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/*
* ezSAT -- A simple and easy to use CNF generator for SAT solvers
*
* Copyright (C) 2013 Claire Xenia Wolf <claire@yosyshq.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 "ezminisat.h"
#include <stdio.h>
#include <assert.h>
#define DIM_X 5
#define DIM_Y 5
#define DIM_Z 5
#define NUM_124 6
#define NUM_223 6
ezMiniSAT ez;
int blockidx = 0;
std::map<int, std::string> blockinfo;
std::vector<int> grid[DIM_X][DIM_Y][DIM_Z];
struct blockgeom_t
{
int center_x, center_y, center_z;
int size_x, size_y, size_z;
int var;
void mirror_x() { center_x *= -1; }
void mirror_y() { center_y *= -1; }
void mirror_z() { center_z *= -1; }
void rotate_x() { int tmp[4] = { center_y, center_z, size_y, size_z }; center_y = tmp[1]; center_z = -tmp[0]; size_y = tmp[3]; size_z = tmp[2]; }
void rotate_y() { int tmp[4] = { center_x, center_z, size_x, size_z }; center_x = tmp[1]; center_z = -tmp[0]; size_x = tmp[3]; size_z = tmp[2]; }
void rotate_z() { int tmp[4] = { center_x, center_y, size_x, size_y }; center_x = tmp[1]; center_y = -tmp[0]; size_x = tmp[3]; size_y = tmp[2]; }
bool operator< (const blockgeom_t &other) const {
if (center_x != other.center_x) return center_x < other.center_x;
if (center_y != other.center_y) return center_y < other.center_y;
if (center_z != other.center_z) return center_z < other.center_z;
if (size_x != other.size_x) return size_x < other.size_x;
if (size_y != other.size_y) return size_y < other.size_y;
if (size_z != other.size_z) return size_z < other.size_z;
if (var != other.var) return var < other.var;
return false;
}
};
// geometry data for spatial symmetry constraints
std::set<blockgeom_t> blockgeom;
int add_block(int pos_x, int pos_y, int pos_z, int size_x, int size_y, int size_z, int blockidx)
{
char buffer[1024];
snprintf(buffer, 1024, "block(%d,%d,%d,%d,%d,%d,%d);", size_x, size_y, size_z, pos_x, pos_y, pos_z, blockidx);
int var = ez.literal();
blockinfo[var] = buffer;
for (int ix = pos_x; ix < pos_x+size_x; ix++)
for (int iy = pos_y; iy < pos_y+size_y; iy++)
for (int iz = pos_z; iz < pos_z+size_z; iz++)
grid[ix][iy][iz].push_back(var);
blockgeom_t bg;
bg.size_x = 2*size_x;
bg.size_y = 2*size_y;
bg.size_z = 2*size_z;
bg.center_x = (2*pos_x + size_x) - DIM_X;
bg.center_y = (2*pos_y + size_y) - DIM_Y;
bg.center_z = (2*pos_z + size_z) - DIM_Z;
bg.var = var;
assert(blockgeom.count(bg) == 0);
blockgeom.insert(bg);
return var;
}
void add_block_positions_124(std::vector<int> &block_positions_124)
{
block_positions_124.clear();
for (int size_x = 1; size_x <= 4; size_x *= 2)
for (int size_y = 1; size_y <= 4; size_y *= 2)
for (int size_z = 1; size_z <= 4; size_z *= 2) {
if (size_x == size_y || size_y == size_z || size_z == size_x)
continue;
for (int ix = 0; ix <= DIM_X-size_x; ix++)
for (int iy = 0; iy <= DIM_Y-size_y; iy++)
for (int iz = 0; iz <= DIM_Z-size_z; iz++)
block_positions_124.push_back(add_block(ix, iy, iz, size_x, size_y, size_z, blockidx++));
}
}
void add_block_positions_223(std::vector<int> &block_positions_223)
{
block_positions_223.clear();
for (int orientation = 0; orientation < 3; orientation++) {
int size_x = orientation == 0 ? 3 : 2;
int size_y = orientation == 1 ? 3 : 2;
int size_z = orientation == 2 ? 3 : 2;
for (int ix = 0; ix <= DIM_X-size_x; ix++)
for (int iy = 0; iy <= DIM_Y-size_y; iy++)
for (int iz = 0; iz <= DIM_Z-size_z; iz++)
block_positions_223.push_back(add_block(ix, iy, iz, size_x, size_y, size_z, blockidx++));
}
}
// use simple built-in random number generator to
// ensure determinism of the program across platforms
uint32_t xorshift32() {
static uint32_t x = 314159265;
x ^= x << 13;
x ^= x >> 17;
x ^= x << 5;
return x;
}
void condense_exclusives(std::vector<int> &vars)
{
std::map<int, std::set<int>> exclusive;
for (int ix = 0; ix < DIM_X; ix++)
for (int iy = 0; iy < DIM_Y; iy++)
for (int iz = 0; iz < DIM_Z; iz++) {
for (int a : grid[ix][iy][iz])
for (int b : grid[ix][iy][iz])
if (a != b)
exclusive[a].insert(b);
}
std::vector<std::vector<int>> pools;
for (int a : vars)
{
std::vector<int> candidate_pools;
for (size_t i = 0; i < pools.size(); i++)
{
for (int b : pools[i])
if (exclusive[a].count(b) == 0)
goto no_candidate_pool;
candidate_pools.push_back(i);
no_candidate_pool:;
}
if (candidate_pools.size() > 0) {
int p = candidate_pools[xorshift32() % candidate_pools.size()];
pools[p].push_back(a);
} else {
pools.push_back(std::vector<int>());
pools.back().push_back(a);
}
}
std::vector<int> new_vars;
for (auto &pool : pools)
{
std::vector<int> formula;
int var = ez.literal();
for (int a : pool)
formula.push_back(ez.OR(ez.NOT(a), var));
formula.push_back(ez.OR(ez.expression(ezSAT::OpOr, pool), ez.NOT(var)));
ez.assume(ez.onehot(pool, true));
ez.assume(ez.expression(ezSAT::OpAnd, formula));
new_vars.push_back(var);
}
printf("Condensed %d variables into %d one-hot pools.\n", int(vars.size()), int(new_vars.size()));
vars.swap(new_vars);
}
int main()
{
printf("\nCreating SAT encoding..\n");
// add 1x2x4 blocks
std::vector<int> block_positions_124;
add_block_positions_124(block_positions_124);
condense_exclusives(block_positions_124);
ez.assume(ez.manyhot(block_positions_124, NUM_124));
// add 2x2x3 blocks
std::vector<int> block_positions_223;
add_block_positions_223(block_positions_223);
condense_exclusives(block_positions_223);
ez.assume(ez.manyhot(block_positions_223, NUM_223));
// add constraint for max one block per grid element
for (int ix = 0; ix < DIM_X; ix++)
for (int iy = 0; iy < DIM_Y; iy++)
for (int iz = 0; iz < DIM_Z; iz++) {
assert(grid[ix][iy][iz].size() > 0);
ez.assume(ez.onehot(grid[ix][iy][iz], true));
}
printf("Found %d possible block positions.\n", int(blockgeom.size()));
// look for spatial symmetries
std::set<std::set<blockgeom_t>> symmetries;
symmetries.insert(blockgeom);
bool keep_running = true;
while (keep_running) {
keep_running = false;
std::set<std::set<blockgeom_t>> old_sym;
old_sym.swap(symmetries);
for (auto &old_sym_set : old_sym)
{
std::set<blockgeom_t> mx, my, mz;
std::set<blockgeom_t> rx, ry, rz;
for (auto &bg : old_sym_set) {
blockgeom_t bg_mx = bg, bg_my = bg, bg_mz = bg;
blockgeom_t bg_rx = bg, bg_ry = bg, bg_rz = bg;
bg_mx.mirror_x(), bg_my.mirror_y(), bg_mz.mirror_z();
bg_rx.rotate_x(), bg_ry.rotate_y(), bg_rz.rotate_z();
mx.insert(bg_mx), my.insert(bg_my), mz.insert(bg_mz);
rx.insert(bg_rx), ry.insert(bg_ry), rz.insert(bg_rz);
}
if (!old_sym.count(mx) || !old_sym.count(my) || !old_sym.count(mz) ||
!old_sym.count(rx) || !old_sym.count(ry) || !old_sym.count(rz))
keep_running = true;
symmetries.insert(old_sym_set);
symmetries.insert(mx);
symmetries.insert(my);
symmetries.insert(mz);
symmetries.insert(rx);
symmetries.insert(ry);
symmetries.insert(rz);
}
}
// add constraints to eliminate all the spatial symmetries
std::vector<std::vector<int>> vecvec;
for (auto &sym : symmetries) {
std::vector<int> vec;
for (auto &bg : sym)
vec.push_back(bg.var);
vecvec.push_back(vec);
}
for (size_t i = 1; i < vecvec.size(); i++)
ez.assume(ez.ordered(vecvec[0], vecvec[1]));
printf("Found and eliminated %d spatial symmetries.\n", int(symmetries.size()));
printf("Generated %d clauses over %d variables.\n", ez.numCnfClauses(), ez.numCnfVariables());
std::vector<int> modelExpressions;
std::vector<bool> modelValues;
for (auto &it : blockinfo) {
ez.freeze(it.first);
modelExpressions.push_back(it.first);
}
int solution_counter = 0;
while (1)
{
printf("\nSolving puzzle..\n");
bool ok = ez.solve(modelExpressions, modelValues);
if (!ok) {
printf("No more solutions found!\n");
break;
}
printf("Puzzle solution:\n");
std::vector<int> constraint;
for (size_t i = 0; i < modelExpressions.size(); i++)
if (modelValues[i]) {
constraint.push_back(ez.NOT(modelExpressions[i]));
printf("%s\n", blockinfo.at(modelExpressions[i]).c_str());
}
ez.assume(ez.expression(ezSAT::OpOr, constraint));
solution_counter++;
}
printf("\nFound %d distinct solutions.\n", solution_counter);
printf("Have a nice day.\n\n");
return 0;
}
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