diff --git a/src/core_test/cases/group_union.cc b/src/core_test/cases/group_union.cc
index cbcbafa..a3e2ba2 100644
--- a/src/core_test/cases/group_union.cc
+++ b/src/core_test/cases/group_union.cc
@@ -1,14 +1,10 @@
 #include <gtest/gtest.h>
 
-#include <format>
 #include <cstdint>
 #include <algorithm>
 
 #include <ranges>
 
-// TODO: only for debug
-#include <iostream>
-
 #include "group/group.h"
 #include "helper/cases.h"
 #include "common_code/common_code.h"
@@ -21,6 +17,7 @@ using klotski::cases::ALL_GROUP_NUM;
 
 TEST(GroupUnion, basic) {
 
+    // TODO: loop for all
     EXPECT_TRUE(GroupUnion::create(0).has_value());
     EXPECT_EQ(GroupUnion::create(0).value().unwrap(), 0);
     EXPECT_FALSE(GroupUnion::create(TYPE_ID_LIMIT).has_value());
@@ -76,60 +73,18 @@ TEST(GroupUnion, size) {
 }
 
 TEST(GroupUnion, group_num) {
-
     for (uint32_t type_id = 0; type_id < TYPE_ID_LIMIT; ++type_id) {
         EXPECT_EQ(GroupUnion::unsafe_create(type_id).group_num(), group_num(type_id));
-
     }
 }
 
 TEST(GroupUnion, cases) {
     for (uint32_t type_id = 0; type_id < klotski::cases::TYPE_ID_LIMIT; ++type_id) {
         auto cases = group_union_cases(type_id);
-        EXPECT_EQ(cases, klotski::cases::GroupUnion::unsafe_create(type_id).cases().codes());
+        EXPECT_EQ(cases, GroupUnion::unsafe_create(type_id).cases().codes());
     }
 }
 
-TEST(GroupUnion, demo) {
-
-    // for (auto i = 0; i < block_nums().size(); ++i) {
-    //     std::cout << block_nums()[i].n_2x1 + block_nums()[i].n_1x2 << ", ";
-    //     std::cout << block_nums()[i].n_2x1 << ", ";
-    //     std::cout << block_nums()[i].n_1x1 << std::endl;
-    // }
-
-    std::vector<std::vector<uint64_t>> pp;
-
-    pp.resize(block_nums().size());
-
-    for (uint64_t head = 0; head < 16; ++head) {
-
-        for (auto range : AllCases::instance().fetch()[head]) {
-            uint64_t common_code = head << 32 | range;
-
-            auto type_id = to_type_id(cal_block_num(common_code));
-
-            pp[type_id].emplace_back(common_code);
-
-        }
-
-    }
-
-    for (uint32_t type_id = 0; type_id < klotski::cases::TYPE_ID_LIMIT; ++type_id) {
-
-        auto cases = klotski::cases::GroupUnion::unsafe_create(type_id).cases();
-
-        std::vector<uint64_t> extend {};
-        for (uint64_t head = 0; head < 16; ++head) {
-            for (auto range : cases[head]) {
-                extend.emplace_back(head << 32 | range);
-            }
-        }
-
-        std::cout << "type_id " << type_id << " -> " << extend.size() << std::endl;
-
-        EXPECT_EQ(extend, pp[type_id]);
-    }
-
+// TODO: test max_group_size
 
-}
+// TODO: verify from_raw_code / from_short_code / from_common_code
diff --git a/src/core_test/cases/helper/block_num.cc b/src/core_test/cases/helper/block_num.cc
index 277d8b4..d68d29d 100644
--- a/src/core_test/cases/helper/block_num.cc
+++ b/src/core_test/cases/helper/block_num.cc
@@ -24,13 +24,26 @@ static std::vector<block_num_t> build_block_nums() {
             }
         }
     }
-
     std::ranges::sort(nums.begin(), nums.end(), [](const auto lhs, const auto rhs) {
         return lhs.first < rhs.first;
     });
     return std::views::all(nums) | std::views::values | std::ranges::to<std::vector>();
 }
 
+/// Build the mapping table from block_num to type_id.
+static std::unordered_map<block_num_t, uint32_t> build_type_id_map() {
+    std::unordered_map<block_num_t, uint32_t> ids;
+    for (uint64_t i = 0; i < block_nums().size(); ++i) {
+        ids.emplace(block_nums()[i], i); // TODO: using `std::views::enumerate`
+    }
+    return ids;
+}
+
+const std::vector<block_num_t>& block_nums() {
+    static auto data = build_block_nums();
+    return data;
+}
+
 block_num_t cal_block_num(uint32_t range) {
     block_num_t result {};
     for (range = range_reverse(range); range; range >>= 2) {
@@ -50,11 +63,6 @@ block_num_t cal_block_num(uint32_t range) {
     return result;
 }
 
-const std::vector<block_num_t>& block_nums() {
-    static auto data = build_block_nums();
-    return data;
-}
-
 block_num_t to_block_num(const uint32_t type_id) {
     if (type_id < block_nums().size()) {
         return block_nums()[type_id];
@@ -63,14 +71,7 @@ block_num_t to_block_num(const uint32_t type_id) {
 }
 
 uint32_t to_type_id(const block_num_t block_num) {
-    static auto data = [] {
-        std::unordered_map<block_num_t, uint32_t> map;
-        for (auto i = 0; i < block_nums().size(); ++i) {
-            map.emplace(block_nums()[i], i); // TODO: using `std::views::enumerate`
-        }
-        return map;
-    }();
-
+    static auto data = build_type_id_map();
     if (const auto match = data.find(block_num); match != data.end()) {
         return match->second;
     }
diff --git a/src/core_test/cases/helper/group_impl.cc b/src/core_test/cases/helper/group_impl.cc
index b5cfbe3..d74cda1 100644
--- a/src/core_test/cases/helper/group_impl.cc
+++ b/src/core_test/cases/helper/group_impl.cc
@@ -1,99 +1,81 @@
-#include <iostream>
-
 #include "cases.h"
 
-/// Filter cases with different type_id from AllCases.
-static std::vector<std::vector<CommonCode>> build_all_cases() {
-    std::vector<std::vector<CommonCode>> codes;
-    for (auto code : AllCases::instance().fetch().codes()) {
-        const auto type_id = to_type_id(cal_block_num(code.unwrap()));
-        if (type_id >= codes.size()) {
-            codes.resize(type_id + 1);
-        }
-        codes[type_id].emplace_back(code);
-    }
-    return codes;
-}
+// TODO: multi-threads builder
 
-std::vector<CommonCode> extend_cases(CommonCode seed) {
-    auto raw_codes = klotski::cases::Group::extend(seed.to_raw_code()); // TODO: using inner build process
+/// Extend ordered Group from the specified CommonCode seed.
+static std::vector<CommonCode> extend_cases(CommonCode seed) {
+    // TODO: using inner build process
+    auto raw_codes = klotski::cases::Group::extend(seed.to_raw_code());
     std::vector<CommonCode> common_codes {raw_codes.begin(), raw_codes.end()};
     std::ranges::sort(common_codes.begin(), common_codes.end());
     return common_codes;
 }
 
-std::vector<CommonCode> remove_sub(const std::vector<CommonCode> &all, const std::vector<CommonCode> &sub) {
-    std::vector<CommonCode> tmp;
-    tmp.reserve(all.size() - sub.size());
-    std::ranges::set_difference(all.begin(), all.end(), sub.begin(), sub.end(), std::back_inserter(tmp));
-    return tmp;
-}
-
+/// Split Groups from the specified ordered list of CommonCodes.
 static std::vector<std::vector<CommonCode>> split_groups(std::vector<CommonCode> codes) {
-
     std::vector<std::vector<CommonCode>> groups;
-
     while (!codes.empty()) {
-        auto sub = extend_cases(codes[0]);
+        auto group = extend_cases(codes[0]); // sorted array
+        groups.emplace_back(group);
 
-        groups.emplace_back(sub);
-        codes = remove_sub(codes, sub);
+        std::vector<CommonCode> remain;
+        remain.reserve(codes.size() - group.size());
+        std::ranges::set_difference(codes.begin(), codes.end(), group.begin(), group.end(), std::back_inserter(remain));
+        codes = remain; // for next loop
     }
-
-    std::ranges::stable_sort(groups.begin(), groups.end(), [](const std::vector<CommonCode> &g1, const std::vector<CommonCode> &g2) {
-        return g1.size() > g2.size();
+    std::ranges::stable_sort(groups.begin(), groups.end(), [](const auto &lhs, const auto &rhs) {
+        return lhs.size() > rhs.size(); // sort with group size
     });
-
     return groups;
+}
 
+/// Filter cases with different type_id from AllCases.
+static const std::vector<std::vector<CommonCode>>& group_union_data() {
+    static auto data = [] {
+        std::vector<std::vector<CommonCode>> codes;
+        codes.resize(block_nums().size());
+        for (auto code: AllCases::instance().fetch().codes()) {
+            codes[to_type_id(cal_block_num(code.unwrap()))].emplace_back(code);
+        }
+        return codes;
+    }();
+    return data;
 }
 
-// TODO: static data of `build_all_cases`
+/// Construct all valid klotski Groups in different GroupUnion.
+static const std::vector<std::vector<std::vector<CommonCode>>>& group_data() {
+    static auto data = [] {
+        std::vector<std::vector<std::vector<CommonCode>>> groups;
+        groups.reserve(group_union_num());
+        for (uint32_t type_id = 0; type_id < group_union_num(); ++type_id) {
+            groups.emplace_back(split_groups(group_union_cases(type_id)));
+        }
+        return groups;
+    }();
+    return data;
+}
 
 uint32_t group_union_num() {
-    static auto data = build_all_cases();
-    return data.size();
+    return group_union_data().size();
 }
 
-const std::vector<CommonCode>& group_union_cases(const uint32_t type_id) {
-    static auto data = build_all_cases();
-    if (type_id < data.size()) {
-        return data[type_id];
+uint32_t group_num(uint32_t type_id) {
+    if (type_id < group_data().size()) {
+        return group_data()[type_id].size();
     }
     std::abort();
 }
 
-// TODO: multi-threads builder
-
-static std::vector<std::vector<std::vector<CommonCode>>> all_groups_builder() {
-
-    std::vector<std::vector<std::vector<CommonCode>>> data;
-
-    for (uint32_t type_id = 0; type_id < group_union_num(); ++type_id) {
-
-        data.emplace_back(split_groups(group_union_cases(type_id)));
-
-    }
-
-    return data;
-
-}
-
-uint32_t group_num(uint32_t type_id) {
-    static auto data = all_groups_builder();
-    if (type_id < data.size()) {
-        return data[type_id].size();
+const std::vector<CommonCode>& group_union_cases(const uint32_t type_id) {
+    if (type_id < group_union_data().size()) {
+        return group_union_data()[type_id];
     }
     std::abort();
 }
 
 const std::vector<CommonCode>& group_cases(uint32_t type_id, uint32_t group_id) {
-
-    static auto data = all_groups_builder();
-
-    if (type_id < data.size() && group_id < data[type_id].size()) {
-        return data[type_id][group_id];
+    if (type_id < group_data().size() && group_id < group_data()[type_id].size()) {
+        return group_data()[type_id][group_id];
     }
-
     std::abort();
 }