Bands and low-clue puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Re: Bands and low-clue puzzles

Postby dobrichev » Sun Jan 08, 2017 10:32 pm

blue wrote:For (the same) 100 random grids, the average dropped from 21.64s to 21.06s, or about ~2.7%.

Thank you Blue.
If you remove the full scan for the shortest effective UA, the difference would grow, but the overall speed will drop down.

BTW, my "random" grids are not much random. Could you share your collection of 100 random grids?

I am stuck in my academic attempt to do sets and cells reordering. The task is very complicated to me - everything depends non-linearly of everything, the number of permutations is huge, and even Monte Carlo wouldn't work.
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Re: Bands and low-clue puzzles

Postby blue » Sun Jan 08, 2017 11:04 pm

dobrichev wrote:BTW, my "random" grids are not much random. Could you share your collection of 100 random grids?

Here they are ...
Hidden Text: Show
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Out of curiosity, are you planning to reorder things "on the fly", after each of the early clues are added ?
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Re: Bands and low-clue puzzles

Postby dobrichev » Mon Jan 09, 2017 12:13 am

coloin wrote:I do hope that searching for a 14 clue solution in 72 clues [with less UA] is more than 18x quicker than searching for a 17 in 81 clues ... is it ?

I can't measure this.
Reducing the number of clues by one in the 16/17/18 search reduces the time by factor of 5 to 10.
17 - 14 = 3; 5^^3 > 100 w/o taking into account the reduced number of cells.
The solver pressure expectingly highly depends on the quality of the UA sets. The minimizer takes tool too.

So, you propose to ignore potential 17s having 222222221 row distribution simultaneously in row and column directions, do 9 rows + 9 columns = 18 times search for 9+(14-), and finally minimize only the entirely populated row to 3+.
Or, being pedantic, search 6 rows + 6 columns = 12 times for 9+(14-) and then minimize to 3+, also search 2 rows + 2 columns = 4 times for 9+(15-) and then minimize to 2+. This will cover also the 222222221 distribution. Is this correct?
Good idea, as always.

From other hand, having process that deals with X+(N-) partial puzzles, the output from scanning 54 cells for N- (typically 13- or 14-), with even less UA, has potential to be reused for checking all ~30 completions for the first 2 bands (column 2 of the table in opening post, ~180/6 row permutations = ~30 unless more are isomorphic).
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Re: Bands and low-clue puzzles

Postby dobrichev » Mon Jan 09, 2017 12:40 am

blue wrote:Out of curiosity, are you planning to reorder things "on the fly", after each of the early clues are added ?

No.
At "consolidation" point I simply rebuild indexes for the survived UA from respective raw bitmaps but with dead clues removed. They are already ordered and with remapped cells. I am doing stable sort by size, keeping the old order within the UA of the same new size. Else disastrous loss of higher order UA composites occurs.
"On the fly" I found that it is better, prior to consolidation, to look forward for several unhit UA, not to choose the first one nor (as by McGuire) to scan the entire collection. Optimal depth is 6 to 10 unhit UA forward. I hope to remove forward search if the initial reordering succeeds, or at least to do it only on first few steps.
It would be simpler for you to take a look on my last code. This file is the iteration process with entry point at the bottom, and the second half of this file is for indexes manipulation.

Thank you for the grids.
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Re: Bands and low-clue puzzles

Postby blue » Mon Jan 09, 2017 3:38 am

coloin wrote:I do hope that searching for a 14 clue solution in 72 clues [with less UA] is more than 18x quicker than searching for a 17 in 81 clues ... is it ?

That is difficult to answer.
I can say something about my "hack" to Gary McGuire (et al.)'s code, but how relevant it is, who's to say (?).

For the same 100 random grids as in my earlier post(s), the average time was ~24.09s per grid.
[ That was keeping the clues in the top row, as the "9+", and looking for 14 more clues in the remaining cells. ]

The average time, was severely impacted by two grids in particular ... one that took 268 seconds, and one that took 819s.
Tossing those two out, the average time dropped to ~13.40s/grid, or ~60% of the time to search for 17's in the same grids.

The code was only looking at UA sets with size <= 12, though, and going to "size <= 14", could help.
[ By "size <= 12" UA's, I mean all minimal UA sets with size <= 12, that don't include a cell in the top row. ]

I say that because for the two bad grids, there were "many many" ways to hit all of the "size <= 12" UAs, with only 11 clues -- leaving the code in a situation where it needed to add every combination of 3 additional ("undead") clues, to get (its interpretation of) all of the "potentially valid" 9+14's.
For the worst case, that lead to ~32 billion (9+)14-clue sets, that (likely) hit all of the UA's with size <= 12.
[ Oddly enough, for the two bad cases, no 9+14 puzzles were produced. In the remaining grids, 367 were found. ]

coloin wrote:For example

say we postulated that all 17s have been found whitch begin with max lex {x..x......} or {xx......} I think we have ...
which means that all non-found 17s have max lex {x..x..x..] or more

This avoids a search for 9+15 puzzles, of course, but why else would one assume such a thing ?
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Re: Bands and low-clue puzzles

Postby coloin » Mon Jan 09, 2017 12:30 pm

blue wrote:So, you propose to ignore potential 17s having 222222221 row distribution simultaneously in row and column directions, do 9 rows + 9 columns = 18 times search for 9+(14-), and finally minimize only the entirely populated row to 3+.

Yes ....but
blue wrote:This avoids a search for 9+15 puzzles, of course, but why else would one assume such a thing ?

Yes ... to get the advantage of a 9+14 ....and approx there are 3 per grid ! But you are right ... we cant really ignore the 222222221 puzzles

champagne only proved the {x..x.....} case - 2 puzzles found from only 72 18-clue patterns here
Code: Select all
...3..5....6....7.1....8....7....3......6...1..4..1....5..3.......7...4.2........
2.......5.....16....8.3.....3.....2......74....15......1..2.......3...8.4........

The {xx.......} case had many many more patterns - so they can not all have been searched but 14 [ or 86 ?] puzzles are known
Code: Select all
.3.....1....7..5....4..2...1.......2...4..6....8.3....54............3.8.....1....
.6....5.......7..6..72.....2......8...3...4......61...4...5.......3...7..5.......
.7..4......2.....1.....1.3....3..5.......84..1.4.......5..6....3......8....2.....
3.......2...4..6....8..1....1.....3....7..5....4.2....54............3.8.....1....
3......1....7..5..8....2.....1...4.....5....2.8..3.....65...........3.8.....1....
3.7...........87......1.5...6.7..........3..1..2....3..5.4.....1......8.....2....
.......8473..........1.......8.5.......2..4...4......72......6......41......37...
......1.7..5...3...6...2......2...8....53....74.......3.1...........4.6.....1....
.12.........1..5...9......85.....3......19...8...6...........69.....8.7....5.....
8......2....9.1...5....7....13..........1..5..9......8......7.9....8.6.....5.....
1......5........72.63.........34....75..........8..6....4...8......75........1...
....41........9.6...5.8......25......8....1........9.4...3...2.84.......1........
......1.94...5........2.3.....1.9...5....7......3......13.......8.....4...9....2.
......3.84...5........2.1.....1.3...5....7......8......13.......8.....2...9....4.

Thanks for even considering it ....and it is interesting that 2 grids had the prolonged search time ...
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Re: Bands and low-clue puzzles

Postby coloin » Mon Jan 09, 2017 3:51 pm

dobrichev wrote:Or, being pedantic, search 6 rows + 6 columns = 12 times for 9+(14-) and then minimize to 3+, also search 2 rows + 2 columns = 4 times for 9+(15-) and then minimize to 2+. This will cover also the 222222221 distribution. Is this correct?

A first i didn't understand !
but it probably would be 9 column x [9+(14)] and 7 row x [9+(14)] only 2 row x [ 9+(15)] which guarantees not catching the single clue in a row
well done !
Last edited by coloin on Sun Jan 15, 2017 10:42 pm, edited 1 time in total.
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Re: Good and bad news in the search of 17s

Postby champagne » Mon Jan 09, 2017 3:52 pm

blue wrote:[ It's so fast now, that nobody would believe me without actually seeing it run. ]

Cheers,
Blue.


Hi Blue,

So we have a challenging investigation. Normally, adding the good options should help.

I finished the revision of my code with good and bad results. The worse thing I did was to introduce in bands 1+2 a step with UAs tables of 64 UAs for UAs not limited to bands 1+2, this comes to close to the last steps for bands 1+2. At the opposite, the last steps are much better.

So I need more days to come with results.
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Re: Bands and low-clue puzzles

Postby blue » Mon Jan 09, 2017 8:35 pm

coloin wrote:
blue wrote:Or, being pedantic, search 6 rows + 6 columns = 12 times for 9+(14-) and then minimize to 3+, also search 2 rows + 2 columns = 4 times for 9+(15-) and then minimize to 2+. This will cover also the 222222221 distribution. Is this correct?

A first i didn't understand !
but it probably would be 9 column x [9+(14)] and 7 row x [9+(14)] only 2 row x [ 9+(15)] which guarantees not catching the single clue in a row
well done !

It wasn't me that wrote it.
I don't understand it. I need a "visual aid", or something.
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Re: Bands and low-clue puzzles

Postby coloin » Mon Jan 09, 2017 8:57 pm

Sorry it was dobrichev's comment ... i apologise.
This 17-puzzle
Code: Select all
+---+---+---+
|...|1..|.38|
|2..|..5|...|
|...|...|...|
+---+---+---+
|.5.|...|4..|
|4..|.3.|...|
|...|7..|..6|
+---+---+---+
|..1|...|.5.|
|...|.6.|2..|
|.6.|..4|...|
+---+---+---+

will only found by one of the the [18] x {9+14} searchs - in this case row 1 has the 3 clues

This 17-puzzle
Code: Select all
+---+---+---+
|3.7|...|...|
|...|..8|7..|
|...|.1.|5..|
+---+---+---+
|.6.|7..|...|
|...|..3|..1|
|..2|...|.3.|
+---+---+---+
|.5.|4..|...|
|1..|...|.8.|
|...|.2.|...|
+---+---+---+

wont be found by the [18] x {9+14} search
but it will be found by any 2 row (9+15} searches
if row 9 is filled - the 9+15 wont be findable
if row 8 is filled - the 9+15 will be findable

maybe academic if a 9+15 proves long winded and gives too many valid puzzles
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Re: Bands and low-clue puzzles

Postby blue » Mon Jan 09, 2017 11:06 pm

Hi Colin,

Thank you. I see it now.
There are also two 17's with this shape:

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . 1 | . . 2 |
| . 3 4 | . 5 . | . 6 . |
+-------+-------+-------+
| . . . | . . 7 | . . 8 |
| . . 5 | . . . | 1 . . |
| . 6 . | 9 . . | . . . |
+-------+-------+-------+
| . . . | 3 . . | . 8 . |
| 1 . . | . 2 . | . . . |
| 7 . . | . . . | . . . |
+-------+-------+-------+

9+13's could find those, though.
9+12's could find anything with 5 clues in a row/col (and <= 2 in each box).

coloin wrote:maybe academic if a 9+15 proves long winded and gives too many valid puzzles

Marking the (remaining) cells in a box as "dead", as soon as the box acquired a 2nd clue, could speed things up.
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Re: Bands and low-clue puzzles

Postby coloin » Mon Jan 09, 2017 11:50 pm

blue wrote:9+12's could find anything with 5 clues in a row/col (and <= 2 in each box).

A few years ago i did a pretty determined non-exaustive search to find 9plus12s [box9 and row9]here
Both searches maxed out for me at the 9plus13 stage [ around 2-4 million puzzles that I found]
The row and box search for 9plus14 misses out the row/col/box - 222222221- as above
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Re: Bands and low-clue puzzles

Postby champagne » Thu Jan 12, 2017 10:34 am

blue wrote:
dobrichev wrote:BTW, my "random" grids are not much random. Could you share your collection of 100 random grids?

Here they are ...


I run a test on that lot with the current code,

I got an average 5 mn per solution grid, with a minimum of 1.4 second and a maximum of 38 mn.

Next step will be to analyze the "worse cases" but this will come later, I have now to mark a pause and prepare our next trip
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Re: Bands and low-clue puzzles

Postby dobrichev » Thu Jan 12, 2017 9:20 pm

Here are my results, about 20 seconds per grid.
Hidden Text: Show
Code: Select all
634258917578916324192437865486795231925143678317862549743529186251684793869371452   puz=0   ch=3991   time 7.215 seconds.
843592167652417398179638542915784623728369451364125879537941286486273915291856734   puz=0   ch=1706   time 6.152 seconds.
794538261815629437362147985459283176231976854678415392527894613186352749943761528   puz=0   ch=3402   time 11.568 seconds.
734215968982367145165498237819623574256749813347851692628174359493586721571932486   puz=0   ch=2464   time 3.796 seconds.
148527396675319824293864751369152487827496135514738962786945213432681579951273648   puz=0   ch=9132   time 20.110 seconds.
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629143587784592163351768249217386495438259671965471328576834912842915736193627854   puz=0   ch=748   time 2.357 seconds.
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657394281341286579289157364463518792975642813128973456894721635716435928532869147   puz=0   ch=22908   time 15.474 seconds.
139564782754892613286173594942735168568419327317628459891357246475286931623941875   puz=0   ch=13583   time 26.046 seconds.
423681957516974328897235614965812473241763895378549162632497581784156239159328746   puz=0   ch=2   time 1.270 seconds.
534687129872931564169245783723854691416792835985163472641328957358479216297516348   puz=0   ch=59636   time 48.646 seconds.

Total time 1921.983 seconds.
dobrichev
2016 Supporter
 
Posts: 1295
Joined: 24 May 2010

Re: Bands and low-clue puzzles

Postby champagne » Fri Jan 13, 2017 6:21 am

Hi mladen,

Currently much better than my code. I suspect that postponing short UAs (UA4 UA6) not in bands 1+2 is the main penalty in my lay-out.
Waiting now for Blue's first shot
champagne
2017 Supporter
 
Posts: 5445
Joined: 02 August 2007
Location: France Brittany

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