
* For text formatting, we do need c and r here.
*/
int c, r, area;
/*
* For any square index, whichblock[i] gives its block index.
*
* For 0 <= b,i < cr, blocks[b][i] gives the index of the ith
* square in block b. nr_squares[b] gives the number of squares
* in block b (also the number of valid elements in blocks[b]).
*
* blocks_data holds the data pointed to by blocks.
*
* nr_squares may be NULL for block structures where all blocks are
* the same size.
*/
int *whichblock, **blocks, *nr_squares, *blocks_data;
int nr_blocks, max_nr_squares;
#ifdef STANDALONE_SOLVER
/*
* Textual descriptions of each block. For normal Sudoku these
* are of the form "(1,3)"; for jigsaw they are "starting at
* (5,7)". So the sensible usage in both cases is to say
* "elimination within block %s" with one of these strings.
*
* Only blocknames itself needs individually freeing; it's all
* one block.
*/
char **blocknames;
#endif
};
struct game_state {
/*
* For historical reasons, I use `cr' to denote the overall
* width/height of the puzzle. It was a natural notation when
* all puzzles were divided into blocks in a grid, but doesn't
* really make much sense given jigsaw puzzles. However, the
* obvious `n' is heavily used in the solver to describe the
* index of a number being placed, so `cr' will have to stay.
*/
int cr;
struct block_structure *blocks;
struct block_structure *kblocks; /* Blocks for killer puzzles. */
bool xtype, killer;
digit *grid, *kgrid;
bool *pencil; /* c*r*c*r elements */
bool *immutable; /* marks which digits are clues */
bool completed, cheated;
};
static game_params *default_params(void)
{
game_params *ret = snew(game_params);
ret->c = ret->r = 3;
ret->xtype = false;
ret->killer = false;
ret->symm = SYMM_ROT2; /* a plausible default */
ret->diff = DIFF_BLOCK; /* so is this */
ret->kdiff = DIFF_KINTERSECT; /* so is this */
return ret;
}
static void free_params(game_params *params)
{
sfree(params);
}
static game_params *dup_params(const game_params *params)
{
game_params *ret = snew(game_params);
*ret = *params; /* structure copy */
return ret;
}
static bool game_fetch_preset(int i, char **name, game_params **params)
{
static struct {
const char *title;
game_params params;
} const presets[] = {
{ "2x2 Trivial", { 2, 2, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, false, false } },
{ "2x3 Basic", { 2, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, false, false } },
{ "3x3 Trivial", { 3, 3, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, false, false } },
{ "3x3 Basic", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, false, false } },
{ "3x3 Basic X", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, true } },
{ "3x3 Intermediate", { 3, 3, SYMM_ROT2, DIFF_INTERSECT, DIFF_KMINMAX, false, false } },
{ "3x3 Advanced", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, false, false } },
{ "3x3 Advanced X", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, true } },
{ "3x3 Extreme", { 3, 3, SYMM_ROT2, DIFF_EXTREME, DIFF_KMINMAX, false, false } },
{ "3x3 Unreasonable", { 3, 3, SYMM_ROT2, DIFF_RECURSIVE, DIFF_KMINMAX, false, false } },
{ "3x3 Killer", { 3, 3, SYMM_NONE, DIFF_BLOCK, DIFF_KINTERSECT, false, true } },
{ "9 Jigsaw Basic", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, false, false } },
{ "9 Jigsaw Basic X", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, true } },
{ "9 Jigsaw Advanced", { 9, 1, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, false, false } },
#ifndef SLOW_SYSTEM
{ "3x4 Basic", { 3, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, false, false } },
{ "4x4 Basic", { 4, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, false, false } },
#endif
};
if (i < 0 || i >= lenof(presets))
return false;
*name = dupstr(presets[i].title);
*params = dup_params(&presets[i].params);
return true;
}
static void decode_params(game_params *ret, char const *string)
{
bool seen_r = false;
ret->c = ret->r = atoi(string);
ret->xtype = false;
ret->killer = false;
while (*string && isdigit((unsigned char)*string)) string++;
if (*string == 'x') {
string++;
ret->r = atoi(string);
seen_r = true;
while (*string && isdigit((unsigned char)*string)) string++;
}
while (*string) {
if (*string == 'j') {
string++;
if (seen_r)
ret->c *= ret->r;
ret->r = 1;
} else if (*string == 'x') {
string++;
ret->xtype = true;
} else if (*string == 'k') {
string++;
ret->killer = true;
} else if (*string == 'r' || *string == 'm' || *string == 'a') {
int sn, sc;
bool sd;
sc = *string++;
if (sc == 'm' && *string == 'd') {
sd = true;
string++;
} else {
sd = false;
}
sn = atoi(string);
while (*string && isdigit((unsigned char)*string)) string++;
if (sc == 'm' && sn == 8)
ret->symm = SYMM_REF8;
if (sc == 'm' && sn == 4)
ret->symm = sd ? SYMM_REF4D : SYMM_REF4;
if (sc == 'm' && sn == 2)
ret->symm = sd ? SYMM_REF2D : SYMM_REF2;
if (sc == 'r' && sn == 4)
ret->symm = SYMM_ROT4;
if (sc == 'r' && sn == 2)
ret->symm = SYMM_ROT2;
if (sc == 'a')
ret->symm = SYMM_NONE;
} else if (*string == 'd') {
string++;
if (*string == 't') /* trivial */
string++, ret->diff = DIFF_BLOCK;
else if (*string == 'b') /* basic */
string++, ret->diff = DIFF_SIMPLE;
else if (*string == 'i') /* intermediate */
string++, ret->diff = DIFF_INTERSECT;
else if (*string == 'a') /* advanced */
string++, ret->diff = DIFF_SET;
else if (*string == 'e') /* extreme */
string++, ret->diff = DIFF_EXTREME;
else if (*string == 'u') /* unreasonable */
string++, ret->diff = DIFF_RECURSIVE;
} else
string++; /* eat unknown character */
}
}
static char *encode_params(const game_params *params, bool full)
{
char str[80];
if (params->r > 1)
sprintf(str, "%dx%d", params->c, params->r);
else
sprintf(str, "%dj", params->c);
if (params->xtype)
strcat(str, "x");
if (params->killer)
strcat(str, "k");
if (full) {
switch (params->symm) {
case SYMM_REF8: strcat(str, "m8"); break;
case SYMM_REF4: strcat(str, "m4"); break;
case SYMM_REF4D: strcat(str, "md4"); break;
case SYMM_REF2: strcat(str, "m2"); break;
case SYMM_REF2D: strcat(str, "md2"); break;
case SYMM_ROT4: strcat(str, "r4"); break;
/* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
case SYMM_NONE: strcat(str, "a"); break;
}
switch (params->diff) {
/* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
case DIFF_SIMPLE: strcat(str, "db"); break;
case DIFF_INTERSECT: strcat(str, "di"); break;
case DIFF_SET: strcat(str, "da"); break;
case DIFF_EXTREME: strcat(str, "de"); break;
case DIFF_RECURSIVE: strcat(str, "du"); break;
}
}
return dupstr(str);
}
static config_item *game_configure(const game_params *params)
{
config_item *ret;
char buf[80];
ret = snewn(8, config_item);
ret[0].name = "Columns of sub-blocks";
ret[0].type = C_STRING;
sprintf(buf, "%d", params->c);
ret[0].u.string.sval = dupstr(buf);
ret[1].name = "Rows of sub-blocks";
ret[1].type = C_STRING;
sprintf(buf, "%d", params->r);
ret[1].u.string.sval = dupstr(buf);
ret[2].name = "\"X\" (require every number in each main diagonal)";
ret[2].type = C_BOOLEAN;
ret[2].u.boolean.bval = params->xtype;
ret[3].name = "Jigsaw (irregularly shaped sub-blocks)";
ret[3].type = C_BOOLEAN;
ret[3].u.boolean.bval = (params->r == 1);
ret[4].name = "Killer (digit sums)";
ret[4].type = C_BOOLEAN;
ret[4].u.boolean.bval = params->killer;
ret[5].name = "Symmetry";
ret[5].type = C_CHOICES;
ret[5].u.choices.choicenames = ":None:2-way rotation:4-way rotation:2-way mirror:"
"2-way diagonal mirror:4-way mirror:4-way diagonal mirror:"
"8-way mirror";
ret[5].u.choices.selected = params->symm;
ret[6].name = "Difficulty";
ret[6].type = C_CHOICES;
ret[6].u.choices.choicenames = ":Trivial:Basic:Intermediate:Advanced:Extreme:Unreasonable";
ret[6].u.choices.selected = params->diff;
ret[7].name = NULL;
ret[7].type = C_END;
return ret;
}
static game_params *custom_params(const config_item *cfg)
{
game_params *ret = snew(game_params);
ret->c = atoi(cfg[0].u.string.sval);
ret->r = atoi(cfg[1].u.string.sval);
ret->xtype = cfg[2].u.boolean.bval;
if (cfg[3].u.boolean.bval) {
ret->c *= ret->r;
ret->r = 1;
}
ret->killer = cfg[4].u.boolean.bval;
ret->symm = cfg[5].u.choices.selected;
ret->diff = cfg[6].u.choices.selected;
ret->kdiff = DIFF_KINTERSECT;
return ret;
}
static const char *validate_params(const game_params *params, bool full)
{
if (params->c < 2)
return "Both dimensions must be at least 2";
if (params->c > ORDER_MAX || params->r > ORDER_MAX)
return "Dimensions greater than "STR(ORDER_MAX)" are not supported";
if ((params->c * params->r) > 31)
return "Unable to support more than 31 distinct symbols in a puzzle";
if (params->killer && params->c * params->r > 9)
return "Killer puzzle dimensions must be smaller than 10";
if (params->xtype && params->c * params->r < 4)
return "X-type puzzle dimensions must be larger than 3";
return NULL;
}
/*
* ----------------------------------------------------------------------
* Block structure functions.
*/
static struct block_structure *alloc_block_structure(int c, int r, int area,
int max_nr_squares,
int nr_blocks)
{
int i;
struct block_structure *b = snew(struct block_structure);
b->refcount = 1;
b->nr_blocks = nr_blocks;
b->max_nr_squares = max_nr_squares;
b->c = c; b->r = r; b->area = area;
b->whichblock = snewn(area, int);
b->blocks_data = snewn(nr_blocks * max_nr_squares, int);
b->blocks = snewn(nr_blocks, int *);
b->nr_squares = snewn(nr_blocks, int);
for (i = 0; i < nr_blocks; i++)
b->blocks[i] = b->blocks_data + i*max_nr_squares;
#ifdef STANDALONE_SOLVER
b->blocknames = (char **)smalloc(c*r*(sizeof(char *)+80));
for (i = 0; i < c * r; i++)
b->blocknames[i] = NULL;
#endif
return b;
}
static void free_block_structure(struct block_structure *b)
{
if (--b->refcount == 0) {
sfree(b->whichblock);
sfree(b->blocks);
sfree(b->blocks_data);
#ifdef STANDALONE_SOLVER
sfree(b->blocknames);
#endif
sfree(b->nr_squares);
sfree(b);
}
}
static struct block_structure *dup_block_structure(struct block_structure *b)
{
struct block_structure *nb;
int i;
nb = alloc_block_structure(b->c, b->r, b->area, b->max_nr_squares,
b->nr_blocks);
memcpy(nb->nr_squares, b->nr_squares, b->nr_blocks * sizeof *b->nr_squares);
memcpy(nb->whichblock, b->whichblock, b->area * sizeof *b->whichblock);
memcpy(nb->blocks_data, b->blocks_data,
b->nr_blocks * b->max_nr_squares * sizeof *b->blocks_data);
for (i = 0; i < b->nr_blocks; i++)
nb->blocks[i] = nb->blocks_data + i*nb->max_nr_squares;
#ifdef STANDALONE_SOLVER
memcpy(nb->blocknames, b->blocknames, b->c * b->r *(sizeof(char *)+80));
{
int i;
for (i = 0; i < b->c * b->r; i++)
if (b->blocknames[i] == NULL)
nb->blocknames[i] = NULL;
else
nb->blocknames[i] = ((char *)nb->blocknames) + (b->blocknames[i] - (char *)b->blocknames);
}
#endif
return nb;
}
static void split_block(struct block_structure *b, int *squares, int nr_squares)
{
int i, j;
int previous_block = b->whichblock[squares[0]];
int newblock = b->nr_blocks;
assert(b->max_nr_squares >= nr_squares);
assert(b->nr_squares[previous_block] > nr_squares);
b->nr_blocks++;
b->blocks_data = sresize(b->blocks_data,
b->nr_blocks * b->max_nr_squares, int);
b->nr_squares = sresize(b->nr_squares, b->nr_blocks, int);
sfree(b->blocks);
b->blocks = snewn(b->nr_blocks, int *);
for (i = 0; i < b->nr_blocks; i++)
b->blocks[i] = b->blocks_data + i*b->max_nr_squares;
for (i = 0; i < nr_squares; i++) {
assert(b->whichblock[squares[i]] == previous_block);
b->whichblock[squares[i]] = newblock;
b->blocks[newblock][i] = squares[i];
}
for (i = j = 0; i < b->nr_squares[previous_block]; i++) {
int k;
int sq = b->blocks[previous_block][i];
for (k = 0; k < nr_squares; k++)
if (squares[k] == sq)
break;
if (k == nr_squares)
b->blocks[previous_block][j++] = sq;
}
b->nr_squares[previous_block] -= nr_squares;
b->nr_squares[newblock] = nr_squares;
}
static void remove_from_block(struct block_structure *blocks, int b, int n)
{
int i, j;
blocks->whichblock[n] = -1;
for (i = j = 0; i < blocks->nr_squares[b]; i++)
if (blocks->blocks[b][i] != n)
blocks->blocks[b][j++] = blocks->blocks[b][i];
assert(j+1 == i);
blocks->nr_squares[b]--;
}
/* ----------------------------------------------------------------------
* Solver.
*
* This solver is used for two purposes:
* + to check solubility of a grid as we gradually remove numbers
* from it
* + to solve an externally generated puzzle when the user selects
* `Solve'.
*
* It supports a variety of specific modes of reasoning. By
* enabling or disabling subsets of these modes we can arrange a
* range of difficulty levels.
*/
/*
* Modes of reasoning currently supported:
*
* - Positional elimination: a number must go in a particular
* square because all the other empty squares in a given
* row/col/blk are ruled out.
*
* - Killer minmax elimination: for killer-type puzzles, a number
* is impossible if choosing it would cause the sum in a killer
* region to be guaranteed to be too large or too small.
*
* - Numeric elimination: a square must have a particular number
* in because all the other numbers that could go in it are
* ruled out.
*
* - Intersectional analysis: given two domains which overlap
* (hence one must be a block, and the other can be a row or
* col), if the possible locations for a particular number in
* one of the domains can be narrowed down to the overlap, then
* that number can be ruled out everywhere but the overlap in
* the other domain too.
*
* - Set elimination: if there is a subset of the empty squares
* within a domain such that the union of the possible numbers
* in that subset has the same size as the subset itself, then
* those numbers can be ruled out everywhere else in the domain.
* (For example, if there are five empty squares and the
* possible numbers in each are 12, 23, 13, 134 and 1345, then
* the first three empty squares form such a subset: the numbers
* 1, 2 and 3 _must_ be in those three squares in some
* permutation, and hence we can deduce none of them can be in
* the fourth or fifth squares.)
* + You can also see this the other way round, concentrating
* on numbers rather than squares: if there is a subset of
* the unplaced numbers within a domain such that the union
* of all their possible positions has the same size as the
* subset itself, then all other numbers can be ruled out for
* those positions. However, it turns out that this is
* exactly equivalent to the first formulation at all times:
* there is a 1-1 correspondence between suitable subsets of
* the unplaced numbers and suitable subsets of the unfilled
* places, found by taking the _complement_ of the union of
* the numbers' possible positions (or the spaces' possible
* contents).
*
* - Forcing chains (see comment for solver_forcing().)
*
* - Recursion. If all else fails, we pick one of the currently
* most constrained empty squares and take a random guess at its
* contents, then continue solving on that basis and see if we
* get any further.
*/
struct solver_usage {
int cr;
struct block_structure *blocks, *kblocks, *extra_cages;
/*
* We set up a cubic array, indexed by x, y and digit; each
* element of this array is true or false according to whether
* or not that digit _could_ in principle go in that position.
*
* The way to index this array is cube[(y*cr+x)*cr+n-1]; there
* are macros below to help with this.
*/
bool *cube;
/*
* This is the grid in which we write down our final
* deductions. y-coordinates in here are _not_ transformed.
*/
digit *grid;
/*
* For killer-type puzzles, kclues holds the secondary clue for
* each cage. For derived cages, the clue is in extra_clues.
*/
digit *kclues, *extra_clues;
/*
* Now we keep track, at a slightly higher level, of what we
* have yet to work out, to prevent doing the same deduction
* many times.
*/
/* row[y*cr+n-1] true if digit n has been placed in row y */
bool *row;
/* col[x*cr+n-1] true if digit n has been placed in row x */
bool *col;
/* blk[i*cr+n-1] true if digit n has been placed in block i */
bool *blk;
/* diag[i*cr+n-1] true if digit n has been placed in diagonal i */
bool *diag; /* diag 0 is \, 1 is / */
int *regions;
int nr_regions;
int **sq2region;
};
#define cubepos2(xy,n) ((xy)*usage->cr+(n)-1)
#define cubepos(x,y,n) cubepos2((y)*usage->cr+(x),n)
#define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
#define cube2(xy,n) (usage->cube[cubepos2(xy,n)])
#define ondiag0(xy) ((xy) % (cr+1) == 0)
#define ondiag1(xy) ((xy) % (cr-1) == 0 && (xy) > 0 && (xy) < cr*cr-1)
#define diag0(i) ((i) * (cr+1))
#define diag1(i) ((i+1) * (cr-1))
/*
* Function called when we are certain that a particular square has
* a particular number in it. The y-coordinate passed in here is
* transformed.
*/
static void solver_place(struct solver_usage *usage, int x, int y, int n)
{
int cr = usage->cr;
int sqindex = y*cr+x;
int i, bi;
assert(cube(x,y,n));
/*
* Rule out all other numbers in this square.
*/
for (i = 1; i <= cr; i++)
if (i != n)
cube(x,y,i) = false;
/*
* Rule out this number in all other positions in the row.
*/
for (i = 0; i < cr; i++)
if (i != y)
cube(x,i,n) = false;
/*
* Rule out this number in all other positions in the column.
*/
for (i = 0; i < cr; i++)
if (i != x)
cube(i,y,n) = false;
/*
* Rule out this number in all other positions in the block.
*/
bi = usage->blocks->whichblock[sqindex];
for (i = 0; i < cr; i++) {
int bp = usage->blocks->blocks[bi][i];
if (bp != sqindex)
cube2(bp,n) = false;
}
/*
* Enter the number in the result grid.
*/
usage->grid[sqindex] = n;
/*
* Cross out this number from the list of numbers left to place
* in its row, its column and its block.
*/
usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
usage->blk[bi*cr+n-1] = true;
if (usage->diag) {
if (ondiag0(sqindex)) {
for (i = 0; i < cr; i++)
if (diag0(i) != sqindex)
cube2(diag0(i),n) = false;
usage->diag[n-1] = true;
}
if (ondiag1(sqindex)) {
for (i = 0; i < cr; i++)
if (diag1(i) != sqindex)
cube2(diag1(i),n) = false;
usage->diag[cr+n-1] = true;
}
}
}
#if defined STANDALONE_SOLVER && defined __GNUC__
/*
* Forward-declare the functions taking printf-like format arguments
* with __attribute__((format)) so as to ensure the argument syntax
* gets debugged.
*/
struct solver_scratch;
static int solver_elim(struct solver_usage *usage, int *indices,
const char *fmt, ...)
__attribute__((format(printf,3,4)));
static int solver_intersect(struct solver_usage *usage,
int *indices1, int *indices2, const char *fmt, ...)
__attribute__((format(printf,4,5)));
static int solver_set(struct solver_usage *usage,
struct solver_scratch *scratch,
int *indices, const char *fmt, ...)
__attribute__((format(printf,4,5)));
#endif
static int solver_elim(struct solver_usage *usage, int *indices
#ifdef STANDALONE_SOLVER
, const char *fmt, ...
#endif
)
{
int cr = usage->cr;
int fpos, m, i;
/*
* Count the number of set bits within this section of the
* cube.
*/
m = 0;
fpos = -1;
for (i = 0; i < cr; i++)
if (usage->cube[indices[i]]) {
fpos = indices[i];
m++;
}
if (m == 1) {
int x, y, n;
assert(fpos >= 0);
n = 1 + fpos % cr;
x = fpos / cr;
y = x / cr;
x %= cr;
if (!usage->grid[y*cr+x]) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
va_list ap;
printf("%*s", solver_recurse_depth*4, "");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n%*s placing %d at (%d,%d)\n",
solver_recurse_depth*4, "", n, 1+x, 1+y);
}
#endif
solver_place(usage, x, y, n);
return +1;
}
} else if (m == 0) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
va_list ap;
printf("%*s", solver_recurse_depth*4, "");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n%*s no possibilities available\n",
solver_recurse_depth*4, "");
}
#endif
return -1;
}
return 0;
}
static int solver_intersect(struct solver_usage *usage,
int *indices1, int *indices2
#ifdef STANDALONE_SOLVER
, const char *fmt, ...
#endif
)
{
int cr = usage->cr;
int ret, i, j;
/*
* Loop over the first domain and see if there's any set bit
* not also in the second.
*/
for (i = j = 0; i < cr; i++) {
int p = indices1[i];
while (j < cr && indices2[j] < p)
j++;
if (usage->cube[p]) {
if (j < cr && indices2[j] == p)
continue; /* both domains contain this index */
else
return 0; /* there is, so we can't deduce */
}
}
/*
* We have determined that all set bits in the first domain are
* within its overlap with the second. So loop over the second
* domain and remove all set bits that aren't also in that
* overlap; return +1 iff we actually _did_ anything.
*/
ret = 0;
for (i = j = 0; i < cr; i++) {
int p = indices2[i];
while (j < cr && indices1[j] < p)
j++;
if (usage->cube[p] && (j >= cr || indices1[j] != p)) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
int px, py, pn;
if (!ret) {
va_list ap;
printf("%*s", solver_recurse_depth*4, "");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n");
}
pn = 1 + p % cr;
px = p / cr;
py = px / cr;
px %= cr;
printf("%*s ruling out %d at (%d,%d)\n",
solver_recurse_depth*4, "", pn, 1+px, 1+py);
}
#endif
ret = +1; /* we did something */
usage->cube[p] = false;
}
}
return ret;
}
struct solver_scratch {
unsigned char *grid, *rowidx, *colidx, *set;
int *neighbours, *bfsqueue;
int *indexlist, *indexlist2;
#ifdef STANDALONE_SOLVER
int *bfsprev;
#endif
};
static int solver_set(struct solver_usage *usage,
struct solver_scratch *scratch,
int *indices
#ifdef STANDALONE_SOLVER
, const char *fmt, ...
#endif
)
{
int cr = usage->cr;
int i, j, n, count;
unsigned char *grid = scratch->grid;
unsigned char *rowidx = scratch->rowidx;
unsigned char *colidx = scratch->colidx;
unsigned char *set = scratch->set;
/*
* We are passed a cr-by-cr matrix of booleans. Our first job
* is to winnow it by finding any definite placements - i.e.
* any row with a solitary 1 - and discarding that row and the
* column containing the 1.
*/
memset(rowidx, 1, cr);
memset(colidx, 1, cr);
for (i = 0; i < cr; i++) {
int count = 0, first = -1;
for (j = 0; j < cr; j++)
if (usage->cube[indices[i*cr+j]])
first = j, count++;
/*
* If count == 0, then there's a row with no 1s at all and
* the puzzle is internally inconsistent.
*/
if (count == 0) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
va_list ap;
printf("%*s", solver_recurse_depth*4,
"");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n%*s solver_set: impossible on entry\n",
solver_recurse_depth*4, "");
}
#endif
return -1;
}
if (count == 1)
rowidx[i] = colidx[first] = 0;
}
/*
* Convert each of rowidx/colidx from a list of 0s and 1s to a
* list of the indices of the 1s.
*/
for (i = j = 0; i < cr; i++)
if (rowidx[i])
rowidx[j++] = i;
n = j;
for (i = j = 0; i < cr; i++)
if (colidx[i])
colidx[j++] = i;
assert(n == j);
/*
* And create the smaller matrix.
*/
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
grid[i*cr+j] = usage->cube[indices[rowidx[i]*cr+colidx[j]]];
/*
* Having done that, we now have a matrix in which every row
* has at least two 1s in. Now we search to see if we can find
* a rectangle of zeroes (in the set-theoretic sense of
* `rectangle', i.e. a subset of rows crossed with a subset of
* columns) whose width and height add up to n.
*/
memset(set, 0, n);
count = 0;
while (1) {
/*
* We have a candidate set. If its size is <=1 or >=n-1
* then we move on immediately.
*/
if (count > 1 && count < n-1) {
/*
* The number of rows we need is n-count. See if we can
* find that many rows which each have a zero in all
* the positions listed in `set'.
*/
int rows = 0;
for (i = 0; i < n; i++) {
bool ok = true;
for (j = 0; j < n; j++)
if (set[j] && grid[i*cr+j]) {
ok = false;
break;
}
if (ok)
rows++;
}
/*
* We expect never to be able to get _more_ than
* n-count suitable rows: this would imply that (for
* example) there are four numbers which between them
* have at most three possible positions, and hence it
* indicates a faulty deduction before this point or
* even a bogus clue.
*/
if (rows > n - count) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
va_list ap;
printf("%*s", solver_recurse_depth*4,
"");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n%*s contradiction reached\n",
solver_recurse_depth*4, "");
}
#endif
return -1;
}
if (rows >= n - count) {
bool progress = false;
/*
* We've got one! Now, for each row which _doesn't_
* satisfy the criterion, eliminate all its set
* bits in the positions _not_ listed in `set'.
* Return +1 (meaning progress has been made) if we
* successfully eliminated anything at all.
*
* This involves referring back through
* rowidx/colidx in order to work out which actual
* positions in the cube to meddle with.
*/
for (i = 0; i < n; i++) {
bool ok = true;
for (j = 0; j < n; j++)
if (set[j] && grid[i*cr+j]) {
ok = false;
break;
}
if (!ok) {
for (j = 0; j < n; j++)
if (!set[j] && grid[i*cr+j]) {
int fpos = indices[rowidx[i]*cr+colidx[j]];
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
int px, py, pn;
if (!progress) {
va_list ap;
printf("%*s", solver_recurse_depth*4,
"");
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
printf(":\n");
}
pn = 1 + fpos % cr;
px = fpos / cr;
py = px / cr;
px %= cr;
printf("%*s ruling out %d at (%d,%d)\n",
solver_recurse_depth*4, "",
pn, 1+px, 1+py);
}
#endif
progress = true;
usage->cube[fpos] = false;
}
}
}
if (progress) {
return +1;
}
}
}
/*
* Binary increment: change the rightmost 0 to a 1, and
* change all 1s to the right of it to 0s.
*/
i = n;
while (i > 0 && set[i-1])
set[--i] = 0, count--;
if (i > 0)
set[--i] = 1, count++;
else
break; /* done */
}
return 0;
}
/*
* Look for forcing chains. A forcing chain is a path of
* pairwise-exclusive squares (i.e. each pair of adjacent squares
* in the path are in the same row, column or block) with the
* following properties:
*
* (a) Each square on the path has precisely two possible numbers.
*
* (b) Each pair of squares which are adjacent on the path share
* at least one possible number in common.
*
* (c) Each square in the middle of the path shares _both_ of its
* numbers with at least one of its neighbours (not the same
* one with both neighbours).
*
* These together imply that at least one of the possible number
* choices at one end of the path forces _all_ the rest of the
* numbers along the path. In order to make real use of this, we
* need further properties:
*
* (c) Ruling out some number N from the square at one end of the
* path forces the square at the other end to take the same
* number N.
*
* (d) The two end squares are both in line with some third
* square.
*
* (e) That third square currently has N as a possibility.
*
* If we can find all of that lot, we can deduce that at least one
* of the two ends of the forcing chain has number N, and that
* therefore the mutually adjacent third square does not.
*
* To find forcing chains, we're going to start a bfs at each
* suitable square, once for each of its two possible numbers.
*/
static int solver_forcing(struct solver_usage *usage,
struct solver_scratch *scratch)
{
int cr = usage->cr;
int *bfsqueue = scratch->bfsqueue;
#ifdef STANDALONE_SOLVER
int *bfsprev = scratch->bfsprev;
#endif
unsigned char *number = scratch->grid;
int *neighbours = scratch->neighbours;
int x, y;
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++) {
int count, t, n;
/*
* If this square doesn't have exactly two candidate
* numbers, don't try it.
*
* In this loop we also sum the candidate numbers,
* which is a nasty hack to allow us to quickly find
* `the other one' (since we will shortly know there
* are exactly two).
*/
for (count = t = 0, n = 1; n <= cr; n++)
if (cube(x, y, n))
count++, t += n;
if (count != 2)
continue;
/*
* Now attempt a bfs for each candidate.
*/
for (n = 1; n <= cr; n++)
if (cube(x, y, n)) {
int orign, currn, head, tail;
/*
* Begin a bfs.
*/
orign = n;
memset(number, cr+1, cr*cr);
head = tail = 0;
bfsqueue[tail++] = y*cr+x;
#ifdef STANDALONE_SOLVER
bfsprev[y*cr+x] = -1;
#endif
number[y*cr+x] = t - n;
while (head < tail) {
int xx, yy, nneighbours, xt, yt, i;
xx = bfsqueue[head++];
yy = xx / cr;
xx %= cr;
currn = number[yy*cr+xx];
/*
* Find neighbours of yy,xx.
*/
nneighbours = 0;
for (yt = 0; yt < cr; yt++)
neighbours[nneighbours++] = yt*cr+xx;
for (xt = 0; xt < cr; xt++)
neighbours[nneighbours++] = yy*cr+xt;
xt = usage->blocks->whichblock[yy*cr+xx];
for (yt = 0; yt < cr; yt++)
neighbours[nneighbours++] = usage->blocks->blocks[xt][yt];
if (usage->diag) {
int sqindex = yy*cr+xx;
if (ondiag0(sqindex)) {
for (i = 0; i < cr; i++)
neighbours[nneighbours++] = diag0(i);
}
if (ondiag1(sqindex)) {
for (i = 0; i < cr; i++)
neighbours[nneighbours++] = diag1(i);
}
}
/*
* Try visiting each of those neighbours.
*/
for (i = 0; i < nneighbours; i++) {
int cc, tt, nn;
xt = neighbours[i] % cr;
yt = neighbours[i] / cr;
/*
* We need this square to not be
* already visited, and to include
* currn as a possible number.
*/
if (number[yt*cr+xt] <= cr)
continue;
if (!cube(xt, yt, currn))
continue;
/*
* Don't visit _this_ square a second
* time!
*/
if (xt == xx && yt == yy)
continue;
/*
* To continue with the bfs, we need
* this square to have exactly two
* possible numbers.
*/
for (cc = tt = 0, nn = 1; nn <= cr; nn++)
if (cube(xt, yt, nn))
cc++, tt += nn;
if (cc == 2) {
bfsqueue[tail++] = yt*cr+xt;
#ifdef STANDALONE_SOLVER
bfsprev[yt*cr+xt] = yy*cr+xx;
#endif
number[yt*cr+xt] = tt - currn;
}
/*
* One other possibility is that this
* might be the square in which we can
* make a real deduction: if it's
* adjacent to x,y, and currn is equal
* to the original number we ruled out.
*/
if (currn == orign &&
(xt == x || yt == y ||
(usage->blocks->whichblock[yt*cr+xt] == usage->blocks->whichblock[y*cr+x]) ||
(usage->diag && ((ondiag0(yt*cr+xt) && ondiag0(y*cr+x)) ||
(ondiag1(yt*cr+xt) && ondiag1(y*cr+x)))))) {
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
const char *sep = "";
int xl, yl;
printf("%*sforcing chain, %d at ends of ",
solver_recurse_depth*4, "", orign);
xl = xx;
yl = yy;
while (1) {
printf("%s(%d,%d)", sep, 1+xl,
1+yl);
xl = bfsprev[yl*cr+xl];
if (xl < 0)
break;
yl = xl / cr;
xl %= cr;
sep = "-";
}
printf("\n%*s ruling out %d at (%d,%d)\n",
solver_recurse_depth*4, "",
orign, 1+xt, 1+yt);
}
#endif
cube(xt, yt, orign) = false;
return 1;
}
}
}
}
}
return 0;
}
static int solver_killer_minmax(struct solver_usage *usage,
struct block_structure *cages, digit *clues,
int b
#ifdef STANDALONE_SOLVER
, const char *extra
#endif
)
{
int cr = usage->cr;
int i;
int ret = 0;
int nsquares = cages->nr_squares[b];
if (clues[b] == 0)
return 0;
for (i = 0; i < nsquares; i++) {
int n, x = cages->blocks[b][i];
for (n = 1; n <= cr; n++)
if (cube2(x, n)) {
int maxval = 0, minval = 0;
int j;
for (j = 0; j < nsquares; j++) {
int m;
int y = cages->blocks[b][j];
if (i == j)
continue;
for (m = 1; m <= cr; m++)
if (cube2(y, m)) {
minval += m;
break;
}
for (m = cr; m > 0; m--)
if (cube2(y, m)) {
maxval += m;
break;
}
}
if (maxval + n < clues[b]) {
cube2(x, n) = false;
ret = 1;
#ifdef STANDALONE_SOLVER
if (solver_show_working)
printf("%*s ruling out %d at (%d,%d) as too low %s\n",
solver_recurse_depth*4, "killer minmax analysis",
n, 1 + x%cr, 1 + x/cr, extra);
#endif
}
if (minval + n > clues[b]) {
cube2(x, n) = false;
ret = 1;
#ifdef STANDALONE_SOLVER
if (solver_show_working)
printf("%*s ruling out %d at (%d,%d) as too high %s\n",
solver_recurse_depth*4, "killer minmax analysis",
n, 1 + x%cr, 1 + x/cr, extra);
#endif
}
}
}
return ret;
}
static int solver_killer_sums(struct solver_usage *usage, int b,
struct block_structure *cages, int clue,
bool cage_is_region
#ifdef STANDALONE_SOLVER
, const char *cage_type
#endif
)
{
int cr = usage->cr;
int i, ret, max_sums;
int nsquares = cages->nr_squares[b];
unsigned long *sumbits, possible_addends;
if (clue == 0) {
assert(nsquares == 0);
return 0;
}
if (nsquares == 0) {
#ifdef STANDALONE_SOLVER
if (solver_show_working)
printf("%*skiller: cage has no usable squares left\n",
solver_recurse_depth*4, "");
#endif
return -1;
}
if (nsquares < 2 || nsquares > 4)
return 0;
if (!cage_is_region) {
int known_row = -1, known_col = -1, known_block = -1;
/*
* Verify that the cage lies entirely within one region,
* so that using the precomputed sums is valid.
*/
for (i = 0; i < nsquares; i++) {
int x = cages->blocks[b][i];
assert(usage->grid[x] == 0);
if (i == 0) {
known_row = x/cr;
known_col = x%cr;
known_block = usage->blocks->whichblock[x];
} else {
if (known_row != x/cr)
known_row = -1;
if (known_col != x%cr)
known_col = -1;
if (known_block != usage->blocks->whichblock[x])
known_block = -1;
}
}
if (known_block == -1 && known_col == -1 && known_row == -1)
return 0;
}
if (nsquares == 2) {
if (clue < 3 || clue > 17)
return -1;
sumbits = sum_bits2[clue];
max_sums = MAX_2SUMS;
} else if (nsquares == 3) {
if (clue < 6 || clue > 24)
return -1;
sumbits = sum_bits3[clue];
max_sums = MAX_3SUMS;
} else {
if (clue < 10 || clue > 30)
return -1;
sumbits = sum_bits4[clue];
max_sums = MAX_4SUMS;
}
/*
* For every possible way to get the sum, see if there is
* one square in the cage that disallows all the required
* addends. If we find one such square, this way to compute
* the sum is impossible.
*/
possible_addends = 0;
for (i = 0; i < max_sums; i++) {
int j;
unsigned long bits = sumbits[i];
if (bits == 0)
break;
for (j = 0; j < nsquares; j++) {
int n;
unsigned long square_bits = bits;
int x = cages->blocks[b][j];
for (n = 1; n <= cr; n++)
if (!cube2(x, n))
square_bits &= ~(1L << n);
if (square_bits == 0) {
break;
}
}
if (j == nsquares)
possible_addends |= bits;
}
/*
* Now we know which addends can possibly be used to
* compute the sum. Remove all other digits from the
* set of possibilities.
*/
if (possible_addends == 0)
return -1;
ret = 0;
for (i = 0; i < nsquares; i++) {
int n;
int x = cages->blocks[b][i];
for (n = 1; n <= cr; n++) {
if (!cube2(x, n))
continue;
if ((possible_addends & (1 << n)) == 0) {
cube2(x, n) = false;
ret = 1;
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
printf("%*s using %s\n",
solver_recurse_depth*4, "killer sums analysis",
cage_type);
printf("%*s ruling out %d at (%d,%d) due to impossible %d-sum\n",
solver_recurse_depth*4, "",
n, 1 + x%cr, 1 + x/cr, nsquares);
}
#endif
}
}
}
return ret;
}
static int filter_whole_cages(struct solver_usage *usage, int *squares, int n,
int *filtered_sum)
{
int b, i, j, off;
*filtered_sum = 0;
/* First, filter squares with a clue. */
for (i = j = 0; i < n; i++)
if (usage->grid[squares[i]])
*filtered_sum += usage->grid[squares[i]];
else
squares[j++] = squares[i];
n = j;
/*
* Filter all cages that are covered entirely by the list of
* squares.
*/
off = 0;
for (b = 0; b < usage->kblocks->nr_blocks && off < n; b++) {
int b_squares = usage->kblocks->nr_squares[b];
int matched = 0;
if (b_squares == 0)
continue;
/*
* Find all squares of block b that lie in our list,
* and make them contiguous at off, which is the current position
* in the output list.
*/
for (i = 0; i < b_squares; i++) {
for (j = off; j < n; j++)
if (squares[j] == usage->kblocks->blocks[b][i]) {
int t = squares[off + matched];
squares[off + matched] = squares[j];
squares[j] = t;
matched++;
break;
}
}
/* If so, filter out all squares of b from the list. */
if (matched != usage->kblocks->nr_squares[b]) {
off += matched;
continue;
}
memmove(squares + off, squares + off + matched,
(n - off - matched) * sizeof *squares);
n -= matched;
*filtered_sum += usage->kclues[b];
}
assert(off == n);
return off;
}
static struct solver_scratch *solver_new_scratch(struct solver_usage *usage)
{
struct solver_scratch *scratch = snew(struct solver_scratch);
int cr = usage->cr;
scratch->grid = snewn(cr*cr, unsigned char);
scratch->rowidx = snewn(cr, unsigned char);
scratch->colidx = snewn(cr, unsigned char);
scratch->set = snewn(cr, unsigned char);
scratch->neighbours = snewn(5*cr, int);
scratch->bfsqueue = snewn(cr*cr, int);
#ifdef STANDALONE_SOLVER
scratch->bfsprev = snewn(cr*cr, int);
#endif
scratch->indexlist = snewn(cr*cr, int); /* used for set elimination */
scratch->indexlist2 = snewn(cr, int); /* only used for intersect() */
return scratch;
}
static void solver_free_scratch(struct solver_scratch *scratch)
{
#ifdef STANDALONE_SOLVER
sfree(scratch->bfsprev);
#endif
sfree(scratch->bfsqueue);
sfree(scratch->neighbours);
sfree(scratch->set);
sfree(scratch->colidx);
sfree(scratch->rowidx);
sfree(scratch->grid);
sfree(scratch->indexlist);
sfree(scratch->indexlist2);
sfree(scratch);
}
/*
* Used for passing information about difficulty levels between the solver
* and its callers.
*/
struct difficulty {
/* Maximum levels allowed. */
int maxdiff, maxkdiff;
/* Levels reached by the solver. */
int diff, kdiff;
};
static void solver(int cr, struct block_structure *blocks,
struct block_structure *kblocks, bool xtype,
digit *grid, digit *kgrid, struct difficulty *dlev)
{
struct solver_usage *usage;
struct solver_scratch *scratch;
int x, y, b, i, n, ret;
int diff = DIFF_BLOCK;
int kdiff = DIFF_KSINGLE;
/*
* Set up a usage structure as a clean slate (everything
* possible).
*/
usage = snew(struct solver_usage);
usage->cr = cr;
usage->blocks = blocks;
if (kblocks) {
usage->kblocks = dup_block_structure(kblocks);
usage->extra_cages = alloc_block_structure (kblocks->c, kblocks->r,
cr * cr, cr, cr * cr);
usage->extra_clues = snewn(cr*cr, digit);
} else {
usage->kblocks = usage->extra_cages = NULL;
usage->extra_clues = NULL;
}
usage->cube = snewn(cr*cr*cr, bool);
usage->grid = grid; /* write straight back to the input */
if (kgrid) {
int nclues;
assert(kblocks);
nclues = kblocks->nr_blocks;
/*
* Allow for expansion of the killer regions, the absolute
* limit is obviously one region per square.
*/
usage->kclues = snewn(cr*cr, digit);
for (i = 0; i < nclues; i++) {
for (n = 0; n < kblocks->nr_squares[i]; n++)
if (kgrid[kblocks->blocks[i][n]] != 0)
usage->kclues[i] = kgrid[kblocks->blocks[i][n]];
assert(usage->kclues[i] > 0);
}
memset(usage->kclues + nclues, 0, cr*cr - nclues);
} else {
usage->kclues = NULL;
}
for (i = 0; i < cr*cr*cr; i++)
usage->cube[i] = true;
usage->row = snewn(cr * cr, bool);
usage->col = snewn(cr * cr, bool);
usage->blk = snewn(cr * cr, bool);
memset(usage->row, 0, cr * cr * sizeof(bool));
memset(usage->col, 0, cr * cr * sizeof(bool));
memset(usage->blk, 0, cr * cr * sizeof(bool));
if (xtype) {
usage->diag = snewn(cr * 2, bool);
memset(usage->diag, 0, cr * 2 * sizeof(bool));
} else
usage->diag = NULL;
usage->nr_regions = cr * 3 + (xtype ? 2 : 0);
usage->regions = snewn(cr * usage->nr_regions, int);
usage->sq2region = snewn(cr * cr * 3, int *);
for (n = 0; n < cr; n++) {
for (i = 0; i < cr; i++) {
x = n*cr+i;
y = i*cr+n;
b = usage->blocks->blocks[n][i];
usage->regions[cr*n*3 + i] = x;
usage->regions[cr*n*3 + cr + i] = y;
usage->regions[cr*n*3 + 2*cr + i] = b;
usage->sq2region[x*3] = usage->regions + cr*n*3;
usage->sq2region[y*3 + 1] = usage->regions + cr*n*3 + cr;
usage->sq2region[b*3 + 2] = usage->regions + cr*n*3 + 2*cr;
}
}
scratch = solver_new_scratch(usage);
/*
* Place all the clue numbers we are given.
*/
for (x = 0; x < cr; x++)
for (y = 0; y < cr; y++) {
int n = grid[y*cr+x];
if (n) {
if (!cube(x,y,n)) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
solver_place(usage, x, y, grid[y*cr+x]);
}
}
/*
* Now loop over the grid repeatedly trying all permitted modes
* of reasoning. The loop terminates if we complete an
* iteration without making any progress; we then return
* failure or success depending on whether the grid is full or
* not.
*/
while (1) {
/*
* I'd like to write `continue;' inside each of the
* following loops, so that the solver returns here after
* making some progress. However, I can't specify that I
* want to continue an outer loop rather than the innermost
* one, so I'm apologetically resorting to a goto.
*/
cont:
/*
* Blockwise positional elimination.
*/
for (b = 0; b < cr; b++)
for (n = 1; n <= cr; n++)
if (!usage->blk[b*cr+n-1]) {
for (i = 0; i < cr; i++)
scratch->indexlist[i] = cubepos2(usage->blocks->blocks[b][i],n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional elimination,"
" %d in block %s", n,
usage->blocks->blocknames[b]
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_BLOCK);
goto cont;
}
}
if (usage->kclues != NULL) {
bool changed = false;
/*
* First, bring the kblocks into a more useful form: remove
* all filled-in squares, and reduce the sum by their values.
* Walk in reverse order, since otherwise remove_from_block
* can move element past our loop counter.
*/
for (b = 0; b < usage->kblocks->nr_blocks; b++)
for (i = usage->kblocks->nr_squares[b] -1; i >= 0; i--) {
int x = usage->kblocks->blocks[b][i];
int t = usage->grid[x];
if (t == 0)
continue;
remove_from_block(usage->kblocks, b, x);
if (t > usage->kclues[b]) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
usage->kclues[b] -= t;
/*
* Since cages are regions, this tells us something
* about the other squares in the cage.
*/
for (n = 0; n < usage->kblocks->nr_squares[b]; n++) {
cube2(usage->kblocks->blocks[b][n], t) = false;
}
}
/*
* The most trivial kind of solver for killer puzzles: fill
* single-square cages.
*/
for (b = 0; b < usage->kblocks->nr_blocks; b++) {
int squares = usage->kblocks->nr_squares[b];
if (squares == 1) {
int v = usage->kclues[b];
if (v < 1 || v > cr) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
x = usage->kblocks->blocks[b][0] % cr;
y = usage->kblocks->blocks[b][0] / cr;
if (!cube(x, y, v)) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
solver_place(usage, x, y, v);
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
printf("%*s placing %d at (%d,%d)\n",
solver_recurse_depth*4, "killer single-square cage",
v, 1 + x%cr, 1 + x/cr);
}
#endif
changed = true;
}
}
if (changed) {
kdiff = max(kdiff, DIFF_KSINGLE);
goto cont;
}
}
if (dlev->maxkdiff >= DIFF_KINTERSECT && usage->kclues != NULL) {
bool changed = false;
/*
* Now, create the extra_cages information. Every full region
* (row, column, or block) has the same sum total (45 for 3x3
* puzzles. After we try to cover these regions with cages that
* lie entirely within them, any squares that remain must bring
* the total to this known value, and so they form additional
* cages which aren't immediately evident in the displayed form
* of the puzzle.
*/
usage->extra_cages->nr_blocks = 0;
for (i = 0; i < 3; i++) {
for (n = 0; n < cr; n++) {
int *region = usage->regions + cr*n*3 + i*cr;
int sum = cr * (cr + 1) / 2;
int nsquares = cr;
int filtered;
int n_extra = usage->extra_cages->nr_blocks;
int *extra_list = usage->extra_cages->blocks[n_extra];
memcpy(extra_list, region, cr * sizeof *extra_list);
nsquares = filter_whole_cages(usage, extra_list, nsquares, &filtered);
sum -= filtered;
if (nsquares == cr || nsquares == 0)
continue;
if (dlev->maxdiff >= DIFF_RECURSIVE) {
if (sum <= 0) {
dlev->diff = DIFF_IMPOSSIBLE;
goto got_result;
}
}
assert(sum > 0);
if (nsquares == 1) {
if (sum > cr) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
x = extra_list[0] % cr;
y = extra_list[0] / cr;
if (!cube(x, y, sum)) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
solver_place(usage, x, y, sum);
changed = true;
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
printf("%*s placing %d at (%d,%d)\n",
solver_recurse_depth*4, "killer single-square deduced cage",
sum, 1 + x, 1 + y);
}
#endif
}
b = usage->kblocks->whichblock[extra_list[0]];
for (x = 1; x < nsquares; x++)
if (usage->kblocks->whichblock[extra_list[x]] != b)
break;
if (x == nsquares) {
assert(usage->kblocks->nr_squares[b] > nsquares);
split_block(usage->kblocks, extra_list, nsquares);
assert(usage->kblocks->nr_squares[usage->kblocks->nr_blocks - 1] == nsquares);
usage->kclues[usage->kblocks->nr_blocks - 1] = sum;
usage->kclues[b] -= sum;
} else {
usage->extra_cages->nr_squares[n_extra] = nsquares;
usage->extra_cages->nr_blocks++;
usage->extra_clues[n_extra] = sum;
}
}
}
if (changed) {
kdiff = max(kdiff, DIFF_KINTERSECT);
goto cont;
}
}
/*
* Another simple killer-type elimination. For every square in a
* cage, find the minimum and maximum possible sums of all the
* other squares in the same cage, and rule out possibilities
* for the given square based on whether they are guaranteed to
* cause the sum to be either too high or too low.
* This is a special case of trying all possible sums across a
* region, which is a recursive algorithm. We should probably
* implement it for a higher difficulty level.
*/
if (dlev->maxkdiff >= DIFF_KMINMAX && usage->kclues != NULL) {
bool changed = false;
for (b = 0; b < usage->kblocks->nr_blocks; b++) {
int ret = solver_killer_minmax(usage, usage->kblocks,
usage->kclues, b
#ifdef STANDALONE_SOLVER
, ""
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0)
changed = true;
}
for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
int ret = solver_killer_minmax(usage, usage->extra_cages,
usage->extra_clues, b
#ifdef STANDALONE_SOLVER
, "using deduced cages"
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0)
changed = true;
}
if (changed) {
kdiff = max(kdiff, DIFF_KMINMAX);
goto cont;
}
}
/*
* Try to use knowledge of which numbers can be used to generate
* a given sum.
* This can only be used if a cage lies entirely within a region.
*/
if (dlev->maxkdiff >= DIFF_KSUMS && usage->kclues != NULL) {
bool changed = false;
for (b = 0; b < usage->kblocks->nr_blocks; b++) {
int ret = solver_killer_sums(usage, b, usage->kblocks,
usage->kclues[b], true
#ifdef STANDALONE_SOLVER
, "regular clues"
#endif
);
if (ret > 0) {
changed = true;
kdiff = max(kdiff, DIFF_KSUMS);
} else if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
}
for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
int ret = solver_killer_sums(usage, b, usage->extra_cages,
usage->extra_clues[b], false
#ifdef STANDALONE_SOLVER
, "deduced clues"
#endif
);
if (ret > 0) {
changed = true;
kdiff = max(kdiff, DIFF_KSUMS);
} else if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
}
}
if (changed)
goto cont;
}
if (dlev->maxdiff <= DIFF_BLOCK)
break;
/*
* Row-wise positional elimination.
*/
for (y = 0; y < cr; y++)
for (n = 1; n <= cr; n++)
if (!usage->row[y*cr+n-1]) {
for (x = 0; x < cr; x++)
scratch->indexlist[x] = cubepos(x, y, n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional elimination,"
" %d in row %d", n, 1+y
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SIMPLE);
goto cont;
}
}
/*
* Column-wise positional elimination.
*/
for (x = 0; x < cr; x++)
for (n = 1; n <= cr; n++)
if (!usage->col[x*cr+n-1]) {
for (y = 0; y < cr; y++)
scratch->indexlist[y] = cubepos(x, y, n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional elimination,"
" %d in column %d", n, 1+x
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SIMPLE);
goto cont;
}
}
/*
* X-diagonal positional elimination.
*/
if (usage->diag) {
for (n = 1; n <= cr; n++)
if (!usage->diag[n-1]) {
for (i = 0; i < cr; i++)
scratch->indexlist[i] = cubepos2(diag0(i), n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional elimination,"
" %d in \\-diagonal", n
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SIMPLE);
goto cont;
}
}
for (n = 1; n <= cr; n++)
if (!usage->diag[cr+n-1]) {
for (i = 0; i < cr; i++)
scratch->indexlist[i] = cubepos2(diag1(i), n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional elimination,"
" %d in /-diagonal", n
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SIMPLE);
goto cont;
}
}
}
/*
* Numeric elimination.
*/
for (x = 0; x < cr; x++)
for (y = 0; y < cr; y++)
if (!usage->grid[y*cr+x]) {
for (n = 1; n <= cr; n++)
scratch->indexlist[n-1] = cubepos(x, y, n);
ret = solver_elim(usage, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "numeric elimination at (%d,%d)",
1+x, 1+y
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SIMPLE);
goto cont;
}
}
if (dlev->maxdiff <= DIFF_SIMPLE)
break;
/*
* Intersectional analysis, rows vs blocks.
*/
for (y = 0; y < cr; y++)
for (b = 0; b < cr; b++)
for (n = 1; n <= cr; n++) {
if (usage->row[y*cr+n-1] ||
usage->blk[b*cr+n-1])
continue;
for (i = 0; i < cr; i++) {
scratch->indexlist[i] = cubepos(i, y, n);
scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
}
/*
* solver_intersect() never returns -1.
*/
if (solver_intersect(usage, scratch->indexlist,
scratch->indexlist2
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in row %d vs block %s",
n, 1+y, usage->blocks->blocknames[b]
#endif
) ||
solver_intersect(usage, scratch->indexlist2,
scratch->indexlist
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in block %s vs row %d",
n, usage->blocks->blocknames[b], 1+y
#endif
)) {
diff = max(diff, DIFF_INTERSECT);
goto cont;
}
}
/*
* Intersectional analysis, columns vs blocks.
*/
for (x = 0; x < cr; x++)
for (b = 0; b < cr; b++)
for (n = 1; n <= cr; n++) {
if (usage->col[x*cr+n-1] ||
usage->blk[b*cr+n-1])
continue;
for (i = 0; i < cr; i++) {
scratch->indexlist[i] = cubepos(x, i, n);
scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
}
if (solver_intersect(usage, scratch->indexlist,
scratch->indexlist2
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in column %d vs block %s",
n, 1+x, usage->blocks->blocknames[b]
#endif
) ||
solver_intersect(usage, scratch->indexlist2,
scratch->indexlist
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in block %s vs column %d",
n, usage->blocks->blocknames[b], 1+x
#endif
)) {
diff = max(diff, DIFF_INTERSECT);
goto cont;
}
}
if (usage->diag) {
/*
* Intersectional analysis, \-diagonal vs blocks.
*/
for (b = 0; b < cr; b++)
for (n = 1; n <= cr; n++) {
if (usage->diag[n-1] ||
usage->blk[b*cr+n-1])
continue;
for (i = 0; i < cr; i++) {
scratch->indexlist[i] = cubepos2(diag0(i), n);
scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
}
if (solver_intersect(usage, scratch->indexlist,
scratch->indexlist2
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in \\-diagonal vs block %s",
n, usage->blocks->blocknames[b]
#endif
) ||
solver_intersect(usage, scratch->indexlist2,
scratch->indexlist
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in block %s vs \\-diagonal",
n, usage->blocks->blocknames[b]
#endif
)) {
diff = max(diff, DIFF_INTERSECT);
goto cont;
}
}
/*
* Intersectional analysis, /-diagonal vs blocks.
*/
for (b = 0; b < cr; b++)
for (n = 1; n <= cr; n++) {
if (usage->diag[cr+n-1] ||
usage->blk[b*cr+n-1])
continue;
for (i = 0; i < cr; i++) {
scratch->indexlist[i] = cubepos2(diag1(i), n);
scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
}
if (solver_intersect(usage, scratch->indexlist,
scratch->indexlist2
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in /-diagonal vs block %s",
n, usage->blocks->blocknames[b]
#endif
) ||
solver_intersect(usage, scratch->indexlist2,
scratch->indexlist
#ifdef STANDALONE_SOLVER
, "intersectional analysis,"
" %d in block %s vs /-diagonal",
n, usage->blocks->blocknames[b]
#endif
)) {
diff = max(diff, DIFF_INTERSECT);
goto cont;
}
}
}
if (dlev->maxdiff <= DIFF_INTERSECT)
break;
/*
* Blockwise set elimination.
*/
for (b = 0; b < cr; b++) {
for (i = 0; i < cr; i++)
for (n = 1; n <= cr; n++)
scratch->indexlist[i*cr+n-1] = cubepos2(usage->blocks->blocks[b][i], n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "set elimination, block %s",
usage->blocks->blocknames[b]
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SET);
goto cont;
}
}
/*
* Row-wise set elimination.
*/
for (y = 0; y < cr; y++) {
for (x = 0; x < cr; x++)
for (n = 1; n <= cr; n++)
scratch->indexlist[x*cr+n-1] = cubepos(x, y, n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "set elimination, row %d", 1+y
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SET);
goto cont;
}
}
/*
* Column-wise set elimination.
*/
for (x = 0; x < cr; x++) {
for (y = 0; y < cr; y++)
for (n = 1; n <= cr; n++)
scratch->indexlist[y*cr+n-1] = cubepos(x, y, n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "set elimination, column %d", 1+x
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SET);
goto cont;
}
}
if (usage->diag) {
/*
* \-diagonal set elimination.
*/
for (i = 0; i < cr; i++)
for (n = 1; n <= cr; n++)
scratch->indexlist[i*cr+n-1] = cubepos2(diag0(i), n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "set elimination, \\-diagonal"
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SET);
goto cont;
}
/*
* /-diagonal set elimination.
*/
for (i = 0; i < cr; i++)
for (n = 1; n <= cr; n++)
scratch->indexlist[i*cr+n-1] = cubepos2(diag1(i), n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "set elimination, /-diagonal"
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_SET);
goto cont;
}
}
if (dlev->maxdiff <= DIFF_SET)
break;
/*
* Row-vs-column set elimination on a single number.
*/
for (n = 1; n <= cr; n++) {
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
scratch->indexlist[y*cr+x] = cubepos(x, y, n);
ret = solver_set(usage, scratch, scratch->indexlist
#ifdef STANDALONE_SOLVER
, "positional set elimination, number %d", n
#endif
);
if (ret < 0) {
diff = DIFF_IMPOSSIBLE;
goto got_result;
} else if (ret > 0) {
diff = max(diff, DIFF_EXTREME);
goto cont;
}
}
/*
* Forcing chains.
*/
if (solver_forcing(usage, scratch)) {
diff = max(diff, DIFF_EXTREME);
goto cont;
}
/*
* If we reach here, we have made no deductions in this
* iteration, so the algorithm terminates.
*/
break;
}
/*
* Last chance: if we haven't fully solved the puzzle yet, try
* recursing based on guesses for a particular square. We pick
* one of the most constrained empty squares we can find, which
* has the effect of pruning the search tree as much as
* possible.
*/
if (dlev->maxdiff >= DIFF_RECURSIVE) {
int best, bestcount;
best = -1;
bestcount = cr+1;
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
if (!grid[y*cr+x]) {
int count;
/*
* An unfilled square. Count the number of
* possible digits in it.
*/
count = 0;
for (n = 1; n <= cr; n++)
if (cube(x,y,n))
count++;
/*
* We should have found any impossibilities
* already, so this can safely be an assert.
*/
assert(count > 1);
if (count < bestcount) {
bestcount = count;
best = y*cr+x;
}
}
if (best != -1) {
int i, j;
digit *list, *ingrid, *outgrid;
diff = DIFF_IMPOSSIBLE; /* no solution found yet */
/*
* Attempt recursion.
*/
y = best / cr;
x = best % cr;
list = snewn(cr, digit);
ingrid = snewn(cr * cr, digit);
outgrid = snewn(cr * cr, digit);
memcpy(ingrid, grid, cr * cr);
/* Make a list of the possible digits. */
for (j = 0, n = 1; n <= cr; n++)
if (cube(x,y,n))
list[j++] = n;
#ifdef STANDALONE_SOLVER
if (solver_show_working) {
const char *sep = "";
printf("%*srecursing on (%d,%d) [",
solver_recurse_depth*4, "", x + 1, y + 1);
for (i = 0; i < j; i++) {
printf("%s%d", sep, list[i]);
sep = " or ";
}
printf("]\n");
}
#endif
/*
* And step along the list, recursing back into the
* main solver at every stage.
*/
for (i = 0; i < j; i++) {
memcpy(outgrid, ingrid, cr * cr);
outgrid[y*cr+x] = list[i];
#ifdef STANDALONE_SOLVER
if (solver_show_working)
printf("%*sguessing %d at (%d,%d)\n",
solver_recurse_depth*4, "", list[i], x + 1, y + 1);
solver_recurse_depth++;
#endif
solver(cr, blocks, kblocks, xtype, outgrid, kgrid, dlev);
#ifdef STANDALONE_SOLVER
solver_recurse_depth--;
if (solver_show_working) {
printf("%*sretracting %d at (%d,%d)\n",
solver_recurse_depth*4, "", list[i], x + 1, y + 1);
}
#endif
/*
* If we have our first solution, copy it into the
* grid we will return.
*/
if (diff == DIFF_IMPOSSIBLE && dlev->diff != DIFF_IMPOSSIBLE)
memcpy(grid, outgrid, cr*cr);
if (dlev->diff == DIFF_AMBIGUOUS)
diff = DIFF_AMBIGUOUS;
else if (dlev->diff == DIFF_IMPOSSIBLE)
/* do not change our return value */;
else {
/* the recursion turned up exactly one solution */
if (diff == DIFF_IMPOSSIBLE)
diff = DIFF_RECURSIVE;
else
diff = DIFF_AMBIGUOUS;
}
/*
* As soon as we've found more than one solution,
* give up immediately.
*/
if (diff == DIFF_AMBIGUOUS)
break;
}
sfree(outgrid);
sfree(ingrid);
sfree(list);
}
} else {
/*
* We're forbidden to use recursion, so we just see whether
* our grid is fully solved, and return DIFF_IMPOSSIBLE
* otherwise.
*/
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
if (!grid[y*cr+x])
diff = DIFF_IMPOSSIBLE;
}
got_result:
dlev->diff = diff;
dlev->kdiff = kdiff;
#ifdef STANDALONE_SOLVER
if (solver_show_working)
printf("%*s%s found\n",
solver_recurse_depth*4, "",
diff == DIFF_IMPOSSIBLE ? "no solution" :
diff == DIFF_AMBIGUOUS ? "multiple solutions" :
"one solution");
#endif
sfree(usage->sq2region);
sfree(usage->regions);
sfree(usage->cube);
sfree(usage->row);
sfree(usage->col);
sfree(usage->blk);
sfree(usage->diag);
if (usage->kblocks) {
free_block_structure(usage->kblocks);
free_block_structure(usage->extra_cages);
sfree(usage->extra_clues);
}
if (usage->kclues) sfree(usage->kclues);
sfree(usage);
solver_free_scratch(scratch);
}
/* ----------------------------------------------------------------------
* End of solver code.
*/
/* ----------------------------------------------------------------------
* Killer set generator.
*/
/* ----------------------------------------------------------------------
* Solo filled-grid generator.
*
* This grid generator works by essentially trying to solve a grid
* starting from no clues, and not worrying that there's more than
* one possible solution. Unfortunately, it isn't computationally
* feasible to do this by calling the above solver with an empty
* grid, because that one needs to allocate a lot of scratch space
* at every recursion level. Instead, I have a much simpler
* algorithm which I shamelessly copied from a Python solver
* written by Andrew Wilkinson (which is GPLed, but I've reused
* only ideas and no code). It mostly just does the obvious
* recursive thing: pick an empty square, put one of the possible
* digits in it, recurse until all squares are filled, backtrack
* and change some choices if necessary.
*
* The clever bit is that every time it chooses which square to
* fill in next, it does so by counting the number of _possible_
* numbers that can go in each square, and it prioritises so that
* it picks a square with the _lowest_ number of possibilities. The
* idea is that filling in lots of the obvious bits (particularly
* any squares with only one possibility) will cut down on the list
* of possibilities for other squares and hence reduce the enormous
* search space as much as possible as early as possible.
*
* The use of bit sets implies that we support puzzles up to a size of
* 32x32 (less if anyone finds a 16-bit machine to compile this on).
*/
/*
* Internal data structure used in gridgen to keep track of
* progress.
*/
struct gridgen_coord { int x, y, r; };
struct gridgen_usage {
int cr;
struct block_structure *blocks, *kblocks;
/* grid is a copy of the input grid, modified as we go along */
digit *grid;
/*
* Bitsets. In each of them, bit n is set if digit n has been placed
* in the corresponding region. row, col and blk are used for all
* puzzles. cge is used only for killer puzzles, and diag is used
* only for x-type puzzles.
* All of these have cr entries, except diag which only has 2,
* and cge, which has as many entries as kblocks.
*/
unsigned int *row, *col, *blk, *cge, *diag;
/* This lists all the empty spaces remaining in the grid. */
struct gridgen_coord *spaces;
int nspaces;
/* If we need randomisation in the solve, this is our random state. */
random_state *rs;
};
static void gridgen_place(struct gridgen_usage *usage, int x, int y, digit n)
{
unsigned int bit = 1 << n;
int cr = usage->cr;
usage->row[y] |= bit;
usage->col[x] |= bit;
usage->blk[usage->blocks->whichblock[y*cr+x]] |= bit;
if (usage->cge)
usage->cge[usage->kblocks->whichblock[y*cr+x]] |= bit;
if (usage->diag) {
if (ondiag0(y*cr+x))
usage->diag[0] |= bit;
if (ondiag1(y*cr+x))
usage->diag[1] |= bit;
}
usage->grid[y*cr+x] = n;
}
static void gridgen_remove(struct gridgen_usage *usage, int x, int y, digit n)
{
unsigned int mask = ~(1 << n);
int cr = usage->cr;
usage->row[y] &= mask;
usage->col[x] &= mask;
usage->blk[usage->blocks->whichblock[y*cr+x]] &= mask;
if (usage->cge)
usage->cge[usage->kblocks->whichblock[y*cr+x]] &= mask;
if (usage->diag) {
if (ondiag0(y*cr+x))
usage->diag[0] &= mask;
if (ondiag1(y*cr+x))
usage->diag[1] &= mask;
}
usage->grid[y*cr+x] = 0;
}
#define N_SINGLE 32
/*
* The real recursive step in the generating function.
*
* Return values: 1 means solution found, 0 means no solution
* found on this branch.
*/
static bool gridgen_real(struct gridgen_usage *usage, digit *grid, int *steps)
{
int cr = usage->cr;
int i, j, n, sx, sy, bestm, bestr;
bool ret;
int *digits;
unsigned int used;
/*
* Firstly, check for completion! If there are no spaces left
* in the grid, we have a solution.
*/
if (usage->nspaces == 0)
return true;
/*
* Next, abandon generation if we went over our steps limit.
*/
if (*steps <= 0)
return false;
(*steps)--;
/*
* Otherwise, there must be at least one space. Find the most
* constrained space, using the `r' field as a tie-breaker.
*/
bestm = cr+1; /* so that any space will beat it */
bestr = 0;
used = ~0;
i = sx = sy = -1;
for (j = 0; j < usage->nspaces; j++) {
int x = usage->spaces[j].x, y = usage->spaces[j].y;
unsigned int used_xy;
int m;
m = usage->blocks->whichblock[y*cr+x];
used_xy = usage->row[y] | usage->col[x] | usage->blk[m];
if (usage->cge != NULL)
used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
if (usage->cge != NULL)
used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
if (usage->diag != NULL) {
if (ondiag0(y*cr+x))
used_xy |= usage->diag[0];
if (ondiag1(y*cr+x))
used_xy |= usage->diag[1];
}
/*
* Find the number of digits that could go in this space.
*/
m = 0;
for (n = 1; n <= cr; n++) {
unsigned int bit = 1 << n;
if ((used_xy & bit) == 0)
m++;
}
if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
bestm = m;
bestr = usage->spaces[j].r;
sx = x;
sy = y;
i = j;
used = used_xy;
}
}
/*
* Swap that square into the final place in the spaces array,
* so that decrementing nspaces will remove it from the list.
*/
if (i != usage->nspaces-1) {
struct gridgen_coord t;
t = usage->spaces[usage->nspaces-1];
usage->spaces[usage->nspaces-1] = usage->spaces[i];
usage->spaces[i] = t;
}
/*
* Now we've decided which square to start our recursion at,
* simply go through all possible values, shuffling them
* randomly first if necessary.
*/
digits = snewn(bestm, int);
j = 0;
for (n = 1; n <= cr; n++) {
unsigned int bit = 1 << n;
if ((used & bit) == 0)
digits[j++] = n;
}
if (usage->rs)
shuffle(digits, j, sizeof(*digits), usage->rs);
/* And finally, go through the digit list and actually recurse. */
ret = false;
for (i = 0; i < j; i++) {
n = digits[i];
/* Update the usage structure to reflect the placing of this digit. */
gridgen_place(usage, sx, sy, n);
usage->nspaces--;
/* Call the solver recursively. Stop when we find a solution. */
if (gridgen_real(usage, grid, steps)) {
ret = true;
break;
}
/* Revert the usage structure. */
gridgen_remove(usage, sx, sy, n);
usage->nspaces++;
}
sfree(digits);
return ret;
}
/*
* Entry point to generator. You give it parameters and a starting
* grid, which is simply an array of cr*cr digits.
*/
static bool gridgen(int cr, struct block_structure *blocks,
struct block_structure *kblocks, bool xtype,
digit *grid, random_state *rs, int maxsteps)
{
struct gridgen_usage *usage;
int x, y;
bool ret;
/*
* Clear the grid to start with.
*/
memset(grid, 0, cr*cr);
/*
* Create a gridgen_usage structure.
*/
usage = snew(struct gridgen_usage);
usage->cr = cr;
usage->blocks = blocks;
usage->grid = grid;
usage->row = snewn(cr, unsigned int);
usage->col = snewn(cr, unsigned int);
usage->blk = snewn(cr, unsigned int);
if (kblocks != NULL) {
usage->kblocks = kblocks;
usage->cge = snewn(usage->kblocks->nr_blocks, unsigned int);
memset(usage->cge, 0, kblocks->nr_blocks * sizeof *usage->cge);
} else {
usage->cge = NULL;
}
memset(usage->row, 0, cr * sizeof *usage->row);
memset(usage->col, 0, cr * sizeof *usage->col);
memset(usage->blk, 0, cr * sizeof *usage->blk);
if (xtype) {
usage->diag = snewn(2, unsigned int);
memset(usage->diag, 0, 2 * sizeof *usage->diag);
} else {
usage->diag = NULL;
}
/*
* Begin by filling in the whole top row with randomly chosen
* numbers. This cannot introduce any bias or restriction on
* the available grids, since we already know those numbers
* are all distinct so all we're doing is choosing their
* labels.
*/
for (x = 0; x < cr; x++)
grid[x] = x+1;
shuffle(grid, cr, sizeof(*grid), rs);
for (x = 0; x < cr; x++)
gridgen_place(usage, x, 0, grid[x]);
usage->spaces = snewn(cr * cr, struct gridgen_coord);
usage->nspaces = 0;
usage->rs = rs;
/*
* Initialise the list of grid spaces, taking care to leave
* out the row I've already filled in above.
*/
for (y = 1; y < cr; y++) {
for (x = 0; x < cr; x++) {
usage->spaces[usage->nspaces].x = x;
usage->spaces[usage->nspaces].y = y;
usage->spaces[usage->nspaces].r = random_bits(rs, 31);
usage->nspaces++;
}
}
/*
* Run the real generator function.
*/
ret = gridgen_real(usage, grid, &maxsteps);
/*
* Clean up the usage structure now we have our answer.
*/
sfree(usage->spaces);
sfree(usage->cge);
sfree(usage->blk);
sfree(usage->col);
sfree(usage->row);
sfree(usage->diag);
sfree(usage);
return ret;
}
/* ----------------------------------------------------------------------
* End of grid generator code.
*/
static int check_killer_cage_sum(struct block_structure *kblocks,
digit *kgrid, digit *grid, int blk)
{
/*
* Returns: -1 if the cage has any empty square; 0 if all squares
* are full but the sum is wrong; +1 if all squares are full and
* they have the right sum.
*
* Does not check uniqueness of numbers within the cage; that's
* done elsewhere (because in error highlighting it needs to be
* detected separately so as to flag the error in a visually
* different way).
*/
int n_squares = kblocks->nr_squares[blk];
int sum = 0, clue = 0;
int i;
for (i = 0; i < n_squares; i++) {
int xy = kblocks->blocks[blk][i];
if (grid[xy] == 0)
return -1;
sum += grid[xy];
if (kgrid[xy]) {
assert(clue == 0);
clue = kgrid[xy];
}
}
assert(clue != 0);
return sum == clue;
}
/*
* Check whether a grid contains a valid complete puzzle.
*/
static bool check_valid(int cr, struct block_structure *blocks,
struct block_structure *kblocks,
digit *kgrid, bool xtype, digit *grid)
{
bool *used;
int x, y, i, j, n;
used = snewn(cr, bool);
/*
* Check that each row contains precisely one of everything.
*/
for (y = 0; y < cr; y++) {
memset(used, 0, cr * sizeof(bool));
for (x = 0; x < cr; x++)
if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
used[grid[y*cr+x]-1] = true;
for (n = 0; n < cr; n++)
if (!used[n]) {
sfree(used);
return false;
}
}
/*
* Check that each column contains precisely one of everything.
*/
for (x = 0; x < cr; x++) {
memset(used, 0, cr * sizeof(bool));
for (y = 0; y < cr; y++)
if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
used[grid[y*cr+x]-1] = true;
for (n = 0; n < cr; n++)
if (!used[n]) {
sfree(used);
return false;
}
}
/*
* Check that each block contains precisely one of everything.
*/
for (i = 0; i < cr; i++) {
memset(used, 0, cr * sizeof(bool));
for (j = 0; j < cr; j++)
if (grid[blocks->blocks[i][j]] > 0 &&
grid[blocks->blocks[i][j]] <= cr)
used[grid[blocks->blocks[i][j]]-1] = true;
for (n = 0; n < cr; n++)
if (!used[n]) {
sfree(used);
return false;
}
}
/*
* Check that each Killer cage, if any, contains at most one of
* everything. If we also know the clues for those cages (which we
* might not, when this function is called early in puzzle
* generation), we also check that they all have the right sum.
*/
if (kblocks) {
for (i = 0; i < kblocks->nr_blocks; i++) {
memset(used, 0, cr * sizeof(bool));
for (j = 0; j < kblocks->nr_squares[i]; j++)
if (grid[kblocks->blocks[i][j]] > 0 &&
grid[kblocks->blocks[i][j]] <= cr) {
if (used[grid[kblocks->blocks[i][j]]-1]) {
sfree(used);
return false;
}
used[grid[kblocks->blocks[i][j]]-1] = true;
}
if (kgrid && check_killer_cage_sum(kblocks, kgrid, grid, i) != 1) {
sfree(used);
return false;
}
}
}
/*
* Check that each diagonal contains precisely one of everything.
*/
if (xtype) {
memset(used, 0, cr * sizeof(bool));
for (i = 0; i < cr; i++)
if (grid[diag0(i)] > 0 && grid[diag0(i)] <= cr)
used[grid[diag0(i)]-1] = true;
for (n = 0; n < cr; n++)
if (!used[n]) {
sfree(used);
return false;
}
memset(used, 0, cr * sizeof(bool));
for (i = 0; i < cr; i++)
if (grid[diag1(i)] > 0 && grid[diag1(i)] <= cr)
used[grid[diag1(i)]-1] = true;
for (n = 0; n < cr; n++)
if (!used[n]) {
sfree(used);
return false;
}
}
sfree(used);
return true;
}
static int symmetries(const game_params *params, int x, int y,
int *output, int s)
{
int c = params->c, r = params->r, cr = c*r;
int i = 0;
#define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
ADD(x, y);
switch (s) {
case SYMM_NONE:
break; /* just x,y is all we need */
case SYMM_ROT2:
ADD(cr - 1 - x, cr - 1 - y);
break;
case SYMM_ROT4:
ADD(cr - 1 - y, x);
ADD(y, cr - 1 - x);
ADD(cr - 1 - x, cr - 1 - y);
break;
case SYMM_REF2:
ADD(cr - 1 - x, y);
break;
case SYMM_REF2D:
ADD(y, x);
break;
case SYMM_REF4:
ADD(cr - 1 - x, y);
ADD(x, cr - 1 - y);
ADD(cr - 1 - x, cr - 1 - y);
break;
case SYMM_REF4D:
ADD(y, x);
ADD(cr - 1 - x, cr - 1 - y);
ADD(cr - 1 - y, cr - 1 - x);
break;
case SYMM_REF8:
ADD(cr - 1 - x, y);
ADD(x, cr - 1 - y);
ADD(cr - 1 - x, cr - 1 - y);
ADD(y, x);
ADD(y, cr - 1 - x);
ADD(cr - 1 - y, x);
ADD(cr - 1 - y, cr - 1 - x);
break;
}
#undef ADD
return i;
}
static char *encode_solve_move(int cr, digit *grid)
{
int i, len;
char *ret, *p;
const char *sep;
/*
* It's surprisingly easy to work out _exactly_ how long this
* string needs to be. To decimal-encode all the numbers from 1
* to n:
*
* - every number has a units digit; total is n.
* - all numbers above 9 have a tens digit; total is max(n-9,0).
* - all numbers above 99 have a hundreds digit; total is max(n-99,0).
* - and so on.
*/
len = 0;
for (i = 1; i <= cr; i *= 10)
len += max(cr - i + 1, 0);
len += cr; /* don't forget the commas */
len *= cr; /* there are cr rows of these */
/*
* Now len is one bigger than the total size of the
* comma-separated numbers (because we counted an
* additional leading comma). We need to have a leading S
* and a trailing NUL, so we're off by one in total.
*/
len++;
ret = snewn(len, char);
p = ret;
*p++ = 'S';
sep = "";
for (i = 0; i < cr*cr; i++) {
p += sprintf(p, "%s%d", sep, grid[i]);
sep = ",";
}
*p++ = '\0';
assert(p - ret == len);
return ret;
}
static void dsf_to_blocks(DSF *dsf, struct block_structure *blocks,
int min_expected, int max_expected)
{
int cr = blocks->c * blocks->r, area = cr * cr;
int i, nb = 0;
for (i = 0; i < area; i++)
blocks->whichblock[i] = -1;
for (i = 0; i < area; i++) {
int j = dsf_canonify(dsf, i);
if (blocks->whichblock[j] < 0)
blocks->whichblock[j] = nb++;
blocks->whichblock[i] = blocks->whichblock[j];
}
assert(nb >= min_expected && nb <= max_expected);
blocks->nr_blocks = nb;
}
static void make_blocks_from_whichblock(struct block_structure *blocks)
{
int i;
for (i = 0; i < blocks->nr_blocks; i++) {
blocks->blocks[i][blocks->max_nr_squares-1] = 0;
blocks->nr_squares[i] = 0;
}
for (i = 0; i < blocks->area; i++) {
int b = blocks->whichblock[i];
int j = blocks->blocks[b][blocks->max_nr_squares-1]++;
assert(j < blocks->max_nr_squares);
blocks->blocks[b][j] = i;
blocks->nr_squares[b]++;
}
}
static char *encode_block_structure_desc(char *p, struct block_structure *blocks)
{
int i, currrun = 0;
int c = blocks->c, r = blocks->r, cr = c * r;
/*
* Encode the block structure. We do this by encoding
* the pattern of dividing lines: first we iterate
* over the cr*(cr-1) internal vertical grid lines in
* ordinary reading order, then over the cr*(cr-1)
* internal horizontal ones in transposed reading
* order.
*
* We encode the number of non-lines between the
* lines; _ means zero (two adjacent divisions), a
* means 1, ..., y means 25, and z means 25 non-lines
* _and no following line_ (so that za means 26, zb 27
* etc).
*/
for (i = 0; i <= 2*cr*(cr-1); i++) {
int x, y, p0, p1;
bool edge;
if (i == 2*cr*(cr-1)) {
edge = true; /* terminating virtual edge */
} else {
if (i < cr*(cr-1)) {
y = i/(cr-1);
x = i%(cr-1);
p0 = y*cr+x;
p1 = y*cr+x+1;
} else {
x = i/(cr-1) - cr;
y = i%(cr-1);
p0 = y*cr+x;
p1 = (y+1)*cr+x;
}
edge = (blocks->whichblock[p0] != blocks->whichblock[p1]);
}
if (edge) {
while (currrun > 25)
*p++ = 'z', currrun -= 25;
if (currrun)
*p++ = 'a'-1 + currrun;
else
*p++ = '_';
currrun = 0;
} else
currrun++;
}
return p;
}
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;
}
/*
* Conservatively stimate the number of characters required for
* encoding a grid of a certain area.
*/
static int grid_encode_space (int area)
{
int t, count;
for (count = 1, t = area; t > 26; t -= 26)
count++;
return count * area;
}
/*
* Conservatively stimate the number of characters required for
* encoding a given blocks structure.
*/
static int blocks_encode_space(struct block_structure *blocks)
{
int cr = blocks->c * blocks->r, area = cr * cr;
return grid_encode_space(area);
}
static char *encode_puzzle_desc(const game_params *params, digit *grid,
struct block_structure *blocks,
digit *kgrid,
struct block_structure *kblocks)
{
int c = params->c, r = params->r, cr = c*r;
int area = cr*cr;
char *p, *desc;
int space;
space = grid_encode_space(area) + 1;
if (r == 1)
space += blocks_encode_space(blocks) + 1;
if (params->killer) {
space += blocks_encode_space(kblocks) + 1;
space += grid_encode_space(area) + 1;
}
desc = snewn(space, char);
p = encode_grid(desc, grid, area);
if (r == 1) {
*p++ = ',';
p = encode_block_structure_desc(p, blocks);
}
if (params->killer) {
*p++ = ',';
p = encode_block_structure_desc(p, kblocks);
*p++ = ',';
p = encode_grid(p, kgrid, area);
}
assert(p - desc < space);
*p++ = '\0';
desc = sresize(desc, p - desc, char);
return desc;
}
static void merge_blocks(struct block_structure *b, int n1, int n2)
{
int i;
/* Move data towards the lower block number. */
if (n2 < n1) {
int t = n2;
n2 = n1;
n1 = t;
}
/* Merge n2 into n1, and move the last block into n2's position. */
for (i = 0; i < b->nr_squares[n2]; i++)
b->whichblock[b->blocks[n2][i]] = n1;
memcpy(b->blocks[n1] + b->nr_squares[n1], b->blocks[n2],
b->nr_squares[n2] * sizeof **b->blocks);
b->nr_squares[n1] += b->nr_squares[n2];
n1 = b->nr_blocks - 1;
if (n2 != n1) {
memcpy(b->blocks[n2], b->blocks[n1],
b->nr_squares[n1] * sizeof **b->blocks);
for (i = 0; i < b->nr_squares[n1]; i++)
b->whichblock[b->blocks[n1][i]] = n2;
b->nr_squares[n2] = b->nr_squares[n1];
}
b->nr_blocks = n1;
}
static bool merge_some_cages(struct block_structure *b, int cr, int area,
digit *grid, random_state *rs)
{
/*
* Make a list of all the pairs of adjacent blocks.
*/
int i, j, k;
struct pair {
int b1, b2;
} *pairs;
int npairs;
pairs = snewn(b->nr_blocks * b->nr_blocks, struct pair);
npairs = 0;
for (i = 0; i < b->nr_blocks; i++) {
for (j = i+1; j < b->nr_blocks; j++) {
/*
* Rule the merger out of consideration if it's
* obviously not viable.
*/
if (b->nr_squares[i] + b->nr_squares[j] > b->max_nr_squares)
continue; /* we couldn't merge these anyway */
/*
* See if these two blocks have a pair of squares
* adjacent to each other.
*/
for (k = 0; k < b->nr_squares[i]; k++) {
int xy = b->blocks[i][k];
int y = xy / cr, x = xy % cr;
if ((y > 0 && b->whichblock[xy - cr] == j) ||
(y+1 < cr && b->whichblock[xy + cr] == j) ||
(x > 0 && b->whichblock[xy - 1] == j) ||
(x+1 < cr && b->whichblock[xy + 1] == j)) {
/*
* Yes! Add this pair to our list.
*/
pairs[npairs].b1 = i;
pairs[npairs].b2 = j;
break;
}
}
}
}
/*
* Now go through that list in random order until we find a pair
* of blocks we can merge.
*/
while (npairs > 0) {
int n1, n2;
unsigned int digits_found;
/*
* Pick a random pair, and remove it from the list.
*/
i = random_upto(rs, npairs);
n1 = pairs[i].b1;
n2 = pairs[i].b2;
if (i != npairs-1)
pairs[i] = pairs[npairs-1];
npairs--;
/* Guarantee that the merged cage would still be a region. */
digits_found = 0;
for (i = 0; i < b->nr_squares[n1]; i++)
digits_found |= 1 << grid[b->blocks[n1][i]];
for (i = 0; i < b->nr_squares[n2]; i++)
if (digits_found & (1 << grid[b->blocks[n2][i]]))
break;
if (i != b->nr_squares[n2])
continue;
/*
* Got one! Do the merge.
*/
merge_blocks(b, n1, n2);
sfree(pairs);
return true;
}
sfree(pairs);
return false;
}
static void compute_kclues(struct block_structure *cages, digit *kclues,
digit *grid, int area)
{
int i;
memset(kclues, 0, area * sizeof *kclues);
for (i = 0; i < cages->nr_blocks; i++) {
int j, sum = 0;
for (j = 0; j < area; j++)
if (cages->whichblock[j] == i)
sum += grid[j];
for (j = 0; j < area; j++)
if (cages->whichblock[j] == i)
break;
assert (j != area);
kclues[j] = sum;
}
}
static struct block_structure *gen_killer_cages(int cr, random_state *rs,
bool remove_singletons)
{
int nr;
int x, y, area = cr * cr;
int n_singletons = 0;
struct block_structure *b = alloc_block_structure (1, cr, area, cr, area);
for (x = 0; x < area; x++)
b->whichblock[x] = -1;
nr = 0;
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++) {
int rnd;
int xy = y*cr+x;
if (b->whichblock[xy] != -1)
continue;
b->whichblock[xy] = nr;
rnd = random_bits(rs, 4);
if (xy + 1 < area && (rnd >= 4 || (!remove_singletons && rnd >= 1))) {
int xy2 = xy + 1;
if (x + 1 == cr || b->whichblock[xy2] != -1 ||
(xy + cr < area && random_bits(rs, 1) == 0))
xy2 = xy + cr;
if (xy2 >= area)
n_singletons++;
else
b->whichblock[xy2] = nr;
} else
n_singletons++;
nr++;
}
b->nr_blocks = nr;
make_blocks_from_whichblock(b);
for (x = y = 0; x < b->nr_blocks; x++)
if (b->nr_squares[x] == 1)
y++;
assert(y == n_singletons);
if (n_singletons > 0 && remove_singletons) {
int n;
for (n = 0; n < b->nr_blocks;) {
int xy, x, y, xy2, other;
if (b->nr_squares[n] > 1) {
n++;
continue;
}
xy = b->blocks[n][0];
x = xy % cr;
y = xy / cr;
if (xy + 1 == area)
xy2 = xy - 1;
else if (x + 1 < cr && (y + 1 == cr || random_bits(rs, 1) == 0))
xy2 = xy + 1;
else
xy2 = xy + cr;
other = b->whichblock[xy2];
if (b->nr_squares[other] == 1)
n_singletons--;
n_singletons--;
merge_blocks(b, n, other);
if (n < other)
n++;
}
assert(n_singletons == 0);
}
return b;
}
static key_label *game_request_keys(const game_params *params, int *nkeys)
{
int i;
int cr = params->c * params->r;
key_label *keys = snewn(cr+1, key_label);
*nkeys = cr + 1;
for (i = 0; i < cr; i++) {
if (i<9) keys[i].button = '1' + i;
else keys[i].button = 'a' + i - 9;
keys[i].label = NULL;
}
keys[cr].button = '\b';
keys[cr].label = NULL;
return keys;
}
static char *new_game_desc(const game_params *params, random_state *rs,
char **aux, bool interactive)
{
int c = params->c, r = params->r, cr = c*r;
int area = cr*cr;
struct block_structure *blocks, *kblocks;
digit *grid, *grid2, *kgrid;
struct xy { int x, y; } *locs;
int nlocs;
char *desc;
int coords[16], ncoords;
int x, y, i, j;
struct difficulty dlev;
precompute_sum_bits();
/*
* Adjust the maximum difficulty level to be consistent with
* the puzzle size: all 2x2 puzzles appear to be Trivial
* (DIFF_BLOCK) so we cannot hold out for even a Basic
* (DIFF_SIMPLE) one.
* Jigsaw puzzles of size 2 and 3 are also all trivial.
*/
dlev.maxdiff = params->diff;
dlev.maxkdiff = params->kdiff;
if ((c == 2 && r == 2) || (r == 1 && c < 4))
dlev.maxdiff = DIFF_BLOCK;
grid = snewn(area, digit);
locs = snewn(area, struct xy);
grid2 = snewn(area, digit);
blocks = alloc_block_structure (c, r, area, cr, cr);
kblocks = NULL;
kgrid = (params->killer) ? snewn(area, digit) : NULL;
#ifdef STANDALONE_SOLVER
assert(!"This should never happen, so we don't need to create blocknames");
#endif
/*
* Loop until we get a grid of the required difficulty. This is
* nasty, but it seems to be unpleasantly hard to generate
* difficult grids otherwise.
*/
while (1) {
/*
* Generate a random solved state, starting by
* constructing the block structure.
*/
if (r == 1) { /* jigsaw mode */
DSF *dsf = divvy_rectangle(cr, cr, cr, rs);
dsf_to_blocks (dsf, blocks, cr, cr);
dsf_free(dsf);
} else { /* basic Sudoku mode */
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
}
make_blocks_from_whichblock(blocks);
if (params->killer) {
if (kblocks) free_block_structure(kblocks);
kblocks = gen_killer_cages(cr, rs, params->kdiff > DIFF_KSINGLE);
}
if (!gridgen(cr, blocks, kblocks, params->xtype, grid, rs, area*area))
continue;
assert(check_valid(cr, blocks, kblocks, NULL, params->xtype, grid));
/*
* Save the solved grid in aux.
*/
{
/*
* We might already have written *aux the last time we
* went round this loop, in which case we should free
* the old aux before overwriting it with the new one.
*/
if (*aux) {
sfree(*aux);
}
*aux = encode_solve_move(cr, grid);
}
/*
* Now we have a solved grid. For normal puzzles, we start removing
* things from it while preserving solubility. Killer puzzles are
* different: we just pass the empty grid to the solver, and use
* the puzzle if it comes back solved.
*/
if (params->killer) {
struct block_structure *good_cages = NULL;
struct block_structure *last_cages = NULL;
int ntries = 0;
memcpy(grid2, grid, area);
for (;;) {
compute_kclues(kblocks, kgrid, grid2, area);
memset(grid, 0, area * sizeof *grid);
solver(cr, blocks, kblocks, params->xtype, grid, kgrid, &dlev);
if (dlev.diff == dlev.maxdiff && dlev.kdiff == dlev.maxkdiff) {
/*
* We have one that matches our difficulty. Store it for
* later, but keep going.
*/
if (good_cages)
free_block_structure(good_cages);
ntries = 0;
good_cages = dup_block_structure(kblocks);
if (!merge_some_cages(kblocks, cr, area, grid2, rs))
break;
} else if (dlev.diff > dlev.maxdiff || dlev.kdiff > dlev.maxkdiff) {
/*
* Give up after too many tries and either use the good one we
* found, or generate a new grid.
*/
if (++ntries > 50)
break;
/*
* The difficulty level got too high. If we have a good
* one, use it, otherwise go back to the last one that
* was at a lower difficulty and restart the process from
* there.
*/
if (good_cages != NULL) {
free_block_structure(kblocks);
kblocks = dup_block_structure(good_cages);
if (!merge_some_cages(kblocks, cr, area, grid2, rs))
break;
} else {
if (last_cages == NULL)
break;
free_block_structure(kblocks);
kblocks = last_cages;
last_cages = NULL;
}
} else {
if (last_cages)
free_block_structure(last_cages);
last_cages = dup_block_structure(kblocks);
if (!merge_some_cages(kblocks, cr, area, grid2, rs))
break;
}
}
if (last_cages)
free_block_structure(last_cages);
if (good_cages != NULL) {
free_block_structure(kblocks);
kblocks = good_cages;
compute_kclues(kblocks, kgrid, grid2, area);
memset(grid, 0, area * sizeof *grid);
break;
}
continue;
}
/*
* Find the set of equivalence classes of squares permitted
* by the selected symmetry. We do this by enumerating all
* the grid squares which have no symmetric companion
* sorting lower than themselves.
*/
nlocs = 0;
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++) {
int i = y*cr+x;
int j;
ncoords = symmetries(params, x, y, coords, params->symm);
for (j = 0; j < ncoords; j++)
if (coords[2*j+1]*cr+coords[2*j] < i)
break;
if (j == ncoords) {
locs[nlocs].x = x;
locs[nlocs].y = y;
nlocs++;
}
}
/*
* Now shuffle that list.
*/
shuffle(locs, nlocs, sizeof(*locs), rs);
/*
* Now loop over the shuffled list and, for each element,
* see whether removing that element (and its reflections)
* from the grid will still leave the grid soluble.
*/
for (i = 0; i < nlocs; i++) {
x = locs[i].x;
y = locs[i].y;
memcpy(grid2, grid, area);
ncoords = symmetries(params, x, y, coords, params->symm);
for (j = 0; j < ncoords; j++)
grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
if (dlev.diff <= dlev.maxdiff &&
(!params->killer || dlev.kdiff <= dlev.maxkdiff)) {
for (j = 0; j < ncoords; j++)
grid[coords[2*j+1]*cr+coords[2*j]] = 0;
}
}
memcpy(grid2, grid, area);
solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
if (dlev.diff == dlev.maxdiff &&
(!params->killer || dlev.kdiff == dlev.maxkdiff))
break; /* found one! */
}
sfree(grid2);
sfree(locs);
/*
* Now we have the grid as it will be presented to the user.
* Encode it in a game desc.
*/
desc = encode_puzzle_desc(params, grid, blocks, kgrid, kblocks);
sfree(grid);
free_block_structure(blocks);
if (params->killer) {
free_block_structure(kblocks);
sfree(kgrid);
}
return desc;
}
static const char *spec_to_grid(const 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;
}
/*
* Create a DSF from a spec found in *pdesc. Update this to point past the
* end of the block spec, and return an error string or NULL if everything
* is OK. The DSF is stored in *PDSF.
*/
static const char *spec_to_dsf(const char **pdesc, DSF **pdsf,
int cr, int area)
{
const char *desc = *pdesc;
int pos = 0;
DSF *dsf;
*pdsf = dsf = dsf_new(area);
while (*desc && *desc != ',') {
int c;
bool adv;
if (*desc == '_')
c = 0;
else if (*desc >= 'a' && *desc <= 'z')
c = *desc - 'a' + 1;
else {
dsf_free(dsf);
return "Invalid character in game description";
}
desc++;
adv = (c != 26); /* 'z' is a special case */
while (c-- > 0) {
int p0, p1;
/*
* Non-edge; merge the two dsf classes on either
* side of it.
*/
if (pos >= 2*cr*(cr-1)) {
dsf_free(dsf);
return "Too much data in block structure specification";
}
if (pos < cr*(cr-1)) {
int y = pos/(cr-1);
int x = pos%(cr-1);
p0 = y*cr+x;
p1 = y*cr+x+1;
} else {
int x = pos/(cr-1) - cr;
int y = pos%(cr-1);
p0 = y*cr+x;
p1 = (y+1)*cr+x;
}
dsf_merge(dsf, p0, p1);
pos++;
}
if (adv)
pos++;
}
*pdesc = desc;
/*
* When desc is exhausted, we expect to have gone exactly
* one space _past_ the end of the grid, due to the dummy
* edge at the end.
*/
if (pos != 2*cr*(cr-1)+1) {
dsf_free(dsf);
return "Not enough data in block structure specification";
}
return NULL;
}
static const 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 const char *validate_block_desc(const char **pdesc, int cr, int area,
int min_nr_blocks, int max_nr_blocks,
int min_nr_squares, int max_nr_squares)
{
const char *err;
DSF *dsf;
err = spec_to_dsf(pdesc, &dsf, cr, area);
if (err) {
return err;
}
if (min_nr_squares == max_nr_squares) {
assert(min_nr_blocks == max_nr_blocks);
assert(min_nr_blocks * min_nr_squares == area);
}
/*
* Now we've got our dsf. Verify that it matches
* expectations.
*/
{
int *canons, *counts;
int i, j, c, ncanons = 0;
canons = snewn(max_nr_blocks, int);
counts = snewn(max_nr_blocks, int);
for (i = 0; i < area; i++) {
j = dsf_canonify(dsf, i);
for (c = 0; c < ncanons; c++)
if (canons[c] == j) {
counts[c]++;
if (counts[c] > max_nr_squares) {
dsf_free(dsf);
sfree(canons);
sfree(counts);
return "A jigsaw block is too big";
}
break;
}
if (c == ncanons) {
if (ncanons >= max_nr_blocks) {
dsf_free(dsf);
sfree(canons);
sfree(counts);
return "Too many distinct jigsaw blocks";
}
canons[ncanons] = j;
counts[ncanons] = 1;
ncanons++;
}
}
if (ncanons < min_nr_blocks) {
dsf_free(dsf);
sfree(canons);
sfree(counts);
return "Not enough distinct jigsaw blocks";
}
for (c = 0; c < ncanons; c++) {
if (counts[c] < min_nr_squares) {
dsf_free(dsf);
sfree(canons);
sfree(counts);
return "A jigsaw block is too small";
}
}
sfree(canons);
sfree(counts);
}
dsf_free(dsf);
return NULL;
}
static const char *validate_desc(const game_params *params, const char *desc)
{
int cr = params->c * params->r, area = cr*cr;
const char *err;
err = validate_grid_desc(&desc, cr, area);
if (err)
return err;
if (params->r == 1) {
/*
* Now we expect a suffix giving the jigsaw block
* structure. Parse it and validate that it divides the
* grid into the right number of regions which are the
* right size.
*/
if (*desc != ',')
return "Expected jigsaw block structure in game description";
desc++;
err = validate_block_desc(&desc, cr, area, cr, cr, cr, cr);
if (err)
return err;
}
if (params->killer) {
if (*desc != ',')
return "Expected killer block structure in game description";
desc++;
err = validate_block_desc(&desc, cr, area, cr, area, 2, cr);
if (err)
return err;
if (*desc != ',')
return "Expected killer clue grid in game description";
desc++;
err = validate_grid_desc(&desc, cr * area, area);
if (err)
return err;
}
if (*desc)
return "Unexpected data at end of game description";
return NULL;
}
static game_state *new_game(midend *me, const game_params *params,
const char *desc)
{
game_state *state = snew(game_state);
int c = params->c, r = params->r, cr = c*r, area = cr * cr;
int i;
precompute_sum_bits();
state->cr = cr;
state->xtype = params->xtype;
state->killer = params->killer;
state->grid = snewn(area, digit);
state->pencil = snewn(area * cr, bool);
memset(state->pencil, 0, area * cr * sizeof(bool));
state->immutable = snewn(area, bool);
memset(state->immutable, 0, area * sizeof(bool));
state->blocks = alloc_block_structure (c, r, area, cr, cr);
if (params->killer) {
state->kblocks = alloc_block_structure (c, r, area, cr, area);
state->kgrid = snewn(area, digit);
} else {
state->kblocks = NULL;
state->kgrid = NULL;
}
state->completed = state->cheated = false;
desc = spec_to_grid(desc, state->grid, area);
for (i = 0; i < area; i++)
if (state->grid[i] != 0)
state->immutable[i] = true;
if (r == 1) {
const char *err;
DSF *dsf;
assert(*desc == ',');
desc++;
err = spec_to_dsf(&desc, &dsf, cr, area);
assert(err == NULL);
dsf_to_blocks(dsf, state->blocks, cr, cr);
dsf_free(dsf);
} else {
int x, y;
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
state->blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
}
make_blocks_from_whichblock(state->blocks);
if (params->killer) {
const char *err;
DSF *dsf;
assert(*desc == ',');
desc++;
err = spec_to_dsf(&desc, &dsf, cr, area);
assert(err == NULL);
dsf_to_blocks(dsf, state->kblocks, cr, area);
dsf_free(dsf);
make_blocks_from_whichblock(state->kblocks);
assert(*desc == ',');
desc++;
desc = spec_to_grid(desc, state->kgrid, area);
}
assert(!*desc);
#ifdef STANDALONE_SOLVER
/*
* Set up the block names for solver diagnostic output.
*/
{
char *p = (char *)(state->blocks->blocknames + cr);
if (r == 1) {
for (i = 0; i < area; i++) {
int j = state->blocks->whichblock[i];
if (!state->blocks->blocknames[j]) {
state->blocks->blocknames[j] = p;
p += 1 + sprintf(p, "starting at (%d,%d)",
1 + i%cr, 1 + i/cr);
}
}
} else {
int bx, by;
for (by = 0; by < r; by++)
for (bx = 0; bx < c; bx++) {
state->blocks->blocknames[by*c+bx] = p;
p += 1 + sprintf(p, "(%d,%d)", bx+1, by+1);
}
}
assert(p - (char *)state->blocks->blocknames < (int)(cr*(sizeof(char *)+80)));
for (i = 0; i < cr; i++)
assert(state->blocks->blocknames[i]);
}
#endif
return state;
}
static game_state *dup_game(const game_state *state)
{
game_state *ret = snew(game_state);
int cr = state->cr, area = cr * cr;
ret->cr = state->cr;
ret->xtype = state->xtype;
ret->killer = state->killer;
ret->blocks = state->blocks;
ret->blocks->refcount++;
ret->kblocks = state->kblocks;
if (ret->kblocks)
ret->kblocks->refcount++;
ret->grid = snewn(area, digit);
memcpy(ret->grid, state->grid, area);
if (state->killer) {
ret->kgrid = snewn(area, digit);
memcpy(ret->kgrid, state->kgrid, area);
} else
ret->kgrid = NULL;
ret->pencil = snewn(area * cr, bool);
memcpy(ret->pencil, state->pencil, area * cr * sizeof(bool));
ret->immutable = snewn(area, bool);
memcpy(ret->immutable, state->immutable, area * sizeof(bool));
ret->completed = state->completed;
ret->cheated = state->cheated;
return ret;
}
static void free_game(game_state *state)
{
free_block_structure(state->blocks);
if (state->kblocks)
free_block_structure(state->kblocks);
sfree(state->immutable);
sfree(state->pencil);
sfree(state->grid);
if (state->kgrid) sfree(state->kgrid);
sfree(state);
}
static char *solve_game(const game_state *state, const game_state *currstate,
const char *ai, const char **error)
{
int cr = state->cr;
char *ret;
digit *grid;
struct difficulty dlev;
/*
* If we already have the solution in ai, save ourselves some
* time.
*/
if (ai)
return dupstr(ai);
grid = snewn(cr*cr, digit);
memcpy(grid, state->grid, cr*cr);
dlev.maxdiff = DIFF_RECURSIVE;
dlev.maxkdiff = DIFF_KINTERSECT;
solver(cr, state->blocks, state->kblocks, state->xtype, grid,
state->kgrid, &dlev);
*error = NULL;
if (dlev.diff == DIFF_IMPOSSIBLE)
*error = "No solution exists for this puzzle";
else if (dlev.diff == DIFF_AMBIGUOUS)
*error = "Multiple solutions exist for this puzzle";
if (*error) {
sfree(grid);
return NULL;
}
ret = encode_solve_move(cr, grid);
sfree(grid);
return ret;
}
static char *grid_text_format(int cr, struct block_structure *blocks,
bool xtype, digit *grid)
{
int vmod, hmod;
int x, y;
int totallen, linelen, nlines;
char *ret, *p, ch;
/*
* For non-jigsaw Sudoku, we format in the way we always have,
* by having the digits unevenly spaced so that the dividing
* lines can fit in:
*
* . . | . .
* . . | . .
* ----+----
* . . | . .
* . . | . .
*
* For jigsaw puzzles, however, we must leave space between
* _all_ pairs of digits for an optional dividing line, so we
* have to move to the rather ugly
*
* . . . .
* ------+------
* . . | . .
* +---+
* . . | . | .
* ------+ |
* . . . | .
*
* We deal with both cases using the same formatting code; we
* simply invent a vmod value such that there's a vertical
* dividing line before column i iff i is divisible by vmod
* (so it's r in the first case and 1 in the second), and hmod
* likewise for horizontal dividing lines.
*/
if (blocks->r != 1) {
vmod = blocks->r;
hmod = blocks->c;
} else {
vmod = hmod = 1;
}
/*
* Line length: we have cr digits, each with a space after it,
* and (cr-1)/vmod dividing lines, each with a space after it.
* The final space is replaced by a newline, but that doesn't
* affect the length.
*/
linelen = 2*(cr + (cr-1)/vmod);
/*
* Number of lines: we have cr rows of digits, and (cr-1)/hmod
* dividing rows.
*/
nlines = cr + (cr-1)/hmod;
/*
* Allocate the space.
*/
totallen = linelen * nlines;
ret = snewn(totallen+1, char); /* leave room for terminating NUL */
/*
* Write the text.
*/
p = ret;
for (y = 0; y < cr; y++) {
/*
* Row of digits.
*/
for (x = 0; x < cr; x++) {
/*
* Digit.
*/
digit d = grid[y*cr+x];
if (d == 0) {
/*
* Empty space: we usually write a dot, but we'll
* highlight spaces on the X-diagonals (in X mode)
* by using underscores instead.
*/
if (xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x)))
ch = '_';
else
ch = '.';
} else if (d <= 9) {
ch = '0' + d;
} else {
ch = 'a' + d-10;
}
*p++ = ch;
if (x == cr-1) {
*p++ = '\n';
continue;
}
*p++ = ' ';
if ((x+1) % vmod)
continue;
/*
* Optional dividing line.
*/
if (blocks->whichblock[y*cr+x] != blocks->whichblock[y*cr+x+1])
ch = '|';
else
ch = ' ';
*p++ = ch;
*p++ = ' ';
}
if (y == cr-1 || (y+1) % hmod)
continue;
/*
* Dividing row.
*/
for (x = 0; x < cr; x++) {
int dwid;
int tl, tr, bl, br;
/*
* Division between two squares. This varies
* complicatedly in length.
*/
dwid = 2; /* digit and its following space */
if (x == cr-1)
dwid--; /* no following space at end of line */
if (x > 0 && x % vmod == 0)
dwid++; /* preceding space after a divider */
if (blocks->whichblock[y*cr+x] != blocks->whichblock[(y+1)*cr+x])
ch = '-';
else
ch = ' ';
while (dwid-- > 0)
*p++ = ch;
if (x == cr-1) {
*p++ = '\n';
break;
}
if ((x+1) % vmod)
continue;
/*
* Corner square. This is:
* - a space if all four surrounding squares are in
* the same block
* - a vertical line if the two left ones are in one
* block and the two right in another
* - a horizontal line if the two top ones are in one
* block and the two bottom in another
* - a plus sign in all other cases. (If we had a
* richer character set available we could break
* this case up further by doing fun things with
* line-drawing T-pieces.)
*/
tl = blocks->whichblock[y*cr+x];
tr = blocks->whichblock[y*cr+x+1];
bl = blocks->whichblock[(y+1)*cr+x];
br = blocks->whichblock[(y+1)*cr+x+1];
if (tl == tr && tr == bl && bl == br)
ch = ' ';
else if (tl == bl && tr == br)
ch = '|';
else if (tl == tr && bl == br)
ch = '-';
else
ch = '+';
*p++ = ch;
}
}
assert(p - ret == totallen);
*p = '\0';
return ret;
}
static bool game_can_format_as_text_now(const game_params *params)
{
/*
* Formatting Killer puzzles as text is currently unsupported. I
* can't think of any sensible way of doing it which doesn't
* involve expanding the puzzle to such a large scale as to make
* it unusable.
*/
if (params->killer)
return false;
return true;
}
static char *game_text_format(const game_state *state)
{
assert(!state->kblocks);
return grid_text_format(state->cr, state->blocks, state->xtype,
state->grid);
}
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.
*/
bool 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 is true, pressing a valid number
* or letter key or Space will enter that number or letter in the grid.
*/
bool 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.
*/
bool hcursor;
};
static game_ui *new_ui(const game_state *state)
{
game_ui *ui = snew(game_ui);
ui->hx = ui->hy = 0;
ui->hpencil = false;
ui->hshow = ui->hcursor = getenv_bool("PUZZLES_SHOW_CURSOR", false);
return ui;
}
static void free_ui(game_ui *ui)
{
sfree(ui);
}
static void game_changed_state(game_ui *ui, const game_state *oldstate,
const game_state *newstate)
{
int cr = newstate->cr;
/*
* 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 * cr + ui->hx] != 0) {
ui->hshow = false;
}
}
static const char *current_key_label(const game_ui *ui,
const game_state *state, int button)
{
if (ui->hshow && (button == CURSOR_SELECT))
return ui->hpencil ? "Ink" : "Pencil";
return "";
}
struct game_drawstate {
bool started, xtype;
int cr;
int tilesize;
digit *grid;
unsigned char *pencil;
unsigned char *hl;
/* This is scratch space used within a single call to game_redraw. */
int nregions, *entered_items;
};
static char *interpret_move(const game_state *state, game_ui *ui,
const game_drawstate *ds,
int x, int y, int button)
{
int cr = state->cr;
int tx, ty;
char buf[80];
button &= ~MOD_MASK;
tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
if (button == LEFT_BUTTON) {
if (state->immutable[ty*cr+tx]) {
ui->hshow = false;
} else if (tx == ui->hx && ty == ui->hy &&
ui->hshow && !ui->hpencil) {
ui->hshow = false;
} else {
ui->hx = tx;
ui->hy = ty;
ui->hshow = true;
ui->hpencil = false;
}
ui->hcursor = false;
return MOVE_UI_UPDATE;
}
if (button == RIGHT_BUTTON) {
/*
* Pencil-mode highlighting for non filled squares.
*/
if (state->grid[ty*cr+tx] == 0) {
if (tx == ui->hx && ty == ui->hy &&
ui->hshow && ui->hpencil) {
ui->hshow = false;
} else {
ui->hpencil = true;
ui->hx = tx;
ui->hy = ty;
ui->hshow = true;
}
} else {
ui->hshow = false;
}
ui->hcursor = false;
return MOVE_UI_UPDATE;
}
}
if (IS_CURSOR_MOVE(button)) {
move_cursor(button, &ui->hx, &ui->hy, cr, cr, false);
ui->hshow = true;
ui->hcursor = true;
return MOVE_UI_UPDATE;
}
if (ui->hshow &&
(button == CURSOR_SELECT)) {
ui->hpencil = !ui->hpencil;
ui->hcursor = true;
return MOVE_UI_UPDATE;
}
if (ui->hshow &&
((button >= '0' && button <= '9' && button - '0' <= cr) ||
(button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
(button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
button == CURSOR_SELECT2 || button == '\b')) {
int n = button - '0';
if (button >= 'A' && button <= 'Z')
n = button - 'A' + 10;
if (button >= 'a' && button <= 'z')
n = button - 'a' + 10;
if (button == CURSOR_SELECT2 || button == '\b')
n = 0;
/*
* Can't overwrite this square. This can only happen here
* if we're using the cursor keys.
*/
if (state->immutable[ui->hy*cr+ui->hx])
return NULL;
/*
* Can't make pencil marks in a filled square. Again, this
* can only become highlighted if we're using cursor keys.
*/
if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
return NULL;
/*
* If you ask to fill a square with what it already contains,
* or blank it when it's already empty, that has no effect...
*/
if ((!ui->hpencil || n == 0) && state->grid[ui->hy*cr+ui->hx] == n) {
bool anypencil = false;
int i;
for (i = 0; i < cr; i++)
anypencil = anypencil ||
state->pencil[(ui->hy*cr+ui->hx) * cr + i];
if (!anypencil) {
/* ... expect to remove the cursor in mouse mode. */
if (!ui->hcursor) {
ui->hshow = false;
return MOVE_UI_UPDATE;
}
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 = false;
return dupstr(buf);
}
if (button == 'M' || button == 'm')
return dupstr("M");
return NULL;
}
static game_state *execute_move(const game_state *from, const char *move)
{
int cr = from->cr;
game_state *ret;
int x, y, n;
if (move[0] == 'S') {
const char *p;
ret = dup_game(from);
ret->completed = ret->cheated = true;
p = move+1;
for (n = 0; n < cr*cr; n++) {
ret->grid[n] = atoi(p);
if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
free_game(ret);
return NULL;
}
while (*p && isdigit((unsigned char)*p)) p++;
if (*p == ',') p++;
}
return ret;
} else if ((move[0] == 'P' || move[0] == 'R') &&
sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
ret = dup_game(from);
if (move[0] == 'P' && n > 0) {
int index = (y*cr+x) * cr + (n-1);
ret->pencil[index] = !ret->pencil[index];
} else {
ret->grid[y*cr+x] = n;
memset(ret->pencil + (y*cr+x)*cr, 0, cr);
/*
* We've made a real change to the grid. Check to see
* if the game has been completed.
*/
if (!ret->completed && check_valid(
cr, ret->blocks, ret->kblocks, ret->kgrid,
ret->xtype, ret->grid)) {
ret->completed = true;
}
}
return ret;
} else if (move[0] == 'M') {
/*
* Fill in absolutely all pencil marks in unfilled squares,
* for those who like to play by the rigorous approach of
* starting off in that state and eliminating things.
*/
ret = dup_game(from);
for (y = 0; y < cr; y++) {
for (x = 0; x < cr; x++) {
if (!ret->grid[y*cr+x]) {
int i;
for (i = 0; i < cr; i++)
ret->pencil[(y*cr+x)*cr + i] = true;
}
}
}
return ret;
} else
return NULL; /* couldn't parse move string */
}
/* ----------------------------------------------------------------------
* Drawing routines.
*/
#define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
#define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
static void game_compute_size(const game_params *params, int tilesize,
const game_ui *ui, int *x, int *y)
{
/* Ick: fake up `ds->tilesize' for macro expansion purposes */
struct { int tilesize; } ads, *ds = &ads;
ads.tilesize = tilesize;
*x = SIZE(params->c * params->r);
*y = SIZE(params->c * params->r);
}
static void game_set_size(drawing *dr, game_drawstate *ds,
const 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_XDIAGONALS * 3 + 0] = 0.9F * ret[COL_BACKGROUND * 3 + 0];
ret[COL_XDIAGONALS * 3 + 1] = 0.9F * ret[COL_BACKGROUND * 3 + 1];
ret[COL_XDIAGONALS * 3 + 2] = 0.9F * ret[COL_BACKGROUND * 3 + 2];
ret[COL_GRID * 3 + 0] = 0.0F;
ret[COL_GRID * 3 + 1] = 0.0F;
ret[COL_GRID * 3 + 2] = 0.0F;
ret[COL_CLUE * 3 + 0] = 0.0F;
ret[COL_CLUE * 3 + 1] = 0.0F;
ret[COL_CLUE * 3 + 2] = 0.0F;
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];
ret[COL_KILLER * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
ret[COL_KILLER * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
ret[COL_KILLER * 3 + 2] = 0.1F * ret[COL_BACKGROUND * 3 + 2];
*ncolours = NCOLOURS;
return ret;
}
static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
{
struct game_drawstate *ds = snew(struct game_drawstate);
int cr = state->cr;
ds->started = false;
ds->cr = cr;
ds->xtype = state->xtype;
ds->grid = snewn(cr*cr, digit);
memset(ds->grid, cr+2, cr*cr);
ds->pencil = snewn(cr*cr*cr, digit);
memset(ds->pencil, 0, cr*cr*cr);
ds->hl = snewn(cr*cr, unsigned char);
memset(ds->hl, 0, cr*cr);
/*
* ds->entered_items needs one row of cr entries per entity in
* which digits may not be duplicated. That's one for each row,
* each column, each block, each diagonal, and each Killer cage.
*/
ds->nregions = cr*3 + 2;
if (state->kblocks)
ds->nregions += state->kblocks->nr_blocks;
ds->entered_items = snewn(cr * ds->nregions, int);
ds->tilesize = 0; /* not decided yet */
return ds;
}
static void game_free_drawstate(drawing *dr, game_drawstate *ds)
{
sfree(ds->hl);
sfree(ds->pencil);
sfree(ds->grid);
sfree(ds->entered_items);
sfree(ds);
}
static void draw_number(drawing *dr, game_drawstate *ds,
const game_state *state, int x, int y, int hl)
{
int cr = state->cr;
int tx, ty, tw, th;
int cx, cy, cw, ch;
int col_killer = (hl & 32 ? COL_ERROR : COL_KILLER);
char str[20];
if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
ds->hl[y*cr+x] == hl &&
!memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
return; /* no change required */
tx = BORDER + x * TILE_SIZE + 1 + GRIDEXTRA;
ty = BORDER + y * TILE_SIZE + 1 + GRIDEXTRA;
cx = tx;
cy = ty;
cw = tw = TILE_SIZE-1-2*GRIDEXTRA;
ch = th = TILE_SIZE-1-2*GRIDEXTRA;
if (x > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x-1])
cx -= GRIDEXTRA, cw += GRIDEXTRA;
if (x+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x+1])
cw += GRIDEXTRA;
if (y > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y-1)*cr+x])
cy -= GRIDEXTRA, ch += GRIDEXTRA;
if (y+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y+1)*cr+x])
ch += GRIDEXTRA;
clip(dr, cx, cy, cw, ch);
/* background needs erasing */
draw_rect(dr, cx, cy, cw, ch,
((hl & 15) == 1 ? COL_HIGHLIGHT :
(ds->xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x))) ? COL_XDIAGONALS :
COL_BACKGROUND));
/*
* Draw the corners of thick lines in corner-adjacent squares,
* which jut into this square by one pixel.
*/
if (x > 0 && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x-1])
draw_rect(dr, tx-GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
if (x+1 < cr && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x+1])
draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
if (x > 0 && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x-1])
draw_rect(dr, tx-GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
if (x+1 < cr && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x+1])
draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
/* pencil-mode highlight */
if ((hl & 15) == 2) {
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);
}
if (state->kblocks) {
int t = GRIDEXTRA * 3;
int kcx, kcy, kcw, kch;
int kl, kt, kr, kb;
bool has_left = false, has_right = false;
bool has_top = false, has_bottom = false;
/*
* In non-jigsaw mode, the Killer cages are placed at a
* fixed offset from the outer edge of the cell dividing
* lines, so that they look right whether those lines are
* thick or thin. In jigsaw mode, however, doing this will
* sometimes cause the cage outlines in adjacent squares to
* fail to match up with each other, so we must offset a
* fixed amount from the _centre_ of the cell dividing
* lines.
*/
if (state->blocks->r == 1) {
kcx = tx;
kcy = ty;
kcw = tw;
kch = th;
} else {
kcx = cx;
kcy = cy;
kcw = cw;
kch = ch;
}
kl = kcx - 1;
kt = kcy - 1;
kr = kcx + kcw;
kb = kcy + kch;
/*
* First, draw the lines dividing this area from neighbouring
* different areas.
*/
if (x == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x-1])
has_left = true, kl += t;
if (x+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x+1])
has_right = true, kr -= t;
if (y == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x])
has_top = true, kt += t;
if (y+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x])
has_bottom = true, kb -= t;
if (has_top)
draw_line(dr, kl, kt, kr, kt, col_killer);
if (has_bottom)
draw_line(dr, kl, kb, kr, kb, col_killer);
if (has_left)
draw_line(dr, kl, kt, kl, kb, col_killer);
if (has_right)
draw_line(dr, kr, kt, kr, kb, col_killer);
/*
* Now, take care of the corners (just as for the normal borders).
* We only need a corner if there wasn't a full edge.
*/
if (x > 0 && y > 0 && !has_left && !has_top
&& state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x-1])
{
draw_line(dr, kl, kt + t, kl + t, kt + t, col_killer);
draw_line(dr, kl + t, kt, kl + t, kt + t, col_killer);
}
if (x+1 < cr && y > 0 && !has_right && !has_top
&& state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x+1])
{
draw_line(dr, kcx + kcw - t, kt + t, kcx + kcw, kt + t, col_killer);
draw_line(dr, kcx + kcw - t, kt, kcx + kcw - t, kt + t, col_killer);
}
if (x > 0 && y+1 < cr && !has_left && !has_bottom
&& state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x-1])
{
draw_line(dr, kl, kcy + kch - t, kl + t, kcy + kch - t, col_killer);
draw_line(dr, kl + t, kcy + kch - t, kl + t, kcy + kch, col_killer);
}
if (x+1 < cr && y+1 < cr && !has_right && !has_bottom
&& state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x+1])
{
draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw - t, kcy + kch, col_killer);
draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw, kcy + kch - t, col_killer);
}
}
if (state->killer && state->kgrid[y*cr+x]) {
sprintf (str, "%d", state->kgrid[y*cr+x]);
draw_text(dr, tx + GRIDEXTRA * 4, ty + GRIDEXTRA * 4 + TILE_SIZE/4,
FONT_VARIABLE, TILE_SIZE/4, ALIGN_VNORMAL | ALIGN_HLEFT,
col_killer, str);
}
/* new number needs drawing? */
if (state->grid[y*cr+x]) {
str[1] = '\0';
str[0] = state->grid[y*cr+x] + '0';
if (str[0] > '9')
str[0] += 'a' - ('9'+1);
draw_text(dr, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
} 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 = npencil = 0; i < cr; i++)
if (state->pencil[(y*cr+x)*cr+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 + TILE_SIZE - GRIDEXTRA;
pt = ty + GRIDEXTRA;
pb = pt + TILE_SIZE - GRIDEXTRA;
if (state->killer) {
/*
* Make space for the Killer cages. We do this
* unconditionally, for uniformity between squares,
* rather than making it depend on whether a Killer
* cage edge is actually present on any given side.
*/
pl += GRIDEXTRA * 3;
pr -= GRIDEXTRA * 3;
pt += GRIDEXTRA * 3;
pb -= GRIDEXTRA * 3;
if (state->kgrid[y*cr+x] != 0) {
/* Make further space for the Killer number. */
pt += TILE_SIZE/4;
/* minph--; */
}
}
/*
* 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 + (TILE_SIZE - fontsize * pw) / 2;
pt = ty + (TILE_SIZE - fontsize * ph) / 2;
/*
* And move it down a bit if it's collided with the
* Killer cage number.
*/
if (state->killer && state->kgrid[y*cr+x] != 0) {
pt = max(pt, ty + GRIDEXTRA * 3 + TILE_SIZE/4);
}
/*
* Now actually draw the pencil marks.
*/
for (i = j = 0; i < cr; i++)
if (state->pencil[(y*cr+x)*cr+i]) {
int dx = j % pw, dy = j / pw;
str[1] = '\0';
str[0] = i + '1';
if (str[0] > '9')
str[0] += 'a' - ('9'+1);
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);
ds->grid[y*cr+x] = state->grid[y*cr+x];
memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
ds->hl[y*cr+x] = hl;
}
static void game_redraw(drawing *dr, game_drawstate *ds,
const game_state *oldstate, const game_state *state,
int dir, const game_ui *ui,
float animtime, float flashtime)
{
int cr = state->cr;
int x, y;
if (!ds->started) {
/*
* Draw the grid. We draw it as a big thick rectangle of
* COL_GRID initially; individual calls to draw_number()
* will poke the right-shaped holes in it.
*/
draw_rect(dr, BORDER-GRIDEXTRA, BORDER-GRIDEXTRA,
cr*TILE_SIZE+1+2*GRIDEXTRA, cr*TILE_SIZE+1+2*GRIDEXTRA,
COL_GRID);
}
/*
* This array is used to keep track of rows, columns and boxes
* which contain a number more than once.
*/
for (x = 0; x < cr * ds->nregions; x++)
ds->entered_items[x] = 0;
for (x = 0; x < cr; x++)
for (y = 0; y < cr; y++) {
digit d = state->grid[y*cr+x];
if (d) {
int box, kbox;
/* Rows */
ds->entered_items[x*cr+d-1]++;
/* Columns */
ds->entered_items[(y+cr)*cr+d-1]++;
/* Blocks */
box = state->blocks->whichblock[y*cr+x];
ds->entered_items[(box+2*cr)*cr+d-1]++;
/* Diagonals */
if (ds->xtype) {
if (ondiag0(y*cr+x))
ds->entered_items[(3*cr)*cr+d-1]++;
if (ondiag1(y*cr+x))
ds->entered_items[(3*cr+1)*cr+d-1]++;
}
/* Killer cages */
if (state->kblocks) {
kbox = state->kblocks->whichblock[y*cr+x];
ds->entered_items[(kbox+3*cr+2)*cr+d-1]++;
}
}
}
/*
* Draw any numbers which need redrawing.
*/
for (x = 0; x < cr; x++) {
for (y = 0; y < cr; y++) {
int highlight = 0;
digit d = state->grid[y*cr+x];
if (flashtime > 0 &&
(flashtime <= FLASH_TIME/3 ||
flashtime >= FLASH_TIME*2/3))
highlight = 1;
/* Highlight active input areas. */
if (x == ui->hx && y == ui->hy && ui->hshow)
highlight = ui->hpencil ? 2 : 1;
/* Mark obvious errors (ie, numbers which occur more than once
* in a single row, column, or box). */
if (d && (ds->entered_items[x*cr+d-1] > 1 ||
ds->entered_items[(y+cr)*cr+d-1] > 1 ||
ds->entered_items[(state->blocks->whichblock[y*cr+x]
+2*cr)*cr+d-1] > 1 ||
(ds->xtype && ((ondiag0(y*cr+x) &&
ds->entered_items[(3*cr)*cr+d-1] > 1) ||
(ondiag1(y*cr+x) &&
ds->entered_items[(3*cr+1)*cr+d-1]>1)))||
(state->kblocks &&
ds->entered_items[(state->kblocks->whichblock[y*cr+x]
+3*cr+2)*cr+d-1] > 1)))
highlight |= 16;
if (d && state->kblocks) {
if (check_killer_cage_sum(
state->kblocks, state->kgrid, state->grid,
state->kblocks->whichblock[y*cr+x]) == 0)
highlight |= 32;
}
draw_number(dr, ds, state, x, y, highlight);
}
}
/*
* Update the _entire_ grid if necessary.
*/
if (!ds->started) {
draw_update(dr, 0, 0, SIZE(cr), SIZE(cr));
ds->started = true;
}
}
static float game_anim_length(const game_state *oldstate,
const game_state *newstate, int dir, game_ui *ui)
{
return 0.0F;
}
static float game_flash_length(const game_state *oldstate,
const game_state *newstate, int dir, game_ui *ui)
{
if (!oldstate->completed && newstate->completed &&
!oldstate->cheated && !newstate->cheated)
return FLASH_TIME;
return 0.0F;
}
static void game_get_cursor_location(const game_ui *ui,
const game_drawstate *ds,
const game_state *state,
const game_params *params,
int *x, int *y, int *w, int *h)
{
if(ui->hshow) {
*x = BORDER + ui->hx * TILE_SIZE + 1 + GRIDEXTRA;
*y = BORDER + ui->hy * TILE_SIZE + 1 + GRIDEXTRA;
*w = *h = TILE_SIZE;
}
}
static int game_status(const game_state *state)
{
return state->completed ? +1 : 0;
}
static void game_print_size(const game_params *params, const game_ui *ui,
float *x, float *y)
{
int pw, ph;
/*
* I'll use 9mm squares by default. They should be quite big
* for this game, because players will want to jot down no end
* of pencil marks in the squares.
*/
game_compute_size(params, 900, ui, &pw, &ph);
*x = pw / 100.0F;
*y = ph / 100.0F;
}
/*
* Subfunction to draw the thick lines between cells. In order to do
* this using the line-drawing rather than rectangle-drawing API (so
* as to get line thicknesses to scale correctly) and yet have
* correctly mitred joins between lines, we must do this by tracing
* the boundary of each sub-block and drawing it in one go as a
* single polygon.
*
* This subfunction is also reused with thinner dotted lines to
* outline the Killer cages, this time offsetting the outline toward
* the interior of the affected squares.
*/
static void outline_block_structure(drawing *dr, game_drawstate *ds,
const game_state *state,
struct block_structure *blocks,
int ink, int inset)
{
int cr = state->cr;
int *coords;
int bi, i, n;
int x, y, dx, dy, sx, sy, sdx, sdy;
/*
* Maximum perimeter of a k-omino is 2k+2. (Proof: start
* with k unconnected squares, with total perimeter 4k.
* Now repeatedly join two disconnected components
* together into a larger one; every time you do so you
* remove at least two unit edges, and you require k-1 of
* these operations to create a single connected piece, so
* you must have at most 4k-2(k-1) = 2k+2 unit edges left
* afterwards.)
*/
coords = snewn(4*cr+4, int); /* 2k+2 points, 2 coords per point */
/*
* Iterate over all the blocks.
*/
for (bi = 0; bi < blocks->nr_blocks; bi++) {
if (blocks->nr_squares[bi] == 0)
continue;
/*
* For each block, find a starting square within it
* which has a boundary at the left.
*/
for (i = 0; i < cr; i++) {
int j = blocks->blocks[bi][i];
if (j % cr == 0 || blocks->whichblock[j-1] != bi)
break;
}
assert(i < cr); /* every block must have _some_ leftmost square */
x = blocks->blocks[bi][i] % cr;
y = blocks->blocks[bi][i] / cr;
dx = -1;
dy = 0;
/*
* Now begin tracing round the perimeter. At all
* times, (x,y) describes some square within the
* block, and (x+dx,y+dy) is some adjacent square
* outside it; so the edge between those two squares
* is always an edge of the block.
*/
sx = x, sy = y, sdx = dx, sdy = dy; /* save starting position */
n = 0;
do {
int cx, cy, tx, ty, nin;
/*
* Advance to the next edge, by looking at the two
* squares beyond it. If they're both outside the block,
* we turn right (by leaving x,y the same and rotating
* dx,dy clockwise); if they're both inside, we turn
* left (by rotating dx,dy anticlockwise and contriving
* to leave x+dx,y+dy unchanged); if one of each, we go
* straight on (and may enforce by assertion that
* they're one of each the _right_ way round).
*/
nin = 0;
tx = x - dy + dx;
ty = y + dx + dy;
nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
blocks->whichblock[ty*cr+tx] == bi);
tx = x - dy;
ty = y + dx;
nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
blocks->whichblock[ty*cr+tx] == bi);
if (nin == 0) {
/*
* Turn right.
*/
int tmp;
tmp = dx;
dx = -dy;
dy = tmp;
} else if (nin == 2) {
/*
* Turn left.
*/
int tmp;
x += dx;
y += dy;
tmp = dx;
dx = dy;
dy = -tmp;
x -= dx;
y -= dy;
} else {
/*
* Go straight on.
*/
x -= dy;
y += dx;
}
/*
* Now enforce by assertion that we ended up
* somewhere sensible.
*/
assert(x >= 0 && x < cr && y >= 0 && y < cr &&
blocks->whichblock[y*cr+x] == bi);
assert(x+dx < 0 || x+dx >= cr || y+dy < 0 || y+dy >= cr ||
blocks->whichblock[(y+dy)*cr+(x+dx)] != bi);
/*
* Record the point we just went past at one end of the
* edge. To do this, we translate (x,y) down and right
* by half a unit (so they're describing a point in the
* _centre_ of the square) and then translate back again
* in a manner rotated by dy and dx.
*/
assert(n < 2*cr+2);
cx = ((2*x+1) + dy + dx) / 2;
cy = ((2*y+1) - dx + dy) / 2;
coords[2*n+0] = BORDER + cx * TILE_SIZE;
coords[2*n+1] = BORDER + cy * TILE_SIZE;
coords[2*n+0] -= dx * inset;
coords[2*n+1] -= dy * inset;
if (nin == 0) {
/*
* We turned right, so inset this corner back along
* the edge towards the centre of the square.
*/
coords[2*n+0] -= dy * inset;
coords[2*n+1] += dx * inset;
} else if (nin == 2) {
/*
* We turned left, so inset this corner further
* _out_ along the edge into the next square.
*/
coords[2*n+0] += dy * inset;
coords[2*n+1] -= dx * inset;
}
n++;
} while (x != sx || y != sy || dx != sdx || dy != sdy);
/*
* That's our polygon; now draw it.
*/
draw_polygon(dr, coords, n, -1, ink);
}
sfree(coords);
}
static void game_print(drawing *dr, const game_state *state, const game_ui *ui,
int tilesize)
{
int cr = state->cr;
int ink = print_mono_colour(dr, 0);
int x, y;
/* Ick: fake up `ds->tilesize' for macro expansion purposes */
game_drawstate ads, *ds = &ads;
game_set_size(dr, ds, NULL, tilesize);
/*
* Border.
*/
print_line_width(dr, 3 * TILE_SIZE / 40);
draw_rect_outline(dr, BORDER, BORDER, cr*TILE_SIZE, cr*TILE_SIZE, ink);
/*
* Highlight X-diagonal squares.
*/
if (state->xtype) {
int i;
int xhighlight = print_grey_colour(dr, 0.90F);
for (i = 0; i < cr; i++)
draw_rect(dr, BORDER + i*TILE_SIZE, BORDER + i*TILE_SIZE,
TILE_SIZE, TILE_SIZE, xhighlight);
for (i = 0; i < cr; i++)
if (i*2 != cr-1) /* avoid redoing centre square, just for fun */
draw_rect(dr, BORDER + i*TILE_SIZE,
BORDER + (cr-1-i)*TILE_SIZE,
TILE_SIZE, TILE_SIZE, xhighlight);
}
/*
* Main grid.
*/
for (x = 1; x < cr; x++) {
print_line_width(dr, TILE_SIZE / 40);
draw_line(dr, BORDER+x*TILE_SIZE, BORDER,
BORDER+x*TILE_SIZE, BORDER+cr*TILE_SIZE, ink);
}
for (y = 1; y < cr; y++) {
print_line_width(dr, TILE_SIZE / 40);
draw_line(dr, BORDER, BORDER+y*TILE_SIZE,
BORDER+cr*TILE_SIZE, BORDER+y*TILE_SIZE, ink);
}
/*
* Thick lines between cells.
*/
print_line_width(dr, 3 * TILE_SIZE / 40);
outline_block_structure(dr, ds, state, state->blocks, ink, 0);
/*
* Killer cages and their totals.
*/
if (state->kblocks) {
print_line_width(dr, TILE_SIZE / 40);
print_line_dotted(dr, true);
outline_block_structure(dr, ds, state, state->kblocks, ink,
5 * TILE_SIZE / 40);
print_line_dotted(dr, false);
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
if (state->kgrid[y*cr+x]) {
char str[20];
sprintf(str, "%d", state->kgrid[y*cr+x]);
draw_text(dr,
BORDER+x*TILE_SIZE + 7*TILE_SIZE/40,
BORDER+y*TILE_SIZE + 16*TILE_SIZE/40,
FONT_VARIABLE, TILE_SIZE/4,
ALIGN_VNORMAL | ALIGN_HLEFT,
ink, str);
}
}
/*
* Standard (non-Killer) clue numbers.
*/
for (y = 0; y < cr; y++)
for (x = 0; x < cr; x++)
if (state->grid[y*cr+x]) {
char str[2];
str[1] = '\0';
str[0] = state->grid[y*cr+x] + '0';
if (str[0] > '9')
str[0] += 'a' - ('9'+1);
draw_text(dr, BORDER + x*TILE_SIZE + TILE_SIZE/2,
BORDER + y*TILE_SIZE + TILE_SIZE/2,
FONT_VARIABLE, TILE_SIZE/2,
ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
}
}
#ifdef COMBINED
#define thegame solo
#endif
const struct game thegame = {
"Solo", "games.solo", "solo",
default_params,
game_fetch_preset, NULL,
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,
NULL, NULL, /* get_prefs, set_prefs */
new_ui,
free_ui,
NULL, /* encode_ui */
NULL, /* decode_ui */
game_request_keys,
game_changed_state,
current_key_label,
interpret_move,
execute_move,
PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
game_colours,
game_new_drawstate,
game_free_drawstate,
game_redraw,
game_anim_length,
game_flash_length,
game_get_cursor_location,
game_status,
true, false, game_print_size, game_print,
false, /* wants_statusbar */
false, NULL, /* timing_state */
REQUIRE_RBUTTON | REQUIRE_NUMPAD, /* flags */
};
#ifdef STANDALONE_SOLVER
int main(int argc, char **argv)
{
game_params *p;
game_state *s;
char *id = NULL, *desc;
const char *err;
bool grade = false;
struct difficulty dlev;
while (--argc > 0) {
char *p = *++argv;
if (!strcmp(p, "-v")) {
solver_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);
dlev.maxdiff = DIFF_RECURSIVE;
dlev.maxkdiff = DIFF_KINTERSECT;
solver(s->cr, s->blocks, s->kblocks, s->xtype, s->grid, s->kgrid, &dlev);
if (grade) {
printf("Difficulty rating: %s\n",
dlev.diff==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
dlev.diff==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
dlev.diff==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
dlev.diff==DIFF_SET ? "Advanced (set elimination required)":
dlev.diff==DIFF_EXTREME ? "Extreme (complex non-recursive techniques required)":
dlev.diff==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
dlev.diff==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
dlev.diff==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
"INTERNAL ERROR: unrecognised difficulty code");
if (p->killer)
printf("Killer difficulty: %s\n",
dlev.kdiff==DIFF_KSINGLE ? "Trivial (single square cages only)":
dlev.kdiff==DIFF_KMINMAX ? "Simple (maximum sum analysis required)":
dlev.kdiff==DIFF_KSUMS ? "Intermediate (sum possibilities)":
dlev.kdiff==DIFF_KINTERSECT ? "Advanced (sum region intersections)":
"INTERNAL ERROR: unrecognised difficulty code");
} else {
printf("%s\n", grid_text_format(s->cr, s->blocks, s->xtype, s->grid));
}
return 0;
}
#endif
/* vim: set shiftwidth=4 tabstop=8: */