ALS-Wing

ALS-Wing is an extension of XY-Wing and DeathBlossom, and is an algorithm that uses the effect of ALS spreading when it becomes a LockedSet.

ALS-Wing includes the base algorithm and is an improvement and generalization of the solving method.
GNPX uses logical operations based on bit representation.

The ALS-Wing "lockedSet" is explained in the following diagram.
Focus on a cell (stem cell) and select the ALS connected to the cell (weak link).
Next, select cell #digit(fake cell digit) to change ALS to LockedSet.

  1. [C]If cell#digit is true,
  2. [B]ALS changes to LockedSet,
  3. If the effect of LockedSet [B->A] is that all the candidate digits in cell [A] are negative,
    (The effect of a weak link from B to A may be multiple #digits.)
  4. [C]Cell #digit is not true.

The basic form of ALS-Wing is shown here, and can be extended as follows. These are independent and can be extended simultaneously.

●ALS-Wing examole

ALS_Wing
Stem Cell: r4c7
ALS_1: r4c4 #68
ALS_2: r3c137 #2469
Eliminated: r3c4 #6


ALS_Wing Connected
Stem Cell: r2c6
ALS_1: r346c4 #1789
ALS_2: r1238c5 #12478
Eliminated: r2c4 #8


ALS_Wing overlapping
Stem Cell: r3c4
ALS_1: r6c4 #78
ALS_2: r4c47 #178
ALS_3: r134c7 #1789
(ALS overlapping cells: r4c7)
Eliminated: r4c6 #8


ALS_Wing Connected overlapping
Stem Cell: r2c5
ALS_1: r137c5 #1478
ALS_2: r138c5 #1247
(ALS overlapping cells: r13c5)
Eliminated: r2c6 #4


7.1..9..8.52...19..8...3.574.3.5.......2.1.......3.7.519.7...3..37...68.8..3..9.1
2.9..3..8.17...63..8...6.259.5.6.......3.2.......9.3.114.6...9..53...48.7..4..2.6


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