Add theory for 复合色链 #5 #11

zhugelianglongming · Mar 19, 2023 · 7c6b57e · 7c6b57e
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diff --git a/技巧/README.md b/技巧/README.md
@@ -598,7 +598,7 @@
 
 [ALS的一般拓展结构]: https://zhuanlan.zhihu.com/p/33770218
 
-[X-Cycle]: 图谱/链/鱼/复杂鱼/X-Cycle.md
+[X-Cycle]: 图谱/链/鱼/复杂鱼/X环.md
 
 [Guardians]: http://www.sudokufans.org.cn/forums/topic/38/?do=findComment&comment=247
 

diff --git a/技巧/图谱/.obsidian/app.json b/技巧/图谱/.obsidian/app.json
@@ -1 +1,3 @@
-{}
+{
+  "alwaysUpdateLinks": true
+}
diff --git a/技巧/图谱/.obsidian/graph.json b/技巧/图谱/.obsidian/graph.json
@@ -55,6 +55,20 @@
         "a": 1,
         "rgb": 5395168
       }
+    },
+    {
+      "query": "tag:#Level/e",
+      "color": {
+        "a": 1,
+        "rgb": 11621088
+      }
+    },
+    {
+      "query": "tag:#Level/d1",
+      "color": {
+        "a": 1,
+        "rgb": 14701233
+      }
     }
   ],
   "collapse-display": false,
@@ -67,6 +81,6 @@
   "repelStrength": 15.4459635416667,
   "linkStrength": 1,
   "linkDistance": 97,
-  "scale": 0.4848509037488175,
+  "scale": 0.7940586382786211,
   "close": true
 }
diff --git a/技巧/图谱/.obsidian/workspace.json b/技巧/图谱/.obsidian/workspace.json
@@ -46,7 +46,7 @@
             "state": {
               "type": "search",
               "state": {
-                "query": "",
+                "query": "视角",
                 "matchingCase": false,
                 "explainSearch": false,
                 "collapseAll": false,
@@ -71,7 +71,8 @@
               "state": {}
             }
           }
-        ]
+        ],
+        "currentTab": 3
       }
     ],
     "direction": "horizontal",
@@ -140,7 +141,7 @@
             }
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-        "currentTab": 2
+        "currentTab": 3
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     "direction": "horizontal",
@@ -159,17 +160,30 @@
   },
   "active": "750e8ad12eb79598",
   "lastOpenFiles": [
-    "链/鱼/二阶鱼.md",
+    "染色法/复合色链.md",
+    "链/鱼/复杂鱼/复杂鱼.md",
+    "链/鱼/复杂鱼/X环.md",
+    "染色法/色链.md",
+    "染色法/色分.md",
+    "链/鱼/标准鱼/二阶鱼.md",
+    "链/鱼/标准鱼/标准鱼.md",
+    "关系/关系.md",
+    "染色法",
+    "链/鱼/复杂鱼",
+    "链/鱼/标准鱼",
+    "四阶鱼.md",
+    "链/鱼/标准鱼/三阶鱼.md",
+    "数组/数组.md",
+    "链/标准链/规则Wing/双分支匹配法.md",
+    "链/标准链/规则Wing/三分支匹配法.md",
+    "链/标准链/规则Wing/四分支匹配法.md",
+    "数组/显性数组/显性四数组.md",
     "链/烟花/四重烟花.md",
     "链/烟花/三重烟花.md",
     "链/烟花/烟花.md",
     "链/鱼",
-    "链/标准链/规则Wing/四分支匹配法.md",
-    "链/标准链/规则Wing/双分支匹配法.md",
-    "链/标准链/规则Wing/三分支匹配法.md",
     "Template/【Tpl】技巧.md",
     "Template",
-    "Level1/数组.md",
     "链/烟花",
     "待定数组/欠一数组/欠一数对.md",
     "待定数组/欠一数组",
@@ -181,20 +195,7 @@
     "区块.md",
     "数组/显性数组/显性数组.md",
     "数组/显性数组/显性数对.md",
-    "数组/隐性数组/隐性三数组.md",
-    "链/标准链/未命名.md",
     "链/标准链/规则Wing",
-    "链/标准链",
-    "数组/显性数组/显性四数组.md",
-    "数组/隐性数组",
-    "数组/显性数组",
-    "链",
-    "数组/隐性数组/隐性四数组.md",
-    "数组/隐性数组/隐性数对.md",
-    "数组/显性数组/显性三数组.md",
-    "数组/隐性数组/隐性数组.md",
-    "Level1/摒除法.md",
-    "关系/关系.md",
-    "Level2/标准链.md"
+    "链/标准链"
   ]
 }
diff --git a/技巧/图谱/关系/关系.md b/技巧/图谱/关系/关系.md
@@ -14,8 +14,8 @@
 
 ## 按强弱分类
 
-- 强关系
-- 弱关系
+- [[强关系]]
+- [[弱关系]]
 
 # 按区域分类
 

diff --git a/技巧/图谱/染色法/复合色链.md b/技巧/图谱/染色法/复合色链.md
@@ -0,0 +1,49 @@
+# 复合色链
+
+<!-- START doctoc generated TOC please keep comment here to allow auto update -->
+<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
+## 目录
+
+- [原理](#%E5%8E%9F%E7%90%86)
+  - [技巧拓展](#%E6%8A%80%E5%B7%A7%E6%8B%93%E5%B1%95)
+  - [技巧组合](#%E6%8A%80%E5%B7%A7%E7%BB%84%E5%90%88)
+  - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
+- [标签](#%E6%A0%87%E7%AD%BE)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+
+## 原理
+
+因为
+- 对于数字`X`
+	- 将盘面的`X`共轭对分别标记为颜色`Color[A,B][+,-]`
+	- `ColorA+`和`ColorA-`中，有且仅有 1 种成立`
+	- `ColorB+`和`ColorB-`中，有且仅有 1 种成立`
+	- 存在区域`Region`
+		- 其中存在`ColorA+`和`ColorB+`
+		- `ColorA+`和`ColorB+`，最多只有 1 种成立
+
+所以
+- `ColorA-`和`ColorB-`的共同影响区域必不填入数字`X`
+
+![Multi-Colouring Strategy](https://www.sudokuwiki.org/PuzImages/mctype2_1.jpg)
+
+###  技巧拓展
+
+- [[色链]]：将 1 个[[共轭对]]扩展为[[弱关系]]
+
+###  技巧组合
+
+- [[链]]：通过[[共轭对]]和[[弱关系]]连接的同数链
+	- [[共轭对]] * n
+	- [[弱关系]] * 1
+
+###  技巧转换
+
+- [[链/鱼/复杂鱼/复杂鱼|复杂鱼]]：从全盘视角观察
+
+## 标签
+
+#Level/d1
+
+> [SudokuWiki.org - Multi-Colouring Strategy](https://www.sudokuwiki.org/Multi_Colouring_Strategy)
diff --git a/技巧/图谱/染色法/色分.md b/技巧/图谱/染色法/色分.md
@@ -0,0 +1,36 @@
+# 色分
+
+<!-- START doctoc generated TOC please keep comment here to allow auto update -->
+<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
+## 目录
+
+- [原理](#%E5%8E%9F%E7%90%86)
+  - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
+- [标签](#%E6%A0%87%E7%AD%BE)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+
+## 原理
+
+因为
+- 对于数字`X`
+	- 将盘面的`X`共轭对分别标记为颜色`Color+`和`Color-`
+	- 同种颜色必须同时成立
+- 对于区域`Region`
+	-  `Color+`的单元格数量 > 1
+
+所以
+- `Color+`的单元格必不填入数字`X`
+- `Color-`的单元格必填入数字`X`
+
+![Twice in a Unit](https://www.sudokuwiki.org/PuzImages/SC_Rule2.png)
+
+###  技巧转换
+
+- [[链/鱼/复杂鱼/复杂鱼|复杂鱼]]：从全盘视角观察
+
+## 标签
+
+#Level/e
+
+> [SudokuWiki.org - Single's Chains](https://www.sudokuwiki.org/Singles_Chains): Rule 2 - Twice in a Unit
diff --git a/技巧/图谱/染色法/色链.md b/技巧/图谱/染色法/色链.md
@@ -0,0 +1,39 @@
+# 色链
+
+<!-- START doctoc generated TOC please keep comment here to allow auto update -->
+<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
+## 目录
+
+- [原理](#%E5%8E%9F%E7%90%86)
+  - [技巧组合](#%E6%8A%80%E5%B7%A7%E7%BB%84%E5%90%88)
+  - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
+- [标签](#%E6%A0%87%E7%AD%BE)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+
+## 原理
+
+因为
+- 对于数字`X`
+	- 将盘面的`X`共轭对分别标记为颜色`Color+`和`Color-`
+	- 2 种颜色有且仅有 1 种成立
+
+所以
+- `Color+`和`Color-`的共同影响区域必不填入数字`X`
+
+![Two colours 'elsewhere'](https://www.sudokuwiki.org/PuzImages/SC_Rule4a.png)
+
+###  技巧组合
+
+- [[链]]：通过[[共轭对]]连接的同数链
+	- [[共轭对]] * n
+
+###  技巧转换
+
+- [[链/鱼/复杂鱼/复杂鱼|复杂鱼]]：从全盘视角观察
+
+## 标签
+
+#Level/d
+
+> [SudokuWiki.org - Single's Chains](https://www.sudokuwiki.org/Singles_Chains): Rule 4 - Two colours 'elsewhere'
diff --git a/技巧/图谱/链/鱼/复杂鱼/X-Cycle.md → 技巧/图谱/链/鱼/复杂鱼/X环.md b/技巧/图谱/链/鱼/复杂鱼/X-Cycle.md → 技巧/图谱/链/鱼/复杂鱼/X环.md
@@ -1,11 +1,11 @@
-# X-Cycle
+# X环
 
 <!-- START doctoc generated TOC please keep comment here to allow auto update -->
 <!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
 ## 目录
 
 - [原理](#%E5%8E%9F%E7%90%86)
-  - [技巧拓展](#%E6%8A%80%E5%B7%A7%E6%8B%93%E5%B1%95)
+  - [技巧组合](#%E6%8A%80%E5%B7%A7%E7%BB%84%E5%90%88)
   - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
 - [标签](#%E6%A0%87%E7%AD%BE)
 
@@ -18,20 +18,21 @@
 	- 存在一条`*-强链-弱链-*`交替形成的环`Loop`
 
 所以
-- 若将环`Loop`中单元格间隔标记为红色和绿色，则
-	- 任一红色单元格与任一绿色单元格的共同影响区域，必不填入数字`X`
+- 若将环`Loop`中单元格间隔标记为颜色`Color+`和`Color-`，则
+	- 任一`Color+`单元格与任一`Color-`单元格的共同影响区域，必不填入数字`X`
 
-> 数字`X`在环`Loop`内，要么都在红色单元格中，要么都在绿色单元格中。
+> 数字`X`在环`Loop`内，要么都在`Color+`单元格中，要么都在`Color-`单元格中。
 
 ![X-Cycle](https://www.sudokuwiki.org/PuzImages/NiceL2.png)
 
-###  技巧拓展
+###  技巧组合
 
-- [[链]]：头尾可以通过弱链连接的链
+- [[环]]：头尾可以通过[[共轭对]]连接的同数链
+	- [[共轭对]] * 2n
 
 ###  技巧转换
 
-- [[链/鱼/复杂鱼/复杂鱼|复杂鱼]]：从全盘某个数字的布局考虑
+- [[链/鱼/复杂鱼/复杂鱼|复杂鱼]]：从全盘视角观察
 
 ## 标签
 

diff --git a/技巧/图谱/链/鱼/复杂鱼/复杂鱼.md b/技巧/图谱/链/鱼/复杂鱼/复杂鱼.md
@@ -5,7 +5,6 @@
 ## 目录
 
 - [原理](#%E5%8E%9F%E7%90%86)
-  - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
 - [标签](#%E6%A0%87%E7%AD%BE)
 
 <!-- END doctoc generated TOC please keep comment here to allow auto update -->
@@ -25,12 +24,8 @@
 
 ![Single's Chains](https://www.sudokuwiki.org/PuzImages/SC_Rule2.png)
 
-###  技巧转换
-
-- [[X-Cycle]]：从单数链的结构考虑
-
 ## 标签
 
-#Level/d
+#Level/d1
 
 > [SudokuWiki.org - Single's Chains](https://www.sudokuwiki.org/Singles_Chains)
diff --git a/技巧/图谱/链/鱼/标准鱼/二阶鱼.md b/技巧/图谱/链/鱼/标准鱼/二阶鱼.md
@@ -5,6 +5,7 @@
 ## 目录
 
 - [原理](#%E5%8E%9F%E7%90%86)
+  - [技巧转换](#%E6%8A%80%E5%B7%A7%E8%BD%AC%E6%8D%A2)
 - [练习](#%E7%BB%83%E4%B9%A0)
 - [标签](#%E6%A0%87%E7%AD%BE)
 
@@ -36,6 +37,10 @@
 
 ![X-Wing](https://www.sudokuwiki.org/PuzImages/XWing1.png)
 
+###  技巧转换
+
+- [[复合色链]]：2 个共轭对的复合色链
+
 ## 练习
 
 -   [三思数独](https://www.12634.com/learning/x-wing/index)