The New Sudoku Players' Forum

by **StrmCkr** » Thu Jan 20, 2022 11:55 pm

Code: Select all: something to mull over:

Code: Select all: 030500600006049050500010009070000080002400000340001006400002800060090027003100000 +--------------------+-------------------------+---------------------+ | 12789 3 14789 | 5 278 78 | 6 147 1248 | | 1278 128 6 | 278(3) 4 9 | 1237 5 1238 | | 5 28 478 | 27-8(36) 1 78(36) | 2347 347 9 | +--------------------+-------------------------+---------------------+ | 169 7 159 | 2369 2356 356 | 123459 8 12345 | | 1689 1589 2 | 4 35678 35678 | 13579 1379 135 | | 3 4 589 | 2789 2578 1 | 2579 79 6 | +--------------------+-------------------------+---------------------+ | 4 159 1579 | 367 3567 2 | 8 1369 135 | | 18 6 158 | (38) 9 3458 | 1345 2 7 | | 2789 2589 3 | 1 5678 45678 | 459 469 45 | +--------------------+-------------------------+---------------------+

can your code find this aic? { - Hybrid Wing type 2: }
i know its not found in hodoku's:
{ works for mine as it considers the mini Row/Cols as option A or B }

Code: Select all: mine: (6) 21 = 23 (6) - (3) 23 = 12 21 (3) - (3) 75 = 75 (8) 21 <> 8

yzf's finds it: Grouped AIC Type 2: (8=3)r8c4 - r23c4 = (3-6)r3c6 = 6r3c4 => r3c4<>8

Code: Select all: how my code sees it.. (6) 21 = 23 (6) - (3) 23 = 3 12 21 (3) - (3) 75 = 75 (8) | . . . | (B) . A | . . . | +---------+-----------------+---------+ | . . . | (3)x / / | . . . | <- digit 3 is box 2: mini Row A or mini row B in box | . . . | (3)x / / | . . . | | \ \ \ | -8(36)@ / (36)y | \ \ \ | <- strong link on 6 +---------+-----------------+---------+ | . . . | * . . | . . . | | . . . | * . . | . . . | | . . . | * . . | . . . | +---------+-----------------+---------+ | . . . | * . . | . . . | | . . . | *(38) . . | . . . | <- 38 represents an N size als {n cells with n+1 digits} . | . . . | * . . | . . . | * cells can be added to the ALs +---------+-----------------+---------+

legend:
/ <> = 3
\ <> 6
* = ALS cells{ N cells with N+1 digit}

this one can be extrapolated for additional eliminations when we expand the 1 size als to its max 6 size.
* cells contain all the "3"s then the @ cell cannot contain any of the als digits not = 3.

if the als also contains the "6" in any of the * cells.
x cells cannot contain the any of the als digits
y cell must = 6 or 3.
any of the * cells not in the als cannot contain digits of the als.

Code: Select all: +---------+-------------------------+---------+ | . . . | -68(3) . . | . . . | | . . . | -68(3) . . | . . . | | . . . | -8(36) . -1245789(36) | . . . | +---------+-------------------------+---------+ | . . . | -368 . . | . . . | | . . . | -368 . . | . . . | | . . . | (368) . . | . . . | +---------+-------------------------+---------+ | . . . | -368 . . | . . . | | . . . | (368) . . | . . . | | . . . | -368 . . | . . . | +---------+-------------------------+---------+ ALS Continuous Nice Loop: 3r3c6 = r123c4 - (3=86)r58c4 - r3c4 = 6r3c6 => r3c6<>1,r3c6<>2,r4679c4<>3,r3c6<>4,r3c6<>5,r4679c4<>6,r3c6<>7,r1234679c4,r3c6<>8,r3c6<>9 note: pleasant surprise its in Yzf's solver already.

by **RSW** » Fri Jan 21, 2022 3:31 am

Yes, my chain finder finds the same chain except in reverse order. This is the output:
(6)r3c4=(6)r3c6-(3)r3c6=(3)r23c4-(3=8)r8c4 => -8r3c4

I'll have to read the rest of your post in more detail. My chain finder doesn't find any additional chains in this state of the puzzle. It does work with any size ALS. However, it's currently limited to non group links in the ALS. Adding grouped ALS links is my next little project.

I should add, that my chain finder does not yet include code for finding the eliminations that are possible when the chain forms a loop. That's another item on the to do list.

by **StrmCkr** » Thu Jan 27, 2022 8:30 am

Thus, we have the shortest chain that gives the -1r2c9 elimination after only two passes. We know that we have the -1r2c9 elimination by default, but there may be more. So, we trace the chain to check for other eliminations, and in doing so, we also find -1r1c3. So, we have:

(1)r1c8 = (1)r12c9 - (1)r5c9 == (3)r4c8 - (3)r4c2 = (3)r3c2 - (3=1)r2c3 => -1r1c3 -1r2c9

== is an als correct? 1239 @R4C1,R56C9

i'm presuming it is as my aic code doesn't have those extensions yet,

the good news is my AIC code finally fixed after a full rebuild , found it easier to start from scratch for its chain finding sequence and finally found the error a type o forcing the sequences to use the wrong information => infinite looping and crashing out my write to screen function or killing the program completely when exceeding max value allowed by the storage systems..

by **RSW** » Thu Jan 27, 2022 9:31 pm

StrmCkr wrote:
(1)r1c8 = (1)r12c9 - (1)r5c9 == (3)r4c8 - (3)r4c2 = (3)r3c2 - (3=1)r2c3 => -1r1c3 -1r2c9

== is an als correct? 1239 @R4C1,R56C9

Yes, it's an ALS. The full output of my chain solver with the ALS info is:
ALS(1239)b6p269 => (1)b6p6=(3)b6p2
(1)r1c8 = (1)r12c9 - (1)r5c9 == (3)r4c8 - (3)r4c2 = (3)r3c2 - (3=1)r2c3 => -1r1c3 -1r2c9

Currently, my ALS code doesn't handle grouped ALS links, just single digit occurrences in the ALS, as in the above example. A good example of a grouped ALS link is Cenoman's solution in the recent puzzle: From "More Homework !" thread by eleven » Tue Jan 25, 2022
123.....45.7......8643..2....6479......8.2......1364....8..7642......3.56.....789

Cenoman wrote:
Code: Select all
+----------------------+---------------------+----------------------+ | 1 2 3 | 7 68 b58 | 589 569 4 | | 5 9 7 | 26 2468 148 | 18 36 1368 | | 8 6 4 | 3 9 a15 | 2 57 a17 | +----------------------+---------------------+----------------------+ | 23 1358 6 | 4 7 9 | 158 235 138 | | 347 e347 19 | 8 5 2 | 19 f367 f367 | | 279 578 259 | 1 3 6 | 4 2579 8-7 | +----------------------+---------------------+----------------------+ | 39 35 8 | 59 1 7 | 6 4 2 | | 2479 e47 29 | 269 2468 b48 | 3 1 5 | | 6 d145 125 | 25 c24 3 | 7 8 9 | +----------------------+---------------------+----------------------+

(7=15)r3c69 - (5=84)r18c6 - r9c5 = r9c2 - (4=73)r58c2 - (3=67)r5c89 => -7 r6c9; ste

My solver finds the first three ALS's in Cenoman's solution because they are single digit strong links, but it currently can't find the final (3=67)r5c89 strong link, because it has multiple occurrences of both link digits 3 and 6.

Grouped ALS's will likely be the next thing I add to my chain solver. The simplest way to implement them is finally becoming clear in my mind.

Edit: Fixed the the incorrect one line puzzle text.

by **StrmCkr** » Fri Jan 28, 2022 1:16 am

What's the rule for re using cells? I can't seem to find a reference for it.

Currently my code can re use all Strong link starting cells(À) of the same digit which makes for some very long chains

by **RSW** » Fri Jan 28, 2022 6:11 am

In my old recursive code, it would remember which strong links had been used, and wouldn't reuse them. When I wrote the new code, I kept the rules as minimal as possible. Since I couldn't find any reason for non-repetition of cells, I didn't put anything in to prevent it. So far, it hasn't produced any invalid chains. On the other hand, it has occasionally produced some rather interesting ones, including one that starts and ends on the same cell after making a loop in the middle of the chain, and then following the same links back to the beginning. I dubbed this a "U-turn" chain.

The U-turn chains no longer occur, because my program now requires that the start and end nodes be different. It was always intended to work that way, but a bug in the program had allowed it to happen. I'm now considering removing that restriction as well, because I can see no reason why it needs to be there. (I think the unique endpoint restriction was put in to prevent endless loop chains, but I don't think there's any way that could occur.)

by **StrmCkr** » Fri Jan 28, 2022 11:00 am

alright that's he same deduction I arrived at as it also hasn't derived invalid eliminations
As long as the reused cells where only the à section of any same digit selected. Makes for interesting chains for sure
I found infinie looping occurs if the list isn't finite where you don't deleted selected chains from a list of valid calls per step.

For the
Als chain do a sum of the sector for n and store those cells. (as the link)
Then store the cells with Digit x not in n, repeat for each x not in n

Eliminations are a bit trickery as it would need to use the set of x cells and match those
instead of all digits left in 1 sector

Adding loops 2... (if n from a is not in end als and It sees all of als n candidates at the end then als is doublly linked)

by **Hajime** » Fri Jan 28, 2022 3:53 pm

When extending the chain and the tail hits the chain in a cell, than this is the time to check for nice loops?

by **StrmCkr** » Fri Jan 28, 2022 4:21 pm

Code: Select all: When extending the chain and the tail hits the chain in a cell, than this is the time to check for nice loops?

a bit more complicated then that.

if the chain start and ends on its self its a closed loop

Code: Select all: +--------------------+--------------------+---------+ | -3456789(12) . . | . -2345789(16) . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +--------------------+--------------------+---------+ | . . . | . . . | . . . | | -1356789(24) . . | . -1235789(46) . | . . . | | . . . | . . . | . . . | +--------------------+--------------------+---------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +--------------------+--------------------+---------+

Code: Select all: (6) 40 = 4 (6) - (1) 4 = 0 (1) - (2) 0 = 36 (2) - (4) 36 = 40 (4)

if the chain starts with a bivalve then the last link happens to be the starting digit and they are visible to each other and not connected
its also a loop { weakly linked}

Code: Select all: +--------------+--------------+------------+ | (12) -1 -1 | -1 (16) -1 | -1 -1 -1 | | -2 . . | . -6 . | . . . | | -2 . . | . -6 . | . . . | +--------------+--------------+------------+ | -2 . . | . -6 . | . . . | | (24) -4 -4 | -4 (46) -4 | -4 -4 -4 | | -2 . . | . -6 . | . . . | +--------------+--------------+------------+ | -2 . . | . -6 . | . . . | | -2 . . | . -6 . | . . . | | -2 . . | . -6 . | . . . | +--------------+--------------+------------+

Code: Select all: (1) 4 = 4 (6) - (6) 40 = 40 (4) - (4) 36= 36 (2) - (2) 0 = 0 (1)

weak chain loop:

Code: Select all: +------------------------+--------------------+---------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +------------------------+--------------------+---------+ | -3456789(12) . . | . -12 . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +------------------------+--------------------+---------+ | (1) -12 -12 | . . . | . . . | | (2) -12 -12 | . . . | . . . | | . (2) (1) | . -3456789(12) . | . . . | +------------------------+--------------------+---------+

for this one both the start and end points must be weakly linked to each other.

Code: Select all: (2) 63 = 36 (2) - (1) 36 = 54 (1) - (1) 74 = 76 (1) - (2) 76 = 73 (2)

notes on this one: when this triggers all strong links are now weak, and all weak links are strong for eliminations

by **StrmCkr** » Mon Jan 31, 2022 3:19 pm

hey RSW
do you have almost Hidden sets programed for the aic + als chain finder?

stuff like this.
http://forum.enjoysudoku.com/almost-hidden-set-xz-rule-t32268.html?hilit=ahs

by **RSW** » Tue Feb 01, 2022 12:24 am

I haven't implemented AHS's yet. I went searching for information on them a few months ago, and found this post about them:
almost-hidden-sets-useful-redundant-t3197.html
At that time, after skimming through it, the logic wasn't immediately clear to me, and I wasn't sure whether an AHS would have a corresponding ALS. I put it on my to do list, and intended to reread it at a later date, to figure out the logic. If they turned out to be a complement of ALS's, then I didn't see any point implementing them, if the existing ALS logic could do the same thing.

I adopted the same philosophy when I was working on basic techniques. Since Hidden subsets have corresponding naked subsets, I never implemented hidden subsets. My naked subset code finds naked subsets of all sizes. While it may seem easier to search for a size 2 set than a size 7 set, computationally, I don't see any significant difference. The binomial values 9C2 and 9C7 are the same value: 36.
9C2 = 9C7 = 36
9C3 = 9C6 = 84
9C4 = 9C5 = 126
So, the number of cell combinations that need to be checked are the same in either case.

In the case of almost hidden sets, I would definitely be interested if it can be shown that they can give eliminations that aren't available from a corresponding ALS.

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

Edited to add:

Somehow, I seem to have overlooked this part of one of your earlier posts:

StrmCkr wrote:
Code: Select all
+-----------+------------+--------------+ | 5 6 123 | 347 389 49 | 38 1238 127 | | 4 8 13 | 37 2 5 | 6 9 17 | | 29 39 7 | 6 38 1 | 5 238 4 | +-----------+------------+--------------+ | 29 39 4 | 1 5 8 | 7 23 6 | | 7 5 238 | 234 39 6 | 348 1238 129 | | 6 1 238 | 234 7 49 | 348 5 29 | +-----------+------------+--------------+ | 3 7 5 | 9 4 2 | 1 6 8 | | 1 4 9 | 8 6 3 | 2 7 5 | | 8 2 6 | 5 1 7 | 9 4 3 | +-----------+------------+--------------+

this grid crashed my code. now to find another bug oh the joys...

edit edit: errors still erroring.

I ran this grid on my solver and it came up with a total of 41344 AICs. That was with an iteration limit set to 5 iterations and 100 chains per target. Of those 41344 chains, 8212 were duplicates (reverse order, etc.) and another 32149 that were unique but gave duplicate eliminations. So, restricting the list to the shortest chains giving unique eliminations, there were 983 that were found. This is a fairly big list, and may explain why your program crashed. Maybe it just ran out of memory?

Other stats from the run:
Total BiLocal links: 35
Total BiValue links: 14
Total UR links: 0
Total ALS links: 31
Group Links: 37

Total strong links: 117
Total weak links: 1120

Some of the chains returned:

Hidden Text: Show

For the 41344 chain run, some timing stats:

Code: Select all: Build strong link array: 10.79 ms Build weak link array: 8.96 ms Chain solve: 960.88 ms (the actual cellular automata part of the program) Chain trace: 5.861 s (process each of the found chains, mainly the time to find subchain eliminations) Chain format: 1.783 s (convert the chains into human readable eureka format) Display Update: 641.18 ms (not insignificant)

What's notable here is that the building of the strong and weak link tables is relatively fast. The finding of the chains is quite fast too, considering the number of them that it found in this case. In a more normal run where there are only a few hundred chains in total, the Chain Solve portion of the run would be 10 to 20 ms., similar to the amount of time that it takes to build the strong and weak link tables. It's the processing of the found chains that takes the most time. So, I may have to look at the chain trace part of the code to see if I can speed it up.

by **StrmCkr** » Tue Feb 01, 2022 6:24 pm

Code: Select all: Somehow, I seem to have overlooked this part of one of your earlier posts:

i did manage to fix my code {presuming atm} so far no errors eliminations.

Maybe it just ran out of memory?

my counting function used integers
which has a limit of 32767 --> when it got stuck in an internal loop it maxed this quickly and crashed.. and a few other issues...

my bi local count is higher: probably because i use Box [ Mini Rows & Mini Cols ]
min Row A or B

Code: Select all: | x / / | | x / / | |/ / / |

In the case of almost hidden sets, I would definitely be interested if it can be shown that they can give eliminations that aren't available from a corresponding ALS.

same here hence the question... i do have als xz and AHS-xz coded the only difference Ive seen between the two is set size differences for same eliminations
since als/ahs are complementary they balance this (9 - given ) = ALS + AHS

edit: should be a more clear partially coded Ahs-xz
the doubly linked rules arent fully coded as well as a few other nuances as they are so much harder to code...

from the example tests i've ran it over it had similar/identical eliminations but AHS relied on post clean up to catch the eliminations not included in the code

it is a project code that i haven't found reasons to finish it.

by **yzfwsf** » Thu Feb 03, 2022 2:03 am

StrmCkr wrote: since als/ahs are complementary they balance this (9 - given ) = ALS + AHS

Code: Select all: .-------------------.-------------------.-------------------. | 145 2 1345 | 3459 3459 369 | 5679 8 13579 | | 458 358 7 | 1 234589 369 | 2569 2469 2359 | | 1458 9 6 | 3458 23458 7 | 25 24 1235 | :-------------------+-------------------+-------------------: | 2578 578 258 | 3589 6 39 | 279 1 4 | | 3 1 9 | 47 47 2 | 8 5 6 | | 24578 6 2458 | 589 589 1 | 3 279 279 | :-------------------+-------------------+-------------------: | 12678 78 128 | 679 179 5 | 4 3 2789 | | 1567 4 135 | 2 1379 8 | 5679 679 579 | | 9 3578 2358 | 367 37 4 | 1 267 2578 | '-------------------'-------------------'-------------------'

Almost Locked Set XZ-Rule: (3=24581)r3c14578 - (1=4593)r1c1345 => r1c6<>3
I think AHS is not as powerful as ALS, at least not as easy to use as ALS. Can your AHS-XZ engine find this elimination found by ALS-XZ?

by **StrmCkr** » Thu Feb 03, 2022 2:15 pm

Code: Select all: Can your AHS-XZ engine find this elimination found by ALS-XZ?

no, in its present half baked form it has limitations.

at least not as easy to use as ALS

one of the main reasons i haven't coded it in full.

probably isn't one as some of the lower ahs-xz land on AIC/nice loops
and i cant see how to make them work as AHS-xz's

Code: Select all: +-------------------+-------------------------+-----------------------+ | 145 2 1345 | 3459 3459 9-3(6) | 59(67) 8 359(17) | | 458 358 7 | 1 234589 369 | 2569 2469 2359 | | 1458 9 6 | 458(3) 2458(3) 7 | 25 24 25(13) | +-------------------+-------------------------+-----------------------+ | 2578 578 258 | 3589 6 39 | 279 1 4 | | 3 1 9 | 47 47 2 | 8 5 6 | | 24578 6 2458 | 589 589 1 | 3 279 279 | +-------------------+-------------------------+-----------------------+ | 12678 78 128 | 679 179 5 | 4 3 2789 | | 1567 4 135 | 2 1379 8 | 5679 679 579 | | 9 3578 2358 | 367 37 4 | 1 267 2578 | +-------------------+-------------------------+-----------------------+

Code: Select all: +----------------------+-------------------------+-----------------------+ | 45(1) 2 345(1) | 3459 3459 9-3(6) | 59(67) 8 359(17) | | 458 358 7 | 1 234589 369 | 2569 2469 2359 | | 458(1) 9 6 | 458(3) 2458(3) 7 | 25 24 25(13) | +----------------------+-------------------------+-----------------------+ | 2578 578 258 | 3589 6 39 | 279 1 4 | | 3 1 9 | 47 47 2 | 8 5 6 | | 24578 6 2458 | 589 589 1 | 3 279 279 | +----------------------+-------------------------+-----------------------+ | 12678 78 128 | 679 179 5 | 4 3 2789 | | 1567 4 135 | 2 1379 8 | 5679 679 579 | | 9 3578 2358 | 367 37 4 | 1 267 2578 | +----------------------+-------------------------+-----------------------+

same thing here: MY CODE cant find these styles either
aHS 123 @ r1c1789
AHS 123 @ r1239c9
x: r1c9,r1c9,r1c9
Z

Code: Select all: +------------------------+-------------------+------------------------+ | -679(123) 4 5 | 67 6789 89 | 68(2) 89(1) -89(123) | | 2369 2369 269 | 1 45689 4589 | 568-2 7 89(23) | | 8 169 1679 | 567 2 3 | 456 459-1 49(1) | +------------------------+-------------------+------------------------+ | 23456 2356 246 | 9 358 7 | 1 4568 48 | | 145679 1569 14679 | 25 158 1258 | 3 45689 4789 | | 13579 8 179 | 4 135 6 | 57 2 79 | +------------------------+-------------------+------------------------+ | 12469 1269 3 | 267 14679 1249 | 2478 148 5 | | 12459 7 1249 | 8 1459 12459 | 24 3 6 | | 12456 1256 8 | 3 14567 1245 | 9 14 -47(12) | +------------------------+-------------------+------------------------+

where the als-xz is this:
Almost Locked Set XZ-Rule: A=r1c45678 {126789}, B=r123456c9 {1234789}, X=1,2 => r2c7<>2, r3c8<>1, r1c1<>6, r1c1,r3c4,r6c7,r9c9<>7, r1c1<>9, r9c9<>4

Code: Select all: +----------------------+---------------------+------------------------+ | 123-679 4 5 | (67) (6789) (89) | (268) (189) (123-89) | | 2369 2369 269 | 1 45689 4589 | 568-2 7 (2389) | | 8 169 1679 | 56-7 2 3 | 456 459-1 (149) | +----------------------+---------------------+------------------------+ | 23456 2356 246 | 9 358 7 | 1 4568 (48) | | 145679 1569 14679 | 25 158 1258 | 3 45689 (4789) | | 13579 8 179 | 4 135 6 | 5-7 2 (79) | +----------------------+---------------------+------------------------+ | 12469 1269 3 | 267 14679 1249 | 2478 148 5 | | 12459 7 1249 | 8 1459 12459 | 24 3 6 | | 12456 1256 8 | 3 14567 1245 | 9 14 12-47 | +----------------------+---------------------+------------------------+

by **yzfwsf** » Fri Feb 04, 2022 2:52 am

StrmCkr wrote:no, in its present half baked form it has limitations.

StrmCkr wrote: one of the main reasons i haven't coded it in full.

This should have shown that AHS-XZ is not as easy to use as ALS-XZ. You have had ideas in this area many years ago, but you have not written the code of AHS-XZ completely, which shows that AHS-XZ is not easy to code.
For human solvers, the logic of AHS-XZ is not as easy to understand as ALS-XZ, such as the example mentioned in your post.

Code: Select all: .-----------------------.-------------------.------------------------. | (123)679 4 5 | 67 6789 89 | (2)68 (1)89 (123)89 | | 2369 2369 269 | 1 45689 4589 | 2568 7 2389 | | 8 169 1679 | 567 2 3 | 456 1459 149 | :-----------------------+-------------------+------------------------: | 23456 2356 246 | 9 358 7 | 1 4568 48 | | 145679 1569 14679 | 25 158 1258 | 3 45689 4789 | | 13579 8 179 | 4 135 6 | 57 2 79 | :-----------------------+-------------------+------------------------: | 12469 1269 3 | 267 14679 1249 | (278)4 (8)14 5 | | 12459 7 1249 | 8 1459 12459 | (2)4 3 6 | | 12456 1256 8 | 3 14567 1245 | 9 14 (27)14 | '---------------------'-------------------'--------------------------' (8r7c8 = 2r8c7)AHS:123r1 - (2r1c7 = 1r1c8)AHS:278b9 => r1c8<>8,r7c8<>1 vs Almost Locked Set XZ-Rule: A=r1c4567 {26789},B=b9p248 {1248}, X=2, Z=8 => r1c8<>8

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