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Potential deletions for general loops

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Thu Oct 14, 2010 3:55 am    Post subject: Potential deletions for general loops Reply with quote
Here is the code after basics for Danny's puzzle dated 10/10/14 B.

Code:
*-----------------------------------------------------------*
 | 9     1     8     | 3     2     5     | 7     4     6     |
 | 2     7     4     | 9     168   168   |a18    5     3     |
 | 6     3     5     | 7     148   148   | 189   2     189   |
 |-------------------+-------------------+-------------------|
 | 4     59    6     | 8     159   3     |b159   7     2     |
 | 3     589   2     |e45    7    d14    | 6    c18   c1489  |
 | 7     589   1     | 6     459   2     | 4589  3     489   |
 |-------------------+-------------------+-------------------|
 | 5     6     9     | 2     48    7     | 3     18    148   |
 | 8     4     7     | 1     3     9     | 2     6     5     |
 | 1     2     3     |f45    4568  468   |g48    9     7     |
 *-----------------------------------------------------------*

Look at the loop labeled abcdefg.

(1)a-b=c-(1=4)d-e=f-(4=8)g-(8=1)a

So the question is: Are deletions possible given this loop. An even better question is: Does anyone know of a thread that addresses the issue of potential deletions for general loops including xy-loops.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu Oct 14, 2010 5:15 am    Post subject: Reply with quote
First, I need to rewrite the loop slightly:

Code:
     a      b      c            d      e      f           g
(8=1)r2c7 - r4c7 = r5c89 - (1=4)r5c6 - r5c4 = r9c4 - (4=8)r9c7 - loop

Next, I need to direct you to a comment of mine here.

Since there aren't any ERI cells in this loop, where are the weak inferences (WIs) and which eliminations can we derive from them?

Code:
WI a-b on <1>  =>  r3c7<>1
WI c-d on <1>  =>  nada because it's already a grouped strong link
WI d-e on <4>  =>  r5c9,r6c5<>4
WI f-g on <4>  =>  r9c56<>4
WI g-a on <8>  =>  r36c7<>8

Final tally: r3c7<>1, r5c9,r6c5,r9c56<>4, r36c7<>8

Regards, Danny
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Fri Oct 15, 2010 2:08 pm    Post subject: Reply with quote
As always, I greatly appreciate your detailed feedback Danny.

I have reviewed this response and the referenced link, and believe I am beginning to see some trees in the forest regarding the "mechanical" usage of WIs, but overall the fog is still way to dense. I am fundamentally unsure of the logical base for deletions nor do I understand/appreciate the implications of ERI candidates.

I really need a primer that provides the logical bases for deletions associated with general loops, but have not been successful in finding a source of that level of information. Maybe I have not been using appropriate terms in my searches.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Oct 15, 2010 5:13 pm    Post subject: Reply with quote
tlanglet wrote:
I really need a primer that provides the logical basis for deletions associated with general loops, but have not been successful in finding a source of that level of information.

I was afraid that you were going to say that. As for a more detailed description, I don't ever recall encountering one. All I recall is a nebulous statement that (roughly) goes "all weak links must be converted into strong links". It was much later, when I wrote my latest chain/loop routine, that I realized what was really happening. Here it is in all of its gory detail.

gory detail wrote:
An AIC-loop can be started at any strong inference. Its eliminations are the AIC eliminations derived from every possible starting point. This is equivalent to converting every weak link into a strong link. If an ERI cell is present, then there is an elimination in it as well.

Here's my continuous loop ...

Code:
     a         b         c            d         e         f           g
(8=1)r2c7 - (1)r4c7 = (1)r5c89 - (1=4)r5c6 - (4)r5c4 = (4)r9c4 - (4=8)r9c7 - loop

... and the AICs resulting from starting at every strong inference.

Code:
     a         b         c            d         e         f           g
(8=1)r2c7 - (1)r4c7 = (1)r5c89 - (1=4)r5c6 - (4)r5c4 = (4)r9c4 - (4=8)r9c7 ; r36c7<>8

   b         c            d         e         f           g           a
(1)r4c7 = (1)r5c89 - (1=4)r5c6 - (4)r5c4 = (4)r9c4 - (4=8)r9c7 - (8=1)r2c7 ; r3c7<>1

     d         e         f           g           a         b         c
(1=4)r5c6 - (4)r5c4 = (4)r9c4 - (4=8)r9c7 - (8=1)r2c7 - (1)r4c7 = (1)r5c89 ; nada

   e         f           g           a         b         c            d
(4)r5c4 = (4)r9c4 - (4=8)r9c7 - (8=1)r2c7 - (1)r4c7 = (1)r5c89 - (1=4)r5c6 ; r5c9,r6c5<>4

     g           a         b         c            d         e         f
(4=8)r9c7 - (8=1)r2c7 - (1)r4c7 = (1)r5c89 - (1=4)r5c6 - (4)r5c4 = (4)r9c4 ; r9c56<>4
_________________________________________________________________________________________

Regards, Danny
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida
PostPosted: Mon Oct 18, 2010 12:25 am    Post subject: Reply with quote
Hi Ted,
If you are having trouble finding more information on this it could be because you are using the wrong terminology. The correct terminology is continuous nice loop, which is often called continuous loop. There is a section on nice loops in Sudopedia. You can also google sudoku nice loop and find a tutorial on this.
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strmckr



Joined: 18 Aug 2009
Posts: 64
PostPosted: Tue Oct 19, 2010 1:21 pm    Post subject: Reply with quote
ERI

it stands for
Empty Rectangle intersection


Code:

| / x / |
| x x x |
| / x / |


what it is specifically is a box whos sum of the candidates are found over a

mini row + min col - the middle cell if active.

the middle cell is the intersection of the combined sets of grouped digits

if a cell sees the intersection of the eri group iit be treated as a strong link A = B

for example
Code:

 .  .  . |  /  a  / |  .  .  .
 . ab  . |  a a-b a |  .  .  .
 .  .  . |  /  a  / |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 . -b  . |  . ab  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 Type E:


this w- wing used the eri on digits A to link around the corner and see the bivalve causing the elimination.


some reading for chains:
http://hodoku.sourceforge.net/en/tech_chains.php


eris are a relatively newish concept with programing... what was written on them was lost in the sudokuplayers forum crash...


found more stuff

http://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm
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