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@ -1,5 +1,56 @@ |
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#pragma once |
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/// CommonCode is a generic klotski encoding that records an valid case using
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/// 36-bits lengths, and stored in a `uint64_t`.
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/// Since there is only one `2x2` block, it is encoded separately. Its upper
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/// left corner is called `head`, it has 12 possible positions and is encoded
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/// using 4-bits length (0 ~ 15).
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///
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/// 00 01 02 03
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/// 04 05 06 07 00 01 02
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/// 08 09 10 11 04 05 06 <- head of 2x2 block
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/// 12 13 14 15 08 09 10 (without 03/07/11/15)
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/// 16 17 18 19 12 13 14
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/// Treat spaces as special blocks, there can be four kinds of blocks in total,
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/// namely `space`, `1x2`, `2x1`, `1x1`. Each of them is represented by 2-bits,
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/// which are `00` `01` `10` `11`. Arrange them according to their position and
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/// size, and we can get a binary sequence.
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/// 2x2 -> # # | 2x1 -> # | 1x2 -> # # | 1x1 -> #
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/// # # | # | |
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/// This sequence can have up to 16 blocks, aka 32-bits in length. Therefore, in
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/// order to be compatible with all cases, the length of this part of the code
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/// is set to 32-bits. In addition, for the convenience of reading, it is
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/// stipulated that the sequence starts from the high bit, and the remaining bits
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/// should be filled with `0`.
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/// Putting the content of the `head` in the upper 4-bits, and the lower 32-bits
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/// to store the sequence content, a 36-bits length code can be obtained, which
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/// corresponds to any valid layout one-to-one. When CommonCode is converted into
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/// a string, just directly export the hexadecimal data, and get a 9-bits string
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/// encoding. Characters are not case-sensitive, but it is recommended to use
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/// uppercase letters. In addition, the last `0` of the string is allowed to be
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/// omitted, and it can be completed to 9 digits when decoding, but note that if
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/// the encoding is all `0`, it should be reduced to the remaining one `0`.
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/// Eg1:
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/// % # # % 2x2 -> head = 1
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/// % # # % 2x1 2x1 2x1 1x2 2x1 1x1 1x1 1x1 space space 1x1 ... ... ... ... ...
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/// @ $ $ @ 10 10 10 01 10 11 11 11 00 00 11 00 00 00 00 00
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/// @ & * @ 1010 1001 1011 1111 0000 1100 0000 0000
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/// * & A 9 B F 0 C 0 0
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/// CommonCode = 0x1A9BF0C00 -> "1A9BF0C"
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/// Eg2:
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/// * @ & % 2x2 -> head = 4
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/// # # $ % 1x1 1x1 1x1 2x1 2x1 2x1 space 1x2 space 1x1 1x2 ... ... ... ... ...
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/// # # $ ^ 11 11 11 10 10 10 00 01 00 11 01 00 00 00 00 00
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/// ~ ~ ^ 1111 1110 1010 0001 0011 0100 0000 0000
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/// @ % % F E A 1 3 4 0 0
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/// CommonCode = 0x4FEA13400 -> "4FEA134"
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#include <string> |
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#include <cstdint> |
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#include <ostream> |
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