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efficient-puzzle
cpp-masssprings/include/puzzle.hpp
Christoph Urlacher 592c4b6cc0 massive state space solver improvement: supercomp took ~10s, now ~40ms 
achieved by imposing a 15 block limit on each board and changing the
internal representation from std::string to 4x uint64_t
2026-03-02 05:26:18 +01:00

482 lines
18 KiB
C++
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#ifndef PUZZLE_HPP_
#define PUZZLE_HPP_
#include "util.hpp"
#include <array>
#include <cstddef>
#include <format>
#include <functional>
#include <ranges>
#include <string>
#include <vector>
#include <bits/fs_fwd.h>
/*
* 8x8 board
* -> 64 (sizes) * 2 (target) * 2 (movable) blocks = 1 Byte
*
* 1. Encode the position inside the board (max 64 cells)
* -> 64 (slots) * 1 Byte (block) = 64 Byte
* 2. Encode the position inside the block (max 64 cells)
* -> 64 (blocks) * 2 Byte (size + pos) = 128 Byte
* 3. Encode the position inside the block (with 15 block limit)
* -> 15 (blocks) * 2 (block) = 30 Byte
*
* Store board size + restricted: +1 Byte
* Store target position: +1 Byte
*
* => Limit to 15 blocks max and use option 3. (4x uint64_t)
*
*/
class puzzle
{
public:
/*
* A block is represented as uint16_t.
* It stores its position, width, height and if it's the target block or immovable.
*/
class block
{
friend class puzzle;
private:
static constexpr uint16_t INVALID = 0x8000;
static constexpr uint8_t IMMOVABLE_S = 0;
static constexpr uint8_t IMMOVABLE_E = 0;
static constexpr uint8_t TARGET_S = 1;
static constexpr uint8_t TARGET_E = 1;
static constexpr uint8_t WIDTH_S = 2;
static constexpr uint8_t WIDTH_E = 4;
static constexpr uint8_t HEIGHT_S = 5;
static constexpr uint8_t HEIGHT_E = 7;
static constexpr uint8_t X_S = 8;
static constexpr uint8_t X_E = 10;
static constexpr uint8_t Y_S = 11;
static constexpr uint8_t Y_E = 13;
/*
* Memory layout:
*
* 154 321 098 765 432 1 0
* B0 YYY XXX HHH WWW T I
* ---------- -----------
* Byte 1 Byte 0
*
* Store the y-position at the most significant bits to obtain a row-major ordering when comparing reprs.
* The block at (0, 0) will be the smallest, the block at (width, height) the largest,
* the block at (1, 0) will be smaller than the block at (0, 1), all independent of block size.
* Then, the block with size (1, 1) will be smaller than the block with size (2, 2),
* the block with size (1, 0) - horizontal - will be smaller than the block with size (0, 1) - vertical.
*
* To mark if a block is empty, the first B bit is set to 1. This is required,
* since otherwise uint16_t{0} would be a valid block. This also makes empty blocks sorted last.
*/
uint16_t repr;
public:
// Produces an invalid block, for usage with std::array<block, MaxBlocks>
block()
: repr(INVALID) {}
explicit block(const uint16_t _repr)
: repr(_repr) {}
block(const int x, const int y, const int w, const int h, const bool t = false, const bool i = false)
: repr(create_repr(x, y, w, h, t, i))
{
if (x < 0 || x + w > MAX_WIDTH || y < 0 || y + h > MAX_HEIGHT) {
throw std::invalid_argument("Block size out of bounds");
}
if (t && i) {
throw std::invalid_argument("Target block can't be immovable");
}
}
auto operator==(const block other) const -> bool
{
return repr == other.repr;
}
auto operator!=(const block other) const -> bool
{
return repr != other.repr;
}
auto operator<(const block other) const -> bool
{
return repr < other.repr;
}
auto operator<=(const block other) const -> bool
{
return repr <= other.repr;
}
auto operator>(const block other) const -> bool
{
return repr > other.repr;
}
auto operator>=(const block other) const -> bool
{
return repr >= other.repr;
}
private:
[[nodiscard]] static auto create_repr(uint8_t x, uint8_t y, uint8_t w, uint8_t h, bool t = false,
bool i = false) -> uint16_t;
// Repr setters
[[nodiscard]] auto set_x(uint8_t x) const -> block;
[[nodiscard]] auto set_y(uint8_t y) const -> block;
[[nodiscard]] auto set_width(uint8_t width) const -> block;
[[nodiscard]] auto set_height(uint8_t height) const -> block;
[[nodiscard]] auto set_target(bool target) const -> block;
[[nodiscard]] auto set_immovable(bool immovable) const -> block;
public:
[[nodiscard]] auto unpack_repr() const -> std::tuple<uint8_t, uint8_t, uint8_t, uint8_t, bool, bool>;
// Repr getters
[[nodiscard]] auto get_x() const -> uint8_t;
[[nodiscard]] auto get_y() const -> uint8_t;
[[nodiscard]] auto get_width() const -> uint8_t;
[[nodiscard]] auto get_height() const -> uint8_t;
[[nodiscard]] auto get_target() const -> bool;
[[nodiscard]] auto get_immovable() const -> bool;
// Util
[[nodiscard]] auto valid() const -> bool;
[[nodiscard]] auto principal_dirs() const -> uint8_t;
[[nodiscard]] auto covers(int _x, int _y) const -> bool;
[[nodiscard]] auto collides(block b) const -> bool;
};
public:
static constexpr uint8_t MAX_BLOCKS = 15;
static constexpr uint8_t MIN_WIDTH = 3;
static constexpr uint8_t MIN_HEIGHT = 3;
static constexpr uint8_t MAX_WIDTH = 8;
static constexpr uint8_t MAX_HEIGHT = 8;
private:
static constexpr uint16_t INVALID = 0x8000;
static constexpr uint8_t RESTRICTED_S = 0;
static constexpr uint8_t RESTRICTED_E = 0;
static constexpr uint8_t GOAL_X_S = 1;
static constexpr uint8_t GOAL_X_E = 3;
static constexpr uint8_t GOAL_Y_S = 4;
static constexpr uint8_t GOAL_Y_E = 6;
static constexpr uint8_t WIDTH_S = 7;
static constexpr uint8_t WIDTH_E = 9;
static constexpr uint8_t HEIGHT_S = 10;
static constexpr uint8_t HEIGHT_E = 12;
static constexpr uint8_t GOAL_S = 13;
static constexpr uint8_t GOAL_E = 13;
struct repr_cooked
{
/*
* Memory layout:
*
* 1543 210 98 7 654 321 0
* B0G HHH WW W YYY XXX R
* ---------- -----------
* Byte 1 Byte 0
*
* To mark if a puzzle is empty, the first B bit is set to 1.
* An extra bit is used to mark if the board has a goal, because we can't store MAX_WIDTH=8 in 3 bits.
*/
uint16_t meta;
// NOTE: For the hashes to work, this array needs to be sorted always.
// NOTE: This array might contain empty blocks at the end. The iterator handles this.
std::array<uint16_t, MAX_BLOCKS> blocks;
// repr_cooked() = delete;
// repr_cooked(const repr_cooked& copy) = delete;
// repr_cooked(repr_cooked&& move) = delete;
} __attribute__((packed));
/**
* With gcc, were allowed to acces the members arbitrarily, even if they're not active (not the ones last written):
* - https://gcc.gnu.org/onlinedocs/gcc-4.7.1/gcc/Structures-unions-enumerations-and-bit_002dfields-implementation.html#Structures-unions-enumerations-and-bit_002dfields-implementation
* - https://gcc.gnu.org/onlinedocs/gcc-4.7.1/gcc/Optimize-Options.html#Type_002dpunning
*/
union repr_u
{
// The representation split into meta information and the blocks array
repr_cooked cooked;
// For 15 blocks, we have sizeof(meta) + blocks.size() * sizeof(block) = 2 + 15 * 2 = 32 Bytes
std::array<uint64_t, 4> raw;
};
repr_u repr;
public:
// Produces an invalid puzzle, for usage with containers
puzzle()
: repr(repr_cooked{INVALID, invalid_blocks()}) {}
explicit puzzle(const uint16_t meta)
: repr(repr_cooked{meta, invalid_blocks()}) {}
// NOTE: This constructor does not sort the blocks and is only for state space generation
puzzle(const std::tuple<uint8_t, uint8_t, uint8_t, uint8_t, bool, bool>& meta,
const std::array<uint16_t, MAX_BLOCKS>& sorted_blocks)
: repr(repr_cooked{create_meta(meta), sorted_blocks}) {}
puzzle(const uint64_t byte_0, const uint64_t byte_1, const uint64_t byte_2, const uint64_t byte_3)
: repr(create_repr(byte_0, byte_1, byte_2, byte_3)) {}
puzzle(const uint16_t meta, const std::array<uint16_t, MAX_BLOCKS>& blocks)
: repr(repr_cooked{meta, blocks}) {}
puzzle(const uint8_t w, const uint8_t h, const uint8_t tx, const uint8_t ty, const bool r, const bool g)
: repr(create_repr(w, h, tx, ty, r, g, invalid_blocks()))
{
if (w < MIN_WIDTH || w > MAX_WIDTH || h < MIN_HEIGHT || h > MAX_HEIGHT) {
throw std::invalid_argument("Board size out of bounds");
}
if (tx >= MAX_WIDTH || ty >= MAX_HEIGHT) {
throw std::invalid_argument("Goal out of bounds");
}
}
puzzle(const uint8_t w, const uint8_t h, const uint8_t tx, const uint8_t ty, const bool r, const bool g,
const std::array<uint16_t, MAX_BLOCKS>& b)
: repr(create_repr(w, h, tx, ty, r, g, b))
{
if (w < MIN_WIDTH || w > MAX_WIDTH || h < MIN_HEIGHT || h > MAX_HEIGHT) {
throw std::invalid_argument("Board size out of bounds");
}
if (tx >= MAX_WIDTH || ty >= MAX_HEIGHT) {
throw std::invalid_argument("Goal out of bounds");
}
}
explicit puzzle(const std::string& string_repr)
: repr(create_repr(string_repr)) {}
public:
auto operator==(const puzzle& other) const -> bool
{
return repr.raw == other.repr.raw;
}
auto operator!=(const puzzle& other) const -> bool
{
return repr.raw != other.repr.raw;
}
auto operator<(const puzzle& other) const -> bool
{
// Start from MSB and go to LSB. If equal, check the next.
for (int i = 3; i >= 0; --i) {
if (repr.raw[i] < other.repr.raw[i]) {
return true;
}
if (repr.raw[i] > other.repr.raw[i]) {
return false;
}
}
// All are equal
return false;
}
auto operator<=(const puzzle& other) const -> bool
{
return *this < other || *this == other;
}
auto operator>(const puzzle& other) const -> bool
{
return !(*this <= other);
}
auto operator>=(const puzzle& other) const -> bool
{
return !(*this < other);
}
auto repr_view() const
{
return std::span<const uint16_t>(repr.cooked.blocks.data(), block_count());
}
auto block_view() const
{
return std::span<const uint16_t>(repr.cooked.blocks.data(), block_count()) | std::views::transform(
[](const uint16_t val)
{
return block(val);
});
}
template <typename T, typename... Rest>
static auto hash_combine(std::size_t& seed, const T& v, const Rest&... rest) -> void;
private:
[[nodiscard]] static constexpr auto invalid_blocks() -> std::array<uint16_t, MAX_BLOCKS>
{
std::array<uint16_t, MAX_BLOCKS> blocks;
for (size_t i = 0; i < MAX_BLOCKS; ++i) {
blocks[i] = block::INVALID;
}
return blocks;
}
[[nodiscard]] static auto create_meta(const std::tuple<uint8_t, uint8_t, uint8_t, uint8_t, bool, bool>& meta) -> uint16_t;
[[nodiscard]] static auto create_repr(uint8_t w, uint8_t h, uint8_t tx, uint8_t ty, bool r, bool g,
const std::array<uint16_t, MAX_BLOCKS>& b) -> repr_cooked;
[[nodiscard]] static auto create_repr(uint64_t byte_0, uint64_t byte_1, uint64_t byte_2,
uint64_t byte_3) -> repr_cooked;
[[nodiscard]] static auto create_repr(const std::string& string_repr) -> repr_cooked;
// Repr setters
[[nodiscard]] auto set_restricted(bool restricted) const -> puzzle;
[[nodiscard]] auto set_width(uint8_t width) const -> puzzle;
[[nodiscard]] auto set_height(uint8_t height) const -> puzzle;
[[nodiscard]] auto set_goal(bool goal) const -> puzzle;
[[nodiscard]] auto set_goal_x(uint8_t target_x) const -> puzzle;
[[nodiscard]] auto set_goal_y(uint8_t target_y) const -> puzzle;
[[nodiscard]] auto set_blocks(std::array<uint16_t, MAX_BLOCKS> blocks) const -> puzzle;
public:
// Repr getters
[[nodiscard]] auto unpack_meta() const -> std::tuple<uint8_t, uint8_t, uint8_t, uint8_t, bool, bool>;
[[nodiscard]] auto get_restricted() const -> bool;
[[nodiscard]] auto get_width() const -> uint8_t;
[[nodiscard]] auto get_height() const -> uint8_t;
[[nodiscard]] auto get_goal() const -> bool;
[[nodiscard]] auto get_goal_x() const -> uint8_t;
[[nodiscard]] auto get_goal_y() const -> uint8_t;
// Util
[[nodiscard]] auto hash() const -> size_t;
[[nodiscard]] auto string_repr() const -> std::string;
[[nodiscard]] static auto try_parse_string_repr(const std::string& string_repr) -> std::optional<repr_cooked>;
[[nodiscard]] auto valid() const -> bool;
[[nodiscard]] auto try_get_invalid_reason() const -> std::optional<std::string>;
[[nodiscard]] auto block_count() const -> uint8_t;
[[nodiscard]] auto goal_reached() const -> bool;
[[nodiscard]] auto try_get_block(uint8_t x, uint8_t y) const -> std::optional<block>;
[[nodiscard]] auto try_get_target_block() const -> std::optional<block>;
[[nodiscard]] auto covers(uint8_t x, uint8_t y, uint8_t _w, uint8_t _h) const -> bool;
[[nodiscard]] auto covers(uint8_t x, uint8_t y) const -> bool;
[[nodiscard]] auto covers(block b) const -> bool;
// Editing
[[nodiscard]] auto toggle_restricted() const -> puzzle;
[[nodiscard]] auto try_set_goal(uint8_t x, uint8_t y) const -> std::optional<puzzle>;
[[nodiscard]] auto clear_goal() const -> puzzle;
[[nodiscard]] auto try_add_column() const -> std::optional<puzzle>;
[[nodiscard]] auto try_remove_column() const -> std::optional<puzzle>;
[[nodiscard]] auto try_add_row() const -> std::optional<puzzle>;
[[nodiscard]] auto try_remove_row() const -> std::optional<puzzle>;
[[nodiscard]] auto try_add_block(block b) const -> std::optional<puzzle>;
[[nodiscard]] auto try_remove_block(uint8_t x, uint8_t y) const -> std::optional<puzzle>;
[[nodiscard]] auto try_toggle_target(uint8_t x, uint8_t y) const -> std::optional<puzzle>;
[[nodiscard]] auto try_toggle_wall(uint8_t x, uint8_t y) const -> std::optional<puzzle>;
// Playing
[[nodiscard]] auto try_move_block_at(uint8_t x, uint8_t y, direction dir) const -> std::optional<puzzle>;
// Statespace
[[nodiscard]] auto try_move_block_at_fast(uint64_t bitmap, uint8_t block_idx,
direction dir) const -> std::optional<puzzle>;
static auto sorted_replace(std::array<uint16_t, MAX_BLOCKS> blocks, uint8_t idx,
uint16_t new_val) -> std::array<uint16_t, MAX_BLOCKS>;
auto blocks_bitmap() const -> uint64_t;
static inline auto bitmap_set_bit(uint64_t bitmap, uint8_t x, uint8_t y) -> uint64_t;
static inline auto bitmap_get_bit(uint64_t bitmap, uint8_t x, uint8_t y) -> bool;
static auto bitmap_clear_block(uint64_t bitmap, block b) -> uint64_t;
static auto bitmap_check_collision(uint64_t bitmap, block b) -> bool;
static auto bitmap_check_collision(uint64_t bitmap, block b, direction dir) -> bool;
template <typename F>
auto for_each_adjacent(F&& callback) const -> void
{
const uint64_t bitmap = blocks_bitmap();
const bool r = get_restricted();
for (uint8_t idx = 0; idx < MAX_BLOCKS; idx++) {
const block b = block(repr.cooked.blocks[idx]);
if (!b.valid()) {
break;
}
if (b.get_immovable()) {
continue;
}
const int dirs = r ? b.principal_dirs() : nor | eas | sou | wes;
for (const direction d : {nor, eas, sou, wes}) {
if (dirs & d) {
if (auto moved = try_move_block_at_fast(bitmap, idx, d)) {
callback(*moved);
}
}
}
}
}
[[nodiscard]] auto explore_state_space() const
-> std::pair<std::vector<puzzle>, std::vector<std::pair<size_t, size_t>>>;
};
// Hash functions for sets and maps
struct puzzle_hasher
{
auto operator()(const puzzle& s) const noexcept -> size_t
{
return s.hash();
}
};
struct link_hasher
{
auto operator()(const std::pair<puzzle, puzzle>& s) const noexcept -> size_t
{
size_t h = 0;
if (s.first < s.second) {
puzzle::hash_combine(h, s.first, s.second);
} else {
puzzle::hash_combine(h, s.second, s.first);
}
return h;
}
};
struct link_equal_to
{
auto operator()(const std::pair<puzzle, puzzle>& a, const std::pair<puzzle, puzzle>& b) const noexcept -> bool
{
return (a.first == b.first && a.second == b.second) || (a.first == b.second && a.second == b.first);
}
};
template <typename T, typename... Rest>
auto puzzle::hash_combine(std::size_t& seed, const T& v, const Rest&... rest) -> void
{
auto h = []<typename HashedType>(const HashedType& val) -> std::size_t
{
if constexpr (std::is_same_v<std::decay_t<HashedType>, puzzle>) {
return puzzle_hasher{}(val);
} else if constexpr (std::is_same_v<std::decay_t<HashedType>, std::pair<puzzle, puzzle>>) {
return link_hasher{}(val);
} else {
return std::hash<std::decay_t<HashedType>>{}(val);
}
};
seed ^= h(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
(hash_combine(seed, rest), ...);
}
#endif
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