
This is data from running tests to see how CHECK_LIMIT affects the
time. The test was to solve a 5x5 puzzle with no initial data. Of
course this means a lot of guesswork is required. In each case the
answer obtained was the same, but there was a significant difference
in the time it took to get that solution.

Briefly:

check_limit:    3       4       5      6       7       8       9       10     11
time:           .49     .52     1.13   3.33    8.31    19.18   39.21    76.21 135.07

Using 2 ran for 6 minutes before I quit, so I set the minimum to 3.

For most puzzles this should not make much of a difference. They can
be solved by deducing without requiring guessing. If CHECK_LIMIT is
set too low they may start to guess rather than calculate all the
values.  This still may be the fastest way to do things.


Here is the full data. Notice the number of guesses is about the same
in each case, the number of failed guesses is very small in all cases,
and there are circuits all the way up to the top. (I deleted the
solutions since they were the same in each case. The solution is
included once at the bottom.)



8:17> time ./sudoku -l3 -5
Solved! list maximum was 43, there were 468 guesses
Looked at 3940 candidates, found 1507 circuits
Circuits:          1         2         3
                1452        10        45
0.40u 0.07s 0:00.49 95.9%

8:17> time ./sudoku -l4 -5
Solved! list maximum was 50, there were 470 guesses
Looked at 6395 candidates, found 1496 circuits
Circuits:          1         2         3         4
                1426        18        12        40
0.39u 0.07s 0:00.52 88.4%

8:17> time ./sudoku -l5 -5
Solved! list maximum was 59, there were 464 guesses
Looked at 9511 candidates, found 1486 circuits
Circuits:          1         2         3         4         5
                1405        20        14         9        38
0.96u 0.13s 0:01.13 96.4%

8:17> time ./sudoku -l6 -5
Solved! list maximum was 111, there were 466 guesses
Looked at 13862 candidates, found 1489 circuits
Circuits:          1         2         3         4         5         6
                1404        18        16        11        36         4
3.14u 0.14s 0:03.33 98.4%

8:17> time ./sudoku -l7 -5
Solved! list maximum was 111, there were 465 guesses
Looked at 19227 candidates, found 1488 circuits
Circuits:          1         2         3         4         5         6         7
                1402        18        16        11        35         3         3
8.20u 0.06s 0:08.31 99.3%
Command took 9 seconds

8:18> time ./sudoku -l8 -5
Solved! list maximum was 111, there were 465 guesses
Looked at 25826 candidates, found 1487 circuits
Circuits:          1         2         3         4         5         6         7         8
                1400        18        16        11        35         2         2         3
19.05u 0.10s 0:19.18 99.8%
Command took 19 seconds

8:18> time ./sudoku -l9 -5
Solved! list maximum was 123, there were 465 guesses
Looked at 33577 candidates, found 1487 circuits
Circuits:          1         2         3         4         5         6         7         8         9
                1400        18        16        11        35         2         1         3         1
39.06u 0.12s 0:39.21 99.9%
Command took 39 seconds

8:19> time ./sudoku -l10 -5
Solved! list maximum was 135, there were 464 guesses
Looked at 42485 candidates, found 1488 circuits
Circuits:          1         2         3         4         5         6         7         8         9        10
                1400        18        16        11        35         2         1         2         0         3
75.83u 0.20s 1:16.21 99.7%
Command took 1 minute 16 seconds

8:46> time ./sudoku -5 -l11
Solved! list maximum was 135
 there were 465 total guesses, 464 guesses in the solution
Looked at 52140 candidates, found 1489 circuits
Circuits:          1         2         3         4         5         6         7         8         9        10        11
                1400        18        16        11        35         2         1         2         0         2         2
134.94u 0.10s 2:15.07 99.9%
Command took 2 minutes 15 seconds


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	 |t s r q p|e d c b a|y x w v u|o n m l k|j i h g f|
	 |o n m l k|y x w v u|j i h g f|e d c b a|t s r q p|
	 |j i h g f|o n m l k|e d c b a|t s r q p|y x w v u|
	 |e d c b a|j i h g f|t s r q p|y x w v u|o n m l k|
	 ---------------------------------------------------
	 |x u y w v|p o n m t|h e l k s|d c g j r|a b f i q|
	 |i f e d c|b l u y s|a w t r q|n m o k x|p j v h g|
	 |p j g t q|k c e a v|d m n f b|l h i y w|s u x r o|
	 |b a l n h|x r i j d|v g o p c|s q f u t|w m y k e|
	 |r k s o m|g f q w h|x y u i j|b p e a v|n l t d c|
	 ---------------------------------------------------
	 |w y k j x|l q g i r|m f d e v|p u s h c|b o a n t|
	 |d c b f g|v u t n y|k h j o w|a l x r m|q p e s i|
	 |a v i r n|m j s h x|l q p u t|k b d o e|f c g y w|
	 |m o u e l|d b p f w|s c a y g|i v q t n|x r k j h|
	 |s p q h t|c a k e o|b r i x n|g f y w j|m v l u d|
	 ---------------------------------------------------
	 |v h x u o|q p y t b|i l s d m|w k n f g|c e j a r|
	 |n b d a e|w m f r g|u p k h y|v t j c i|l q o x s|
	 |l r t i s|a k j c e|f b g n x|q o p m h|u y d w v|
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	 |k w f c y|n v d u i|q j e a o|x r l s b|g h p t m|
	 ---------------------------------------------------
	 |c e o x r|i t b k q|p a f w l|h j v n s|d g u m y|
	 |u t v p d|r y a s m|c k q j i|f g b x o|h w n e l|
	 |g q a y i|u w v x c|n o b m h|r e t d l|k f s p j|
	 |h m n s b|f g l d j|r u y t e|c w k p q|v a i o x|
	 |f l j k w|h e o p n|g v x s d|m a u i y|r t q c b|
	 ---------------------------------------------------
