/* * ezSAT -- A simple and easy to use CNF generator for SAT solvers * * Copyright (C) 2013 Clifford Wolf <clifford@clifford.at> * * 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; }