The New Sudoku Players' Forum

[StrmCkr]

There is another type of RCC in AHS, where all non AHS candidates in two AHS form a strong region.

what? exactly constitutes non AHS candidates?

when AHS is defined as:
n digits in N+1 Cells?

if its not part of the AHS then its part of an ALS

i dont comprehend your other comment as treat everything as weak-links when my definitions don't use weak-links at all,

I have weak inferences for eliminations and connectivity

where two als are a strong link via 1 or 2 mutually shared sectors for 1 / 2 digits.

independently its a weak inference for the shared digit between two als and a loop has two weak inferences for the different digits.

i don't use weaklinks in the sense of Nice-loops definitions { bivavle/bilocal plotting of cells} where on implies off etc.

instead i have bi-direction sector inference points for a table of: digit strong links{types 1-6}, als dof strong links, almost fish strong links, AHS dof strong links.

[yzfwsf]

what? exactly constitutes non AHS candidates?
when AHS is defined as:
n digits in N+1 Cells?

N+1 cells include both AHS and non AHS candidates.If a common non AHS candidates from two AHS form a strong region, this is a RCC for that two AHS.

[StrmCkr]

if i comprehend that...

if i have a hypothetical:
digits 123 in cells 4567
digits 124 in cells 1479

x: 47, z 47

your saying that if cells 5,9 happen to have a sector locked between them for say digit "9"

that this outside interaction constitutes a 3rd type of RCC

if that's what your suggesting... then ALS -xz etc functions are also missing a 2nd type of RCC using the interaction of the hidden set outside the scope of the als.
that would internally reduce the als from N+1 digits to N digits

[yzfwsf]

Code: Select all

,---------------------------------,---------------------------------,---------------------------------,
| 123456789  78         123456789 | 456789     123456789  456789    | 123456789  456789     456789    |
| 12345678   123456789  12345678  | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 12345678   123456789  12345678  | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123789     123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123789     123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123789     123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123789     123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
'---------------------------------'---------------------------------'---------------------------------'

AHS1: 123r1c1257
AHS2: 456r2368c2
RCC Type 3: 9b1

[StrmCkr]

exactly what i thought 9 is locked to two sets via 1 sector but sits outside of the scope of the ahs used ie a third set.

to me that would be an
aaahs + AHS + AHS

with 2 cells shared by each ahs

aka DDS using ahs (instead of als.)

If it was 2 cells I'd label it ahs xy rule

[yzfwsf]

RCC for AHS need be focused on cells, not the candidates.

[StrmCkr]

RCC for AHS need be focused on cells, not the candidates.

type 1: cells shared by both sets, these cells do not contain overlapping candidates shared by both sets.
type 2: common digit of set A & B: cells for set A that only contain common digit, cells for set b that only contain common digit : these cells share a sector.

for me the definition's I've been using relate to the sets used. { just like ALS only uses information of the two sets provided: digits of the sets, and cells}
to add the "9" id have to add another set to the mix, as the "9" isn't directly part to the cells of the sets used.

which is where i'm suggesting it would fall into DDS category or AHS - chaining as its now using three AHS

don't get me wrong here it is an interesting thought, and its definitely got my attention a fair amount.

i am thinking its possible for ALS- xz to have something similar where the RCC cell is also part of an internal AHS: so that the internal AHS of both sets also produces extra elimination based on there positions as RCC is true +AHS cell is now locked, or RCC is true + AHS cell is now locked

here we go an example:

Code: Select all

+-----------------+----------------+-----------------+
| .  (1234)  .    | .  (13)  .     | .       (12)  . |
| .  .       .    | .  .     -3    | -2      .     . |
| .  .       .    | .  .     -3    | -2      .     . |
+-----------------+----------------+-----------------+
| .  (124)   (15) | .  .     (135) | (1235)  .     . |
| .  .       .    | .  -3    .     | .       -2    . |
| .  .       .    | .  -3    .     | .       -2    . |
+-----------------+----------------+-----------------+
| .  .       .    | .  .     .     | .       .     . |
| .  .       .    | .  .     .     | .       .     . |
| .  .       .    | .  .     .     | .       .     . |
+-----------------+----------------+-----------------+

als a) 1234 @ r1c258
als b)12345 @ r4c2367
x: 4 in r14c2. (4 is also a strong link for c2)
Ahs of A) 23 @ r1c258
Ahs of b) 23 @ r4c267
x in A or B turns ahs A or B into locked sets for 2,3

2 is pretty clear as an underpinned skyscraper but the 3 is a different beast on its own.

I'd probably just use the ahs xy between the three sets (23) (4) (23)
(R1c58=r1c2) - (r1c2= r4c2) - (r4c2 =r4c67) => peers of 2&2 and peers of 3&3 are excluded.

[yzfwsf]

Code: Select all

+--------------------------+-----------------------+-----------------+
| 124579    1579-2  1579-4 | 2468   246789  24689  | 45679  3   5679 |
| 6         (279)   (479)  | 5      234-79  234-9  | 1      8   (79) |
| 4579      8       3      | 46     1       469    | 45679  2   5679 |
+--------------------------+-----------------------+-----------------+
| 248-1     (12)    (14)   | 9      5       7      | 3      46  68-1 |
| 34578-1   6       57-14  | 148    348     1348   | 578    9   2    |
| 345789-1  3579-1  579-14 | 12468  23468   123468 | 578    47  1578 |
+--------------------------+-----------------------+-----------------+
| 37        37      6      | 18     89      189    | 2      5   4    |
| 59        4       8      | 7      26      256    | 69     1   3    |
| 1579      1579    2      | 3      46      456    | 6789   67  6789 |
+--------------------------+-----------------------+-----------------+

anyone know if its possible to invert this als-xz to showcase it as an ahs-xz

so far i don't think its possible to use AHS-xz rules on two sectors that don't overlap.

bridging the intersections with 2 strong links on 2 & 4 makes it double linked ahs-xz style elimination...

(c2=c563)AHS:234r2 - (c3=c1892)AHS:2468r4 Loop => r156c3<>4, r2c56<>9, r4c19<>1, r1c2<>2, r2c5<>7

[StrmCkr]

Nice !

Code: Select all

+-------------------------+--------------------------+---------------------+
| 124579   1579-2  1579-4 | 2468   246789    24689   | 45679  3     5679   |
| 6        79(2)   79(4)  | 5      -79(234)  -9(234) | 1      8     79     |
| 4579     8       3      | 46     1         469     | 45679  2     5679   |
+-------------------------+--------------------------+---------------------+
| -1(248)  1(2)    1(4)   | 9      5         7       | 3      (46)  -1(68) |
| 134578   6       157-4  | 148    348       1348    | 578    9     2      |
| 1345789  13579   1579-4 | 12468  23468     123468  | 578    47    1578   |
+-------------------------+--------------------------+---------------------+
| 37       37      6      | 18     89        189     | 2      5     4      |
| 59       4       8      | 7      26        256     | 69     1     3      |
| 1579     1579    2      | 3      46        456     | 6789   67    6789   |
+-------------------------+--------------------------+---------------------+




i take it that you have AHS- XZ {1,2} RCC rules operating in your solver now ?

any plans to expand this into AHS -XY, {2,3} RCC rules ? {or beyond with chains}

[yzfwsf]

Yes, AHS-XZ Rule has been written, and AHS-W-Wing, AHS-XY-Wing, and AHS chain are also in the plan, but I am busy with work handover recently and don't have time.

ps: AHS encoding is much more complicated than ALS encoding, and the running time is also much worse than ALS. Determining RCC requires considering multiple situations, while ALS only needs to consider candidates.

[yzfwsf]

Code: Select all

,--------------------,----------------------,-----------------,
| 125    6      135  | 12579  2579   4      | 8     357   23  |
| 1245   125    7    | 1258   235    12358  | 3456  356   9   |
| 8      9      345  | 6      257    2357   | 3457  1     234 |
:--------------------+----------------------+-----------------:
| 56     4      568  | 2589   1      2568   | 369   236   7   |
| 167    178    2    | 3      679    678    | 69    4     5   |
| 3      57     9    | 257    4      2567   | 1     26    8   |
:--------------------+----------------------+-----------------:
| 12457  12578  1458 | 1257   2357   9      | 3457  3578  6   |
| 1567   3      1456 | 157    8      1567   | 2     9     14  |
| 9      12578  1568 | 4      23567  123567 | 357   3578  13  |
'--------------------'----------------------'-----------------'

Almost Locked Set XZ-Rule: A=r678c4 {1257},B=b2p12589 {123579}, X=1, Z=25 => r2c4<>2 r2c4<>5
Vs
Almost Hidden Set XZ-Rule: A=89{r124c4},B=18{b2p146},X=(9r1c4-1r1c4), Z=(8r2c4=18r2c4) => r2c4<>2,r2c4<>5

[StrmCkr]

ps: AHS encoding is much more complicated than ALS encoding, and the running time is also much worse than ALS. Determining RCC requires considering multiple situations, while ALS only needs to consider candidates.

100% agree, which is why i haven't done much with these either mostly fun theory work as coding is a nightmare and more so for the eliminations as they are all internal + some external

ps nice examples