feat: next group theory

src/core/CMakeLists.txt

@@ -25,6 +25,7 @@ set(KLOTSKI_CORE_SRC
 
         group/internal/group_union.cc
         group/internal/group.cc
+        group/internal/group_pro.cc
         group/internal/group_cases.cc
 
         ranges/internal/spawn.cc

src/core/group/group.h

@@ -79,6 +79,7 @@ typedef std::vector<codec::RawCode> RawCodes;
 typedef std::vector<codec::CommonCode> CommonCodes;
 
 class Group;
+class GroupPro;
 
 // TODO: add constexpr
 class GroupUnion {
@@ -107,6 +108,13 @@ public:
     /// Get the upper limit of the group size.
     [[nodiscard]] constexpr uint32_t max_group_size() const;
 
+    // ------------------------------------------------------------------------------------- //
+    /// TODO: new interface
+
+    [[nodiscard]] constexpr uint32_t pattern_num() const;
+
+    [[nodiscard]] std::vector<GroupPro> groups_pro() const;
+
     // ------------------------------------------------------------------------------------- //
 
     /// Get all cases under the current type id.
@@ -145,8 +153,65 @@ private:
     // ------------------------------------------------------------------------------------- //
 };
 
+// TODO: add `==` and `std::hash`
+
 // TODO: add debug output
 
+class GroupPro {
+public:
+    GroupPro() = delete;
+
+    enum class MirrorType {
+        FullMirror = 0,
+        HorizontalMirror = 1,
+        CentroMirror = 2,
+        VerticalMirror = 3,
+        NonMirror = 4,
+    };
+
+    // NOTE: using enum `MirrorTowards`
+    static GroupPro unsafe_create(uint32_t type_id, uint32_t pattern_id, uint32_t mirror_toward) {
+        return {type_id, pattern_id, mirror_toward};
+    }
+
+    [[nodiscard]] constexpr uint32_t type_id() const {
+        return type_id_;
+    }
+
+    [[nodiscard]] constexpr uint32_t pattern_id() const {
+        return pattern_id_;
+    }
+
+    [[nodiscard]] constexpr uint32_t mirror_toward() const {
+        return mirror_toward_;
+    }
+
+    [[nodiscard]] constexpr uint32_t size() const;
+
+    [[nodiscard]] constexpr MirrorType mirror_type() const;
+
+    [[nodiscard]] constexpr bool is_vertical_mirror() const;
+    [[nodiscard]] constexpr bool is_horizontal_mirror() const;
+
+    [[nodiscard]] constexpr GroupPro to_vertical_mirror() const;
+    [[nodiscard]] constexpr GroupPro to_horizontal_mirror() const;
+
+    RangesUnion cases() const;
+
+private:
+    uint32_t type_id_;
+    uint32_t pattern_id_;
+    uint32_t mirror_toward_;
+
+    GroupPro(uint32_t type_id, uint32_t pattern_id, uint32_t mirror_toward) {
+        type_id_ = type_id;
+        pattern_id_ = pattern_id;
+        mirror_toward_ = mirror_toward;
+    }
+
+    [[nodiscard]] constexpr uint32_t flat_id() const;
+};
+
 class Group {
 public:
     Group() = delete;
@@ -281,3 +346,5 @@ public:
 #include "internal/group_union.inl"
 #include "internal/group_cases.inl"
 #include "internal/group.inl"
+
+#include "internal/group_pro.inl"

src/core/group/internal/constant/group_union.h

@@ -25,6 +25,24 @@ constexpr auto GROUP_NUM = std::to_array<uint16_t>({
 
 constexpr auto GROUP_OFFSET = to_offset<uint16_t, 203>(GROUP_NUM);
 
+constexpr auto PATTERN_NUM = std::to_array<uint16_t>({
+    1 , 1  , 1  , 1  , 1  , 1  , 1 , 1  , 1  , 1  , 1  , 1  , 1 , 1  , 1  , 1  ,
+    1 , 1  , 1  , 1  , 1  , 1  , 1 , 1  , 1  , 1  , 1  , 4  , 1 , 1  , 1  , 1  ,
+    1 , 1  , 1  , 1  , 1  , 1  , 1 , 1  , 2  , 1  , 1  , 1  , 1 , 1  , 1  , 1  ,
+    1 , 1  , 2  , 22 , 1  , 1  , 1 , 1  , 1  , 1  , 1  , 1  , 1 , 6  , 36 , 1  ,
+    1 , 1  , 1  , 1  , 1  , 1  , 1 , 1  , 1  , 5  , 1  , 1  , 1 , 1  , 1  , 1  ,
+    1 , 6  , 70 , 1  , 1  , 1  , 1 , 1  , 1  , 3  , 37 , 211, 1 , 1  , 1  , 1  ,
+    1 , 1  , 5  , 25 , 131, 1  , 1 , 1  , 1  , 1  , 1  , 1  , 2 , 24 , 1  , 1  ,
+    1 , 1  , 1  , 17 , 150, 1  , 1 , 1  , 1  , 6  , 89 , 436, 1 , 1  , 1  , 3  ,
+    22, 122, 589, 1  , 1  , 1  , 2 , 9  , 42 , 265, 1  , 1  , 1 , 1  , 1  , 3  ,
+    41, 1  , 1  , 1  , 15 , 129, 1 , 1  , 4  , 82 , 433, 2  , 3 , 27 , 160, 658,
+    1 , 5  , 24 , 123, 665, 1  , 1 , 4  , 20 , 230, 1  , 1  , 1 , 1  , 21 , 1  ,
+    1 , 36 , 4  , 32 , 148, 8  , 48, 276, 9  , 53 , 295, 4  , 46, 306, 3  , 5  ,
+    58, 2  , 6  , 15 , 1  , 11 , 12, 31 , 24 , 19 , 6  ,
+});
+
+const auto PATTERN_OFFSET = to_offset<uint16_t, 203>(PATTERN_NUM);
+
 /// The maximum Group size in each GroupUnion.
 constexpr auto MAX_GROUP_SIZE = std::to_array<uint32_t>({
     12    , 192   , 1440  , 6720  , 21840 , 52416 , 96096 , 137280, 154440, 137280, 96096 , 52416 ,

src/core/group/internal/group_pro.cc

@@ -0,0 +1,38 @@
+#include <algorithm>
+
+#include "group/group.h"
+
+using klotski::cases::GroupPro;
+
+using klotski::codec::CommonCode;
+
+using klotski::cases::RangesUnion;
+
+using klotski::cases::GROUP_PRO_SEED;
+
+RangesUnion GroupPro::cases() const {
+    auto seed = CommonCode::unsafe_create(GROUP_PRO_SEED[flat_id()]);
+
+    // NOTE: convert as RawCode directly
+    if (mirror_toward_ == 1) {
+        seed = seed.to_horizontal_mirror();
+    } else if (mirror_toward_ == 2) {
+        seed = seed.to_vertical_mirror();
+    } else if (mirror_toward_ == 3) {
+        // NOTE: avoid multi convert
+        seed = seed.to_vertical_mirror().to_horizontal_mirror();
+    }
+
+    auto codes = Group::extend(seed.to_raw_code(), size());
+
+    RangesUnion data;
+    for (auto raw_code : codes) {
+        auto common_code = raw_code.to_common_code().unwrap();
+        data[common_code >> 32].emplace_back(static_cast<uint32_t>(common_code));
+    }
+
+    for (int head = 0; head < 16; ++head) {
+        std::stable_sort(data[head].begin(), data[head].end());
+    }
+    return data;
+}

src/core/group/internal/group_pro.inl

@@ -0,0 +1,111 @@
+#pragma once
+
+#include "constant/group_pro.h"
+
+namespace klotski::cases {
+
+constexpr uint32_t GroupPro::flat_id() const {
+    return PATTERN_OFFSET[type_id_] + pattern_id_;
+}
+
+constexpr uint32_t GroupPro::size() const {
+    return GROUP_PRO_SIZE[flat_id()];
+}
+
+constexpr GroupPro::MirrorType GroupPro::mirror_type() const {
+    switch (GROUP_PRO_TYPE[flat_id()]) {
+        case 0:
+            return MirrorType::FullMirror;
+        case 1:
+            return MirrorType::HorizontalMirror;
+        case 2:
+            return MirrorType::CentroMirror;
+        case 3:
+            return MirrorType::VerticalMirror;
+        case 4:
+            return MirrorType::NonMirror;
+    }
+}
+
+constexpr bool GroupPro::is_vertical_mirror() const {
+    switch (mirror_type()) {
+        case MirrorType::FullMirror:
+            return true;
+        case MirrorType::HorizontalMirror:
+            return false;
+        case MirrorType::CentroMirror:
+            return false;
+        case MirrorType::VerticalMirror:
+            return true;
+        case MirrorType::NonMirror:
+            return false;
+    }
+}
+
+constexpr bool GroupPro::is_horizontal_mirror() const {
+    switch (mirror_type()) {
+        case MirrorType::FullMirror:
+            return true;
+        case MirrorType::HorizontalMirror:
+            return true;
+        case MirrorType::CentroMirror:
+            return false;
+        case MirrorType::VerticalMirror:
+            return false;
+        case MirrorType::NonMirror:
+            return false;
+    }
+}
+
+constexpr GroupPro GroupPro::to_vertical_mirror() const {
+    switch (mirror_type()) {
+        case MirrorType::FullMirror:
+            return *this;
+        case MirrorType::HorizontalMirror:
+            if (mirror_toward_ == 0) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 2);
+            }
+            return GroupPro::unsafe_create(type_id_, pattern_id_, 0);
+        case MirrorType::CentroMirror:
+            if (mirror_toward_ == 0) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 1);
+            }
+            return GroupPro::unsafe_create(type_id_, pattern_id_, 0);
+        case MirrorType::VerticalMirror:
+            return *this;
+        case MirrorType::NonMirror:
+            if (mirror_toward_ == 0) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 2);
+            } else if (mirror_toward_ == 1) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 3);
+            } else if (mirror_toward_ == 2) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 0);
+            }
+            return GroupPro::unsafe_create(type_id_, pattern_id_, 1);
+    }
+}
+
+constexpr GroupPro GroupPro::to_horizontal_mirror() const {
+    switch (mirror_type()) {
+        case MirrorType::FullMirror:
+        case MirrorType::HorizontalMirror:
+            return *this;
+        case MirrorType::CentroMirror:
+        case MirrorType::VerticalMirror:
+            if (mirror_toward_ == 0) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 1);
+            }
+            return GroupPro::unsafe_create(type_id_, pattern_id_, 0);
+        case MirrorType::NonMirror:
+            if (mirror_toward_ == 0) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 2);
+            } else if (mirror_toward_ == 1) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 3);
+            } else if (mirror_toward_ == 2) {
+                return GroupPro::unsafe_create(type_id_, pattern_id_, 0);
+            }
+            return GroupPro::unsafe_create(type_id_, pattern_id_, 1);
+    }
+}
+
+} // namespace klotski::cases

src/core/group/internal/group_union.inl

@@ -53,6 +53,39 @@ inline std::optional<Group> GroupUnion::group(const uint32_t group_id) const {
 	return std::nullopt;
 }
 
+// ----------------------------------------------------------------------------------------- //
+// TODO: new interface
+
+constexpr uint32_t GroupUnion::pattern_num() const {
+    return PATTERN_NUM[type_id_];
+}
+
+inline std::vector<GroupPro> GroupUnion::groups_pro() const {
+    std::vector<GroupPro> groups;
+    groups.reserve(group_num());
+    for (uint32_t pattern_id = 0; pattern_id < pattern_num(); ++pattern_id) {
+        auto group = GroupPro::unsafe_create(type_id_, pattern_id, 0);
+        groups.emplace_back(group);
+        switch (group.mirror_type()) {
+            case GroupPro::MirrorType::FullMirror:
+                continue;
+            case GroupPro::MirrorType::HorizontalMirror:
+                groups.emplace_back(GroupPro::unsafe_create(type_id_, pattern_id, 2));
+                break;
+            case GroupPro::MirrorType::CentroMirror:
+            case GroupPro::MirrorType::VerticalMirror:
+                groups.emplace_back(GroupPro::unsafe_create(type_id_, pattern_id, 1));
+                break;
+            case GroupPro::MirrorType::NonMirror:
+                groups.emplace_back(GroupPro::unsafe_create(type_id_, pattern_id, 1));
+                groups.emplace_back(GroupPro::unsafe_create(type_id_, pattern_id, 2));
+                groups.emplace_back(GroupPro::unsafe_create(type_id_, pattern_id, 3));
+                break;
+        }
+    }
+    return groups;
+}
+
 // ----------------------------------------------------------------------------------------- //
 
 inline GroupUnion GroupUnion::from_raw_code(const codec::RawCode raw_code) {

src/core/main.cc

@@ -27,6 +27,7 @@ using klotski::codec::CommonCode;
 using klotski::cases::GroupUnion;
 
 using klotski::cases::Group;
+using klotski::cases::GroupPro;
 using klotski::cases::GroupCases;
 using klotski::cases::GroupUnion;
 
@@ -52,10 +53,34 @@ int main() {
 //    std::cout << GroupCases::fast_obtain(CommonCode::unsafe_create(0x1A9BF0C00)) << std::endl;
 //    std::cout << GroupCases::fast_obtain(CommonCode::unsafe_create(0x4FEA13400)) << std::endl;
 
-    auto group = Group::unsafe_create(123, 1446);
+    auto gu = GroupUnion::unsafe_create(169);
+    std::cout << gu.pattern_num() << std::endl;
 
-    std::cout << group.to_horizontal_mirror().group_id() << std::endl;
+    std::cout << gu.group_num() << std::endl;
-    std::cout << group.to_vertical_mirror().group_id() << std::endl;
+    std::cout << gu.groups_pro().size() << std::endl;
+
+    const auto g = gu.groups_pro()[1];
+    std::cout << std::format("{}-{}-{}\n", g.type_id(), g.pattern_id(), g.mirror_toward());
+
+    const auto codes = g.cases().codes();
+    std::cout << codes.size() << std::endl;
+    for (const auto code : codes) {
+        if (code == 0x1A9BF0C00) {
+            std::cout << "get it" << std::endl;
+        }
+    }
+
+    std::cout << g.is_vertical_mirror() << std::endl;
+    std::cout << g.is_horizontal_mirror() << std::endl;
+
+    auto g1 = g.to_vertical_mirror();
+    std::cout << std::format("{}-{}-{}\n", g1.type_id(), g1.pattern_id(), g1.mirror_toward());
+    auto g2 = g.to_horizontal_mirror();
+    std::cout << std::format("{}-{}-{}\n", g2.type_id(), g2.pattern_id(), g2.mirror_toward());
+
+//    auto gp = GroupPro::unsafe_create(169, 0, 0);
+//    std::cout << gp.size() << std::endl;
+//    std::cout << (int)gp.mirror_type() << std::endl;
 
     std::cerr << std::chrono::system_clock::now() - start << std::endl;