The New Sudoku Players' Forum

[denis_berthier]

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This is again about my systematic procedure for generating high B puzzles in T&E(1) from minimal puzzles in T&E(3) or T&E(2).

Initially, I thought it was successful due to the continued presence of a tridagon or some degenerate form of it. But my recent results involving non-tridagon puzzles prove it is not the case. I've now run the procedure on 3 sets of minimal puzzles:
1) mith's latest collection mith-TE3 of T&E(3) puzzles (all of which have a non-degenerate tridagon);
2) the collection col-TE2 of mastermins-1-to-15 assembled by coloin (and found mainly by coloin, Hendrik Monard and Paquita), all in T&E(2) with BxB ≥ 7 (all of which have a non-degenerate tridagon);
3) a sub-collection el-TE2 of eleven's tamagotchi high SER puzzles (none of which has a non-degenerate tridagon).

I've measured the throughput as the ratio: output-nb-minimals-in-B12+ / input-nb-min-expands.
I think this is the right quotient to consider (because the effective input is the min-expands, not the minimals).
The results allow no appeal; the success of the procedure can't be due only to the tridagon pattern (though it may play some role within T&E(2)):

- 1.285 B12+ minimal puzzle for each min-expand in mith-TE3
- 7.30 B12+ minimal puzzle for each min-expand in col-TE2
- 2.68 B12+ minimal puzzle for each min-expand in el-TE2

Why T&E(2) puzzles give better results than T&E(3) ones may be because T&E(2) is closer to T&E(1) than T&E(3). It may also be due to the saturation of mith-TE3 by minimisation of the min-expands, which could imply proportionately fewer p1U puzzles (but the stats don't confirm this).
Why, within T&E(2), the puzzles with BxB≥7 give better results, tends to contradict the previous first pseudo-explanation.

Conclusion: clear facts; no real explanation of the results.
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[denis_berthier]

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All the definitions and results reported in this thread - and much more- are now available in the 3rd edition of [HCCS]:
http://forum.enjoysudoku.com/hierarchical-classifications-in-constraint-satisfaction-t42076.html
https://www.lulu.com/shop/denis-berthier/hierarchical-classifications-in-constraint-satisfaction-third-edition/paperback/product-4587d42.html?page=1&pageSize=4

One of the topics not discussed here is the (1+BRT) distance of a T&E(n) puzzle to the T&E(n) border. Indeed several notions of distance can be defined, including the most natural one related to the shortest (1+BRT)-expansion paths.

One apparently surprising result for the latter is, whereas the maximum length of expansion paths increases drastically from T&E(3) to T&E(1), it is not the case for the thickness of the T&E(n) domains.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(3) kingdom via (1+BRT)-expansion of T&E(3) minimal puzzles, as described in [HCCS3], have been published:
All-time latest release: https://doi.org/10.5281/zenodo.17500794
Download all (2.5 GB), unzip and see the README.md file for details.

Similar data for the T&E(2) and T&E(1) kingdoms will be published soon.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(1) kingdom via (1+BRT)-expansion of T&E(1) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17505247
Download all (1 GB), unzip (=> 20 GB) and see the README.md file for details.

Similar data for the T&E(2) kingdom will be published later.
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[denis_berthier]

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All the data relevant to the exploration of the pre-tridagon, low BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17510758
Download all (500 MB), unzip (=> 10 GB) and see the README.md file for details.

Similar data for the post-tridagon, high BxB part of the T&E(2) kingdom will be published later.
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[denis_berthier]

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Finally, all the data relevant to the exploration of the post-tridagon, high BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:https://zenodo.org/records/17529657
Download all, unzip and see the README.md file for details.

Note that additional data used in [HCCS3] had already been published:
https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection
https://github.com/denis-berthier/Sudoku-classif
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[denis_berthier]

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[Moved from the "BxB classification" thread.
The collection referred to was defined here: http://forum.enjoysudoku.com/the-bxb-classification-of-t-e-2-puzzles-t41922-375.html and next posts.]

After analysing Paquita's new high BxB puzzles (as collated by coloin) by my (1+BRT)-expansion technique, the record of the longest expansion path in T&E(2) is beaten: 13 (instead of 12 previously):

Code: Select all

.23...78.45.78..237.8...5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 43c +BRT -> --p13EU
.23...78.45.78..237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 42c +p13
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +BRT -> --p12EU
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +p12
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +BRT -> --p11EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +p11
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +BRT -> --p10EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +p10
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +BRT -> --p9EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +p9
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +BRT -> --p8EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +p8
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +BRT -> --p7EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +p7
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +BRT -> --p6EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +p6
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +BRT -> --p5EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +p5
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +BRT -> --p4EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +p4
.2....7..45.7...237.....5.42.5..73..37...2.58.84..52.7...9.4..284...3......1.8... 32c +BRT -> --p3EU
.2....7..45.7...237.....5.42....73..37...2.58.84..52.7...9.4..284...3......1.8... 31c +p3
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +BRT -> --p2EU
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +p2
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +BRT -> --p1EU
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +p1
.2.......45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 28c +BRT -> --p0EU
.2.......45.....237.....5.4.....73..37...2.58.84..5..7...9.4..284...3......1.8... 27c +p0
computation-time = 2.68s

There are actually 3 puzzles in the collection with such a path. The upper terminations of the paths are related to each other by permutation of clues in some UR1.

[Edit]: as noted by an attentive reader of [HCCS3], the T&E(2) record is not broken; it was already 13, as mentioned in [HCCS3, section 7.2.3]. What's broken is the record for the part of T&E(2) with BxB ≥ 7.
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[denis_berthier]

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Following Paquita's publication of a new collection of hard puzzles (https://drive.google.com/file/d/1_vC06xr0bWLWqJ8hROcs3zusiuYB0fEb/view?usp=sharing), I've applied the (1+BRT)-expansion technique to it
As usual, there are some preliminary preparations:
- eliminate 4 non-valid puzzles (==> 62,355 puzzles);
- replace a few non-minimal puzzles by their minimals (==> 63,128 minimals);
- split the collection according to T&E-depth (==> 45,274 minimals in T&E(2) and 17,854 minimals in T&E(3))

This post is about the T&E(2) part (45,274 minimals), more precisely about the subpart with BxB ≥ 7 (i.e. 7,249 minimals, corresponding to 1,099 different solution grids).
My purpose was to see if any meaningful differences appeared wrt the previous T&E(2) collections, namely the Mastermins 1 to 15 collected by coloin.
First thing to notice: in Paquita's collection, the minimals and min-expands are not cross-saturated in T&E(2). My first step was therefore to cross-saturate them:
- compute the min-expands;
- find all their minimals (10,840 minimals, guaranteed to be in T&E(≥2);
- split them according to T&E-depth: 10,812 minimals in T&E(2), guaranteed to have BxB ≥ 7; and 28 minimals in T&E(3);
- keep only those in T&E(2) (and therefore with BxB≥7);
- compute their min-expands (3,437 min-expands).
At this point, cross-saturation is guaranteed.
(Note: I didn't check whether some puzzles were already in the Mastermins).

Now, the full (1+BRT)-expansion procedure can be applied in a totally automated way - using SudoRules command "(SGS-script-compute-TE2-expansion-phases-upto-k 15)". It doesn't seem to produce anything new wrt Mastermins. Here are the basic stats:
- 9.84 minimals per solution grid (9.36 in Mastermins);
- 3.13 min-expands per solution grid (3.22 in Mastermins);
- 3.15 minimals per min-expand (2.91 in Mastermins);
- 49.41 T&E(2)-expand per solution grid (53.60 in Mastermins).
Note that I didn't cross-saturate the minimals wrt the T&E(2)-expands - nor was it done systematically in the Mastermins (though the last figure suggests some cross-saturation beyond min-expands may have been done). The reason is, whereas this is possible in T&E(3), this would lead to extremely long calculations in T&E(2).


One can also check the detailed expansion profiles, with the same peak at phase 4, and with the same reasons why combinatorial explosion is contained.
The longest expansion path has length 11, close to the 13 for the larger Mastermins collection (in which very few paths have length 12 or 13).

Code: Select all

T&E(2) expansion phase p0
10812 mins puzzles
10812 ME puzzles
3437 MEU puzzles

T&E(2) expansion phase p1
168272 p1 puzzles
167468 p1U puzzles
126070 p1U-d2 puzzles
104404 p1EU-d2 puzzles

T&E(2) expansion phase p2
4953195 p1EU-d2-p2 puzzles
4206766 p1EU-d2-p2U puzzles
654173 p1EU-d2-p2U-d2 puzzles
273609 p1EU-d2--p2EU-d2 puzzles

T&E(2) expansion phase p3
12677562 p1EU-d2--p2EU-d2-p3 puzzles
11259918 p1EU-d2--p2EU-d2-p3U puzzles
1081062 p1EU-d2--p2EU-d2-p3U-d2 puzzles
319628 p1EU-d2--p3EU-d2 puzzles

T&E(2) expansion phase p4
14542692 p1EU-d2--p3EU-d2-p4 puzzles
13251971 p1EU-d2--p3EU-d2-p4U puzzles
961529 p1EU-d2--p3EU-d2-p4U-d2 puzzles
239989 p1EU-d2--p4EU-d2 puzzles

T&E(2) expansion phase p5
10728259 p1EU-d2--p4EU-d2-p5 puzzles
9949464 p1EU-d2--p4EU-d2-p5U puzzles
576475 p1EU-d2--p4EU-d2-p5U-d2 puzzles
134194 p1EU-d2--p5EU-d2 puzzles

T&E(2) expansion phase p6
5888449 p1EU-d2--p5EU-d2-p6 puzzles
5535379 p1EU-d2--p5EU-d2-p6U puzzles
257180 p1EU-d2--p5EU-d2-p6U-d2 puzzles
58188 p1EU-d2--p6EU-d2 puzzles

T&E(2) expansion phase p7
2502134 p1EU-d2--p6EU-d2-p7 puzzles
2381658 p1EU-d2--p6EU-d2-p7U puzzles
88218 p1EU-d2--p6EU-d2-p7U-d2 puzzles
19710 p1EU-d2--p7EU-d2 puzzles

T&E(2) expansion phase p8
828755 p1EU-d2--p7EU-d2-p8 puzzles
799267 p1EU-d2--p7EU-d2-p8U puzzles
23021 p1EU-d2--p7EU-d2-p8U-d2 puzzles
5065 p1EU-d2--p8EU-d2 puzzles

T&E(2) expansion phase p9
207694 p1EU-d2--p8EU-d2-p9 puzzles
202882 p1EU-d2--p8EU-d2-p9U puzzles
4461 p1EU-d2--p8EU-d2-p9U-d2 puzzles
967 p1EU-d2--p9EU-d2 puzzles

T&E(2) expansion phase p10
38572 p1EU-d2--p9EU-d2-p10 puzzles
38105 p1EU-d2--p9EU-d2-p10U puzzles
511 p1EU-d2--p9EU-d2-p10U-d2 puzzles
133 p1EU-d2--p10EU-d2 puzzles

T&E(2) expansion phase p11
5174 p1EU-d2--p10EU-d2-p11 puzzles
5149 p1EU-d2--p10EU-d2-p11U puzzles
11 p1EU-d2--p10EU-d2-p11U-d2 puzzles
5 p1EU-d2--p11EU-d2 puzzles

T&E(2) expansion phase p12
199 p1EU-d2--p11EU-d2-p12 puzzles
199 p1EU-d2--p11EU-d2-p12U puzzles
0 p1EU-d2--p11EU-d2-p12U-d2 puzzles
0 p1EU-d2--p12EU-d2 puzzles

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[denis_berthier]

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Here's now my analysis for the T&E(3) part.
At the start, i.e. after the cleaning described in the previous post, there are 17,854 T&E(3) minimal puzzles in 988 different solution grids.

After cross-saturation with min-expands, there are 26,819 minimals.

After cross-saturation with T&E(3)-expands, which is doable (contrary to the T&E(2) puzzles), there are 46,281 minimals (almost 3 times more than at the start). They will be the starting point for the detailed analyses.

1. Basic stats and comparison with mith's largest collection and with coloin's T&E(3) collection analysed in the T&E(3) thread.
Note: all these collections are (almost) cross-saturated with T&E(3)-expands.

Code: Select all

46.84 minimals per grid vs 68.61 for mith, 21.35 for coloin

7.11 min-expands per grid vs 9.89 for mith, 5.07 for coloin

6.59 minimals per min-expand vs 6.94 for mith, 4.21 for coloin

1.081 T&E(3)-expands per grid vs 1.079 for mith, 1.055 for coloin

6.59 min-expands per T&E(3)-expand vs 9.16 for mith, 4.80 for coloin

In the above-mentioned thread, I had underlined the difference between mith's and coloin's collections. It seems Paquita's (saturated) collection lies in-between the two.
As little is know about how Paquita's collection was generated (which seeds were used), it's difficult to draw any conclusion.

2. Expansion stats
The expansion profile is the same as for the other two collections, with a peak at phase 2. Details below:

Code: Select all

T&E(3) expansion phase p0
46281 mins puzzles
46281 ME puzzles
7023 MEU puzzles

T&E(3) expansion phase p1
348546 p1 puzzles
345276 p1U puzzles
20579 p1U-d3 puzzles
9061 p1EU-d3 puzzles

T&E(3) expansion phase p2
445414 p1EU-d3-p2 puzzles
437630 p1EU-d3-p2U puzzles
21227 p1EU-d3-p2U-d3 puzzles
6051 p1EU-d3--p2EU-d3 puzzles

T&E(3) expansion phase p3
294053 p1EU-d3--p2EU-d3-p3 puzzles
288719 p1EU-d3--p2EU-d3-p3U puzzles
12930 p1EU-d3--p2EU-d3-p3U-d3 puzzles
3054 p1EU-d3--p3EU-d3 puzzles

T&E(3) expansion phase p4
146255 p1EU-d3--p3EU-d3-p4 puzzles
143737 p1EU-d3--p3EU-d3-p4U puzzles
5632 p1EU-d3--p3EU-d3-p4U-d3 puzzles
1237 p1EU-d3--p4EU-d3 puzzles

T&E(3) expansion phase p5
58221 p1EU-d3--p4EU-d3-p5 puzzles
57304 p1EU-d3--p4EU-d3-p5U puzzles
1744 p1EU-d3--p4EU-d3-p5U-d3 puzzles
386 p1EU-d3--p5EU-d3 puzzles

T&E(3) expansion phase p6
17809 p1EU-d3--p5EU-d3-p6 puzzles
17571 p1EU-d3--p5EU-d3-p6U puzzles
348 p1EU-d3--p5EU-d3-p6U-d3 puzzles
86 p1EU-d3--p6EU-d3 puzzles

T&E(3) expansion phase p7
3883 p1EU-d3--p6EU-d3-p7 puzzles
3847 p1EU-d3--p6EU-d3-p7U puzzles
49 p1EU-d3--p6EU-d3-p7U-d3 puzzles
16 p1EU-d3--p7EU-d3 puzzles

T&E(3) expansion phase p8
702 p1EU-d3--p7EU-d3-p8 puzzles
701 p1EU-d3--p7EU-d3-p8U puzzles
4 p1EU-d3--p7EU-d3-p8U-d3 puzzles
2 p1EU-d3--p8EU-d3 puzzles

T&E(3) expansion phase p9
85 p1EU-d3--p8EU-d3-p9 puzzles
85 p1EU-d3--p8EU-d3-p9U puzzles
0 p1EU-d3--p8EU-d3-p9U-d3 puzzles
0 p1EU-d3--p9EU-d3 puzzles

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