TDP versus FORCING BRAIDS

Advanced methods and approaches for solving Sudoku puzzles

Re: TDP versus FORCING BRAIDS

Postby eleven » Tue Aug 25, 2020 9:51 pm

Agreed again, and a good sample.
As a manual solver i would definitely not find the "pattern" of the whip for a very long time, and i would not know, how to practice to find it faster.
Whereas the ALS version is something, i naturally would try after some time. And to practice that is straightforward (find n cells for n+1 digits in a house and look, which one leads to a chain).
And i never saw an "elegant" solution from Denis' rules (also don't remember one from TDP). So they have their worth elsewhere.
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Re: TDP versus FORCING BRAIDS

Postby denis_berthier » Wed Aug 26, 2020 6:25 am

https://dictionary.cambridge.org/dictionary/english/not wrote:not
adverb
UK /nɒt/ US /nɑːt/
A1
used to form a negative phrase after verbs like "be", "can", "have", "will", "must", etc., usually used in the short form "n't" in speech:
    He's not fat!
    I won't tell her.
    I can't go.
    Don't you like her?
    It isn't hard (= it is easy).
    I'm just not interested.
    He's not bad-looking (= he is fairly attractive).
    He's not as tall as his father.


https://dictionary.cambridge.org/dictionary/english/not wrote:part
noun
UK /pɑːt/ US /pɑːrt/
part noun (SOME)
A2 [ U ]
some but not all of a thing:
    Part of my steak isn't cooked properly.
    Part of this form seems to be missing.
    I think part of her problem is that she doesn't listen carefully enough to what other people say.
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Re: TDP versus FORCING BRAIDS

Postby SpAce » Wed Aug 26, 2020 2:18 pm

Finally I can see the pattern!!! It's a ship:

Code: Select all
               .----------(5)r2c6      .------------------(3)b3p5     
              /           ||          /                   ||           
(7-4)r2c9 = (4-9)r2c6 = (9-5)r2c2 = (5)r2c8 - (5=3)r7c8 - (3)b3p8 = (3-4)b3p7 = !4b3!
  \           ||          ||                              ||          ||
   \----------(9)r2c9     ||                              ||          ||
    \                     ||                              ||          ||
     \--------------------(5)r2c9                         ||          ||
      \                                                   ||          ||
       \--------------------------------------------------(3)b3p6     ||
        \                                                             ||
         '------------------------------------------------------------(4)b3p6


=> -7r2c9

(Btw, is 4r2c9 (4b3p6) counted as a z-candidate? Originally I thought it should be, then I changed my mind (and the previous post). Looking at that picture makes me think it might yet be, because it's in two roles. I'm not expecting an answer, but it would be nice to know.)

Denis, you can claim as much as you like that the tz-candidates aren't part of your chains (or was it an admission that elegance isn't?), but that doesn't change the reality. It would make sense only if you could show that the abstract core chain is somehow visible as a pattern without executing a T&E procedure that eliminates the tz-candidates along the way.

I could accept the idea with z-candidates only, because as alternate endpoints they can be erased with a single stroke right off the bat. It's a viable tactic even with an AIC by using a nested chain. However, it's not so easy with t-candidates. In our example, even if we factor out the z-candidates, the nested chain still has the two t-memories:

Code: Select all
(7-3|4|5|9)r2c9 = [!4r2 = (4^-9)r2c6 = (9)r2c2 - (5)r2c2^6 = (5%)r2c8 - (5=3)r7c8 - (3)b3p8%5 = (3-4)r3c7 = !4b3] => -7 r2c9

Of course it would be easy to replace those two memories with a subset and a group node, but then it wouldn't be equivalent to the whip. I can't see any reasonable way to factor out the t-candidates to end up with the abstract core chain.

Fact is, the presence of t-candidates adds a lot more complexity than z-candidates, and it's much less credible to claim that they're not part of the chain. The z-candidates are linked to the single target, so they're easier to consider irrelevant. On the other hand, a t-candidate can be linked to any previous right-linking candidate, which can be tedious to find in a long chain unless marked somehow.

I'm not being serious, but one might ask why even bother listing the left-linking candidates. After all, they get erased by the same procedure as the tz-candidates. Thus, we could raise the abstraction level even higher and simply do this:

Code: Select all
(+7r2c9 ->singles-> (7r2c9, 4r2c6, 9r2c2, 5r2c8, 3r7c8, 3r3c7) -> !4b3) => -7r2c9

Robert should like that. Where is he anyway?
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Re: TDP versus FORCING BRAIDS

Postby Mauriès Robert » Wed Sep 16, 2020 5:22 pm

Hi Space,
SpAce wrote:I'm not being serious, but one might ask why even bother listing the left-linking candidates. After all, they get erased by the same procedure as the tz-candidates. Thus, we could raise the abstraction level even higher and simply do this:

Code: Select all
(+7r2c9 ->singles-> (7r2c9, 4r2c6, 9r2c2, 5r2c8, 3r7c8, 3r3c7) -> !4b3) => -7r2c9

Robert should like that. Where is he anyway?


Yes, I like it when you use notations that I understand well and a lead that leads to a contradiction!
I've been too absent to follow the debates in this thread, but I've noticed that you prefer to look for truths, which is what conjugated tracks.
Sincerely
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Re: TDP versus FORCING BRAIDS

Postby SpAce » Thu Sep 17, 2020 12:45 am

Hi Robert,

Good to hear from you! I was a bit worried when you disappeared and there was no sign of activity even on your website.

Mauriès Robert wrote:Yes, I like it when you use notations that I understand well and a lead that leads to a contradiction!

Glad you liked it :)

I've been too absent to follow the debates in this thread

You haven't missed anything.

I've noticed that you prefer to look for truths, which is what conjugated tracks.

Indeed. When that approach fails (or I'm just being lazy), I do make exceptions, though. However, I don't really count such solutions, unless T&E is the only reasonable possibility. I also don't see much point in notating such steps except for the non-basic parts. If one can be reasonably notated, then it can be easily turned into a verity too.
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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