From e0b1ea23ca23b162b13290296d09e2d669e69d4d Mon Sep 17 00:00:00 2001 From: Dnomd343 Date: Fri, 26 Jun 2020 16:14:00 +0800 Subject: [PATCH] Update Readme --- README.md | 134 +++++++++++++++++++++++++-- images/illegal_1+2.png | Bin 0 -> 5870 bytes images/illegal_1.png | Bin 3600 -> 0 bytes images/illegal_2.png | Bin 3998 -> 0 bytes images/illegal_3+4.png | Bin 0 -> 6040 bytes images/illegal_3.png | Bin 3955 -> 0 bytes images/illegal_4.png | Bin 3895 -> 0 bytes images/legal_1+2.png | Bin 0 -> 5870 bytes images/legal_1.png | Bin 3938 -> 0 bytes images/legal_2.png | Bin 3633 -> 0 bytes images/legal_3+4.png | Bin 0 -> 4516 bytes images/legal_3.png | Bin 3121 -> 0 bytes images/legal_4.png | Bin 2008 -> 0 bytes style_count.md | 205 +++++++++++++++++++++++++++++++++++++++++ 14 files changed, 333 insertions(+), 6 deletions(-) create mode 100644 images/illegal_1+2.png delete mode 100644 images/illegal_1.png delete mode 100644 images/illegal_2.png create mode 100644 images/illegal_3+4.png delete mode 100644 images/illegal_3.png delete mode 100644 images/illegal_4.png create mode 100644 images/legal_1+2.png delete mode 100644 images/legal_1.png delete mode 100644 images/legal_2.png create mode 100644 images/legal_3+4.png delete mode 100644 images/legal_3.png delete mode 100644 images/legal_4.png create mode 100644 style_count.md diff --git a/README.md b/README.md index 1a2c626..ac81f8f 100644 --- a/README.md +++ b/README.md @@ -14,15 +14,18 @@ 合法华容道布局共有29334498种 - ### 合法布局举例： -legal_1legal_2legal_3legal_4 +legal_1+2 + +legal_3+4 ### 非法布局举例： -illegal_1illegal_2illegal_3illegal_4 +illegal_1+2 + +illegal_3+4 ### 布局间的关系 @@ -102,6 +105,7 @@ **编码举例** + **例1：** exp-1A9BF0C00 @@ -153,7 +157,8 @@ 0 -因此，布局编码为**1A9BF0C00**，可简写为**1A9BF0C** +因此，布局编码为1A9BF0C00，可简写为1A9BF0C + **例2：** @@ -206,7 +211,7 @@ 0 -因此，布局编码为**4FEA13400**，可简写为**4FEA134** +因此，布局编码为4FEA13400，可简写为4FEA134 **例3：** @@ -261,4 +266,121 @@ 0 -因此，布局编码为**5DC02F800**，可简写为**5DC02F8** \ No newline at end of file +因此，布局编码为5DC02F800，可简写为5DC02F8 + + + +## 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... diff --git a/images/illegal_1+2.png b/images/illegal_1+2.png new file mode 100644 index 0000000000000000000000000000000000000000..361d8e4c73494f58f8492b8a4967e1f01d556d4f GIT binary patch literal 5870 zcmeI0dstF=8pn@z$2BV%nMsX$8Vkowr@XD2T8@`&O2bmi8)@YwR7wSJ5M9!f4*)Dk0|0I4(#7CP6)F8S_@x!^C zO{UIt=pyiX*|8l5;sLGS0{_~VSH>-K#~Are9Gg&<`xYjB`7#rAlu7s``! z`BqeLzjf7J-DP{MZ5Ng&E`n}r)Lym%w(ROLq+3M^u<8X$Xx(A?_A zFS@ato=dgx7(C^ukLBsswKxJ}^~J1gMt>Z*!{g@M`=YH;1OgNQ)?P;}1c0R*AX)%$ zI^6{TP97{;@w;VRY~dZaId&9P7$lKI^;*pKxVFeTugpXQHfvJR3e-Tb%(>V!&-RuR z=VEykiDdbZf0J}sx_8*9Ccc9=u?5xN$&aF1R*|ZP#CwoQVJBLa!vibJV78;RBN7-w z)HUkPRWdX}cybrTJ}$D9n1If+7-zLHgD?fgR8!{#vG?lCNDStbEJjk_^)>oC+|KhZ zqH{wzR7rR%J)6dfJyS`N8>Bf;olRGFTXSZLgLZg3wIPWU-9Ch22~we zUvpqTH4nbOGLKSV6geoEnG6sl&qPZ|{j=B?(@oC@OBk|pYjj!K*#i#sd&8ji9#$-T 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