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generator.c
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generator.c
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/* cdok -- Calcudoku solver/generator
* Copyright (C) 2012 Daniel Beer <dlbeer@gmail.com>
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#include <stdlib.h>
#include <string.h>
#include "cdok.h"
#include "solver.h"
#include "generator.h"
/************************************************************************
* Puzzle generator: grid generation
*/
/* Generate a random permutation of the numbers [1..size] */
static void gen_permutation(int size, uint8_t *values)
{
int i;
for (i = 0; i < size; i++)
values[i] = i + 1;
for (i = size - 1; i >= 1; i--) {
int src = random() % (i + 1);
int tmp = values[i];
values[i] = values[src];
values[src] = tmp;
}
}
/* Recursive grid fill. The grid is filled by picking the next empty
* cell in the sequence, and trying each of the possible values in random
* order. If we reach a cell for which there are no possible values, we
* need to backtrack and try again.
*/
struct fill_context {
int size;
uint8_t *grid;
cdok_set_t rows_used[CDOK_SIZE];
cdok_set_t cols_used[CDOK_SIZE];
};
static int fill_grid(struct fill_context *ctx, int x, int y)
{
cdok_set_t used;
uint8_t choices[CDOK_SIZE];
int i;
cdok_pos_t c;
if (x >= ctx->size) {
x = 0;
y++;
}
if (y >= ctx->size)
return 0;
gen_permutation(ctx->size, choices);
used = ctx->rows_used[y] | ctx->cols_used[x];
c = CDOK_POS(x, y);
for (i = 0; i < ctx->size; i++) {
const int v = choices[i];
const cdok_set_t mask = CDOK_SET_SINGLE(v);
if (used & mask)
continue;
ctx->rows_used[y] |= mask;
ctx->cols_used[x] |= mask;
ctx->grid[c] = v;
if (!fill_grid(ctx, x + 1, y))
return 0;
ctx->rows_used[y] &= ~mask;
ctx->cols_used[x] &= ~mask;
}
return -1;
}
/* Generate a random valid solution grid. */
void cdok_generate_grid(uint8_t *values, int size)
{
struct fill_context ctx;
uint8_t top_row[CDOK_SIZE];
int i;
memset(values, 0, CDOK_CELLS * sizeof(values[0]));
memset(&ctx, 0, sizeof(ctx));
ctx.size = size;
ctx.grid = values;
gen_permutation(size, top_row);
for (i = 0; i < size; i++) {
values[CDOK_POS(i, 0)] = top_row[i];
ctx.cols_used[i] = CDOK_SET_SINGLE(top_row[i]);
}
if (fill_grid(&ctx, 0, 1) < 0)
abort();
}
/************************************************************************
* Puzzle generator: basic group operations (invariant-breaking)
*
* These operations preserve the group_map, but may violate geometry
* constraints.
*/
/* Find an unused group and return the index. */
static int group_alloc(struct cdok_puzzle *puz)
{
int i;
for (i = 0; i < CDOK_GROUPS; i++)
if (!puz->groups[i].size)
return i;
return CDOK_GROUP_NONE;
}
/* Destroy a group and turn all its members back into value cells. */
static void group_destroy(struct cdok_puzzle *puz, int grp,
const uint8_t *solution)
{
struct cdok_group *g = &puz->groups[grp];
int i;
for (i = 0; i < g->size; i++) {
const cdok_pos_t c = g->members[i];
puz->values[c] = solution[c];
puz->group_map[c] = CDOK_GROUP_NONE;
}
g->size = 0;
}
/* Remove the given cell from the group. */
static void group_remove(struct cdok_puzzle *puz, int grp,
cdok_pos_t victim,
const uint8_t *solution)
{
struct cdok_group *g = &puz->groups[grp];
int i;
for (i = 0; i < g->size; i++) {
const cdok_pos_t c = g->members[i];
if (c == victim) {
g->members[i] = g->members[g->size - 1];
g->size--;
puz->values[c] = solution[c];
puz->group_map[c] = CDOK_GROUP_NONE;
break;
}
}
}
/* Add the given cell to the group if it doesn't already belong to one.
* No geometry checks are performed.
*/
static void group_add(struct cdok_puzzle *puz, int grp, cdok_pos_t c)
{
struct cdok_group *g = &puz->groups[grp];
if (puz->group_map[c] != CDOK_GROUP_NONE)
return;
if (g->size >= CDOK_GROUP_SIZE)
return;
g->members[g->size++] = c;
puz->values[c] = 0;
puz->group_map[c] = grp;
}
/* Update the target value for a group, if it can possibly be
* constructed. Returns 0 for success, -1 if no valid target exists for
* this combination of values and group type.
*/
static int group_update_target(struct cdok_puzzle *puz, int grp,
const uint8_t *solution,
cdok_flags_t f)
{
struct cdok_group *g = &puz->groups[grp];
int sum = 0;
int product = 1;
int max = -1;
int i;
if (!g->size)
return 0;
if ((g->type == CDOK_DIFFERENCE || g->type == CDOK_RATIO) &&
g->size > 2 && (f & CDOK_FLAGS_TWO_CELL))
return -1;
for (i = 0; i < g->size; i++) {
const uint8_t v = solution[g->members[i]];
if (v > max)
max = v;
sum += v;
product *= v;
}
switch (g->type) {
case CDOK_SUM:
g->target = sum;
break;
case CDOK_DIFFERENCE:
if (max < 0 || max * 2 < sum)
return -1;
g->target = max * 2 - sum;
break;
case CDOK_PRODUCT:
g->target = product;
break;
case CDOK_RATIO:
if ((max * max) % product)
return -1;
g->target = max * max / product;
break;
}
return 0;
}
/************************************************************************
* Puzzle generator: mutations (invariant-preserving)
*/
/* Choose a cell at random. */
static cdok_pos_t choose_cell(int size)
{
return CDOK_POS(random() % size, random() % size);
}
/* Randomly choose one of the given cell's four neighbours. */
static cdok_pos_t choose_neighbour(int size, cdok_pos_t c)
{
int x = CDOK_POS_X(c);
int y = CDOK_POS_Y(c);
int xn = x + 1, yn = y + 1;
if (xn >= size || (x && (random() & 1)))
xn = x - 1;
if (yn >= size || (y && (random() & 1)))
yn = y - 1;
if (random() & 1)
return CDOK_POS(xn, y);
return CDOK_POS(x, yn);
}
/* Correct the geometry of a group and cut off any non-contigous
* regions.
*/
static void cut_islands(struct cdok_puzzle *puz, int grp,
const uint8_t *solution)
{
uint8_t map_copy[CDOK_CELLS];
struct cdok_group *g = &puz->groups[grp];
cdok_pos_t start = g->members[0];
int len = 0;
int i;
if (!g->size)
return;
memcpy(map_copy, puz->group_map, sizeof(map_copy));
cdok_flood_fill(map_copy, grp, CDOK_POS_X(start), CDOK_POS_Y(start));
for (i = 0; i < g->size; i++) {
cdok_pos_t c = g->members[i];
if (map_copy[c] != CDOK_GROUP_NONE) {
puz->values[c] = solution[c];
puz->group_map[c] = CDOK_GROUP_NONE;
} else {
g->members[len++] = c;
}
}
g->size = len;
if (g->size < 2)
group_destroy(puz, grp, solution);
}
/* Randomly alter the type of the given group. Guaranteed to set a type
* which is valid for the group's values.
*/
static void mut_alter_type(struct cdok_puzzle *puz, int grp,
const uint8_t *solution, cdok_flags_t f)
{
cdok_gtype_t types[] = {
CDOK_SUM,
CDOK_DIFFERENCE,
CDOK_PRODUCT,
CDOK_RATIO
};
int i;
for (i = 3; i >= 1; i--) {
int j = random() % (i + 1);
int tmp = types[i];
types[i] = types[j];
types[j] = tmp;
}
for (i = 0; i < 4; i++) {
puz->groups[grp].type = types[i];
if (!group_update_target(puz, grp, solution, f))
break;
}
}
/* Remove the given cell from its group. If necessary, the group will
* be destroyed and/or pruned to maintain geometry constraints. The
* group type may also be altered if necessary.
*/
static void mut_remove_cell(struct cdok_puzzle *puz, cdok_pos_t c,
const uint8_t *solution, cdok_flags_t f)
{
int grp = puz->group_map[c];
if (grp == CDOK_GROUP_NONE)
return;
if (puz->groups[grp].size <= 2) {
group_destroy(puz, grp, solution);
return;
}
group_remove(puz, grp, c, solution);
cut_islands(puz, grp, solution);
if (group_update_target(puz, grp, solution, f) < 0)
mut_alter_type(puz, grp, solution, f);
}
/* Join the given cell (c) so that it belongs to the same group as its
* neighbour. A group will be created if (n) doesn't belong to one. If
* (c) already belongs to a group, it will be removed from that group.
*
* Adjustments are made to both groups if necessary to preserve geometry
* and type/target constraints.
*/
static void mut_join_cells(struct cdok_puzzle *puz,
cdok_pos_t c, cdok_pos_t n,
const uint8_t *solution,
cdok_flags_t f)
{
int ngrp = puz->group_map[n];
int cgrp = puz->group_map[c];
if (cgrp != CDOK_GROUP_NONE) {
if (ngrp == cgrp)
return;
mut_remove_cell(puz, c, solution, f);
}
if (ngrp != CDOK_GROUP_NONE) {
group_add(puz, ngrp, c);
if (group_update_target(puz, ngrp, solution, f) < 0)
mut_alter_type(puz, ngrp, solution, f);
} else {
int g = group_alloc(puz);
if (g == CDOK_GROUP_NONE)
return;
group_add(puz, g, c);
group_add(puz, g, n);
mut_alter_type(puz, g, solution, f);
}
}
/************************************************************************
* Puzzle generator
*/
/* Ensure that the first cell in each group is the one with the smallest
* grid index.
*/
static void normalize_labels(struct cdok_puzzle *puz)
{
int i;
for (i = 0; i < CDOK_GROUPS; i++) {
struct cdok_group *g = &puz->groups[i];
int min = 0;
int j;
if (!g->size)
continue;
for (j = 1; j < g->size; j++)
if (g->members[j] < g->members[min])
min = j;
j = g->members[min];
g->members[min] = g->members[0];
g->members[0] = j;
}
}
/* Perform a hardening iteration on the given puzzle. We make 10 random
* invariant-preserving changes to the puzzle in sequence. After each
* change, we check to see if there's a unique solution. If so, and the
* puzzle has become more difficult, save it.
*/
static int harden(struct cdok_puzzle *puz, const uint8_t *solution,
int best_score_in, cdok_flags_t fl, int limit)
{
int best_score = best_score_in;
struct cdok_puzzle work;
int i;
memcpy(&work, puz, sizeof(work));
for (i = 0; i < 10; i++) {
cdok_pos_t c = choose_cell(puz->size);
cdok_pos_t cn = choose_neighbour(puz->size, c);
int score = 0;
int r;
mut_join_cells(&work, c, cn, solution, fl);
r = cdok_solve(&work, NULL, &score);
if (!r && (score > best_score) &&
(limit <= 0 || score <= limit)) {
memcpy(puz, &work, sizeof(*puz));
best_score = score;
}
}
return best_score;
}
/* Create a puzzle with the given solution and harden it until we reach
* the maximum iteration count or the difficulty threshold.
*/
int cdok_generate(struct cdok_puzzle *puz,
const uint8_t *solution, int size,
cdok_flags_t fl, int iterations, int limit, int target)
{
int best_score = 0;
int i;
if (size < 2)
return 0;
cdok_init_puzzle(puz, size);
memcpy(puz->values, solution, sizeof(puz->values));
for (i = 0; i < iterations; i++) {
if (target > 0 && best_score >= target)
break;
best_score = harden(puz, solution, best_score, fl,
limit);
}
normalize_labels(puz);
return best_score;
}