The New Sudoku Players' Forum

[yzfwsf]

I was talking in terms of pure ALS-xz rule, ofc my Discontinuous Loops algorithm also finds this solution

Ok, but I only see 2 AHS + 2 strong links VS 2 ALS+2 strong links, where ALS xz is 2 ALS+1 or 2 weak link


Use your latest version, Full scan

Code: Select all

FULL SCAN :

+--------------+--------------+--------------+
|5789 5689 5689|579  <2>  <1> |589  <4>  <3> |
|579  34   34  |<6>  <8>  79  |59   <1>  <2> |
|<1>  589  <2> |59   <3>  <4> |589  <6>  <7> |
+--------------+--------------+--------------+
|589  458  459 |79   <6>  <2> |<3>  78   <1> |
|<2>  389  39  |<1>  79   <5> |<4>  78   <6> |
|<6>  <1>  <7> |<3>  <4>  <8> |<2>  <5>  <9> |
+--------------+--------------+--------------+
|59   5679 569 |<8>  79   <3> |<1>  <2>  <4> |
|<3>  <2>  <1> |<4>  <5>  <6> |<7>  <9>  <8> |
|<4>  789  89  |<2>  <1>  79  |<6>  <3>  <5> |
+--------------+--------------+--------------+

Almost Hidden Sets--------------------------------

r1c4 == 7

Almost Locked Sets--------------------------------

r3c7 <> 5

Almost Locked Sets Chain--------------------------

r3c7 <> 5
r5c2 <> 8
r4c8 <> 8
r4c1 <> 9
r4c4 <> 7
r3c4 <> 9
r1c2 <> 8
r1c1 <> 5
r2c1 <> 9
r2c1 <> 5
r4c3 <> 9
r1c4 <> 5
r1c4 <> 9
r4c2 <> 8

[MAGREMENT]

ALS xz is 2 ALS+1 or 2 weak link

Actually ALS-xz is more than 1 or 2 links as each rcc candidates from ALS 1 has to see (have a weak link with) each rcc candidate from ALS 2. So if both ALS have 2 cells with rcc candidate for example, that is 4 weak link (2 x 2).

Use your latest version, Full scan

I'm sorry but I'm missing your point. I simply stated that my "AHS-xz" rule could find solution my ALS-xz rule did not. I never said that there were not better options for finding such an elimination. Also, the strategy replicating this elimination that you show in my full scan is the ALS-Chain, which I'd argue is more complex to find than simple "AHS-xz".

[yzfwsf]

Code: Select all

.....67...5.1...3...9.2...42..........8.4...29.46.2........7.6....3..1..8.......5

This puzzle has MSLS or Multifish, but your solver's "set equivalence" cannot find it.
MSLS:16 Cells r1278c1359,16 Links 13r1,67r2,13r7,67r8,4c1,2c3,589c5,89c9,5b7
20 Eliminations:r1c28,r7c2<>1,r9c3<>2,r7c27,r1c2<>3,r46c5<>5,r2c7,r8c2<>6,r8c28<>7,r46c59<>8,r4c59,r9c5<>9

[MAGREMENT]

This puzzle has MSLS or Multifish, but your solver's "set equivalence" cannot find it.

That's cause my Set Equivalence strategy doesn't check every possible unit (sector) combination as it would take way too much time. It only checks for Row x Columns and Blocks x 2 Row + 2 Column. I've had in mind coding a smarter approach than testing every combination possible for quite a bit of time but I've not had the courage to do it yet.

I might try doing something right now and see how it goes (Nvm I'm too sleep deprived I'll look into it tomorrow)

[yzfwsf]

Code: Select all

+--------------------+--------------------+--------------------+
|1578   1258   <4>   |12389  13789  289   |<6>    123578 2378  |
|<3>    12568  12678 |1248   14678  248   |578    <9>    2578  |
|1678   <9>    12678 |1238   13678  <5>   |78     12378  <4>   |
+--------------------+--------------------+--------------------+
|148    <7>    189   |23489  <5>    23489 |89     38     <6>   |
|4568   468    <3>   |489    489    <1>   |<2>    578    5789  |
|<2>    58     89    |<7>    38     <6>   |<1>    <4>    3589  |
+--------------------+--------------------+--------------------+
|1478   1248   <5>   |<6>    1489   489   |<3>    278    2789  |
|<9>    1348   178   |13458  <2>    348   |4578   <6>    578   |
|468    234    268   |4589   3489   <7>   |4589   258    <1>   |
+--------------------+--------------------+--------------------+


Maybe bug in your Digit Forcing Net. Missing strong links 7r5,4c7.
Path if on :
9r5c9 - 9r7c9 = 9r9c7 - 5r9c7 = 5r2c7 - 5r1c8 = 5r9c8 -5r9c4 = ALS : (3,4,8,9)r7c6, r8c6, r9c4, r9c5 - 9r7c5 =9r7c6 - 9r4c6
Path if off
9r5c9 = PR : 9r5c45 - 9r4c6

[StrmCkr]

Hodoku is coded as niceloops turbot name was kept as a nod to the Nick
( It's actually all x-cycles not x-chains)
turbot
Ps. You can see this from the chain outputs as it Includes the eliminations as part of the chain.

Even his aic engine lacks true capacity as it only labels aic when the niceloop is a closed Continousloop

Unfortunately hodoku author passed away befor we could finish our collaboration, many unfinished projects was supposed to go into it including changing to aic logic.

niceloops
Use bivavlue/bivalve plotting via cell to cell (cellular Atama)

Are always closed loops and include the elimination cells as part of the chain for discontinuous loops, or they prove themselves true for continous. (forcing implication network!)

This is not coded in hodoku:
à.i.c
Digit based mini sector to mini sector for strong links only uses strong links exclusivly as logic XOR gates
Weakinferences run edgewise as a not gate between nodes. Bidirectional network from every chain link.


als Elim rule

DDS

Alc, pair, TRIP

alc-SoS

[MAGREMENT]

Maybe bug in your Digit Forcing Net. Missing strong links 7r5,4c7.

I see your point, these strong links are not really missing but just not highlighted, as Net's highlighting needs a bit more work

[StrmCkr]

Actually ALS-xz is more than 1 or 2 links as each rcc candidates from ALS 1 has to see (have a weak link with

No, there is only 2 strong link or 3 strong links and 1 or 2 weakinferences in the chain.

There is (n-Rcc) elimination values between common digits of the sets that are not the rcc.
Where n is the combined tôtal shared digits between a & b

Minimally 1, but can be more. (these are not weak inferences)

Als xz example xyz wing

À)(1=23) bp19 - (2=1) r1c4 => r1c23<> 1

In the case of 2 rcc, set a&b are now a locked set,
(als xz aka naked triple aka xyz ring

(A=BC) als À - (c=dA)als b - (a=BC) als à =>loop
B is locked to als a ,
D IS locked to als b

C is locked to A&B
A is locked to A&B

Ps if you want overlaps
Rcc cannot be in shared cells between sets.

[MAGREMENT]

Ps if you want overlaps
Rcc cannot be in shared cells between sets.

I wonder if this overlap rule can also be applied to AHS. Right now, my AHS-xz rule need 2 AHS with no candidates in common. I'll look into it

[StrmCkr]

ahs-xz

Yes, they can see my last posts for the 2nd rcc type
Cells in adjacent sectors And the cells dont overlap..

Ahs use sectors or cells for sharing.

Ps.
Ahs - xz, x wing is a 2rcc rule example. Using 2 shared sectors.

[MAGREMENT]

Could anyone provide me a list of Sudoku's solved by using MSLS ?

I can test my code that way

[yzfwsf]

Code: Select all

.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5
........9...78..2...81.2....3.5..6..5....7..4..7.2......1.7..9.6.......5.4....3..
98.7..6....5.4.........9.3.6......9..3....8....2.7...5.5.........1.27......4.1..7
..34...8......92..6...3.......8..4.......2.9..7..1...6.1.......5...7...176....9..
1.........5.....36....3.5.4.1..6.3....82.....9....7....629.8...7.......8....4.6..
.2....7..4...8...6..9...1...7.8..9....15...2.5....4............8...4...3....63.7.
3.....5...8.4...2...1.....7.4.8.6........9.8.......2.4.....73...6.9.....5.7.....1
..3.5....4....9....8.2....1..5.34......8....69.....3.....7..81..1....6.7..2......
98.7.....7.6...9......5....4......3..6.5.........24..1.9.8..5......3..92.....1.4.
.......391......6...6.9......8.3...6.7...45...1.2.........8..5..4.7.....2....18..
1.....5...8.4...2...3.....7.4.8.6........9.6.......2.4.....73...2.9.....5.7.....1
1.....5...8.4...2...3.....7.4.8.9........6.8.......2.4.....73...6.9.....5.7.....1
98.7..6..7.5.......6..8....6...7.4.....3...5......2..1.9....8....4..5..2...1...3.
.......93.....81....3.16...4.......5..16..9...7.....2..5..6...72....7.4....8..3..
...2............85..6.5......8.3...9.7...23..1..4..6....9....3..2.7..9..4....1...
98.7.....7.6...8.........754...3..2...9...6.......1..4..79..5......4...1.....2.3.
.......8..2.....69..9.8........7...6.1.2..7..5....43....6.9..3.2..1......4...5...
98.7.....6.....8....5....747...5..3...69..........2..1..96..4......1...5.....3.2.
98.7.....6.7...8......5....4...3..2..7....9.......1..4.9.6..5....8.2..3......4..1
98.7.....7.6...8......5....4....3.2..9..1...4..7...9....95..6......2...3.....4.1.
98.7.....7.6...9......5....4...3..2..7...1..4..9...8....75..6......4...1.....2.3.
98.7..6..7...9..8..5.......5...8..9....4....6.....32...7..1......1..2..4...6..3..
98.76....5.............98..7....85.....6...4.....3...2.9....1....72...6...1.4...3
98.76....7....58...5.......5.....4....4.3..2....1....6.7...89.....6....3....2..1.
98.7.....7.6...8......5....4....3.2..9..1...4..7..59....95..6......2..3......4..1
98.7.....6.7...8......85...4...3..2..9....6.......1..4.6.5..9......4...3.....2.1.
98.7.....7.6...8......5....4...3..2..9...1..4..8...6....95..7......4...1.....2.3.
98.7.....7.6...8......85...4....3.2..6....9......1...4.7.5..6......2..1......4..3
98.7.....7.6...8......5....4...3..2..9...1..4..8...5....96..7......4...1.....2.3.
98.7.....7.6...8.........5.4...3...2..89..........4.1...76..5......1..3......2..4
98.7.....7.6...8.........5.4...3...2.7...1.4...9...6....79..5......4..1......2..3
98.7.......6...9.........758..5..7...6..4...3.....2.1.6..9......1...3..2....1..4.
98.7.....6.7...8......5....4....3.2...6...9......1...4..98..5......2...1.....4.3.
98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2
98.7.....7.6...8......5....4...3..2..7.6..........4..1.6.9..5......1..4......2..3
98.7.....7.6...8......5....4....3.2..7....6......1...4.9.5..7......4...1.....2.3.
98.7.....7.6...9......5....4......3...85.........42..1..76..8......3..2......1..4
98.7.....7.6...9......5....4....3.2...7...6......1...4..86..5......4...1.....2.3.
98.7.......6...9.........754...3...2.6....5.......1.4..9.5..8......2..3......4..1
98.7.......6...9......5..7.4....3.2..6.5.........4...1.9.8..5......2...4.....1.3.
98.7.....6...5.8.......8...5...6.9.....4...3......7..2.9....1....5..2.4...13....7
98.7.....6.7...8......5....4....3.2..6....9....9.1...4.9.5..7....6..4..3....2..1.
98.7.....6.7...8......5....4....3.2..6...59....9.1...4.9.5..7......2..1......4..3
98.7.....7...6.........97..5.....4.....3...6.....2...1.7...85....56....3..4.1..2.
98.7.....7...6.........97..5....48.....6...3.....2...1.9....5....5.3...6..41...2.
98.7.....7.6...8......5....4...3..2..9.6..........4..1.6.5..7......2..4......1..3
98.7.....7.6...8......5....4...3..2..9.6..........4..1.6.9..5......1...4.....2.3.
98.7.....7.6...9......5....4....3.2..6.8.........4...1.7.9..5......1..3......2..4
98.7.....7.6...9......5....4....3.2..6.8.......9.4...1.9.5..8......1..4......2..3
98.7.....7.6...9......5....4....3.2..7....5......1...4.6.9..8......2...3.....4.1.
98.7..6....5.4.........9.3.3....6..9.4.5.......7.8....2....1..3.7.....92.......1.
98.7..6....59...4.....3...92....9..7.4.....5...6...8..1....2..3.6...31......1....
.......12.....3..4..4.2......1.....5.3...6...7..8..9....5.9..4..8.7.5...6..3..5..
.......12.....3..4..4.2......1.....5.3...6...7..8..9....5.9..4..8.3.5...6..7..5..
........1.....2..3..3.1..4...4.....5.2...67..8..9.......5.7..3..9.2..5..6..5.8...
........1....12.3...1.4.2....2.5.1...6......37......8...9..4....3.5...6.8..9....7
.......12....34..5..51..6....23...6..7...8...9...4......6....2..8..7.5..4....9..6
..............1.23..2.3...4..5....4..1...6...7..8..5....9.2...5.6...79..8..1.....
..............1.23..2..4..5..5..3..6.1..7....8...9......6....3..9.8..6..7...1.4..
........1....23.4...21.5.....1.5...4.6....7..8..4...9...3.1.....7.9...6.9.....8..
........1.....2.34..4.1..5...3....1..2.6.....7....8.....9.4...5.8.2..9..6....7...
........1....23.4...24.5.......5..3..6...78..9..3....7..4.3..1..7......98.....6..
........1....23.4...24.5.....35..1...6...78..7...3...9..53...1..8......69.....7..
........1.....2.34..1.4..5...5.3..1..6.2.....71.8.......9.....5.8...69..2..7.....
........1.....2.34..1.4..5....6.......7.3..1.89.2.......3.....5.2.9.....6....87..
........1....23.4...24.5.....3.5..1..6....7..8..2....9..5.4.....7....8..9....7..6
........1....23.4...24.5.....3.4.....6....7..8....6..9..5.3..1..9....6..7..2....8
........1....23.4...24.5.....3.4.....6....7..8....6..9..5.3..1..7....6..9..2....8
........1.....2.34..1.4..5...3.....5.2.6.....7....89....9.3..1..6.7.....8..2..5..
........1.....2.34..1.4..5...5.3..1..6.2..5..7..8.......9.....5.8...69..2..7.....
........1.....2.34..3.4..5...4.3..1..6...7...8..2..9....9.....5.7.6.....2....81..
........1.....2.34..3.4..5...1.....5.2...61..7..8.......9.3..1..6.2..9..8....7...
........1.....2.34..3.4..5...4.1...5.6...7...8..2.......9....1..2.6..9..7....85..
........1.....2.34..3.4..5...1.....5.2.6.....7....8.....9.3..1..6...75..8..2..9..
.......12.....34....1.45......3..5...6...4..78...7..9...54..2...7.....8.9.......6
........1....23.4...245.........4.5..6......78...7.9....3..5.1..7....8..9..2....6
........1....23.4...245.........4.5..6..7.8..9..5....7..3..5.1..8......97.....6..
........1....23.4...245......1..4.3..6....7..8..5....9..3..5....9....6..7...9...8
........1.....2.34..3.4..5...5.....3.2...6...7..8.......9.5..1..8...79..6..2..3..
........1.....2.34..3.4..5...4.....3.2...6...7..8.......9.5..1..8...73..6..2..9..
.......12....134....145......3..5....6......78...6..9...4..12...7.....6.9..5....8
........1.....2.34..1.3..5...3.1..4..6.2.....7..8..9....9.....5.8.7.....2....6...
........1....23.4...25.4.....34......6......78....69....53...1..9......87...4.6..
........1.....2.34..1.4..5...5.3..1..6...7...8..2.......9.....3.7...6...2..8..9..
........1....23.4...25.4.......5..3..6...78..9..4....7..3.4..1..7....6..8.......9
........1....23.4...25.4.....1.3..5..6....7..8..4....9..3.4.....7......69....78..
........1....23.4...56..7.......1.2..8..4...39..8.......67..9..5.......77.9....1.
........1....23.4...25.4.......3..5..6......78....79....1.4..2..9....8..7..3....6
........1.....2.34..1.4..5...4.5..1..6.2.....71.8.......9.....3.8...79..2..6.....
........1....23.4...25.4.....13...5..6......78...4.9....34......7....8..9....7..6
........1....23.4...25.4......4...3..6....7..8....7..9..53...1..7......69...4.8..
........1....23.4...25.4......4...3..6....7..8....7..9..53...1..7..4...69.....8..
........1.....2.34..4.3..5...5....1..2.6.....7....8.....9.4...3.6...79..8..29....
........1.....2.34..3.1..5...4.....3.2.6.....7....89....9.4..1..8...7...6..2.....
........1.....2.34..3.4..5...5.....3.2...67..8..9.......7.5..1.56.2.....9....8...
........1....23.4...25.4......4...3..6...7..89...3.7....53...1..8....6..7.......9
........1.....2.34..3.1..5...4.....3.2.6..7..8....9.....7.5..1..9.2.....6....83..
........1.....2.34..1.3..5...3....4..2...67..8..9..5....4.7...5.9.2.....6....8...
........1.....2.34..4.1..5......6.....1.3..4.78.2.......9.....3.2.8..9..6....7...
........1....23.4...254.........5.1..6..7.8..9..2....7..3..2.5..7......98.....6..
........1....23.4...254.........5.3..6......78...7.9....5..2.1..9......87..4..6..
........1.....2.34..3.1..5...5.6..4..7...86..9..2.......6.....3.8.9.....23...7...
........1.....2.34..1.4..5...5....4..2...67..8..9.......7.5...3.9.2.....6....8...
........1....23.4...56..7.......1.2..8..4...39..8.......79..5..5.9.....46......9.
........1....23.4...56..7.......1.2..8..4...39..8.......69..5..5.9.....47......9.
........1.....2.34..3.4..5...1.5..4..6...78..9..2.......8.....3.2...65..7..9.....
........1.....2.34..3.1..5...1.....3.2...6...7..8.......9.5..4..8.2..9..6..7..3..
........1.....2.34..3.1..5...1.....3.2...6...7..8.......9.5..4..8.2..9..6....73..
.......12.....34....1.45......5..3...6.....7.8...71..9..24..1...7......89......6.
.......12.....34....1.54.....25..1...6......78......9...34......7......89...72.6.
.......12.....34....1.54.....25..1...6......78......9...34......9......87...92.6.
........1....23.4...24.5........6..7..35.....68..4.9....12...3..9....6..7.......8
.......12.....34....1.54........6..7..53.....68..4..9...24..5...7.....8.9.......6
........1....23.4...254.........5.3..6..7....8..2..9.7..3..2.1..7....6..9.......8
........1....23.4...245......3..2.1..6......78.....9....5..4....7......89..27.6..
.......12.....3..4..4.2......5..1..6.3.7.....8....9.....6.1..4..9...85..7..3..6..
........1.....2.34..4.3..5...5..1..3.2...6...7..8..9....9.1..4..6...7...8..2.....
........1.....2.34..4.3..5...5..1..3.2...67..8..9.......7.1..4..9.2.....6....8...
........1.....2.34..3.1..5...5.4...3.6...7...8..2.......9..4.1..2...6...7..8..9..
........1.....2.34..4.3..5...5.4..1..6...7...8..2.......9..4..3.2...8...7..6..9..
........1.....2.34..4.3..5...5.4..1..6...7...8..2.......9..4..3.7...6...2..8..9..
........1.....2..3..4.3..5...3..5..4.2...6...7..8.......9.5..1..8.2..9..6....74..
........1.....2.34..3.4..5...4..5..3.2...6...7..8.......9.5..1..8...7...6..2..9..
........1....23.4...245.........5.3..6......78..37.9....5..2.1..9....8..7.......6
........1....23.4...25.4......4...3..6....7..8...37..9..53...1..7......69.....8..
........1....23.4...245.........4.3..6.3..7..8.3.7...9..1..2.5..9....6..7.......8
........1.....2..3..4.3..5...1.5...4.6...71..8..2.......9....1..7.8..9..2...964..
.......12.....34....145......3..5.2..6......78...6..9...4..12...7.....6.9..5....8
........1.....2.34..1.3......5....4..2..567..8..9..5....7.4...5.6.2.....9....8...
........1.....1.23..123..4...4.1..3..5...6...7..8.......9.....2.8...79..6..5.....
........1....23.4...25.4.....32...1..6......78.....9....54..1...9.3..6..7...5...8
...........1..2..3.2..3.45.....4......4.5..16.5.2..3.....3....7.3...452.8..59....
........1..2..3....4..5..23.....5.1..6.4..7..8...9.5....1..2..7.9..6....4..8.....
........1.....2.34..3.4..5...5.....3.6.7.....23...89....9.5..1..7...6...8..2.....
........1.....2.34..4.3..5...5....1..2.6.....7....8.....9.4...3.6.3.79..8..2.....
........1.....2.3...3.1..4...1.4..5..6...7...8..2.......9.....4.7.6..9..2....857.
..............1.23..2.3..4...3.4..5..6...7...8..1.......9.....4.7.6..9..1....857.
........1....23.4...254......13......3..6...768...49....34...5..7....6..9.......8
........1.....2.34..4.1..5...163..4..6.2.....7....8.....9.....3.8...6...2..7..9..
........1.....2.34..4.1..5...1.36..5.6...7...8..2.......9....4..7.6.....2....89..
........1.....2.34..4.3..5...3.46..5.6...7...8..2.......9....1..7.6..9..2....8...
........1....23.4...25.4......3...1..6......78....79....54...3..9......67....18..
........1....23.4...25.4.....14...5..6......78....19....53......9...7..87.....6..
........1....23.4...245.........5.3..6......78...7.9....5..2.1..9..1...87.....6..
........1....23.4...245.........5.3..6......78...7.9....5..2.1..9....8..7...1...6
........1....23.4...25.4.....13...5..6......78....19....34......7...9..89.....6..
........1....23.4...25.4.....13...5..6......78....19....34......9...7..67.....8..
........1....23.4...25.4.....13...5..6...17..83......9..34......7......89....76..
..............1.23..2.3..4...4.2..5..6...7...8..1.......9.....4.7.8..9..14...65..
.......12.....34....1.54......5..3...6...7..18...4..79..24..1...9......87......6.
.......12.....34....1.54......5..3...6...7..18...4..97..24..1...7......89......6.
.......12.....34....1.54......5..3...6...7..18...4..97..24..1...9......87......6.
........1.....2.34..1.34.5...5..1.4..2..6....7..8.......9.....3.8..7....6..2..9..
.......12.....3..4..4.2......5.....6.3.7.....8....9.....6.1..4..9.6.85..7..3..6..
........1.....2..3..3.1..4...5.....6.2...7...8..9.......6.4..3..9.2..6..7..6.85..
........1.....2.3..34.5.2.........6..25..37..8..5......572..3...8..47..29...3....
........1.....2.3..34.1.5.....6......15.7...38......5..57.3..1..8...14.79........
........1.....2.34..4.3..5...3.....5.2...6.7.7..8..9....5.9..1..6.2.....8....7...
........1.....2.34..4.1.52...3.4...2.6...5...7..8.......9....1..8...7...5..6..9..
........1.....1.23..1.3.45...5....3..4...6...7..8..9....9.1...2.8.7.....6....4...
........1..2..3....1..4..32..3..2..5.6.4.....7...8......9....1..4..6.5..8..7..9..
........1....23.4...245......15...2..6....7..8...3...9..43......9..7...67.....8..
........1....23.4...245.........5.3..6......78...7.9....5..2.1..9..4...87.....6..
........1....23.4...245.........5.3..6......78...7.9....5..2.1..9......87...4.6..
........1....23.4...25.4.....3.5.....6....7..8....6..9..5.4..1..9......67....58..
........1....23.4...254......13......6......78...6.9....42...5..7..3.8..9.......6
........1....23.4...245......1..5.3..6....7..8...4...9..5..2....9......87...9.6..
........1....23.4...25.4......4...3..6....7..8....7..9..53...1..7...2..69.....8..
........1.....2.3...3.1..4...5....6..2.7.....8....9.....6.3...4.7.2.65..9....86..
.......12.....34....1.54......5..3...6...7...8...4..79..24..1...7...5..69......8.
........1....23.4...245.........4.3..6....7..8..27...9..1..2.5..9....6..7...4...8
........1....23.4...245.........4.5..6..7.8..9..5...67..1..5.3..7....9..8.......6
.................1..2.34.5...3.6.7...4..25.6.5.6.......248......3.9....46....2.3.
........1.....2.....3.4..5........6...43..5.7.6..5...4..5.6..3..8...59..9...3..4.
...........1..2..3.3..4..21..2..1..5.6.4.....7...8......9....3..4..7.5..8..6..9..
........1....23.4...245.........5.3..6......78...7.9....5..2.1..9......87...3.6..
........1....23.4...245.........5.3..6......78...7.9....1..2.5..9......87...3.6..
........1.....2.34..1.3..5...3.....5.2...6.7.7..8..9....5.9..4..6.2.....8....7...
........1.....2.34..3.1..5...5.4...3.6...78..9..2.......8....1..2...6..77..9.....
.......12.....3..4..1.2.53...2.4...3.6...7...8..5.......9....4..5.6..9..7....8...
........1.....2.34..3.4.52...4.3...2.5...6...7..8.......9....1..8.5.....6....79..
........1.....2....34.1..5......1.35.56.4.1..7......46...8.6....61.5...49........
........1.....2....13.4..5......6.47.45.3.1..1......35...8.1....51.7...497.......
.................1..2.34.5...36......4.7....38...2..4..3..52.8.2.4..89..5.8......
........1.....2....13.4..5......6.47.45.3.1..1......35...8.1....5..7...497.....1.
........1.....2....13.4..5......6.47.45.3.1..1......35...8......51.7...497.....1.
........1....23.45..41.......5....1..2...63..7...8.9....94....3.6...2...8...7....
........1....23.45..41.......54....2.6...7...8...3......9....1..7..6.9..3....82..
........1....23.45..51.......24...5..6..327..8...9.2....7.....2.3..8....9....6...
........1....23.45..51.......45....2.6...7...8...3......9....1..7..8.9..3....62..
........1....23.45..51.......45....2.6...7...8...3......9....1..7..6.9..3....82..
........1....23.45..54.......45....2.6...7...8...3......9....1..7..6.9..3....82..
........1.....2.34..3.4..5......6.....7.3..4.89.2.4.....1.....5.2.9.....6....87..
.......12.....3..4..4.2......5.....6.3...7..88..9.......6.1..2..9...86..7..3..5..
........1....23.4...25.4.....3.5.....6...17..8....6..9..5.4..1..9......67.....8..
.............12.34..1.5.2....2.3.1...6......78......4...9..5....7.9...6.4..3....8
........1....23.4...245......35......6..7...875..1.9....52...1..9......78.....6..
........1....23.4...24.5.....3.5..1..6......78.....9....5.4.....7...98..9....2..6
........1....23.4...25.4.......5..3..6...2..78....79....3.4..1..9......67.....8..
........1....23.4...24.5.....3.4.....6...27..8....6..9..5.3..1..9....6..7.......8
........1....23.4...24.5.....4.3..1..6......78.....9....5.4.....7...98..9....2..6
........1....23.4...24.5.....1.3..5..6......78.....9....3.4.....7...9..69....28..
........1....23.4...24.5......3...5..6...4..78....79....15...3..7....6..9.......8
........1....23.4...245......3..5....6..3...78...6.9....4..2.1..7....6..9.......8
........1....23.4...245.........5.3..6..3...78...7.9....5..2.1..9......87.....6..
........1....23.4...245.........5.3..6..3...78...7.9....5..2.1..9....8..7.......6
........1....23.4...25.4.....3.4.....6...2..78....69....5.3..1..7....6..9.......8
........1....23.4...25.4.....1.3..5..6......78.....9....3.4.....7...96..9....2..8
........1....23.4...245......1..5.3..6......78.....9....5..2....9..7.8..7...3...6
........1....23.4...25.4.....13...5..6......78.....9....34......7...9..89....56..
........1....23.4...25.4.....34..1...6...5..78....69....53...1..7....6..9.......8
........1....23.4...245.........4.3..6....7..8.327...9..1..2.5..9....6..7.......8
........1.....2.34..3.41.5...1.5..4..6...78..9..2.......8..5..3.2...6...7..9.....
..............1..2..2.3.45...4.....6.25..4..78...5.2....8.......4..2.38.5.39.....
..............1..2..2.3.45...4........5..4.16.3..5.2...23.....7.589.....4...2.53.
..............1234..2.5.6....3...76..47.3...262..78..3.764....828.....7.3.4..7.26
..............1..2..3.4..15.341....6.7.38..418.1.6...7.478.....16.4.3.7.3.8.76...
..............1..2..3.4..15.341.6..7.7.38..418.1.7...6.478.....16.4.3.7.3.8.67...


[MAGREMENT]

Thanks for the list, my implementation seems to be able to find all of them.

Aren't there more complex MSLS formation than the simple 4 Rows x 4 Columns tho ?

[yzfwsf]

Try it out, can you find this？

[MAGREMENT]

Try it out, can you find this？

Nope. The thing is, I can easily find the MSLS in any given set of cells but the problem is finding the apropriate set of cells in a puzzle as checking everything takes way too much time. I found one of your post you posted a year ago mentioning how you implemented MSLS. Is this still how you do things ?

Reply to forum friends' questions about how I programmed MSLS：
Cyclic detection of the cross cells (X Cells) structure formed by each m rows * n columns
1. If there are too many fixed cells, skip the structure (x+2 or 1<m*n), and enter the next structure detection
2. Find the minimum coverset for each kind of candidate so that it can cover all these candidates in the structure
3. If coverset(links)=X then we find MSLS
4. If the condition in 3 is not met, set a condition such as links-X<2 or 3, and cache the structure as AMSLS (Almost MSLS)
5. Loop through the AMSLS collection, pre-delete by the links, and then find an locked set with Rank < 0. If there is, include it in the structure, which will reduce the Rank of the structure.
Rank drops to 0, then we find MSLS