## Low/Hi Clue Thresholds

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

### Re: LCT Project Review

Hi Serg,

Serg wrote:Do you mean that each line in the table above represents number of ED grids, for which minimal number of clues in valid puzzles is equal to 17C, 18C, etc?

Not exactly. Let's look at the current grid status table, adding column KM = "Known Min" (ie. there is no puzzle with less clues):

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`               Grids   Known Min     ---------------------------     17C:      46301       46301       18C:  219375245     19C: 5253040692       59242      20C:     268296      268296      21C:          4           4          ----------------------          5472730538      373843`

The status for each category:

• 17C: all are KM, since it is known that there are no 16C puzzles
• 18C: we can't know for sure that any of these are KM until such time as we complete LCT-17 (blue's rigorous 17C search)
• 19C: we know that 59242 are KM because they have been tested with blue's rigorous Find18C function. The number is small because this is an expensive test (~4s per grid). But for all other grids we don't yet know the KM status.
• 20C: we know that every one of these grids has no 19C or less puzzle
• 21C: we know that every one of these grids has no 20C or less puzzle

For 19C grids, we keep a KM status indicator, that gets set whenever we explicitly test that grid with Find18C and find no 18C. If we do find an 18C puzzle, the 19C catalog record is converted into an 18C entry.

We don't have a KM flag for 18C grids, because we don't have an explicit Find17C test. But LCT-17, on completion, will have identified any remaining 17C's. Then we can say that any catalog entry of type 18C is definitely KM.

The big "black hole" we are left with after LCT-17 completes will be the ~5 billion 19C grids for which we can't be sure are KM until such time as they are explicitly tested, OR we come up with an efficient way to identify ALL 18C grids.

Cheers,
Jim Mathimagics
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### Re: Low/Hi Clue Thresholds

Hi, Mathimagics!
Thank you for clarification. Very complicated project, very ambitious goals! And great results already found! I mean exhaustive searches for 21C and 20C.
Well done!

Serg
Serg
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### LCT-18 Progress

Results for recent batches produced by LCT-18 workers:

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`Date              Batches     ED grids     New grids   Yield     Total 18C--------------------------------------------------------------------------22 Nov 2019      81 -   96   15,674,304    5,359,776   34.19% 23 Nov 2019      97 -  112   15,563,744    5,379,546   34.56%23 Nov 2019     113 -  128   15,740,306    5,202,150   33.05%   24 Nov 2019     129 -  144   15,667,837    5,061,052   32.30%  236,494,78225 Nov 2019         (Colin)   3,687,978    1,157,767   31.39%  237,652,549 25 Nov 2019     145 -  160   15,623,621    4,941,106   31.63%  242,593,655`

[EDIT] this means we have found ~25% of the predicted 968 million (+/- 13 million) 18C grids. Mathimagics
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### LCt-18 Progres

Results for recent batches produced by LCT-18 workers:

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`Date              Batches     ED grids     New grids    Yield-------------------------------------------------------------25 Nov 2019     161 -  176   15,667,897    4,692,544   29.95%26 Nov 2019     177 -  192   15,737,238    4,565,802   29.01%28 Nov 2019     193 -  208   15,673,691    4,348,479   27.74%28 Nov 2018     209 -  224   15,685,814    4,480,898   28.57%29 Nov 2019     225 -  240   15,562,115    4,183,054   26.88%30 Nov 2019     241 -  256   15,761,383    4,291,692   27.23%01 Dec 2019     257 -  272   15,751,756    4,246,077   26.96%02 Dec 2019     273 -  288   15,701,212    4,020,863   25.61%02 Dec 2019     289 -  304   15,660,397    3,864,569   24.68%03 Dec 2019     305 -  320   15,668,936    3,888,474   24.82%04 Dec 2019     321 -  336   15,689,167    3,617,314   23.06%05 Dec 2019     337 -  352   15,578,272    3,674,002   23.58%05 Dec 2019     353 -  368   15,703,846    3,610,967   22.99%06 Dec 2019     369 -  384   15,622,537    3,521,177   22.54%07 Dec 2019     385 -  400   15,791,640    3,512,622   22.24%  `

Total 18C grids found = 310,062,298 Mathimagics
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### LCT-18 Progress

Batches produced by Gen18H since the last post:

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`Date              Batches     ED grids     New grids    Yield-------------------------------------------------------------08 Dec 2019     401 -  416   15,548,298    3,322,085   21.37%09 Dec 2019     417 -  432   15,662,851    3,506,261   22.39%10 Dec 2019     433 -  448   15,716,955    3,330,571   21.19%11 Dec 2019     449 -  464   15,769,076    3,128,583   19.84%11 Dec 2019     465 -  480   15,753,254    3,130,577   19.87%12 Dec 2019     481 -  496   15,730,394    3,188,506   20.27%13 Dec 2019     497 -  512   15,562,815    3,020,245   19.41%14 Dec 2019     513 -  528   15,684,137    2,965,126   18.91%15 Dec 2019     529 -  544   15,540,220    3,052,064   19.64%15 Dec 2019     545 -  560   15,822,752    2,925,451   18.94%16 Dec 2019     561 -  576   15,632,390    2,876,672   18.40%17 Dec 2019     577 -  592   15,697,059    2,603,041   16.58%18 Dec 3019     593 -  608   15,615,527    2,640,300   16.91%19 Dec 2019     609 -  624   15,680,362    2,584,728   16.48%20 Dec 2019     625 -  640   15,817,157    2,643,581   16.71%23 Dec 2019     641 -  656   15,590,684    2,375,455   15.24%23 Dec 2019     657 -  672   15,639,328    2,426,678   15.52%24 Dec 2019     673 -  688   15,586,865    2,306,292   14.80%26 Dec 2019     689 -  704   15,850,464    2,348,249   14.82%26 Dec 2019     705 =  720   15,560,133    2,371,526   15.24%27 Dec 2019     721 -  736   15,446,247    2,210,284   14.31%28 Dec 2019     737 -  752   15,760,107    2,247,959   14.26%29 Dec 2019     753 -  768   15,594,851    2,183,202   14.00%30 Dec 2019     769 -  784   15,566,469    2,222,574   14.28%31 Dec 2012     785 -  800   15,700,898    2,258,725   14.39%`

Together with coloin's contributions for the same period (~25 million new grids), the total 18C grid count is now 402,552,192. Mathimagics
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### LCT-18 Progress

Batches/yields for the past month:

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[/code]
01 Jan 2020 801 - 816 15,654,671 2,175,172 13.89%
02 Jan 2020 817 - 832 15,599,456 2,010,565 12.89%
03 Jan 2020 833 - 848 15,581,950 2,014,135 12.93%
04 Jan 2020 849 - 864 15,633,450 2,110,141 13.50%
06 Jan 2020 865 - 880 15,635,523 1,944,318 12.44%
07 Jan 2020 881 - 896 15,604.645 1,946,872 12.48%
08 Jan 2020 897 - 912 15,576,636 1,921,768 12.34%
09 Jan 2020 913 - 928 15,738,552 1,974,022 12.54%
09 Jan 2020 929 - 944 15,658,147 1,880,430 12.01%
10 Jan 2020 945 - 960 15,626,962 1,933,528 12.37%
11 Jan 2020 961 - 976 15,610,712 1,890,443 12.11%
12 Jan 2020 977 - 992 15,560,565 1,841,618 11.84%
13 Jan 2020 993 - 1008 15,687,289 1,725,013 11.00%
14 Jan 2020 1009 - 1024 15,528,053 1,669,829 10.75%
15 Jan 2020 1025 - 1040 15,716,740 1,896,595 12.07%
16 Jan 2020 1041 - 1056 15,875,183 1,849,322 11.65%
17 Jan 2020 1057 - 1072 15,590,512 1,757,688 11.27%
18 Jan 2020 1073 - 1088 15,700,861 1,691,541 10.77%
19 Jan 2020 1089 - 1104 15,562,761 1,735,197 11.15%
20 Jan 2020 1105 - 1120 15,717,935 1,624,633 10.34%
21 Jan 2020 1121 - 1136 15,634,336 1,622,490 10.38%
22 Jan 2020 1137 - 1152 15,760,133 1,719,249 10.91%
23 Jan 2020 1153 - 1168 15,583,101 1,617,306 10.38%
24 Jan 2020 1169 - 1184 15,704,603 1,712,694 10.91%
25 Jan 2020 1185 - 1200 15,574,694 1,572,282 10.10%
26 Jan 2020 1201 - 1216 16,254,907 1,630,985 10.01%
26 Jan 2020 1217 - 1232 15,523,157 1,501,681 9.67%
27 Jan 2020 1233 - 1248 15,853,058 1,607,707 10.14%
28 Jan 2020 1249 - 1264 15,604,715 1,538,526 9.86%
29 Jan 2020 1265 - 1280 15,755,886 1,503,860 9.54%
30 Jan 2020 1281 - 1296 15,503,457 1,512,875 9.76%
31 Jan 2020 1297 - 1312 15,687,032 1,501,163 9.57%[/code]

Net yields are now down to ~9%. And I have had to cut down the number of worker processes from 22 to 16, due to the alarming power consumption revealed by our recent electricity bills!

The total grid count is now 466,504,364, so we have about 48% of blue's estimate of 968 million.

coloin has made a very interesting discovery, namely that, for an 18C puzzle, a fast way to run a limited search of the {-2, +2} vicinity is this:

• choose the clue with the least # of 17C solutions (ie # of solutions with that clue removed)
• search this 17C puzzle with {-1, +2}

This procedure will generally identify the clue with the highest {-2, +2} yield (or close), but is 15 times faster than the full {-2, +2} search.

Can this lead to a Gen18C process with a better yield? We are investigating this ... Mathimagics
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### LCT-18 Progress

I have completed the initial round of tests of Gen18Z, which is a worker process that is based on coloin's "selective {-2, +2}" search method, as outlined above.

First a quick review of the existing process, Gen18H. This uses random morphing of 19C puzzles, "Harvesting" any puzzles with redundant clues which gives us 18C puzzles. This has been the main source of new 18C grids over the past few months.

16 worker processes are running on JACK (my 16-core PC), and currently their output is a steady 15.5 million ED grids every 22 hours on average. The percentage of these grids that are found to be new (ie: no 18C already found) is currently about 9%, and this %yield is slowly decreasing. We have found about half of the likely total of 18C grids so far.

Averaging by worker-hours, the current Gen18H workers thus produce about 44,000 ED grids/hour (GPH), of which ~4,000 are new grids (NPH). So absolute progress is measured by NPH, the number of new grids per worker-hour. But the %yield (NPH v GPH) is still of interest, since any method that provides higher %yields, even at lower production levels (NPH), is of interest when we consider the task ahead (the 50% of 18C grids that are not yet found).

An overview of Gen18Z:

• Seed generation: select a random grid from the catalog, one for which 19-clues is the best known result. Use blue's Find18C function to test it for 18C. If this function fails, mark the grid as "No 18C" (so it doesn't get selected again) and try another grid.
• List propagation: use the selective {-2,+2} method to enumerate new 18C puzzles. Collect any new puzzles for list propagation in a subsequent pass. Repeat this process until no new puzzles found (closure), or until some operational limit is reached.
• List reduction: reduce the collection to one puzzle per ED grid, save this list as a new batch.

The cost of selective {-2,+2} enumeration is still relatively expensive - on average 2s per puzzle (full {-2,+2} enumeration costs 40-60s per puzzle). The main parameter used to limit the list propagation is a limit on the number of puzzles to be {-2,+2} tested (NTEST). Evidence suggests that, when the list propagation is self-sustaining, pursuing additional passes leads ultimately to diminishing new grid yields.

The first round of tests was done with NTEST = 2000, but this was applied within each propagation pass, so the batch times (where propagation was self-sustaining) vary from 1 to 3 hours. In future tests NTEST will specify the absolute total limit, and the batch times should then be fairly constant.

The first test results are shown below. Each batch corresponds to a single seed grid, and the entry lists the time (in minutes), the #of ED grids (ed), and the # of new grids (ng). For grids with sustained propagation, the %yield and approximate NPH value are shown.
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`Batch    6:   72.17m, ed =  30505, ng =   2773   9.09%, nph = 2305Batch    7:   72.58m, ed =  15688, ng =   2541  16.20%, nph = 2100Batch    8:    0.95m, ed =      1, ng =      1Batch    9:    3.43m, ed =      6, ng =      5Batch   10:   88.02m, ed =  27553, ng =   5019  18.22%, nph = 3421Batch   11:   72.48m, ed =  21985, ng =   4534  20.62%, nph = 3753Batch   12:   81.02m, ed =  32247, ng =   1741   5.40%, nph = 1289Batch   13:   89.85m, ed =  17804, ng =   3549  19.93%, nph = 2370Batch   14:    0.52m, ed =      2, ng =      2Batch   15:    1.62m, ed =      1, ng =      1Batch   16:    4.23m, ed =      1, ng =      1Batch   17:   62.02m, ed =  30106, ng =   1274   4.23%, nph = 1233Batch   18:    0.40m, ed =      2, ng =      1Batch   19:   87.97m, ed =  22280, ng =   4605  20.67%, nph = 3141Batch   20:    0.53m, ed =      1, ng =      1Batch   21:  149.50m, ed =  42468, ng =   5435  12.80%, nph = 2181Batch   22:    0.28m, ed =      1, ng =      1Batch   23:  150.08m, ed =  13952, ng =   3575  25.62%, nph = 1429Batch   24:  102.67m, ed =  31270, ng =   4931  15.77%, nph = 2882Batch   25:    0.53m, ed =      1, ng =      1Batch   26:    1.45m, ed =      3, ng =      1Batch   27:   26.53m, ed =   7738, ng =   1357  17.54%, nph = 3069Batch   28:  111.70m, ed =  36821, ng =   4761  12.93%, nph = 2557Batch   29:   88.75m, ed =  23078, ng =   3303  14.31%, nph = 2233Batch   30:   90.95m, ed =  34722, ng =   2971   8.56%, nph = 1960Batch   31:  109.37m, ed =  34143, ng =   4979  14.58%, nph = 2732Batch   32:  138.78m, ed =  28961, ng =   4914  16.97%, nph = 2124Batch   33:    0.45m, ed =      1, ng =      1Batch   34:   67.65m, ed =  29880, ng =   2274   7.61%, nph = 2017Batch   35:   74.35m, ed =  25248, ng =   2796  11.07%, nph = 2256Batch   36:   18.23m, ed =   6068, ng =    852  14.04%, nph = 2804Batch   37:    0.08m, ed =      1, ng =      1Batch   38:   59.48m, ed =  21516, ng =   2459  11.43%, nph = 2480Batch   39:    0.35m, ed =      1, ng =      1Batch   40:   68.98m, ed =  16019, ng =   2444  15.26%, nph = 2126Batch   41:  118.82m, ed =  24434, ng =   5900  24.15%, nph = 2979Batch   42:   65.78m, ed =  38504, ng =   1962   5.10%, nph = 1790Batch   43:    0.20m, ed =      1, ng =      1Batch   44:    0.97m, ed =      1, ng =      1Batch   45:    0.42m, ed =      1, ng =      1Batch   46:    0.40m, ed =      1, ng =      1Batch   47:    1.98m, ed =      1, ng =      1Batch   48:   98.65m, ed =  26657, ng =   5507  20.66%, nph = 3349Batch   49:  108.95m, ed =  27484, ng =   5900  21.47%, nph = 3249Batch   50:    0.77m, ed =      1, ng =      1Batch   51:   92.22m, ed =  28282, ng =   4257  15.05%, nph = 2770Batch   52:   73.95m, ed =  15872, ng =   3704  23.34%, nph = 3005Batch   53:   71.78m, ed =  21817, ng =   2483  11.38%, nph = 2075Batch   54:   92.82m, ed =  28393, ng =   3639  12.82%, nph = 2352Batch   55:   93.12m, ed =  14793, ng =   4232  28.61%, nph = 2727------------------------------------------------------------------    Total : 2718.78m, ed = 776316, ng = 110695  14.26%, nph = 2443`

As you can see, 1 in every 3 grids "failed", ie didn't result in any sustained {-2,+2} propagation. The selective {-2,+2} enumeration tends to favour the most productive cases, but this is by no means guaranteed. In the next round of tests I will make a complete {-2,+2} enumeration of the initial seed puzzle, and we will see if that reduces the "failed" cases.

On the surface, it would appear that the NPH rates (average ~2200) are much less than the current Gen18H workers. But encouragement is found in the incidence of %yields that are often much higher. This (hopefully) suggests that this method will ultimately be more effective in finding "remote" 18C grids. Mathimagics
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### Re: LCT-18 Progress

Mathimagics wrote:As you can see, 1 in every 3 grids "failed", ie didn't result in any sustained {-2,+2} propagation. The selective {-2,+2} enumeration tends to favour the most productive cases, but this is by no means guaranteed. In the next round of tests I will make a complete {-2,+2} enumeration of the initial seed puzzle, and we will see if that reduces the "failed" cases.

There were 19 cases in the initial test set that failed to propagate. After re-running them with full {-2,+2} enumeration (for the seed puzzle) worked for 13 of them:

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`Batch   56:    0.37m, ed =      3, ng =      2Batch   57:   61.58m, ed =  27103, ng =   2342   8.64%, nph = 2282Batch   58:   61.95m, ed =  16404, ng =    851   5.19%, nph =  824Batch   59:   59.55m, ed =  13365, ng =   2777  20.78%, nph = 2798Batch   60:   68.88m, ed =  15830, ng =   2577  16.28%, nph = 2245Batch   61:    0.35m, ed =      1, ng =      1Batch   62:    0.38m, ed =      4, ng =      4Batch   63:    0.47m, ed =      3, ng =      1Batch   64:    0.42m, ed =      2, ng =      2Batch   65:   56.50m, ed =  30360, ng =   2180   7.18%, nph = 2315Batch   66:   59.58m, ed =  33299, ng =    981   2.95%, nph =  988Batch   67:   61.07m, ed =  22795, ng =   2821  12.38%, nph = 2772Batch   68:   65.42m, ed =  21196, ng =   1581   7.46%, nph = 1450Batch   69:   61.23m, ed =  31343, ng =   2054   6.55%, nph = 2013Batch   70:   64.28m, ed =  15176, ng =   1986  13.09%, nph = 1854Batch   71:   71.83m, ed =  30011, ng =   2652   8.84%, nph = 2215Batch   72:    0.35m, ed =      1, ng =      1Batch   73:   73.45m, ed =  11693, ng =   2516  21.52%, nph = 2055Batch   74:   56.88m, ed =  26949, ng =   2033   7.54%, nph = 2144------------------------------------------------------------------    Total :  824.55m, ed = 295538, ng =  27362   9.26%, nph = 1991` Mathimagics
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### Re: Low/Hi Clue Thresholds

Pretty good ....we are half way !!
An excellent effort I think !!

But the fast gen19c continues for now on my PC ...
Interesting that some of the yields are up [24% wow !] , and i suppose that when you get into "non-remote / already found" territory thats when the yield will plummet....

I mentioned that perhaps a selective selective {-1,-1+2}might be the way.
When one removes the best [least sol] clue of the 18 - the number of sols determines the remoteness to an extent .
Instead of trying to process every seed - if we are selective and only process those seeds which have a highish eg 100 sol - maybe this will tend to keep us out of the non-remote/already found territory.
There wont be so many puzzles made however ...
coloin

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### Re: Low/Hi Clue Thresholds

coloin wrote:Instead of trying to process every seed - if we are selective and only process those seeds which have a highish eg 100 sol - maybe this will tend to keep us out of the non-remote/already found territory.
There wont be so many puzzles made however ...

This might work, the trouble is that testing it is tricky and time-consuming. Perhaps an option to keep up our sleeve for when the search really gets difficult ...

Meanwhile, some good news, I think!

I have found a bug in blue's PM1 code. He only searched 1/2 of the possible puzzles. Even with this fixed, it is still 4x faster than my version.

For current workers (Gen18H) the impact will be slightly slower morph test times, but higher yields ultimately ... we will see in a few days time when the new version has generated a few batch sets.

For Gen18Z this could also be significant - if I can make a {-1,+2} version of blue's PM1 code, it should be much faster than the current version! Mathimagics
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### Gen18Z Testing

Results for a full days work for 4 workers running Gen18Z. Note in particular the results for batches #1010, #1046 and #1075.

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`Batch 1001:   59.08m, ed =  16920, ng =   3259  19.26%, nph = 3310Batch 1002:    0.67m, ed =      4, ng =      3Batch 1003:   62.55m, ed =  30280, ng =   1733   5.72%, nph = 1662Batch 1004:   63.67m, ed =  29866, ng =   1933   6.47%, nph = 1822Batch 1005:   68.37m, ed =  10541, ng =   2890  27.42%, nph = 2536Batch 1006:   61.43m, ed =  20340, ng =   2297  11.29%, nph = 2243Batch 1007:   63.80m, ed =  20929, ng =   2979  14.23%, nph = 2802Batch 1008:   62.40m, ed =  13572, ng =   2535  18.68%, nph = 2437Batch 1009:   73.37m, ed =  11542, ng =   2768  23.98%, nph = 2264Batch 1010:   65.45m, ed =  11528, ng =   3923  34.03%, nph = 3596  **Batch 1011:   70.12m, ed =  15763, ng =   2799  17.76%, nph = 2395Batch 1012:   63.97m, ed =  30717, ng =   1685   5.49%, nph = 1581Batch 1013:   68.75m, ed =  14773, ng =   4078  27.60%, nph = 3559Batch 1014:   61.05m, ed =  25847, ng =   2318   8.97%, nph = 2278Batch 1015:   63.85m, ed =  26679, ng =   2114   7.92%, nph = 1987Batch 1016:   64.90m, ed =  14304, ng =   2020  14.12%, nph = 1867Batch 1017:   70.27m, ed =  20854, ng =   2209  10.59%, nph = 1886Batch 1018:   72.07m, ed =  23015, ng =   1858   8.07%, nph = 1547Batch 1019:   73.08m, ed =   7568, ng =   2630  34.75%, nph = 2159Batch 1020:   84.33m, ed =  21352, ng =   3201  14.99%, nph = 2277Batch 1021:   90.77m, ed =  23804, ng =   2870  12.06%, nph = 1897Batch 1022:   64.30m, ed =  47674, ng =    993   2.08%, nph =  927Batch 1023:   59.53m, ed =  13135, ng =   3350  25.50%, nph = 3376Batch 1024:   70.25m, ed =  19441, ng =   3440  17.69%, nph = 2938Batch 1025:    2.68m, ed =      1, ng =      1Batch 1026:   74.27m, ed =  16160, ng =   2887  17.87%, nph = 2332Batch 1027:   58.82m, ed =  19746, ng =   1751   8.87%, nph = 1786Batch 1028:   56.75m, ed =  19654, ng =   2143  10.90%, nph = 2266Batch 1029:    0.38m, ed =      2, ng =      2Batch 1030:   61.58m, ed =  22378, ng =   2796  12.49%, nph = 2724Batch 1031:   67.88m, ed =  15049, ng =   1895  12.59%, nph = 1675Batch 1032:   60.55m, ed =  12082, ng =   2775  22.97%, nph = 2750Batch 1033:   65.12m, ed =  15908, ng =   2930  18.42%, nph = 2700Batch 1034:   67.50m, ed =  24119, ng =   2099   8.70%, nph = 1866Batch 1035:   71.18m, ed =  18125, ng =   2010  11.09%, nph = 1694Batch 1036:   61.35m, ed =  18588, ng =   1894  10.19%, nph = 1852Batch 1037:   64.65m, ed =  13693, ng =   2027  14.80%, nph = 1881Batch 1038:   60.50m, ed =  20083, ng =   2563  12.76%, nph = 2542Batch 1039:    1.60m, ed =      1, ng =      1Batch 1040:    0.70m, ed =      4, ng =      3Batch 1041:   64.88m, ed =  14322, ng =   2139  14.94%, nph = 1978Batch 1042:   59.75m, ed =  21896, ng =   1491   6.81%, nph = 1497Batch 1043:   59.95m, ed =  26806, ng =   2277   8.49%, nph = 2279Batch 1044:   62.00m, ed =  16952, ng =   2232  13.17%, nph = 2160Batch 1045:   66.87m, ed =  28922, ng =   2395   8.28%, nph = 2149Batch 1046:   65.85m, ed =  13883, ng =   4455  32.09%, nph = 4059  **Batch 1047:   57.12m, ed =  28021, ng =   1737   6.20%, nph = 1825Batch 1048:   62.85m, ed =  18968, ng =   2459  12.96%, nph = 2347Batch 1049:   61.78m, ed =  18244, ng =   4362  23.91%, nph = 4236Batch 1050:   67.02m, ed =  14123, ng =   3129  22.16%, nph = 2801Batch 1051:   59.77m, ed =  19337, ng =   2549  13.18%, nph = 2559Batch 1052:   59.30m, ed =  10634, ng =   3479  32.72%, nph = 3520Batch 1053:   61.68m, ed =  30788, ng =   1334   4.33%, nph = 1298Batch 1054:   64.32m, ed =  22325, ng =   1828   8.19%, nph = 1705Batch 1055:   63.37m, ed =  23236, ng =   2100   9.04%, nph = 1988Batch 1056:   57.90m, ed =  20702, ng =   1838   8.88%, nph = 1905Batch 1057:   61.27m, ed =  18394, ng =   3496  19.01%, nph = 3424Batch 1058:   63.65m, ed =  27558, ng =   1907   6.92%, nph = 1798Batch 1059:   61.62m, ed =  15268, ng =   3512  23.00%, nph = 3420Batch 1060:   60.45m, ed =  27807, ng =   2125   7.64%, nph = 2109Batch 1061:   61.17m, ed =  17146, ng =   2530  14.76%, nph = 2482Batch 1062:    1.47m, ed =      2, ng =      2Batch 1063:   63.37m, ed =  18771, ng =   3108  16.56%, nph = 2943Batch 1064:   58.15m, ed =  16950, ng =   3260  19.23%, nph = 3364Batch 1065:   65.28m, ed =  15011, ng =   2336  15.56%, nph = 2147Batch 1066:   71.33m, ed =  24450, ng =   2958  12.10%, nph = 2488Batch 1067:   72.12m, ed =  16644, ng =   2719  16.34%, nph = 2262Batch 1068:   66.08m, ed =  23515, ng =   2376  10.10%, nph = 2157Batch 1069:   71.47m, ed =  20407, ng =   2442  11.97%, nph = 2050Batch 1070:   59.93m, ed =  21242, ng =   2579  12.14%, nph = 2582Batch 1071:   58.95m, ed =  16445, ng =   2988  18.17%, nph = 3041Batch 1072:    0.43m, ed =      2, ng =      1Batch 1073:   67.63m, ed =  23913, ng =   2379   9.95%, nph = 2110Batch 1074:   65.97m, ed =   9443, ng =   2984  31.60%, nph = 2714   Batch 1075:   57.95m, ed =  14226, ng =   4454  31.31%, nph = 4612   ***Batch 1076:    1.03m, ed =      2, ng =      2Batch 1077:   65.28m, ed =  13405, ng =   1975  14.73%, nph = 1815Batch 1078:    0.75m, ed =      2, ng =      2Batch 1079:   57.00m, ed =  16929, ng =   2411  14.24%, nph = 2538Batch 1080:    2.10m, ed =      7, ng =      6Batch 1081:   58.88m, ed =  14224, ng =   2280  16.03%, nph = 2323Batch 1082:   58.22m, ed =  13671, ng =   3374  24.68%, nph = 3477Batch 1083:   58.57m, ed =  17531, ng =   3227  18.41%, nph = 3306Batch 1084:   73.47m, ed =  20985, ng =   1391   6.63%, nph = 1136Batch 1085:   69.27m, ed =  13139, ng =   3038  23.12%, nph = 2632Batch 1086:    0.80m, ed =      1, ng =      1Batch 1087:   73.58m, ed =  24306, ng =   1344   5.53%, nph = 1096Batch 1088:   71.98m, ed =  16619, ng =   2038  12.26%, nph = 1699Batch 1089:   74.90m, ed =  26037, ng =   2135   8.20%, nph = 1710Batch 1090:   74.48m, ed =  33400, ng =   1458   4.37%, nph = 1174Batch 1091:   67.58m, ed =  21166, ng =   3014  14.24%, nph = 2676Batch 1092:   71.38m, ed =  27184, ng =   2736  10.06%, nph = 2300Batch 1093:   65.72m, ed =  19549, ng =   1887   9.65%, nph = 1723------------------------------------------------------------------    Total : 5361.22m, ed =1620551, ng = 207941  12.83%, nph = 2327`

If we can reduce the cost of doing the {-1,+2} tests, this could be really prove to be a gun method! Mathimagics
2017 Supporter

Posts: 1538
Joined: 27 May 2015
Location: Canberra

### Re: Low/Hi Clue Thresholds

Well that is progress !!!
Is each batch from a single 17C subpuzzle ?
coloin

Posts: 1906
Joined: 05 May 2005

### Re: Low/Hi Clue Thresholds

Each batch begins with single 18C seed puzzle. This is always a new grid - I use Blue's Find18C function to get this puzzle, and only look at grids that aren't already known to have an 18C, or known NOT to have one.

For the seed puzzle I do a complete enumeration of {-2, +2}. As I explained above, although this takes 40-60 seconds, it is worth the effort because it picks up many cases where the selective ("best 17C subpuzzle") enumeration would not otherwise find anything to propagate.

All of the {-2, +2} tests except for this first one are done in selective mode (ie via the "best17C subpuzzle").

======================================== ListSPC.zip

Sub-Puzzle Count tool: a sub-puzzle is a given puzzle with 1 clue removed. This tool takes a puzzle, and removes the clue with the lowest subpuzzle solution count.
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`> ListSPC 1.3........6.....2.....254.......6....7..8........4..5.9..6.....7.....2.....1.3..1.3........6.....2.....254.......6.......8........4..5.9..6.....7.....2.....1.3..`

A file of puzzles can be used:
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`> ListSPC Test18C.txt`

The tool can also list all sub-puzzle solution counts for a given puzzle. Example:
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`c:> ListSPC -x 1.3........6.....2.....254.......6....7..8........4..5.9..6.....7.....2.....1.3..Puzzle has 18 cluesClue 01 = 1:  solns =   22468Clue 03 = 3:  solns =   52738Clue 12 = 6:  solns =   92137Clue 18 = 2:  solns =    1147Clue 24 = 2:  solns =  187609Clue 25 = 5:  solns =    5944Clue 26 = 4:  solns =  158243Clue 34 = 6:  solns =   35139Clue 39 = 7:  solns =      45Clue 42 = 8:  solns =   17870Clue 51 = 4:  solns =   38394Clue 54 = 5:  solns =     788Clue 56 = 9:  solns =    1677Clue 59 = 6:  solns =  110334Clue 65 = 7:  solns =    5249Clue 71 = 2:  solns =    5047Clue 77 = 1:  solns =    7598Clue 79 = 3:  solns =    3523`
Last edited by Mathimagics on Sun Feb 09, 2020 5:27 pm, edited 1 time in total. Mathimagics
2017 Supporter

Posts: 1538
Joined: 27 May 2015
Location: Canberra

### Gen18Z Tests

Ok, one more day of batch testing for the new Gen18Z process.

I finally understand exactly what blue's {-1,+1} code does, and the principle is quite simple. For each subpuzzle ie {-1}, we test all the {+1} candidates, in the usual fashion. But we also keep a list of distinct solutions, and by using clever bitmasking, we can ask whether a value D has occurred in cell CN in some solution already found, and whether this has occurred twice.

So when we come to testing CN = D, we can skip this solver call if we know that CN = D has occurred twice in the solution list for this {-1} subpuzzle. This reduces the solver calls by roughly half.

When blue first gave me this code, the puzzle generation time was in fact reduced by a factor of ~4, not 2. It turns out he had a bug in the outer loop, he only added clue values to the right of the {-1} clue, and ignored the possibilities to the left. I only found this by comparing his code with mine on a per-puzzle basis, and noticed that I was finding more {-1,+1} puzzles.

And what about the impact of this on Gen18H yields? Fixing the bug certainly had the expected slowdown of the process, as it takes on average of 31 hours to produce a batch in "full-search mode", compared to just 22 hours previously. Sadly, however, this didn't translate to any noticable increased grid %yield, so the absolute yield (NPH) is greatly reduced! The bottom line is that Gen18H, which is basically {-1,+1} processing throughout, runs best in "half-search mode"!

===============================================

Ok, we will return to this issue later on. For Gen18Z we take a 17-clue puzzle and do a {-1, +2} search. For each {-1} we need to add 2 clues at a time, and it is not a simple matter to translate blue's method into 2 clue mode. But we can use it in a simple outer loop as follows:

• for each possible 18c puzzle corresponding to the 17-clue base puzzle plus 1 added clue, do a (blue) {-1, +1} search

Using this approach has the desired effect, reducing batch generation time by ~40%, and thus to improved NPH results. This set of batch results shows avg NPH = 3880 over a day's work. (A couple of batches, 1201 + 1202, show %yields of 50% !!)
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`Batch 1102:   38.77m, ed =  27473, ng =   2626   9.56%, nph = 4064Batch 1103:   43.67m, ed =  19627, ng =   1649   8.40%, nph = 2266Batch 1104:   46.15m, ed =  19737, ng =   2981  15.10%, nph = 3876Batch 1105:   46.53m, ed =  19737, ng =   2981  15.10%, nph = 3844Batch 1106:    0.78m, ed =      3, ng =      2Batch 1107:    0.65m, ed =      3, ng =      2Batch 1108:   44.73m, ed =  14982, ng =   4845  32.34%, nph = 6499Batch 1109:   42.68m, ed =  19845, ng =   2507  12.63%, nph = 3524Batch 1110:   42.78m, ed =  19845, ng =   2507  12.63%, nph = 3516Batch 1111:   46.63m, ed =  12294, ng =   3490  28.39%, nph = 4490Batch 1112:   40.48m, ed =  49518, ng =   1136   2.29%, nph = 1684Batch 1113:   40.02m, ed =  20755, ng =   1930   9.30%, nph = 2894Batch 1114:    0.45m, ed =      2, ng =      1Batch 1115:   42.27m, ed =  18436, ng =   3010  16.33%, nph = 4273Batch 1116:   42.50m, ed =  18436, ng =   3010  16.33%, nph = 4249Batch 1117:   42.30m, ed =  14262, ng =   4058  28.45%, nph = 5756Batch 1118:   46.57m, ed =  49412, ng =   1930   3.91%, nph = 2487Batch 1119:   54.63m, ed =  18118, ng =   3708  20.47%, nph = 4072Batch 1120:   55.03m, ed =  18118, ng =   3708  20.47%, nph = 4043Batch 1121:   50.13m, ed =  29112, ng =   4088  14.04%, nph = 4893Batch 1122:   41.20m, ed =  14909, ng =   3545  23.78%, nph = 5163Batch 1123:   42.53m, ed =  12517, ng =   2995  23.93%, nph = 4225Batch 1124:   47.33m, ed =  22620, ng =   3443  15.22%, nph = 4364Batch 1125:   99.18m, ed =  30828, ng =   2093   6.79%, nph = 1266Batch 1126:   99.22m, ed =  30828, ng =   2093   6.79%, nph = 1266Batch 1127:   37.73m, ed =  17562, ng =   2233  12.71%, nph = 3551Batch 1128:   46.45m, ed =   9824, ng =   2301  23.42%, nph = 2972Batch 1129:   43.05m, ed =  26903, ng =   2974  11.05%, nph = 4145Batch 1130:   43.13m, ed =  26903, ng =   2974  11.05%, nph = 4137Batch 1131:   43.57m, ed =  16413, ng =   3145  19.16%, nph = 4331Batch 1132:   45.92m, ed =  10777, ng =   3965  36.79%, nph = 5181Batch 1133:    0.53m, ed =      1, ng =      1Batch 1134:   46.67m, ed =  16468, ng =   3810  23.14%, nph = 4899Batch 1135:   46.60m, ed =  16468, ng =   3810  23.14%, nph = 4906Batch 1136:    0.70m, ed =      3, ng =      3Batch 1137:    0.72m, ed =      3, ng =      3Batch 1138:   44.80m, ed =  17768, ng =   1674   9.42%, nph = 2242Batch 1139:   50.90m, ed =  31882, ng =   2305   7.23%, nph = 2717Batch 1140:    1.38m, ed =      1, ng =      1Batch 1141:   49.12m, ed =  10235, ng =   3828  37.40%, nph = 4676Batch 1142:   49.08m, ed =  10235, ng =   3828  37.40%, nph = 4679Batch 1143:   44.15m, ed =  20928, ng =   4882  23.33%, nph = 6635Batch 1144:   43.57m, ed =  36640, ng =   2552   6.97%, nph = 3515Batch 1145:   43.80m, ed =  21311, ng =   2108   9.89%, nph = 2888Batch 1146:   43.85m, ed =  21311, ng =   2108   9.89%, nph = 2884Batch 1147:   40.03m, ed =  13503, ng =    776   5.75%, nph = 1163Batch 1148:   48.37m, ed =  23461, ng =   2441  10.40%, nph = 3028Batch 1149:   43.77m, ed =  40100, ng =   1672   4.17%, nph = 2292Batch 1150:   43.88m, ed =  40100, ng =   1672   4.17%, nph = 2286Batch 1151:   41.80m, ed =  15418, ng =   2968  19.25%, nph = 4260Batch 1152:    0.58m, ed =      2, ng =      2Batch 1153:   44.22m, ed =  28115, ng =   2414   8.59%, nph = 3276Batch 1154:   43.98m, ed =  51994, ng =    854   1.64%, nph = 1165Batch 1155:   44.10m, ed =  51994, ng =    854   1.64%, nph = 1162Batch 1156:   37.55m, ed =  15035, ng =   3890  25.87%, nph = 6216Batch 1157:   44.37m, ed =  14198, ng =   2933  20.66%, nph = 3966Batch 1158:    0.95m, ed =      1, ng =      1Batch 1159:   41.52m, ed =  25996, ng =   2733  10.51%, nph = 3950Batch 1160:   41.48m, ed =  25996, ng =   2733  10.51%, nph = 3953Batch 1161:   36.15m, ed =   4084, ng =   1958  47.94%, nph = 3250Batch 1162:   49.20m, ed =  26194, ng =   1949   7.44%, nph = 2377Batch 1163:   53.18m, ed =  12820, ng =   4490  35.02%, nph = 5065Batch 1164:   53.17m, ed =  12820, ng =   4490  35.02%, nph = 5067Batch 1165:   39.40m, ed =  11782, ng =   3742  31.76%, nph = 5698Batch 1166:   49.52m, ed =  12097, ng =   3332  27.54%, nph = 4037Batch 1167:   39.57m, ed =  21970, ng =   2315  10.54%, nph = 3511Batch 1168:   39.75m, ed =  21970, ng =   2315  10.54%, nph = 3494Batch 1169:   39.35m, ed =  18897, ng =   3616  19.14%, nph = 5514Batch 1170:   40.75m, ed =  57824, ng =    584   1.01%, nph =  860Batch 1171:    0.78m, ed =      2, ng =      1Batch 1172:   35.93m, ed =  36391, ng =   1947   5.35%, nph = 3251Batch 1173:   40.00m, ed =  18790, ng =   3798  20.21%, nph = 5697Batch 1174:   40.22m, ed =  18790, ng =   3798  20.21%, nph = 5666Batch 1175:    1.40m, ed =      1, ng =      1Batch 1176:    1.43m, ed =      1, ng =      1Batch 1177:   37.73m, ed =  10474, ng =   3409  32.55%, nph = 5421Batch 1178:   44.93m, ed =  20623, ng =   2538  12.31%, nph = 3389Batch 1179:   44.93m, ed =  20623, ng =   2538  12.31%, nph = 3389Batch 1180:   40.85m, ed =  20913, ng =   3648  17.44%, nph = 5358Batch 1181:    0.60m, ed =      2, ng =      2Batch 1182:   56.45m, ed =  30904, ng =   2093   6.77%, nph = 2225Batch 1183:   40.65m, ed =  36996, ng =   1583   4.28%, nph = 2337Batch 1184:   40.75m, ed =  36996, ng =   1583   4.28%, nph = 2331Batch 1185:   40.03m, ed =  17304, ng =   3195  18.46%, nph = 4789Batch 1186:   38.60m, ed =  28927, ng =   2945  10.18%, nph = 4578Batch 1187:   35.60m, ed =  34878, ng =   1310   3.76%, nph = 2208Batch 1188:    0.70m, ed =      2, ng =      2Batch 1189:   38.80m, ed =  22652, ng =   3577  15.79%, nph = 5531Batch 1190:   38.87m, ed =  22652, ng =   3577  15.79%, nph = 5522Batch 1191:   37.93m, ed =  19550, ng =   3617  18.50%, nph = 5721Batch 1192:   39.45m, ed =  18764, ng =   3676  19.59%, nph = 5591Batch 1193:   41.37m, ed =  20425, ng =   3065  15.01%, nph = 4446Batch 1194:   41.50m, ed =  20425, ng =   3065  15.01%, nph = 4431Batch 1195:   44.00m, ed =  24719, ng =   2734  11.06%, nph = 3728Batch 1196:   42.35m, ed =  10612, ng =   3866  36.43%, nph = 5477Batch 1197:   37.15m, ed =  40565, ng =   1100   2.71%, nph = 1777Batch 1198:   49.13m, ed =  24069, ng =   3239  13.46%, nph = 3955Batch 1199:   48.93m, ed =  24069, ng =   3239  13.46%, nph = 3972Batch 1200:   36.10m, ed =  22853, ng =   2015   8.82%, nph = 3349Batch 1201:   38.35m, ed =  20712, ng =   2805  13.54%, nph = 4389Batch 1202:   39.95m, ed =   6884, ng =   3530  51.28%, nph = 5302Batch 1203:   39.92m, ed =   6884, ng =   3530  51.28%, nph = 5306Batch 1204:   41.25m, ed =  20915, ng =   3411  16.31%, nph = 4961Batch 1205:   38.20m, ed =  15449, ng =   3139  20.32%, nph = 4930Batch 1206:   41.63m, ed =  15600, ng =   3004  19.26%, nph = 4329Batch 1207:   41.57m, ed =  15600, ng =   3004  19.26%, nph = 4336Batch 1208:   42.45m, ed =  26396, ng =   2177   8.25%, nph = 3077Batch 1209:   41.80m, ed =  19486, ng =   1833   9.41%, nph = 2631Batch 1210:   41.18m, ed =  33083, ng =   2301   6.96%, nph = 3352Batch 1211:   41.20m, ed =  33083, ng =   2301   6.96%, nph = 3351Batch 1212:   41.32m, ed =  23680, ng =   2865  12.10%, nph = 4161Batch 1213:   40.45m, ed =  23683, ng =   2670  11.27%, nph = 3960Batch 1214:    0.37m, ed =      1, ng =      1Batch 1215:    1.77m, ed =      3, ng =      2Batch 1216:   50.53m, ed =  20133, ng =   3842  19.08%, nph = 4562Batch 1217:   50.53m, ed =  20133, ng =   3842  19.08%, nph = 4562Batch 1218:    0.63m, ed =      3, ng =      3Batch 1219:    0.62m, ed =      3, ng =      3Batch 1220:   39.75m, ed =  16861, ng =   2896  17.18%, nph = 4371Batch 1221:   47.47m, ed =  20455, ng =   2178  10.65%, nph = 2753Batch 1222:   43.68m, ed =  16100, ng =   2346  14.57%, nph = 3222Batch 1223:   43.68m, ed =  16100, ng =   2346  14.57%, nph = 3222Batch 1224:   41.05m, ed =  33109, ng =   1999   6.04%, nph = 2922Batch 1225:   38.60m, ed =  20668, ng =   2515  12.17%, nph = 3909Batch 1226:   43.00m, ed =  12315, ng =   4404  35.76%, nph = 6145Batch 1227:   43.00m, ed =  12315, ng =   4404  35.76%, nph = 6145Batch 1228:   46.95m, ed =  22639, ng =   1924   8.50%, nph = 2459Batch 1229:   44.00m, ed =  14463, ng =   3579  24.75%, nph = 4880Batch 1230:    0.62m, ed =      7, ng =      6Batch 1231:    0.40m, ed =      1, ng =      1Batch 1232:   42.50m, ed =  16701, ng =   3289  19.69%, nph = 4643Batch 1233:   42.63m, ed =  16701, ng =   3289  19.69%, nph = 4629Batch 1234:    0.58m, ed =      3, ng =      2Batch 1235:    0.48m, ed =      3, ng =      2Batch 1236:   41.70m, ed =  18410, ng =   2286  12.42%, nph = 3289Batch 1237:   42.07m, ed =  25948, ng =   3571  13.76%, nph = 5093Batch 1238:   44.75m, ed =  33487, ng =   2445   7.30%, nph = 3278Batch 1239:   44.88m, ed =  33487, ng =   2445   7.30%, nph = 3268Batch 1240:   45.97m, ed =  13315, ng =   3163  23.76%, nph = 4129Batch 1241:   42.78m, ed =  21133, ng =   3973  18.80%, nph = 5572Batch 1242:    0.42m, ed =      1, ng =      1Batch 1243:   40.40m, ed =  16132, ng =   4251  26.35%, nph = 6313Batch 1244:   40.27m, ed =  16132, ng =   4251  26.35%, nph = 6334Batch 1245:   38.80m, ed =  24502, ng =   1869   7.63%, nph = 2890Batch 1246:   38.12m, ed =  19783, ng =   2607  13.18%, nph = 4104Batch 1247:   51.30m, ed =  27142, ng =   2026   7.46%, nph = 2370Batch 1248:   51.40m, ed =  27142, ng =   2026   7.46%, nph = 2365Batch 1249:   38.77m, ed =  16799, ng =   1476   8.79%, nph = 2284Batch 1250:   37.23m, ed =  19808, ng =   3730  18.83%, nph = 6011Batch 1251:   36.53m, ed =  15054, ng =   4091  27.18%, nph = 6719Batch 1252:   37.42m, ed =  14904, ng =   3006  20.17%, nph = 4820Batch 1253:   46.92m, ed =  47748, ng =   1584   3.32%, nph = 2026Batch 1254:   47.02m, ed =  47748, ng =   1584   3.32%, nph = 2021------------------------------------------------------------------    Total : 5735.62m, ed =2942927, ng = 370870  12.60%, nph = 3880`

So Gen18Z is now roughly on a par with Gen18H (in "half-search" mode), but is actually running in "full-search" mode, so maybe it can do even better. Another round of tests is scheduled! Mathimagics
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Posts: 1538
Joined: 27 May 2015
Location: Canberra

### Re: Low/Hi Clue Thresholds

More good news, it seems!

I tested the same 3 seed grids with some parameter changes. NTEST is the limit on number of {-2,+2} tests done for each seed, ie batch, and HS is an option to operate in "half-search mode" (see above).

a) with NTEST = 2000 (the current default)
Code: Select all
`Batch 1239:   44.88m, ed =  33487, ng =   2445   7.30%, nph = 3268Batch 1240:   45.97m, ed =  13315, ng =   3163  23.76%, nph = 4129Batch 1241:   42.78m, ed =  21133, ng =   3973  18.80%, nph = 5572`

b) with NTEST = 3000
Code: Select all
`Batch 1239:   62.63m, ed =  54107, ng =   3808   7.04%, nph = 3648Batch 1240:   63.32m, ed =  19023, ng =   4592  24.14%, nph = 4351Batch 1241:   59.25m, ed =  31485, ng =   6051  19.22%, nph = 6128`

c) with NTEST = 3000 + HS
Code: Select all
`Batch 1239:   36.68m, ed =  41685, ng =   2991   7.18%, nph = 4892Batch 1240:   36.35m, ed =  14593, ng =   3362  23.04%, nph = 5549Batch 1241:   34.92m, ed =  27676, ng =   5133  18.55%, nph = 8820`

d) with NTEST = 5000 + HS
Code: Select all
`Batch 1239:   62.08m, ed =  64034, ng =   4529   7.07%, nph = 4377Batch 1240:   60.45m, ed =  20068, ng =   4839  24.11%, nph = 4803Batch 1241:   58.62m, ed =  41971, ng =   8050  19.18%, nph = 8240`

Test (b) indicates that we can increase NTEST without yield loss, in fact in all cases the NPH was actually increased.

Test (c) suggests that "half-search mode" finds fewer grids, which you would expect, but is much faster and produces even higher NPH. That's really good news!

Test (d) hints at diminishing returns for increased NTEST settings, but these are still very good yields. Mathimagics
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Posts: 1538
Joined: 27 May 2015
Location: Canberra

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