The New Sudoku Players' Forum

[dyguests]

I try to convert a Sudoku puzzle to a Exact Cover, It works.
Convert a Killer Sudoku, It works to.
But a Killer Sudoku that have not sum of cage. How to convert to a Exact Cover?

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For a Killer Sudoku, like:
-------------
AA. ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...

AA=3
-------------

The AA cage can be convert to Exact Cover like:
100
011

--------------------------------------------------------------------------------------------------------

For a Killer Sudoku that have not sum of cage, like:
-------------
AA. ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...

(no hint of sum of AA)
-------------

How to convert AA cage to Exact Cover?

[creint]

killer cage = all different + sum cage
If you don't know the sum you can't apply the sum cage.
Your example does not give more constraints than a regular sudoku.
What do you want? More details help.

[dyguests]

Problem solved, thinks.

I found it can be solved by dlx with secondary columns.

-------------------------------------
some details:
1. DLX. https://en.wikipedia.org/wiki/Dancing_Links
secondary columns: show "Optional constraints".
2. Convert sudoku to a DLX. https://blog.csdn.net/mu399/article/details/7627862

[dyguests]

I forget how to use "secondary columns" to slove the problem. What happened 3 years ago???

My new solution:

例：二个格子，总和5。

可能结果：
1,4 2,3 3,2 4,1

精确匹配：

格子索引（主列） | 数字1~4(辅助列)
10 | 1000
01 | 0001

10 | 0100
01 | 0010

很明显上面是两组解：1,4 和 2,3。
但是
10 | 1000
01 | 0010
也是精确匹配的一组解：1,3。不是杀手框的解。

---------------------------------

新的方案：
对于第一个格子，不采用`10 1000`的格式。
而是采用`10 1110`的格式。

其中 `10 1110` 表示
1... ：数字2
.11. ：禁止2,3

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我不确认这个方案是否能解决 多组解中出现重复数字 的问题