The New Sudoku Players' Forum

[P.O.]

a value that is placed collects all the values of its BRT-expansion minus those already placed so a value that has in its BRT-expansion all the other values regardless of its position in the path will collect all the remaining values
it is unlikely that from the 36 values i have i will get a longer expansion path than the one you found because in this selection there are 10 such values so there are 26 values left to organize into expansion steps before ending with any of the 10
what is important in this exercise is to have a good starting selection

here the BRT-expansion of your values:

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1: ((13 7))
1: ((17 2))
1: ((20 9))
1: ((23 3))
1: ((26 6))
1: ((36 7))
1: ((42 4))
1: ((51 8))
1: ((52 4))
1: ((56 4))
1: ((66 9))
2: ((10 4) (20 9))
2: ((15 9) (20 9))
2: ((24 2) (20 9))
2: ((79 9) (66 9))
2: ((80 4) (56 4))
3: ((4 4) (10 4) (20 9))
3: ((14 8) (13 7) (23 3))
3: ((27 4) (26 6) (23 3))
4: ((1 1) (10 4) (20 9) (2 2))
4: ((2 2) (1 1) (10 4) (20 9))
4: ((48 7) (36 7) (74 7) (56 4))
4: ((74 7) (56 4) (48 7) (36 7))
6: ((41 7) (48 7) (36 7) (74 7) (13 7) (56 4))
9: ((38 1) (1 1) (10 4) (48 7) (74 7) (20 9) (2 2) (56 4) (36 7))


[denis_berthier]

it is unlikely that from the 36 values i have i will get a longer expansion path than the one you found

it's not only unlikely but impossible. My algorithm finds all the longest expansion paths.[/quote]
But I was talking of your example with 2x4 backdoors
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[P.O.]

My algorithm finds all the longest expansion paths

so it is not this algorithm that built this expansion

[denis_berthier]

My algorithm finds all the longest expansion paths

so it is not this algorithm that built this expansion

The longest expansion path for the minimal puzzle has 18 expansion steps.It's clearly not the one you mention. It's the result of the full expansion process.

If you're alluding to another of my algorithms that didn't find the shortest 1-step path out of T&E(3), it's a completely separate process, a small process coming after the full expansion one, just as a fallout of it. There was a bug in it, now corrected. Fortunately, I hadn't done lots of calculations with it yet. I was and I still am more interested in the longest paths than in the shortest ones.
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