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合法华容道布局共有29334498种 合法华容道布局共有29334498种
### 合法布局举例： ### 合法布局举例：
<img src="/images/legal_1.png" alt="legal_1" style="zoom: 40%;" /><img src="/images/legal_2.png" alt="legal_2" style="zoom:40%;" /><img src="/images/legal_3.png" alt="legal_3" style="zoom:40%;" /><img src="/images/legal_4.png" alt="legal_4" style="zoom:40%;" /> <img src="/images/legal_1+2.png" alt="legal_1+2" style="zoom: 40%;" />
<img src="/images/legal_3+4.png" alt="legal_3+4" style="zoom: 40%;" />
### 非法布局举例： ### 非法布局举例：
<img src="/images/illegal_1.png" alt="illegal_1" style="zoom: 40%;" /><img src="/images/illegal_2.png" alt="illegal_2" style="zoom:40%;" /><img src="/images/illegal_3.png" alt="illegal_3" style="zoom:40%;" /><img src="/images/illegal_4.png" alt="illegal_4" style="zoom:40%;" /> <img src="/images/illegal_1+2.png" alt="illegal_1+2" style="zoom: 40%;" />
<img src="/images/illegal_3+4.png" alt="illegal_3+4" style="zoom: 40%;" />
### 布局间的关系 ### 布局间的关系
@ -102,6 +105,7 @@
**编码举例** **编码举例**
**例1：** **例1：**
<img src="/images/code_exp_1.png" alt="exp-1A9BF0C00" style="zoom: 60%;" /> <img src="/images/code_exp_1.png" alt="exp-1A9BF0C00" style="zoom: 60%;" />
@ -153,7 +157,8 @@
<td colspan="2"><b>0</b></td> <td colspan="2"><b>0</b></td>
</tr> </tr>
</table> </table>
因此，布局编码为**1A9BF0C00**，可简写为**1A9BF0C** 因此，布局编码为<b>1A9BF0C00</b>，可简写为<b>1A9BF0C</b>
**例2：** **例2：**
@ -206,7 +211,7 @@
<td colspan="2"><b>0</b></td> <td colspan="2"><b>0</b></td>
</tr> </tr>
</table> </table>
因此，布局编码为**4FEA13400**，可简写为**4FEA134** 因此，布局编码为<b>4FEA13400</b>，可简写为<b>4FEA134</b>
**例3：** **例3：**
@ -261,4 +266,121 @@
<td colspan="2"><b>0</b></td> <td colspan="2"><b>0</b></td>
</tr> </tr>
</table> </table>
因此，布局编码为**5DC02F800**，可简写为**5DC02F8** 因此，布局编码为<b>5DC02F800</b>，可简写为<b>5DC02F8</b>
## 分类
由于共有29334498种布局，将它们从小到大排列，进而得到唯一的id(0 ~ 29334497)；
### 摆列方式分类
将2 x 1（1 x 2）的数量称为jiang_num，1 x 1的数量称为bing_num；
据此可分为64种情况，统计如下：
| jiang_num | bing_num | 数量 |
| :-: | :-: | :-: |
| 0 | 0 | 12 |
| 0 | 1 | 192 |
| 0 | 2 | 1440 |
| 0 | 3 | 6720 |
| 0 | 4 | 21840 |
| 0 | 5 | 52416 |
| 0 | 6 | 96096 |
| 0 | 7 | 137280 |
| 0 | 8 | 154440 |
| 0 | 9 | 137280 |
| 0 | 10 | 96096 |
| 0 | 11 | 52416 |
| 0 | 12 | 21840 |
| 0 | 13 | 6720 |
| 0 | 14 | 1440 |
| 1 | 0 | 256 |
| 1 | 1 | 3584 |
| 1 | 2 | 23296 |
| 1 | 3 | 93184 |
| 1 | 4 | 256256 |
| 1 | 5 | 512512 |
| 1 | 6 | 768768 |
| 1 | 7 | 878592 |
| 1 | 8 | 768768 |
| 1 | 9 | 512512 |
| 1 | 10 | 256256 |
| 1 | 11 | 93184 |
| 1 | 12 | 23296 |
| 2 | 0 | 2138 |
| 2 | 1 | 25656 |
| 2 | 2 | 141108 |
| 2 | 3 | 470360 |
| 2 | 4 | 1058310 |
| 2 | 5 | 1693296 |
| 2 | 6 | 1975512 |
| 2 | 7 | 1693296 |
| 2 | 8 | 1058310 |
| 2 | 9 | 470360 |
| 2 | 10 | 141108 |
| 3 | 0 | 8974 |
| 3 | 1 | 89740 |
| 3 | 2 | 403830 |
| 3 | 3 | 1076880 |
| 3 | 4 | 1884540 |
| 3 | 5 | 2261448 |
| 3 | 6 | 1884540 |
| 3 | 7 | 1076880 |
| 3 | 8 | 403830 |
| 4 | 0 | 20224 |
| 4 | 1 | 161792 |
| 4 | 2 | 566272 |
| 4 | 3 | 1132544 |
| 4 | 4 | 1415680 |
| 4 | 5 | 1132544 |
| 4 | 6 | 566272 |
| 5 | 0 | 24232 |
| 5 | 1 | 145392 |
| 5 | 2 | 363480 |
| 5 | 3 | 484640 |
| 5 | 4 | 363480 |
| 6 | 0 | 14330 |
| 6 | 1 | 57320 |
| 6 | 2 | 85980 |
| 7 | 0 | 3508 |
进而，将2 x 1的数量称为style_num，于是有style_num恒小于或等于jiang_num；
此时可分出203种情况（注意不存在 *jiang_num-bing_num-style_num = 7-0-0* 的情况）：
[203种分类的元素数量](./style_count.md)
### 群
表述：群是有限个不同布局的集合，该集合必须满足定义的条件；
定义：群中任意一个布局无论如何移动，其结果仍在该群内；
性质：群是封闭的，群中所有元素构成一个关系网；
最简性：只需群中任意一个布局，即可复原出群中的所有元素；
### 按群继续分类
对于一个特定的 *jiang_num-bing_num-style_num* 分组，可拆分出n个群；将分出的群按元素数量从大到小排列，若存在元素数量相同的群，则取其中的最小元素排序；对这些群进行编号得0 ~ (n - 1) 共n个群，编号记为group_num；
因而对于某一群，存在一个唯一编号 *jiang_num-bing_num-style_num-group_num* ；由于群中的元素个数是确定的，将其中的元素按编码从小到大排列，其中的元素可得唯一编号group_index；
所以，对于任意布局，可得唯一编号 *jiang_num-bing_num-style_num-group_num-group_index*；
## 层级关系
未完待续...

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| jiang_num | bing_num | style_num | COUNT |
| :-: | :-: | :-: | :-: |
| 0 | 0 | 0 | 12 |
| 0 | 1 | 0 | 192 |
| 0 | 2 | 0 | 1440 |
| 0 | 3 | 0 | 6720 |
| 0 | 4 | 0 | 21840 |
| 0 | 5 | 0 | 52416 |
| 0 | 6 | 0 | 96096 |
| 0 | 7 | 0 | 137280 |
| 0 | 8 | 0 | 154440 |
| 0 | 9 | 0 | 137280 |
| 0 | 10 | 0 | 96096 |
| 0 | 11 | 0 | 52416 |
| 0 | 12 | 0 | 21840 |
| 0 | 13 | 0 | 6720 |
| 0 | 14 | 0 | 1440 |
| 1 | 0 | 0 | 132 |
| 1 | 0 | 1 | 124 |
| 1 | 1 | 0 | 1848 |
| 1 | 1 | 1 | 1736 |
| 1 | 2 | 0 | 12012 |
| 1 | 2 | 1 | 11284 |
| 1 | 3 | 0 | 48048 |
| 1 | 3 | 1 | 45136 |
| 1 | 4 | 0 | 132132 |
| 1 | 4 | 1 | 124124 |
| 1 | 5 | 0 | 264264 |
| 1 | 5 | 1 | 248248 |
| 1 | 6 | 0 | 396396 |
| 1 | 6 | 1 | 372372 |
| 1 | 7 | 0 | 453024 |
| 1 | 7 | 1 | 425568 |
| 1 | 8 | 0 | 396396 |
| 1 | 8 | 1 | 372372 |
| 1 | 9 | 0 | 264264 |
| 1 | 9 | 1 | 248248 |
| 1 | 10 | 0 | 132132 |
| 1 | 10 | 1 | 124124 |
| 1 | 11 | 0 | 48048 |
| 1 | 11 | 1 | 45136 |
| 1 | 12 | 0 | 12012 |
| 1 | 12 | 1 | 11284 |
| 2 | 0 | 0 | 582 |
| 2 | 0 | 1 | 1044 |
| 2 | 0 | 2 | 512 |
| 2 | 1 | 0 | 6984 |
| 2 | 1 | 1 | 12528 |
| 2 | 1 | 2 | 6144 |
| 2 | 2 | 0 | 38412 |
| 2 | 2 | 1 | 68904 |
| 2 | 2 | 2 | 33792 |
| 2 | 3 | 0 | 128040 |
| 2 | 3 | 1 | 229680 |
| 2 | 3 | 2 | 112640 |
| 2 | 4 | 0 | 288090 |
| 2 | 4 | 1 | 516780 |
| 2 | 4 | 2 | 253440 |
| 2 | 5 | 0 | 460944 |
| 2 | 5 | 1 | 826848 |
| 2 | 5 | 2 | 405504 |
| 2 | 6 | 0 | 537768 |
| 2 | 6 | 1 | 964656 |
| 2 | 6 | 2 | 473088 |
| 2 | 7 | 0 | 460944 |
| 2 | 7 | 1 | 826848 |
| 2 | 7 | 2 | 405504 |
| 2 | 8 | 0 | 288090 |
| 2 | 8 | 1 | 516780 |
| 2 | 8 | 2 | 253440 |
| 2 | 9 | 0 | 128040 |
| 2 | 9 | 1 | 229680 |
| 2 | 9 | 2 | 112640 |
| 2 | 10 | 0 | 38412 |
| 2 | 10 | 1 | 68904 |
| 2 | 10 | 2 | 33792 |
| 3 | 0 | 0 | 1320 |
| 3 | 0 | 1 | 3382 |
| 3 | 0 | 2 | 3180 |
| 3 | 0 | 3 | 1092 |
| 3 | 1 | 0 | 13200 |
| 3 | 1 | 1 | 33820 |
| 3 | 1 | 2 | 31800 |
| 3 | 1 | 3 | 10920 |
| 3 | 2 | 0 | 59400 |
| 3 | 2 | 1 | 152190 |
| 3 | 2 | 2 | 143100 |
| 3 | 2 | 3 | 49140 |
| 3 | 3 | 0 | 158400 |
| 3 | 3 | 1 | 405840 |
| 3 | 3 | 2 | 381600 |
| 3 | 3 | 3 | 131040 |
| 3 | 4 | 0 | 277200 |
| 3 | 4 | 1 | 710220 |
| 3 | 4 | 2 | 667800 |
| 3 | 4 | 3 | 229320 |
| 3 | 5 | 0 | 332640 |
| 3 | 5 | 1 | 852264 |
| 3 | 5 | 2 | 801360 |
| 3 | 5 | 3 | 275184 |
| 3 | 6 | 0 | 277200 |
| 3 | 6 | 1 | 710220 |
| 3 | 6 | 2 | 667800 |
| 3 | 6 | 3 | 229320 |
| 3 | 7 | 0 | 158400 |
| 3 | 7 | 1 | 405840 |
| 3 | 7 | 2 | 381600 |
| 3 | 7 | 3 | 131040 |
| 3 | 8 | 0 | 59400 |
| 3 | 8 | 1 | 152190 |
| 3 | 8 | 2 | 143100 |
| 3 | 8 | 3 | 49140 |
| 4 | 0 | 0 | 1632 |
| 4 | 0 | 1 | 5344 |
| 4 | 0 | 2 | 7248 |
| 4 | 0 | 3 | 4680 |
| 4 | 0 | 4 | 1320 |
| 4 | 1 | 0 | 13056 |
| 4 | 1 | 1 | 42752 |
| 4 | 1 | 2 | 57984 |
| 4 | 1 | 3 | 37440 |
| 4 | 1 | 4 | 10560 |
| 4 | 2 | 0 | 45696 |
| 4 | 2 | 1 | 149632 |
| 4 | 2 | 2 | 202944 |
| 4 | 2 | 3 | 131040 |
| 4 | 2 | 4 | 36960 |
| 4 | 3 | 0 | 91392 |
| 4 | 3 | 1 | 299264 |
| 4 | 3 | 2 | 405888 |
| 4 | 3 | 3 | 262080 |
| 4 | 3 | 4 | 73920 |
| 4 | 4 | 0 | 114240 |
| 4 | 4 | 1 | 374080 |
| 4 | 4 | 2 | 507360 |
| 4 | 4 | 3 | 327600 |
| 4 | 4 | 4 | 92400 |
| 4 | 5 | 0 | 91392 |
| 4 | 5 | 1 | 299264 |
| 4 | 5 | 2 | 405888 |
| 4 | 5 | 3 | 262080 |
| 4 | 5 | 4 | 73920 |
| 4 | 6 | 0 | 45696 |
| 4 | 6 | 1 | 149632 |
| 4 | 6 | 2 | 202944 |
| 4 | 6 | 3 | 131040 |
| 4 | 6 | 4 | 36960 |
| 5 | 0 | 0 | 1044 |
| 5 | 0 | 1 | 4392 |
| 5 | 0 | 2 | 7284 |
| 5 | 0 | 3 | 7120 |
| 5 | 0 | 4 | 3444 |
| 5 | 0 | 5 | 948 |
| 5 | 1 | 0 | 6264 |
| 5 | 1 | 1 | 26352 |
| 5 | 1 | 2 | 43704 |
| 5 | 1 | 3 | 42720 |
| 5 | 1 | 4 | 20664 |
| 5 | 1 | 5 | 5688 |
| 5 | 2 | 0 | 15660 |
| 5 | 2 | 1 | 65880 |
| 5 | 2 | 2 | 109260 |
| 5 | 2 | 3 | 106800 |
| 5 | 2 | 4 | 51660 |
| 5 | 2 | 5 | 14220 |
| 5 | 3 | 0 | 20880 |
| 5 | 3 | 1 | 87840 |
| 5 | 3 | 2 | 145680 |
| 5 | 3 | 3 | 142400 |
| 5 | 3 | 4 | 68880 |
| 5 | 3 | 5 | 18960 |
| 5 | 4 | 0 | 15660 |
| 5 | 4 | 1 | 65880 |
| 5 | 4 | 2 | 109260 |
| 5 | 4 | 3 | 106800 |
| 5 | 4 | 4 | 51660 |
| 5 | 4 | 5 | 14220 |
| 6 | 0 | 0 | 270 |
| 6 | 0 | 1 | 1836 |
| 6 | 0 | 2 | 3196 |
| 6 | 0 | 3 | 4288 |
| 6 | 0 | 4 | 3084 |
| 6 | 0 | 5 | 1260 |
| 6 | 0 | 6 | 396 |
| 6 | 1 | 0 | 1080 |
| 6 | 1 | 1 | 7344 |
| 6 | 1 | 2 | 12784 |
| 6 | 1 | 3 | 17152 |
| 6 | 1 | 4 | 12336 |
| 6 | 1 | 5 | 5040 |
| 6 | 1 | 6 | 1584 |
| 6 | 2 | 0 | 1620 |
| 6 | 2 | 1 | 11016 |
| 6 | 2 | 2 | 19176 |
| 6 | 2 | 3 | 25728 |
| 6 | 2 | 4 | 18504 |
| 6 | 2 | 5 | 7560 |
| 6 | 2 | 6 | 2376 |
| 7 | 0 | 1 | 342 |
| 7 | 0 | 2 | 464 |
| 7 | 0 | 3 | 1036 |
| 7 | 0 | 4 | 772 |
| 7 | 0 | 5 | 626 |
| 7 | 0 | 6 | 180 |
| 7 | 0 | 7 | 88 |
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