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Author: Marc OlschokMarc Olschok Date: Jan 11, 2008 17:12
Albert van der Horst wrote:> Recently I got interested in the following problem:
>
> Given is a partial function from a set A to a domain D.
___________________________________________^^^^^^^^^^^^^
did you mean "with domain D" here?
> Also given a number of subsets of A: A_i.
> The problem is to find an extension of the function to the
> whole set, where each restriction to A_i is a bijection.
>
> Familiar, anyone?
Not really. Of course such an extension does not always exist.
Do you know anything more about the sets A_i?
Marc
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Author: Albert van der HorstAlbert van der Horst Date: Jan 12, 2008 01:56
In article aioe.org>,
Marc Olschok wrote:>Albert van der Horst wrote:>> Recently I got interested in the following problem:
>>
>> Given is a partial function from a set A to a domain D.
>___________________________________________^^^^^^^^^^^^^
>did you mean "with domain D" here?
I should have said to som other set B.
>
>> Also given a number of subsets of A: A_i.
>> The problem is to find an extension of the function to the
>> whole set, where each restriction to A_i is a bijection.
>>
>> Familiar, anyone?
>
>Not really. Of course such an extension does not always exist.
This _is_ a familiar problem. In line with some critics on this forum
here again we're talking about Sodoku solvers.
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Author: Marc OlschokMarc Olschok Date: Jan 12, 2008 12:59
Albert van der Horst wrote:> In article aioe.org>,
> Marc Olschok wrote:>>Albert van der Horst wrote:>>> Recently I got interested in the following problem:
>>>
>>> Given is a partial function from a set A to a domain D.
>>___________________________________________^^^^^^^^^^^^^
>>did you mean "with domain D" here?
>
> I should have said to som other set B.
>>
>>> Also given a number of subsets of A: A_i.
>>> The problem is to find an extension of the function to the
>>> whole set, where each restriction to A_i is a bijection.
>>>
>>> Familiar, anyone?
>>
>>Not really. Of course such an extension does not always exist.
> ...
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Author: Albert van der HorstAlbert van der Horst Date: Jan 13, 2008 16:15
In article aioe.org>,
Marc Olschok wrote:>Albert van der Horst wrote:>> In article aioe.org>,
>> Marc Olschok wrote:>>>Albert van der Horst wrote:>>>> Recently I got interested in the following problem:
>>>>
>>>> Given is a partial function from a set A to a domain D.
>>>___________________________________________^^^^^^^^^^^^^
>>>did you mean "with domain D" here?
>>
>> I should have said to som other set B.
>>>
>>>> Also given a number of subsets of A: A_i.
>>>> The problem is to find an extension of the function to the
>>>> whole set, where each restriction to A_i is a bijection.
>>>>
>>>> Familiar, anyone?
>>> ...
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Author: Albert van der HorstAlbert van der Horst Date: Jan 14, 2008 09:03
Clean restatement of the problem
Given is a partial function from a set A to some other set B,
( partial i.e. only defined on a subset of A.)
Also given a number of subsets of A: A_i.
The problem is to find an extension of the function to the
whole set, where each restriction to A_i is a bijection.
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Author: Albert van der HorstAlbert van der Horst Date: Jan 15, 2008 00:55
In article aioe.org>,
Marc Olschok wrote:>Albert van der Horst wrote:>> Clean restatement of the problem
>>
>> Given is a partial function from a set A to some other set B,
>> ( partial i.e. only defined on a subset of A.)
>>
>> Also given a number of subsets of A: A_i.
>> The problem is to find an extension of the function to the
>> whole set, where each restriction to A_i is a bijection.
>>
>> In article aioe.org>,
>> Marc Olschok wrote:>>>Albert van der Horst wrote:>>
>>>>>>
>>>>>> Familiar, anyone?
>>>>>
>>>>>Not really. Of course such an extension does not always exist. ...
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Author: Marc OlschokMarc Olschok Date: Jan 15, 2008 11:58
Albert van der Horst wrote:> In article aioe.org>,
> Marc Olschok wrote:>>Albert van der Horst wrote:>>> Clean restatement of the problem
>>>
>>> Given is a partial function from a set A to some other set B,
>>> ( partial i.e. only defined on a subset of A.)
>>>
>>> Also given a number of subsets of A: A_i.
>>> The problem is to find an extension of the function to the
>>> whole set, where each restriction to A_i is a bijection.
>>>
>>> In article aioe.org>,
>>> Marc Olschok wrote:>>>>Albert van der Horst wrote:>>>
>>>>>>>
>>>>>>> Familiar, anyone?
>>>>>> ...
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Author: Anton ErtlAnton Ertl Date: Jan 15, 2008 12:11
Albert van der Horst writes:>My point is that if you don't assume beforehand that the subsets
>are the rows, small rectangles and columns in the sodoku puzzle,
>this leads the way to a straightforward and fast implementation
>of a solver.
I have not followed your discussion closely, but sometime after
writing my partial Sudoku solver
< http://www.complang.tuwien.ac.at/forth/programs/sudoku3.fs>, I
realized that it would have been much simpler and more general if I
had represented the rows, columns, and regions through indirection
arrays:
Simpler: Then rows, columns, and regions could all have been treated
more uniformly. Just have one word for walking through them, and pass
that word the indirection array.
More general: By using a different indirection array for regions, one
could have attacked the unusual Sudoku variants (with non-square
regions) that I see in the newspaper now and then.
When I find the time to resume programming my Sudoku solver ...
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Author: Albert van der HorstAlbert van der Horst Date: Jan 23, 2008 02:54
In article ,
Albert van der Horst wrote:>Clean restatement of the problem
>
>Given is a partial function from a set A to some other set B,
>( partial i.e. only defined on a subset of A.)
>
>Also given a number of subsets of A: A_i.
>The problem is to find an extension of the function to the
>whole set, where each restriction to A_i is a bijection.
>
>In article aioe.org>,
>Marc Olschok wrote:>>Albert van der Horst wrote:>
>>>>>
>>>>> Familiar, anyone?
>>>>
>>>>Not really. Of course such an extension does not always exist.
>>> ...
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Author: Marcel HendrixMarcel Hendrix Date: Jan 23, 2008 11:32
Albert van der Horst writes Re: A set problem
[..]
CREATE grid19
rg 5 0 0 1 0 0 3 0 0
rg 7 0 0 6 0 0 0 0 0
rg 0 0 9 0 4 7 6 0 2
rg 0 0 3 0 0 0 0 0 7
rg 0 1 0 0 0 0 0 8 0
rg 2 9 0 0 0 1 4 0 0
rg 8 0 0 0 0 0 0 0 0
rg 0 0 0 0 0 6 0 1 5
rg 0 0 0 5 3 8 0 0 0
," Albert van der Horst's Python example"
That's not a very hard one ( 0.19 ms with Robert Spykerman's
Forth algorithm )
Try this.
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