puzzle3d.cc

Go to the documentation of this file.

/*
 *  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;
}