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Add theory for Almost Locked Set #5 #11
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zhugelianglongming committed Mar 26, 2023
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25 changes: 25 additions & 0 deletions 技巧/图谱/结构/严格共享候选数.md
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<!-- 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

- [定义](#%E5%AE%9A%E4%B9%89)
- [性质](#%E6%80%A7%E8%B4%A8)
- [标签](#%E6%A0%87%E7%AD%BE)

<!-- END doctoc generated TOC please keep comment here to allow auto update -->

# 定义
- 对于候选数`X`,存在 2 个[[定区域准集合数组]]`ALS1``ALS2`
- `ALS1`的准集合候选数包含`X`
- `ALS2`的准集合候选数包含`X`
- `ALS1`中的`X`和`ALS2`中的`X`是[[弱关系]]
- 则候选数`X``ALS1``ALS2`的严格共享候选数

# 性质

- `ALS1`中的`X``ALS2`中的`X`为以下 2 种关系之一:
- [[同区域同数弱关系]]
- [[跨区域同数弱关系]]

# 标签
- #Concept
22 changes: 22 additions & 0 deletions 技巧/图谱/结构/关系/弱关系.md
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@@ -0,0 +1,22 @@
<!-- 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

- [定义](#%E5%AE%9A%E4%B9%89)
- [标签](#%E6%A0%87%E7%AD%BE)

<!-- END doctoc generated TOC please keep comment here to allow auto update -->

# 定义
- 两个命题的弱关系:两个命题不可同时为真

即,若`P``Q`是弱关系,则
- P∧Q ⇔ F
- P⇒¬Q
- Q⇒¬P

# 标签

- #Concept

> [SudokuWiki.org - Weak and Strong Links](https://www.sudokuwiki.org/Weak_and_Strong_Links)
22 changes: 22 additions & 0 deletions 技巧/图谱/结构/关系/强关系.md
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@@ -0,0 +1,22 @@
<!-- 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

- [定义](#%E5%AE%9A%E4%B9%89)
- [标签](#%E6%A0%87%E7%AD%BE)

<!-- END doctoc generated TOC please keep comment here to allow auto update -->

# 定义
- 两个命题的强关系:两个命题不可同时为假

即,若`P``Q`是强关系,则
- P∨Q ⇔ T
- ¬P⇒Q
- ¬Q⇒P

# 标签

- #Concept

> [SudokuWiki.org - Weak and Strong Links](https://www.sudokuwiki.org/Weak_and_Strong_Links)
34 changes: 34 additions & 0 deletions 技巧/图谱/结构/定区域准集合数组.md
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# 定区域准集合数组

<!-- 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

- [定义](#%E5%AE%9A%E4%B9%89)
- [技巧拓展](#%E6%8A%80%E5%B7%A7%E6%8B%93%E5%B1%95)
- [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 -->

## 定义

- 在单一区域`Region`
- `N`个单元格共有`N+1`个候选数

### 技巧拓展

- [[数组]]:扩展候选数的数量
- `N`→`N+1`

## 技巧转换

- [[同区域异数强关系]]`N+1`个候选数中,任意 2 个不同候选数是同区域异数强关系
- 即:`N`个单元格中,不可同时没有任意 2 种候选数

## 标签

- #Level/3
- #Concept

> [SudokuWiki.org - Almost Locked Sets](https://www.sudokuwiki.org/Almost_Locked_Sets)
2 changes: 1 addition & 1 deletion 技巧/图谱/融合式待定数组(SdC).md
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- [[伪数组]]
- [[跨区数组]]
- [[待定数组]]
- [[定集合准区域数组]]


## 按公共数分类
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因为
- 对于单元格`Cell`的候选数`X`,存在2 条链`Chain[1,2]`
- 若单元格填入数字`X`,由`Chain[1]`可推得结论`Solution`成立
- 若单元格不填入数字`X`,由`Chain[2]`可推得结论`Solution`成立
- 若单元格填入数字`X`,由`Chain[1]`可推得命题`Statement`成立
- 若单元格不填入数字`X`,由`Chain[2]`可推得命题`Statement`成立

所以
- 结论`Solution`成立。

- 命题`Statement`成立。

### 技巧转换

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