docs: update AllCases description

src/core/all_cases/all_cases.h

@@ -8,17 +8,19 @@
 
 /// As we all know, a space or 1x1 block will occupy 1 slot, 1x2 and 2x1 block
 /// will occupy 2 slots, and together they fill 16 positions, so all possible
-/// combinations can be calculated, this number is 204, each combination can
+/// combinations can be calculated, the number is 204. Since there are no cases
-/// produce different permutations. After mathematical calculations, there are
+/// with seven 2x1 blocks, we need to remove one combination, which leaves 203
-/// a total of 7311921 possible permutations. The goal of BasicRanges is to
+/// situations. Therefore, each combination can produce different permutations,
-/// find these permutations, sort them and store in a uint32_t array.
+/// after mathematical calculations, there are a total of `7311885` possible
+/// permutations. The goal of BasicRanges is to find these permutations, sort
+/// them and store in a uint32_t array.
 
 /// AllCases is used to generate all valid CommonCodes, its works based on all
 /// permutations generated by BasicRanges, which will use different 2x2 block
 /// positions to check respectively. On the 5x4 chessboard, it has 12 possible
 /// positions, and the numbers are distributed in 0 ~ 15, witch called `head`.
-/// For the convenience of calculation, here use an array of length 16 for
+/// For the convenience of calculation, here we use an array of length 16 for
-/// storage, of course, the position of 3/7/11/15 will be empty.
+/// storage, note that the position of 3/7/11/15 will be empty.
 
 ///   00 01 02 03
 ///   04 05 06 07    00 01 02
@@ -27,8 +29,8 @@
 ///   16 17 18 19    12 13 14
 
 /// After all the work is done, we will have 29334498 cases, distributed in 16
-/// arrays. Each of them is a uint32_t array storing the ranges, this is to
+/// arrays. Each of them is a uint32_t array storing the ranges, which can be
-/// save memory, otherwise the 64-bit length must be consumed.
+/// used to save memory, otherwise the 64-bit length must be consumed.
 
 /// By the way, due to the performance considerations of the checking process,
 /// the resulting data of BasicRanges will be flipped every 2-bit, which will

src/core/all_cases/internal/constant.inl

@@ -4,8 +4,9 @@
 
 namespace klotski::cases {
 
-// ------------------------------------------------------------------------------------- //
+// ----------------------------------------------------------------------------------------- //
 
+/// Number of cases corresponding to the head value.
 constexpr auto ALL_CASES_NUM = std::to_array({
     2942906, 2260392, 2942906, 0,
     2322050, 1876945, 2322050, 0,
@@ -17,8 +18,9 @@ constexpr auto ALL_CASES_NUM_ = array_sum(ALL_CASES_NUM);
 
 constexpr auto ALL_CASES_OFFSET = to_offset(ALL_CASES_NUM);
 
-// ------------------------------------------------------------------------------------- //
+// ----------------------------------------------------------------------------------------- //
 
+/// Number of ranges corresponding to the type_id.
 constexpr auto BASIC_RANGES_NUM = std::to_array({
     1     , 16    , 120   , 560   , 1820 , 4368 , 8008  , 11440 ,
     12870 , 11440 , 8008  , 4368  , 1820 , 560  , 120   , 15    ,
@@ -52,6 +54,6 @@ constexpr auto BASIC_RANGES_NUM_ = array_sum(BASIC_RANGES_NUM);
 
 constexpr auto BASIC_RANGES_OFFSET = to_offset(BASIC_RANGES_NUM);
 
-// ------------------------------------------------------------------------------------- //
+// ----------------------------------------------------------------------------------------- //
 
 } // namespace klotski::cases