Les séquences démêlées pour vous

15 mars 2017

Un excellent résumé qui fait un tour d’horizon des séquences (et des particularités de chacunes) pour les bases de données les plus populaires.


MySQL en vrac (5)

16 février 2016

Un sondage sur le déploiment et la gestion de bases de données open source ici.

On vous demande votre utilisation des SQL Modes ici.

Une présentation sur PERFORMANCE_SCHEMA.

La taille du buffer pool : quelques précisions ici.

L’allocation de mémoire des buffers pour le performance schema dans MySQL 5.7 : quelques conseils.

La perte de données au démarrage de MySQL : des explications.


Bases de données et Pharo

4 avril 2015

Un article datant de janvier mais qui reste d’actualité tant on peut constater un intérêt soudain et marqué pour Pharo 4 et les moyens de persister des données sur les mailing lists ces temps-ci.


Enterprise NoSQL for Dummies

7 juillet 2014

La version de Enterprise NoSQL for Dummies (fichier PDF de 75 pages) de MarkLogic est gratuitement téléchargeable ici.  Dépêchez-vous!  C’est concis et bien expliqué.


Comment presser un citron (troisième partie)

27 mai 2013

1. Un problème n’arrive jamais seul

Dans la deuxième partie de cet article (le premier article étant ici), nous nous sommes laissés sur un exemple extrême (i.e. une grille avec des lignes et des colonnes vides) afin de vérifier la validité et l’efficacité de la solution présentée dans un des pires scénarios envisageable :

Avant même de débuter, rappelez-vous qu’il est primordial d’exécuter la commande suivante dans votre session pour éviter d’avoir à attendre une éternité, que ce soit pour la requête SQL ou pour un EXPLAIN!

set @@optimizer_search_depth = 3;

Qu’arriverait-il si nous avions à solutionner un sudoku contenant à la fois des lignes et des colonnes vides, comme dans l’exemple ci-haut avec la requête suivante:

SELECT *
FROM sudoku_combined_view
WHERE
(r2c2 = 3) AND (r2c3 = 4) AND (r2c4 = 8) AND (r2c5 = 2) AND
(r2c6 = 5) AND (r2c7 = 6) AND (r2c8 = 9) AND (r3c2 = 5) AND
(r3c3 = 9) AND (r3c4 = 3) AND (r3c5 = 6) AND (r3c6 = 4) AND
(r3c7 = 1) AND (r3c8 = 8) AND (r4c2 = 9) AND (r4c3 = 7) AND
(r4c4 = 1) AND (r4c5 = 8) AND (r4c6 = 2) AND (r4c7 = 5) AND
(r4c8 = 6) AND (r6c2 = 8) AND (r6c3 = 1) AND (r6c4 = 4) AND
(r6c5 = 7) AND (r6c6 = 6) AND (r6c7 = 2) AND (r6c8 = 3) AND
(r7c2 = 2) AND (r7c3 = 5) AND (r7c4 = 6) AND (r7c5 = 4) AND
(r7c6 = 1) AND (r7c7 = 9) AND (r7c8 = 7) AND (r8c2 = 7) AND
(r8c3 = 6) AND (r8c4 = 5) AND (r8c5 = 3) AND (r8c6 = 8) AND
(r8c7 = 4) AND (r8c8 = 2);

Examinons le résultat du EXPLAIN pour la grille en question:

+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+----------------------------------------------------------+
| id | select_type | table | type        | possible_keys                                                                                                                                      | key         | key_len | ref                           | rows | Extra                                                    |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+----------------------------------------------------------+
|  1 | SIMPLE      | col3  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i38,i48 | 2,2,2   | NULL                          |   64 | Using intersect(i23,i38,i48); Using where                |
|  1 | SIMPLE      | r2    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i58     | 2,2     | NULL                          |   68 | Using intersect(i23,i58); Using where; Using join buffer |
|  1 | SIMPLE      | r3    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i56     | 2,2     | NULL                          |   68 | Using intersect(i78,i56); Using where; Using join buffer |
|  1 | SIMPLE      | r4    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i38,i46     | 2,2     | NULL                          |   68 | Using intersect(i38,i46); Using where; Using join buffer |
|  1 | SIMPLE      | r6    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i67     | 2,2     | NULL                          |   68 | Using intersect(i23,i67); Using where; Using join buffer |
|  1 | SIMPLE      | r7    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i38,i56     | 2,2     | NULL                          |   68 | Using intersect(i38,i56); Using where; Using join buffer |
|  1 | SIMPLE      | r8    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer |
|  1 | SIMPLE      | col2  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer |
|  1 | SIMPLE      | col4  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i46     | 2,2     | NULL                          |   68 | Using intersect(i78,i46); Using where; Using join buffer |
|  1 | SIMPLE      | col5  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer |
|  1 | SIMPLE      | col6  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i67     | 2,2     | NULL                          |   68 | Using intersect(i23,i67); Using where; Using join buffer |
|  1 | SIMPLE      | col7  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer |
|  1 | SIMPLE      | col8  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i24     | 2,2     | NULL                          |   68 | Using intersect(i37,i24); Using where; Using join buffer |
|  1 | SIMPLE      | col1  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23         | 2       | sudoku.r2.c1,sudoku.r3.c1     | 5040 | Using where                                              |
|  1 | SIMPLE      | r1    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c1,sudoku.col2.c1 | 5040 | Using where                                              |
|  1 | SIMPLE      | r5    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c5,sudoku.col2.c5 | 5040 | Using where                                              |
|  1 | SIMPLE      | r9    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c9,sudoku.col2.c9 | 5040 | Using where                                              |
|  1 | SIMPLE      | col9  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.r1.c9,sudoku.r2.c9     | 5040 | Using where                                              |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+----------------------------------------------------------+
18 rows in set (0.20 sec)

À première vue, tout semble correct! Aucun table scan et les indexes sont utilisés pour chaque colonne et chaque rangée non vide!

Et en combien de temps MySQL peut-il « solutionner » cette grille ?

Fantastique!  1.5 seconde!  Tout est réglé!  Malheureusement, non…

2. Le pire scénario possible

Il existe une catégorie de sudokus que nombre de mathématiciens et d’informaticiens étudient depuis des années : ces grilles minimales n’ont seulement que 17 révélés, le minimum théorique (une conjecture encore non prouvée de façon mathématique par Gary McGuire, Bastian Tugemann et Gilles Civario, un autre intéressant article ici) pouvant mener à une solution unique.  Plusieurs de ces grilles spéciales (17 révélés) sont depuis des années compilées par Gordon Royle, professeur à l’université d’Australie Occidentale.

Comme celle-ci :

Vous remarquerez que cette grille ne contient aucune ligne ni aucune colonne vide! Essayons donc de voir en combien de temps MySQL pourra résoudre celle-ci :

mysql> SELECT *
 -> FROM sudoku_combined_view
 -> WHERE
 -> (r1c8 = 1) AND
 -> (r2c1 = 4) AND
 -> (r3c2 = 2) AND
 -> (r4c5 = 5) AND
 -> (r4c7 = 4) AND
 -> (r4c9 = 7) AND
 -> (r5c3 = 8) AND
 -> (r5c7 = 3) AND
 -> (r6c3 = 1) AND
 -> (r6c5 = 9) AND
 -> (r7c1 = 3) AND
 -> (r7c4 = 4) AND
 -> (r7c7 = 2) AND
 -> (r8c2 = 5) AND
 -> (r8c4 = 1) AND
 -> (r9c4 = 8) AND
 -> (r9c6 = 6);
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| r1c1 | r1c2 | r1c3 | r1c4 | r1c5 | r1c6 | r1c7 | r1c8 | r1c9 | r2c1 | r2c2 | r2c3 | r2c4 | r2c5 | r2c6 | r2c7 | r2c8 | r2c9 | r3c1 | r3c2 | r3c3 | r3c4 | r3c5 | r3c6 | r3c7 | r3c8 | r3c9 | r4c1 | r4c2 | r4c3 | r4c4 | r4c5 | r4c6 | r4c7 | r4c8 | r4c9 | r5c1 | r5c2 | r5c3 | r5c4 | r5c5 | r5c6 | r5c7 | r5c8 | r5c9 | r6c1 | r6c2 | r6c3 | r6c4 | r6c5 | r6c6 | r6c7 | r6c8 | r6c9 | r7c1 | r7c2 | r7c3 | r7c4 | r7c5 | r7c6 | r7c7 | r7c8 | r7c9 | r8c1 | r8c2 | r8c3 | r8c4 | r8c5 | r8c6 | r8c7 | r8c8 | r8c9 | r9c1 | r9c2 | r9c3 | r9c4 | r9c5 | r9c6 | r9c7 | r9c8 | r9c9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
|   6  |   9  |   3  |   7  |   8  |   4  |   5  |   1  |   2  |   4  |   8  |   7  |   5  |   1  |   2  |   9  |   3  |   6  |   1  |   2  |   5  |   9  |   6  |   3  |   8  |   7  |   4  |   9  |   3  |   2  |   6  |   5  |   1  |   4  |   8  |   7  |   5  |   6  |   8  |   2  |   4  |   7  |   3  |   9  |   1  |   7  |   4  |   1  |   3  |   9  |   8  |   6  |   2  |   5  |   3  |   1  |   9  |   4  |   7  |   5  |   2  |   6  |   8  |   8  |   5  |   6  |   1  |   2  |   9  |   7  |   4  |   3  |   2  |   7  |   4  |   8  |   3  |   6  |   1  |   5  |   9  |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
1 row in set (2 min 20.83 sec)

Ouch!  Je ne suis pas arrivé à descendre sour la barre des 40 secondes malgré mes tentatives répétées et ce, sur différents serveurs avec différentes configurations (et même différentes autres grilles de 17 révélés). Les résultats pour solutionner cette grille vont de près de 40 secondes à plus de 33 minutes. Le résultat du EXPLAIN parle par lui-même :

+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+---------+---------+-------------------------------+------+----------------------------------------------------------+
| id | select_type | table | type        | possible_keys                                                                                                                                      | key     | key_len | ref                           | rows | Extra                                                    |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+---------+---------+-------------------------------+------+----------------------------------------------------------+
|  1 | SIMPLE      | r4    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i57,i59 | 2,2     | NULL                          |  624 | Using intersect(i57,i59); Using where                    |
|  1 | SIMPLE      | r7    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i14,i47 | 2,2     | NULL                          |  624 | Using intersect(i14,i47); Using where; Using join buffer |
|  1 | SIMPLE      | col4  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i89 | 2,2     | NULL                          |  624 | Using intersect(i78,i89); Using where; Using join buffer |
|  1 | SIMPLE      | col7  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i45,i47 | 2,2     | NULL                          |  624 | Using intersect(i45,i47); Using where; Using join buffer |
|  1 | SIMPLE      | r8    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i24     | 2       | const,const                   | 5000 | Using where                                              |
|  1 | SIMPLE      | r9    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i46     | 2       | const,const                   | 5001 | Using where                                              |
|  1 | SIMPLE      | col1  | range       | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i27     | 2       | NULL                          | 5000 | Using where; Using join buffer                           |
|  1 | SIMPLE      | r5    | range       | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37     | 2       | NULL                          | 5001 | Using where; Using join buffer                           |
|  1 | SIMPLE      | r6    | range       | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i35     | 2       | NULL                          | 5001 | Using where; Using join buffer                           |
|  1 | SIMPLE      | col3  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i45     | 2       | sudoku.r4.c3,const            | 5040 | Using where                                              |
|  1 | SIMPLE      | col2  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i34     | 2       | const,sudoku.r4.c2            | 5040 | Using where                                              |
|  1 | SIMPLE      | r2    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | const,sudoku.col2.c2          | 5040 | Using where                                              |
|  1 | SIMPLE      | col5  | range       | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i46     | 2       | NULL                          | 5001 | Using where; Using join buffer                           |
|  1 | SIMPLE      | r3    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | sudoku.col1.c3,const          | 5040 | Using where                                              |
|  1 | SIMPLE      | col8  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | const,sudoku.r2.c8            | 5040 | Using where                                              |
|  1 | SIMPLE      | r1    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | sudoku.col1.c1,sudoku.col2.c1 | 5040 | Using where                                              |
|  1 | SIMPLE      | col9  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | sudoku.r1.c9,sudoku.r2.c9     | 5040 | Using where                                              |
|  1 | SIMPLE      | col6  | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12     | 2       | sudoku.r1.c6,sudoku.r2.c6     | 5040 | Using where                                              |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+---------+---------+-------------------------------+------+----------------------------------------------------------+
18 rows in set (2.59 sec)

Observez la colonne rows dans le résultat du EXPLAIN pour comprendre le nombre astronomique de jointures possibles que MySQL aura à effectuer et à tester…  Dans la très grande majorité des cas, ce chiffre est supérieur à 5000!

Il devient maintenant évident que notre solution ne tient plus la route…

3. Ne pas céder au découragement!

Il existe bon nombre d’autres possibilités d’optimisations que nous n’avons toujours pas envisagées.  Par exemple, dans certains cas il pourrait être avantageux de chercher par boîtes (carré de 3×3 dans le sudoku).  Certaines grilles de 17 révélés pourraient grandement en bénéficier mais il nous faudrait alors joindre 27 tables!  Ce qui est gagné d’un côté est perdu de l’autre.

Nous pourrions également créer des partitions mais dans ce cas, quelles seraient les chances qu’une colonne ou une rangée contienne la donnée permettant de discriminer et de choisir la partition requise?

Nous pourrions augmenter la taille de l’index pour passer de 2 colones à 3 mais l’impact de cette mesure serait inutile pour les grilles de 17 révélés.

Qu’arriverait-il si nous passions du format de table MyISAM à InnoDb ?  Absolument rien, le problème demeure entier : MySQL n’est pas assez rapide pour lire les données (ou les indexes) sur disque puis les joindre efficacement dans un cas aussi extrême.

L’idée à la base de cette série d’article était d’arriver à solutionner un sudoku valide en n’utilisant que du SQL.  Un sudoku valide, par définition, a une seule solution.  Nous aurions pu ajouter LIMIT 1 à chacune de nos vues mais hélas, ce faisant, nos vues seraient contraintes d’utiliser l’algorithme TEMPTABLE au lieu de MERGE, ce qui serait catastrophique!

Évidemment, quelques autres astuces existent, comme augmenter la taille des variables key_buffer_size et join_buffer_size, diminuer la valeur du optimizer_search_depth, etc.  Évidemment dans le cas des 2 premières variables, je ne peux rien vous suggérer comme ces paramètres dépendent de la mémoire RAM disponible sur votre machine, le système d’exploitation utilisé, etc.  Quant à la valeur de la variable optimizer_search_depth, diminuer celle-ci n’aura pas d’impact significatif comme le problème réside dans la lenteur des accès au disque dur et au nombre effarant de jointures et de rangées à examnier (et à retrouver puis lire).

4. Éplucher toutes les options

Il existe un type de table, MEMORY, en MySQL qui nous permettrait d’éviter d’avoir à lire les données (ou les indexes) sur disque, ce qui pourrait avoir un impact majeur dans notre cas.  Nous allons donc créer cette table en mémoire et la remplir tout en créant les indexes nécessaires (exactement les mêmes vues et indexes que la table de format MyISAM).

Mais avant de procéder, prenez bien soin de vous assurez que la variable max_heap_table_size soit supérieure à 216Mb ( 226492416) sinon vous vous heurterez à une tonne d’erreurs 1114 (table full).  Si ce n’est pas le cas, vous pouvez fixer la valeur de cette variable à 216Mb comme suit :

set @@max_heap_table_size =  226492416;

Une fois cette précaution prise, construisez la table et les indexes nécessaires comme suit:

USE sudoku;

DROP TABLE IF EXISTS positions_memory;
CREATE TABLE positions_memory (
 c1 TINYINT UNSIGNED NOT NULL,
 c2 TINYINT UNSIGNED NOT NULL,
 c3 TINYINT UNSIGNED NOT NULL,
 c4 TINYINT UNSIGNED NOT NULL,
 c5 TINYINT UNSIGNED NOT NULL,
 c6 TINYINT UNSIGNED NOT NULL,
 c7 TINYINT UNSIGNED NOT NULL,
 c8 TINYINT UNSIGNED NOT NULL,
 c9 TINYINT UNSIGNED NOT NULL
) ENGINE=MEMORY;

INSERT INTO positions_memory (c1, c2, c3, c4, c5, c6, c7, c8, c9)
SELECT c1, c2, c3, c4, c5, c6, c7, c8, c9 FROM positions;

CREATE INDEX i12 ON positions_memory(c1, c2) USING HASH; CREATE INDEX i13 ON positions_memory(c1, c3) USING HASH;
CREATE INDEX i14 ON positions_memory(c1, c4) USING HASH; CREATE INDEX i15 ON positions_memory(c1, c5) USING HASH;
CREATE INDEX i16 ON positions_memory(c1, c6) USING HASH; CREATE INDEX i17 ON positions_memory(c1, c7) USING HASH;
CREATE INDEX i18 ON positions_memory(c1, c8) USING HASH; CREATE INDEX i19 ON positions_memory(c1, c9) USING HASH;
CREATE INDEX i23 ON positions_memory(c2, c3) USING HASH; CREATE INDEX i24 ON positions_memory(c2, c4) USING HASH;
CREATE INDEX i25 ON positions_memory(c2, c5) USING HASH; CREATE INDEX i26 ON positions_memory(c2, c6) USING HASH;
CREATE INDEX i27 ON positions_memory(c2, c7) USING HASH; CREATE INDEX i28 ON positions_memory(c2, c8) USING HASH;
CREATE INDEX i29 ON positions_memory(c2, c9) USING HASH; CREATE INDEX i34 ON positions_memory(c3, c4) USING HASH;
CREATE INDEX i35 ON positions_memory(c3, c5) USING HASH; CREATE INDEX i36 ON positions_memory(c3, c6) USING HASH;
CREATE INDEX i37 ON positions_memory(c3, c7) USING HASH; CREATE INDEX i38 ON positions_memory(c3, c8) USING HASH;
CREATE INDEX i39 ON positions_memory(c3, c9) USING HASH; CREATE INDEX i45 ON positions_memory(c4, c5) USING HASH;
CREATE INDEX i46 ON positions_memory(c4, c6) USING HASH; CREATE INDEX i47 ON positions_memory(c4, c7) USING HASH;
CREATE INDEX i48 ON positions_memory(c4, c8) USING HASH; CREATE INDEX i49 ON positions_memory(c4, c9) USING HASH;
CREATE INDEX i56 ON positions_memory(c5, c6) USING HASH; CREATE INDEX i57 ON positions_memory(c5, c7) USING HASH;
CREATE INDEX i58 ON positions_memory(c5, c8) USING HASH; CREATE INDEX i59 ON positions_memory(c5, c9) USING HASH;
CREATE INDEX i67 ON positions_memory(c6, c7) USING HASH; CREATE INDEX i68 ON positions_memory(c6, c8) USING HASH;
CREATE INDEX i69 ON positions_memory(c6, c9) USING HASH; CREATE INDEX i78 ON positions_memory(c7, c8) USING HASH;
CREATE INDEX i79 ON positions_memory(c7, c9) USING HASH; CREATE INDEX i89 ON positions_memory(c8, c9) USING HASH;
CREATE INDEX i9 ON positions_memory(c9) USING HASH;

Maintenant, il s’agit de recréer les trois mêmes vues que nous avons créées pour le type de table MYISAM mais pour notre nouvelle table.

En premier lieu, la vue sur les rangées.

USE sudoku;

DROP VIEW IF EXISTS sudoku_memory_rows_view;
CREATE VIEW sudoku_memory_rows_view AS
SELECT
r1.c1 as r1c1, r1.c2 as r1c2, r1.c3 as r1c3, r1.c4 as r1c4, r1.c5 as r1c5, r1.c6 as r1c6, r1.c7 as r1c7, r1.c8 as r1c8, r1.c9 as r1c9, r2.c1 as r2c1,
r2.c2 as r2c2, r2.c3 as r2c3, r2.c4 as r2c4, r2.c5 as r2c5, r2.c6 as r2c6, r2.c7 as r2c7, r2.c8 as r2c8, r2.c9 as r2c9, r3.c1 as r3c1, r3.c2 as r3c2,
r3.c3 as r3c3, r3.c4 as r3c4, r3.c5 as r3c5, r3.c6 as r3c6, r3.c7 as r3c7, r3.c8 as r3c8, r3.c9 as r3c9, r4.c1 as r4c1, r4.c2 as r4c2, r4.c3 as r4c3,
r4.c4 as r4c4, r4.c5 as r4c5, r4.c6 as r4c6, r4.c7 as r4c7, r4.c8 as r4c8, r4.c9 as r4c9, r5.c1 as r5c1, r5.c2 as r5c2, r5.c3 as r5c3, r5.c4 as r5c4,
r5.c5 as r5c5, r5.c6 as r5c6, r5.c7 as r5c7, r5.c8 as r5c8, r5.c9 as r5c9, r6.c1 as r6c1, r6.c2 as r6c2, r6.c3 as r6c3, r6.c4 as r6c4, r6.c5 as r6c5,
r6.c6 as r6c6, r6.c7 as r6c7, r6.c8 as r6c8, r6.c9 as r6c9, r7.c1 as r7c1, r7.c2 as r7c2, r7.c3 as r7c3, r7.c4 as r7c4, r7.c5 as r7c5, r7.c6 as r7c6,
r7.c7 as r7c7, r7.c8 as r7c8, r7.c9 as r7c9, r8.c1 as r8c1, r8.c2 as r8c2, r8.c3 as r8c3, r8.c4 as r8c4, r8.c5 as r8c5, r8.c6 as r8c6, r8.c7 as r8c7,
r8.c8 as r8c8, r8.c9 as r8c9, r9.c1 as r9c1, r9.c2 as r9c2, r9.c3 as r9c3, r9.c4 as r9c4, r9.c5 as r9c5, r9.c6 as r9c6, r9.c7 as r9c7, r9.c8 as r9c8,
r9.c9 as r9c9

FROM
positions_memory r1, positions_memory r2, positions_memory r3,
positions_memory r4, positions_memory r5, positions_memory r6,
positions_memory r7, positions_memory r8, positions_memory r9

WHERE
-- Nombres uniques dans chaque colonne
(r1.c1 <> r2.c1) AND (r1.c1 <> r3.c1) AND (r1.c1 <> r4.c1) AND (r1.c1 <> r5.c1) AND (r1.c1 <> r6.c1) AND (r1.c1 <> r7.c1) AND (r1.c1 <> r8.c1) AND (r1.c1 <> r9.c1) AND (r1.c2 <> r2.c2) AND (r1.c2 <> r3.c2) AND (r1.c2 <> r4.c2) AND (r1.c2 <> r5.c2) AND (r1.c2 <> r6.c2) AND (r1.c2 <> r7.c2) AND (r1.c2 <> r8.c2) AND (r1.c2 <> r9.c2) AND
(r1.c3 <> r2.c3) AND (r1.c3 <> r3.c3) AND (r1.c3 <> r4.c3) AND (r1.c3 <> r5.c3) AND (r1.c3 <> r6.c3) AND (r1.c3 <> r7.c3) AND (r1.c3 <> r8.c3) AND (r1.c3 <> r9.c3) AND (r1.c4 <> r2.c4) AND (r1.c4 <> r3.c4) AND (r1.c4 <> r4.c4) AND (r1.c4 <> r5.c4) AND (r1.c4 <> r6.c4) AND (r1.c4 <> r7.c4) AND (r1.c4 <> r8.c4) AND (r1.c4 <> r9.c4) AND
(r1.c5 <> r2.c5) AND (r1.c5 <> r3.c5) AND (r1.c5 <> r4.c5) AND (r1.c5 <> r5.c5) AND (r1.c5 <> r6.c5) AND (r1.c5 <> r7.c5) AND (r1.c5 <> r8.c5) AND (r1.c5 <> r9.c5) AND (r1.c6 <> r2.c6) AND (r1.c6 <> r3.c6) AND (r1.c6 <> r4.c6) AND (r1.c6 <> r5.c6) AND (r1.c6 <> r6.c6) AND (r1.c6 <> r7.c6) AND (r1.c6 <> r8.c6) AND (r1.c6 <> r9.c6) AND
(r1.c7 <> r2.c7) AND (r1.c7 <> r3.c7) AND (r1.c7 <> r4.c7) AND (r1.c7 <> r5.c7) AND (r1.c7 <> r6.c7) AND (r1.c7 <> r7.c7) AND (r1.c7 <> r8.c7) AND (r1.c7 <> r9.c7) AND (r1.c8 <> r2.c8) AND (r1.c8 <> r3.c8) AND (r1.c8 <> r4.c8) AND (r1.c8 <> r5.c8) AND (r1.c8 <> r6.c8) AND (r1.c8 <> r7.c8) AND (r1.c8 <> r8.c8) AND (r1.c8 <> r9.c8) AND
(r1.c9 <> r2.c9) AND (r1.c9 <> r3.c9) AND (r1.c9 <> r4.c9) AND (r1.c9 <> r5.c9) AND (r1.c9 <> r6.c9) AND (r1.c9 <> r7.c9) AND (r1.c9 <> r8.c9) AND (r1.c9 <> r9.c9) AND (r2.c1 <> r3.c1) AND (r2.c1 <> r4.c1) AND (r2.c1 <> r5.c1) AND (r2.c1 <> r6.c1) AND (r2.c1 <> r7.c1) AND (r2.c1 <> r8.c1) AND (r2.c1 <> r9.c1) AND (r2.c2 <> r3.c2) AND
(r2.c2 <> r4.c2) AND (r2.c2 <> r5.c2) AND (r2.c2 <> r6.c2) AND (r2.c2 <> r7.c2) AND (r2.c2 <> r8.c2) AND (r2.c2 <> r9.c2) AND (r2.c3 <> r3.c3) AND (r2.c3 <> r4.c3) AND (r2.c3 <> r5.c3) AND (r2.c3 <> r6.c3) AND (r2.c3 <> r7.c3) AND (r2.c3 <> r8.c3) AND (r2.c3 <> r9.c3) AND (r2.c4 <> r3.c4) AND (r2.c4 <> r4.c4) AND (r2.c4 <> r5.c4) AND
(r2.c4 <> r6.c4) AND (r2.c4 <> r7.c4) AND (r2.c4 <> r8.c4) AND (r2.c4 <> r9.c4) AND (r2.c5 <> r3.c5) AND (r2.c5 <> r4.c5) AND (r2.c5 <> r5.c5) AND (r2.c5 <> r6.c5) AND (r2.c5 <> r7.c5) AND (r2.c5 <> r8.c5) AND (r2.c5 <> r9.c5) AND (r2.c6 <> r3.c6) AND (r2.c6 <> r4.c6) AND (r2.c6 <> r5.c6) AND (r2.c6 <> r6.c6) AND (r2.c6 <> r7.c6) AND
(r2.c6 <> r8.c6) AND (r2.c6 <> r9.c6) AND (r2.c7 <> r3.c7) AND (r2.c7 <> r4.c7) AND (r2.c7 <> r5.c7) AND (r2.c7 <> r6.c7) AND (r2.c7 <> r7.c7) AND (r2.c7 <> r8.c7) AND (r2.c7 <> r9.c7) AND (r2.c8 <> r3.c8) AND (r2.c8 <> r4.c8) AND (r2.c8 <> r5.c8) AND (r2.c8 <> r6.c8) AND (r2.c8 <> r7.c8) AND (r2.c8 <> r8.c8) AND (r2.c8 <> r9.c8) AND
(r2.c9 <> r3.c9) AND (r2.c9 <> r4.c9) AND (r2.c9 <> r5.c9) AND (r2.c9 <> r6.c9) AND (r2.c9 <> r7.c9) AND (r2.c9 <> r8.c9) AND (r2.c9 <> r9.c9) AND (r3.c1 <> r4.c1) AND (r3.c1 <> r5.c1) AND (r3.c1 <> r6.c1) AND (r3.c1 <> r7.c1) AND (r3.c1 <> r8.c1) AND (r3.c1 <> r9.c1) AND (r3.c2 <> r4.c2) AND (r3.c2 <> r5.c2) AND (r3.c2 <> r6.c2) AND
(r3.c2 <> r7.c2) AND (r3.c2 <> r8.c2) AND (r3.c2 <> r9.c2) AND (r3.c3 <> r4.c3) AND (r3.c3 <> r5.c3) AND (r3.c3 <> r6.c3) AND (r3.c3 <> r7.c3) AND (r3.c3 <> r8.c3) AND (r3.c3 <> r9.c3) AND (r3.c4 <> r4.c4) AND (r3.c4 <> r5.c4) AND (r3.c4 <> r6.c4) AND (r3.c4 <> r7.c4) AND (r3.c4 <> r8.c4) AND (r3.c4 <> r9.c4) AND (r3.c5 <> r4.c5) AND
(r3.c5 <> r5.c5) AND (r3.c5 <> r6.c5) AND (r3.c5 <> r7.c5) AND (r3.c5 <> r8.c5) AND (r3.c5 <> r9.c5) AND (r3.c6 <> r4.c6) AND (r3.c6 <> r5.c6) AND (r3.c6 <> r6.c6) AND (r3.c6 <> r7.c6) AND (r3.c6 <> r8.c6) AND (r3.c6 <> r9.c6) AND (r3.c7 <> r4.c7) AND (r3.c7 <> r5.c7) AND (r3.c7 <> r6.c7) AND (r3.c7 <> r7.c7) AND (r3.c7 <> r8.c7) AND
(r3.c7 <> r9.c7) AND (r3.c8 <> r4.c8) AND (r3.c8 <> r5.c8) AND (r3.c8 <> r6.c8) AND (r3.c8 <> r7.c8) AND (r3.c8 <> r8.c8) AND (r3.c8 <> r9.c8) AND (r3.c9 <> r4.c9) AND (r3.c9 <> r5.c9) AND (r3.c9 <> r6.c9) AND (r3.c9 <> r7.c9) AND (r3.c9 <> r8.c9) AND (r3.c9 <> r9.c9) AND (r4.c1 <> r5.c1) AND (r4.c1 <> r6.c1) AND (r4.c1 <> r7.c1) AND
(r4.c1 <> r8.c1) AND (r4.c1 <> r9.c1) AND (r4.c2 <> r5.c2) AND (r4.c2 <> r6.c2) AND (r4.c2 <> r7.c2) AND (r4.c2 <> r8.c2) AND (r4.c2 <> r9.c2) AND (r4.c3 <> r5.c3) AND (r4.c3 <> r6.c3) AND (r4.c3 <> r7.c3) AND (r4.c3 <> r8.c3) AND (r4.c3 <> r9.c3) AND (r4.c4 <> r5.c4) AND (r4.c4 <> r6.c4) AND (r4.c4 <> r7.c4) AND (r4.c4 <> r8.c4) AND
(r4.c4 <> r9.c4) AND (r4.c5 <> r5.c5) AND (r4.c5 <> r6.c5) AND (r4.c5 <> r7.c5) AND (r4.c5 <> r8.c5) AND (r4.c5 <> r9.c5) AND (r4.c6 <> r5.c6) AND (r4.c6 <> r6.c6) AND (r4.c6 <> r7.c6) AND (r4.c6 <> r8.c6) AND (r4.c6 <> r9.c6) AND (r4.c7 <> r5.c7) AND (r4.c7 <> r6.c7) AND (r4.c7 <> r7.c7) AND (r4.c7 <> r8.c7) AND (r4.c7 <> r9.c7) AND
(r4.c8 <> r5.c8) AND (r4.c8 <> r6.c8) AND (r4.c8 <> r7.c8) AND (r4.c8 <> r8.c8) AND (r4.c8 <> r9.c8) AND (r4.c9 <> r5.c9) AND (r4.c9 <> r6.c9) AND (r4.c9 <> r7.c9) AND (r4.c9 <> r8.c9) AND (r4.c9 <> r9.c9) AND (r5.c1 <> r6.c1) AND (r5.c1 <> r7.c1) AND (r5.c1 <> r8.c1) AND (r5.c1 <> r9.c1) AND (r5.c2 <> r6.c2) AND (r5.c2 <> r7.c2) AND
(r5.c2 <> r8.c2) AND (r5.c2 <> r9.c2) AND (r5.c3 <> r6.c3) AND (r5.c3 <> r7.c3) AND (r5.c3 <> r8.c3) AND (r5.c3 <> r9.c3) AND (r5.c4 <> r6.c4) AND (r5.c4 <> r7.c4) AND (r5.c4 <> r8.c4) AND (r5.c4 <> r9.c4) AND (r5.c5 <> r6.c5) AND (r5.c5 <> r7.c5) AND (r5.c5 <> r8.c5) AND (r5.c5 <> r9.c5) AND (r5.c6 <> r6.c6) AND (r5.c6 <> r7.c6) AND
(r5.c6 <> r8.c6) AND (r5.c6 <> r9.c6) AND (r5.c7 <> r6.c7) AND (r5.c7 <> r7.c7) AND (r5.c7 <> r8.c7) AND (r5.c7 <> r9.c7) AND (r5.c8 <> r6.c8) AND (r5.c8 <> r7.c8) AND (r5.c8 <> r8.c8) AND (r5.c8 <> r9.c8) AND (r5.c9 <> r6.c9) AND (r5.c9 <> r7.c9) AND (r5.c9 <> r8.c9) AND (r5.c9 <> r9.c9) AND (r6.c1 <> r7.c1) AND (r6.c1 <> r8.c1) AND
(r6.c1 <> r9.c1) AND (r6.c2 <> r7.c2) AND (r6.c2 <> r8.c2) AND (r6.c2 <> r9.c2) AND (r6.c3 <> r7.c3) AND (r6.c3 <> r8.c3) AND (r6.c3 <> r9.c3) AND (r6.c4 <> r7.c4) AND (r6.c4 <> r8.c4) AND (r6.c4 <> r9.c4) AND (r6.c5 <> r7.c5) AND (r6.c5 <> r8.c5) AND (r6.c5 <> r9.c5) AND (r6.c6 <> r7.c6) AND (r6.c6 <> r8.c6) AND (r6.c6 <> r9.c6) AND
(r6.c7 <> r7.c7) AND (r6.c7 <> r8.c7) AND (r6.c7 <> r9.c7) AND (r6.c8 <> r7.c8) AND (r6.c8 <> r8.c8) AND (r6.c8 <> r9.c8) AND (r6.c9 <> r7.c9) AND (r6.c9 <> r8.c9) AND (r6.c9 <> r9.c9) AND (r7.c1 <> r8.c1) AND (r7.c1 <> r9.c1) AND (r7.c2 <> r8.c2) AND (r7.c2 <> r9.c2) AND (r7.c3 <> r8.c3) AND (r7.c3 <> r9.c3) AND (r7.c4 <> r8.c4) AND
(r7.c4 <> r9.c4) AND (r7.c5 <> r8.c5) AND (r7.c5 <> r9.c5) AND (r7.c6 <> r8.c6) AND (r7.c6 <> r9.c6) AND (r7.c7 <> r8.c7) AND (r7.c7 <> r9.c7) AND (r7.c8 <> r8.c8) AND (r7.c8 <> r9.c8) AND (r7.c9 <> r8.c9) AND (r7.c9 <> r9.c9) AND (r8.c1 <> r9.c1) AND (r8.c2 <> r9.c2) AND (r8.c3 <> r9.c3) AND (r8.c4 <> r9.c4) AND (r8.c5 <> r9.c5) AND
(r8.c6 <> r9.c6) AND (r8.c7 <> r9.c7) AND (r8.c8 <> r9.c8) AND (r8.c9 <> r9.c9) AND
-- Nombres uniques dans chaque maison de 3x3
(r1.c1 <> r2.c2) AND (r1.c1 <> r2.c3) AND (r1.c1 <> r3.c2) AND (r1.c1 <> r3.c3) AND (r1.c2 <> r2.c1) AND (r1.c2 <> r2.c3) AND (r1.c2 <> r3.c1) AND (r1.c2 <> r3.c3) AND (r1.c3 <> r2.c1) AND (r1.c3 <> r2.c2) AND (r1.c3 <> r3.c1) AND (r1.c3 <> r3.c2) AND (r1.c4 <> r2.c5) AND (r1.c4 <> r2.c6) AND (r1.c4 <> r3.c5) AND (r1.c4 <> r3.c6) AND
(r1.c5 <> r2.c4) AND (r1.c5 <> r2.c6) AND (r1.c5 <> r3.c4) AND (r1.c5 <> r3.c6) AND (r1.c6 <> r2.c4) AND (r1.c6 <> r2.c5) AND (r1.c6 <> r3.c4) AND (r1.c6 <> r3.c5) AND (r1.c7 <> r2.c8) AND (r1.c7 <> r2.c9) AND (r1.c7 <> r3.c8) AND (r1.c7 <> r3.c9) AND (r1.c8 <> r2.c7) AND (r1.c8 <> r2.c9) AND (r1.c8 <> r3.c7) AND (r1.c8 <> r3.c9) AND
(r1.c9 <> r2.c7) AND (r1.c9 <> r2.c8) AND (r1.c9 <> r3.c7) AND (r1.c9 <> r3.c8) AND (r2.c1 <> r3.c2) AND (r2.c1 <> r3.c3) AND (r2.c2 <> r3.c1) AND (r2.c2 <> r3.c3) AND (r2.c3 <> r3.c1) AND (r2.c3 <> r3.c2) AND (r2.c4 <> r3.c5) AND (r2.c4 <> r3.c6) AND (r2.c5 <> r3.c4) AND (r2.c5 <> r3.c6) AND (r2.c6 <> r3.c4) AND (r2.c6 <> r3.c5) AND
(r2.c7 <> r3.c8) AND (r2.c7 <> r3.c9) AND (r2.c8 <> r3.c7) AND (r2.c8 <> r3.c9) AND (r2.c9 <> r3.c7) AND (r2.c9 <> r3.c8) AND (r4.c1 <> r5.c2) AND (r4.c1 <> r5.c3) AND (r4.c1 <> r6.c2) AND (r4.c1 <> r6.c3) AND (r4.c2 <> r5.c1) AND (r4.c2 <> r5.c3) AND (r4.c2 <> r6.c1) AND (r4.c2 <> r6.c3) AND (r4.c3 <> r5.c1) AND (r4.c3 <> r5.c2) AND
(r4.c3 <> r6.c1) AND (r4.c3 <> r6.c2) AND (r4.c4 <> r5.c5) AND (r4.c4 <> r5.c6) AND (r4.c4 <> r6.c5) AND (r4.c4 <> r6.c6) AND (r4.c5 <> r5.c4) AND (r4.c5 <> r5.c6) AND (r4.c5 <> r6.c4) AND (r4.c5 <> r6.c6) AND (r4.c6 <> r5.c4) AND (r4.c6 <> r5.c5) AND (r4.c6 <> r6.c4) AND (r4.c6 <> r6.c5) AND (r4.c7 <> r5.c8) AND (r4.c7 <> r5.c9) AND
(r4.c7 <> r6.c8) AND (r4.c7 <> r6.c9) AND (r4.c8 <> r5.c7) AND (r4.c8 <> r5.c9) AND (r4.c8 <> r6.c7) AND (r4.c8 <> r6.c9) AND (r4.c9 <> r5.c7) AND (r4.c9 <> r5.c8) AND (r4.c9 <> r6.c7) AND (r4.c9 <> r6.c8) AND (r5.c1 <> r6.c2) AND (r5.c1 <> r6.c3) AND (r5.c2 <> r6.c1) AND (r5.c2 <> r6.c3) AND (r5.c3 <> r6.c1) AND (r5.c3 <> r6.c2) AND
(r5.c4 <> r6.c5) AND (r5.c4 <> r6.c6) AND (r5.c5 <> r6.c4) AND (r5.c5 <> r6.c6) AND (r5.c6 <> r6.c4) AND (r5.c6 <> r6.c5) AND (r5.c7 <> r6.c8) AND (r5.c7 <> r6.c9) AND (r5.c8 <> r6.c7) AND (r5.c8 <> r6.c9) AND (r5.c9 <> r6.c7) AND (r5.c9 <> r6.c8) AND (r7.c1 <> r8.c2) AND (r7.c1 <> r8.c3) AND (r7.c1 <> r9.c2) AND (r7.c1 <> r9.c3) AND
(r7.c2 <> r8.c1) AND (r7.c2 <> r8.c3) AND (r7.c2 <> r9.c1) AND (r7.c2 <> r9.c3) AND (r7.c3 <> r8.c1) AND (r7.c3 <> r8.c2) AND (r7.c3 <> r9.c1) AND (r7.c3 <> r9.c2) AND (r7.c4 <> r8.c5) AND (r7.c4 <> r8.c6) AND (r7.c4 <> r9.c5) AND (r7.c4 <> r9.c6) AND (r7.c5 <> r8.c4) AND (r7.c5 <> r8.c6) AND (r7.c5 <> r9.c4) AND (r7.c5 <> r9.c6) AND
(r7.c6 <> r8.c4) AND (r7.c6 <> r8.c5) AND (r7.c6 <> r9.c4) AND (r7.c6 <> r9.c5) AND (r7.c7 <> r8.c8) AND (r7.c7 <> r8.c9) AND (r7.c7 <> r9.c8) AND (r7.c7 <> r9.c9) AND (r7.c8 <> r8.c7) AND (r7.c8 <> r8.c9) AND (r7.c8 <> r9.c7) AND (r7.c8 <> r9.c9) AND (r7.c9 <> r8.c7) AND (r7.c9 <> r8.c8) AND (r7.c9 <> r9.c7) AND (r7.c9 <> r9.c8) AND
(r8.c1 <> r9.c2) AND (r8.c1 <> r9.c3) AND (r8.c2 <> r9.c1) AND (r8.c2 <> r9.c3) AND (r8.c3 <> r9.c1) AND (r8.c3 <> r9.c2) AND (r8.c4 <> r9.c5) AND (r8.c4 <> r9.c6) AND (r8.c5 <> r9.c4) AND (r8.c5 <> r9.c6) AND (r8.c6 <> r9.c4) AND (r8.c6 <> r9.c5) AND (r8.c7 <> r9.c8) AND (r8.c7 <> r9.c9) AND (r8.c8 <> r9.c7) AND (r8.c8 <> r9.c9) AND
(r8.c9 <> r9.c7) AND (r8.c9 <> r9.c8);

En second lieu, la vue sur les colonnes.

USE sudoku;

DROP VIEW IF EXISTS sudoku_memory_columns_view;
CREATE VIEW sudoku_memory_columns_view AS
SELECT
col1.c1 as r1c1, col1.c2 as r2c1, col1.c3 as r3c1, col1.c4 as r4c1, col1.c5 as r5c1,col1.c6 as r6c1, col1.c7 as r7c1, col1.c8 as r8c1, col1.c9 as r9c1, col2.c1 as r1c2,
col2.c2 as r2c2, col2.c3 as r3c2, col2.c4 as r4c2, col2.c5 as r5c2, col2.c6 as r6c2,col2.c7 as r7c2, col2.c8 as r8c2, col2.c9 as r9c2, col3.c1 as r1c3, col3.c2 as r2c3,
col3.c3 as r3c3, col3.c4 as r4c3, col3.c5 as r5c3, col3.c6 as r6c3, col3.c7 as r7c3,col3.c8 as r8c3, col3.c9 as r9c3, col4.c1 as r1c4, col4.c2 as r2c4, col4.c3 as r3c4,
col4.c4 as r4c4, col4.c5 as r5c4, col4.c6 as r6c4, col4.c7 as r7c4, col4.c8 as r8c4,col4.c9 as r9c4, col5.c1 as r1c5, col5.c2 as r2c5, col5.c3 as r3c5, col5.c4 as r4c5,
col5.c5 as r5c5, col5.c6 as r6c5, col5.c7 as r7c5, col5.c8 as r8c5, col5.c9 as r9c5,col6.c1 as r1c6, col6.c2 as r2c6, col6.c3 as r3c6, col6.c4 as r4c6, col6.c5 as r5c6,
col6.c6 as r6c6, col6.c7 as r7c6, col6.c8 as r8c6, col6.c9 as r9c6, col7.c1 as r1c7,col7.c2 as r2c7, col7.c3 as r3c7, col7.c4 as r4c7, col7.c5 as r5c7, col7.c6 as r6c7,
col7.c7 as r7c7, col7.c8 as r8c7, col7.c9 as r9c7, col8.c1 as r1c8, col8.c2 as r2c8,col8.c3 as r3c8, col8.c4 as r4c8, col8.c5 as r5c8, col8.c6 as r6c8, col8.c7 as r7c8,
col8.c8 as r8c8, col8.c9 as r9c8, col9.c1 as r1c9, col9.c2 as r2c9, col9.c3 as r3c9,col9.c4 as r4c9, col9.c5 as r5c9, col9.c6 as r6c9, col9.c7 as r7c9, col9.c8 as r8c9,
col9.c9 as r9c9
FROM
positions_memory col1, positions_memory col2, positions_memory col3, positions_memory col4,
positions_memory col5, positions_memory col6, positions_memory col7, positions_memory col8, positions_memory col9
WHERE
-- Nombres uniques dans chaque rangee
(col1.c1 <> col2.c1) AND (col1.c1 <> col3.c1) AND (col1.c1 <> col4.c1) AND (col1.c1 <> col5.c1) AND (col1.c1 <> col6.c1) AND (col1.c1 <> col7.c1) AND (col1.c1 <> col8.c1) AND (col1.c1 <> col9.c1) AND (col1.c2 <> col2.c2) AND (col1.c2 <> col3.c2) AND (col1.c2 <> col4.c2) AND (col1.c2 <> col5.c2) AND (col1.c2 <> col6.c2) AND (col1.c2 <> col7.c2) AND (col1.c2 <> col8.c2) AND (col1.c2 <> col9.c2) AND (col1.c3 <> col2.c3) AND (col1.c3 <> col3.c3) AND (col1.c3 <> col4.c3) AND (col1.c3 <> col5.c3) AND (col1.c3 <> col6.c3) AND (col1.c3 <> col7.c3) AND (col1.c3 <> col8.c3) AND (col1.c3 <> col9.c3) AND (col1.c4 <> col2.c4) AND (col1.c4 <> col3.c4) AND (col1.c4 <> col4.c4) AND (col1.c4 <> col5.c4) AND (col1.c4 <> col6.c4) AND (col1.c4 <> col7.c4) AND (col1.c4 <> col8.c4) AND (col1.c4 <> col9.c4) AND
(col1.c5 <> col2.c5) AND (col1.c5 <> col3.c5) AND (col1.c5 <> col4.c5) AND (col1.c5 <> col5.c5) AND (col1.c5 <> col6.c5) AND (col1.c5 <> col7.c5) AND (col1.c5 <> col8.c5) AND (col1.c5 <> col9.c5) AND (col1.c6 <> col2.c6) AND (col1.c6 <> col3.c6) AND (col1.c6 <> col4.c6) AND (col1.c6 <> col5.c6) AND (col1.c6 <> col6.c6) AND (col1.c6 <> col7.c6) AND (col1.c6 <> col8.c6) AND (col1.c6 <> col9.c6) AND (col1.c7 <> col2.c7) AND (col1.c7 <> col3.c7) AND (col1.c7 <> col4.c7) AND (col1.c7 <> col5.c7) AND (col1.c7 <> col6.c7) AND (col1.c7 <> col7.c7) AND (col1.c7 <> col8.c7) AND (col1.c7 <> col9.c7) AND (col1.c8 <> col2.c8) AND (col1.c8 <> col3.c8) AND (col1.c8 <> col4.c8) AND (col1.c8 <> col5.c8) AND (col1.c8 <> col6.c8) AND (col1.c8 <> col7.c8) AND (col1.c8 <> col8.c8) AND (col1.c8 <> col9.c8) AND
(col1.c9 <> col2.c9) AND (col1.c9 <> col3.c9) AND (col1.c9 <> col4.c9) AND (col1.c9 <> col5.c9) AND (col1.c9 <> col6.c9) AND (col1.c9 <> col7.c9) AND (col1.c9 <> col8.c9) AND (col1.c9 <> col9.c9) AND (col2.c1 <> col3.c1) AND (col2.c1 <> col4.c1) AND (col2.c1 <> col5.c1) AND (col2.c1 <> col6.c1) AND (col2.c1 <> col7.c1) AND (col2.c1 <> col8.c1) AND (col2.c1 <> col9.c1) AND (col2.c2 <> col3.c2) AND (col2.c2 <> col4.c2) AND (col2.c2 <> col5.c2) AND (col2.c2 <> col6.c2) AND (col2.c2 <> col7.c2) AND (col2.c2 <> col8.c2) AND (col2.c2 <> col9.c2) AND (col2.c3 <> col3.c3) AND (col2.c3 <> col4.c3) AND (col2.c3 <> col5.c3) AND (col2.c3 <> col6.c3) AND (col2.c3 <> col7.c3) AND (col2.c3 <> col8.c3) AND (col2.c3 <> col9.c3) AND (col2.c4 <> col3.c4) AND (col2.c4 <> col4.c4) AND (col2.c4 <> col5.c4) AND
(col2.c4 <> col6.c4) AND (col2.c4 <> col7.c4) AND (col2.c4 <> col8.c4) AND (col2.c4 <> col9.c4) AND (col2.c5 <> col3.c5) AND (col2.c5 <> col4.c5) AND (col2.c5 <> col5.c5) AND (col2.c5 <> col6.c5) AND (col2.c5 <> col7.c5) AND (col2.c5 <> col8.c5) AND (col2.c5 <> col9.c5) AND (col2.c6 <> col3.c6) AND (col2.c6 <> col4.c6) AND (col2.c6 <> col5.c6) AND (col2.c6 <> col6.c6) AND (col2.c6 <> col7.c6) AND (col2.c6 <> col8.c6) AND (col2.c6 <> col9.c6) AND (col2.c7 <> col3.c7) AND (col2.c7 <> col4.c7) AND (col2.c7 <> col5.c7) AND (col2.c7 <> col6.c7) AND (col2.c7 <> col7.c7) AND (col2.c7 <> col8.c7) AND (col2.c7 <> col9.c7) AND (col2.c8 <> col3.c8) AND (col2.c8 <> col4.c8) AND (col2.c8 <> col5.c8) AND (col2.c8 <> col6.c8) AND (col2.c8 <> col7.c8) AND (col2.c8 <> col8.c8) AND (col2.c8 <> col9.c8) AND
(col2.c9 <> col3.c9) AND (col2.c9 <> col4.c9) AND (col2.c9 <> col5.c9) AND (col2.c9 <> col6.c9) AND (col2.c9 <> col7.c9) AND (col2.c9 <> col8.c9) AND (col2.c9 <> col9.c9) AND (col3.c1 <> col4.c1) AND (col3.c1 <> col5.c1) AND (col3.c1 <> col6.c1) AND (col3.c1 <> col7.c1) AND (col3.c1 <> col8.c1) AND (col3.c1 <> col9.c1) AND (col3.c2 <> col4.c2) AND (col3.c2 <> col5.c2) AND (col3.c2 <> col6.c2) AND (col3.c2 <> col7.c2) AND (col3.c2 <> col8.c2) AND (col3.c2 <> col9.c2) AND (col3.c3 <> col4.c3) AND (col3.c3 <> col5.c3) AND (col3.c3 <> col6.c3) AND (col3.c3 <> col7.c3) AND (col3.c3 <> col8.c3) AND (col3.c3 <> col9.c3) AND (col3.c4 <> col4.c4) AND (col3.c4 <> col5.c4) AND (col3.c4 <> col6.c4) AND (col3.c4 <> col7.c4) AND (col3.c4 <> col8.c4) AND (col3.c4 <> col9.c4) AND (col3.c5 <> col4.c5) AND
(col3.c5 <> col5.c5) AND (col3.c5 <> col6.c5) AND (col3.c5 <> col7.c5) AND (col3.c5 <> col8.c5) AND (col3.c5 <> col9.c5) AND (col3.c6 <> col4.c6) AND (col3.c6 <> col5.c6) AND (col3.c6 <> col6.c6) AND (col3.c6 <> col7.c6) AND (col3.c6 <> col8.c6) AND (col3.c6 <> col9.c6) AND (col3.c7 <> col4.c7) AND (col3.c7 <> col5.c7) AND (col3.c7 <> col6.c7) AND (col3.c7 <> col7.c7) AND (col3.c7 <> col8.c7) AND (col3.c7 <> col9.c7) AND (col3.c8 <> col4.c8) AND (col3.c8 <> col5.c8) AND (col3.c8 <> col6.c8) AND (col3.c8 <> col7.c8) AND (col3.c8 <> col8.c8) AND (col3.c8 <> col9.c8) AND (col3.c9 <> col4.c9) AND (col3.c9 <> col5.c9) AND (col3.c9 <> col6.c9) AND (col3.c9 <> col7.c9) AND (col3.c9 <> col8.c9) AND (col3.c9 <> col9.c9) AND (col4.c1 <> col5.c1) AND (col4.c1 <> col6.c1) AND (col4.c1 <> col7.c1) AND
(col4.c1 <> col8.c1) AND (col4.c1 <> col9.c1) AND (col4.c2 <> col5.c2) AND (col4.c2 <> col6.c2) AND (col4.c2 <> col7.c2) AND (col4.c2 <> col8.c2) AND (col4.c2 <> col9.c2) AND (col4.c3 <> col5.c3) AND (col4.c3 <> col6.c3) AND (col4.c3 <> col7.c3) AND (col4.c3 <> col8.c3) AND (col4.c3 <> col9.c3) AND (col4.c4 <> col5.c4) AND (col4.c4 <> col6.c4) AND (col4.c4 <> col7.c4) AND (col4.c4 <> col8.c4) AND (col4.c4 <> col9.c4) AND (col4.c5 <> col5.c5) AND (col4.c5 <> col6.c5) AND (col4.c5 <> col7.c5) AND (col4.c5 <> col8.c5) AND (col4.c5 <> col9.c5) AND (col4.c6 <> col5.c6) AND (col4.c6 <> col6.c6) AND (col4.c6 <> col7.c6) AND (col4.c6 <> col8.c6) AND (col4.c6 <> col9.c6) AND (col4.c7 <> col5.c7) AND (col4.c7 <> col6.c7) AND (col4.c7 <> col7.c7) AND (col4.c7 <> col8.c7) AND (col4.c7 <> col9.c7) AND
(col4.c8 <> col5.c8) AND (col4.c8 <> col6.c8) AND (col4.c8 <> col7.c8) AND (col4.c8 <> col8.c8) AND (col4.c8 <> col9.c8) AND (col4.c9 <> col5.c9) AND (col4.c9 <> col6.c9) AND (col4.c9 <> col7.c9) AND (col4.c9 <> col8.c9) AND (col4.c9 <> col9.c9) AND (col5.c1 <> col6.c1) AND (col5.c1 <> col7.c1) AND (col5.c1 <> col8.c1) AND (col5.c1 <> col9.c1) AND (col5.c2 <> col6.c2) AND (col5.c2 <> col7.c2) AND (col5.c2 <> col8.c2) AND (col5.c2 <> col9.c2) AND (col5.c3 <> col6.c3) AND (col5.c3 <> col7.c3) AND (col5.c3 <> col8.c3) AND (col5.c3 <> col9.c3) AND (col5.c4 <> col6.c4) AND (col5.c4 <> col7.c4) AND (col5.c4 <> col8.c4) AND (col5.c4 <> col9.c4) AND (col5.c5 <> col6.c5) AND (col5.c5 <> col7.c5) AND (col5.c5 <> col8.c5) AND (col5.c5 <> col9.c5) AND (col5.c6 <> col6.c6) AND (col5.c6 <> col7.c6) AND
(col5.c6 <> col8.c6) AND (col5.c6 <> col9.c6) AND (col5.c7 <> col6.c7) AND (col5.c7 <> col7.c7) AND (col5.c7 <> col8.c7) AND (col5.c7 <> col9.c7) AND (col5.c8 <> col6.c8) AND (col5.c8 <> col7.c8) AND (col5.c8 <> col8.c8) AND (col5.c8 <> col9.c8) AND (col5.c9 <> col6.c9) AND (col5.c9 <> col7.c9) AND (col5.c9 <> col8.c9) AND (col5.c9 <> col9.c9) AND (col6.c1 <> col7.c1) AND (col6.c1 <> col8.c1) AND (col6.c1 <> col9.c1) AND (col6.c2 <> col7.c2) AND (col6.c2 <> col8.c2) AND (col6.c2 <> col9.c2) AND (col6.c3 <> col7.c3) AND (col6.c3 <> col8.c3) AND (col6.c3 <> col9.c3) AND (col6.c4 <> col7.c4) AND (col6.c4 <> col8.c4) AND (col6.c4 <> col9.c4) AND (col6.c5 <> col7.c5) AND (col6.c5 <> col8.c5) AND (col6.c5 <> col9.c5) AND (col6.c6 <> col7.c6) AND (col6.c6 <> col8.c6) AND (col6.c6 <> col9.c6) AND
(col6.c7 <> col7.c7) AND (col6.c7 <> col8.c7) AND (col6.c7 <> col9.c7) AND (col6.c8 <> col7.c8) AND (col6.c8 <> col8.c8) AND (col6.c8 <> col9.c8) AND (col6.c9 <> col7.c9) AND (col6.c9 <> col8.c9) AND (col6.c9 <> col9.c9) AND (col7.c1 <> col8.c1) AND (col7.c1 <> col9.c1) AND (col7.c2 <> col8.c2) AND (col7.c2 <> col9.c2) AND (col7.c3 <> col8.c3) AND (col7.c3 <> col9.c3) AND (col7.c4 <> col8.c4) AND (col7.c4 <> col9.c4) AND (col7.c5 <> col8.c5) AND (col7.c5 <> col9.c5) AND (col7.c6 <> col8.c6) AND (col7.c6 <> col9.c6) AND (col7.c7 <> col8.c7) AND (col7.c7 <> col9.c7) AND (col7.c8 <> col8.c8) AND (col7.c8 <> col9.c8) AND (col7.c9 <> col8.c9) AND (col7.c9 <> col9.c9) AND (col8.c1 <> col9.c1) AND (col8.c2 <> col9.c2) AND (col8.c3 <> col9.c3) AND (col8.c4 <> col9.c4) AND (col8.c5 <> col9.c5) AND
(col8.c6 <> col9.c6) AND (col8.c7 <> col9.c7) AND (col8.c8 <> col9.c8) AND (col8.c9 <> col9.c9) AND
-- Nombres uniques dans chaque maison de 3x3
(col1.c1 <> col1.c2) AND (col1.c1 <> col1.c3) AND (col1.c1 <> col2.c2) AND (col1.c1 <> col2.c3) AND (col1.c1 <> col3.c2) AND (col1.c1 <> col3.c3) AND (col1.c2 <> col1.c3) AND (col1.c2 <> col2.c1) AND (col1.c2 <> col2.c3) AND (col1.c2 <> col3.c1) AND (col1.c2 <> col3.c3) AND (col1.c3 <> col2.c1) AND (col1.c3 <> col2.c2) AND (col1.c3 <> col3.c1) AND (col1.c3 <> col3.c2) AND (col1.c4 <> col1.c5) AND (col1.c4 <> col1.c6) AND (col1.c4 <> col2.c5) AND (col1.c4 <> col2.c6) AND (col1.c4 <> col3.c5) AND (col1.c4 <> col3.c6) AND (col1.c5 <> col1.c6) AND (col1.c5 <> col2.c4) AND (col1.c5 <> col2.c6) AND (col1.c5 <> col3.c4) AND (col1.c5 <> col3.c6) AND (col1.c6 <> col2.c4) AND (col1.c6 <> col2.c5) AND (col1.c6 <> col3.c4) AND (col1.c6 <> col3.c5) AND (col1.c7 <> col1.c8) AND (col1.c7 <> col1.c9) AND
(col1.c7 <> col2.c8) AND (col1.c7 <> col2.c9) AND (col1.c7 <> col3.c8) AND (col1.c7 <> col3.c9) AND (col1.c8 <> col1.c9) AND (col1.c8 <> col2.c7) AND (col1.c8 <> col2.c9) AND (col1.c8 <> col3.c7) AND (col1.c8 <> col3.c9) AND (col1.c9 <> col2.c7) AND (col1.c9 <> col2.c8) AND (col1.c9 <> col3.c7) AND (col1.c9 <> col3.c8) AND (col2.c1 <> col2.c2) AND (col2.c1 <> col2.c3) AND (col2.c1 <> col3.c2) AND (col2.c1 <> col3.c3) AND (col2.c2 <> col2.c3) AND (col2.c2 <> col3.c1) AND (col2.c2 <> col3.c3) AND (col2.c3 <> col3.c1) AND (col2.c3 <> col3.c2) AND (col2.c4 <> col2.c5) AND (col2.c4 <> col2.c6) AND (col2.c4 <> col3.c5) AND (col2.c4 <> col3.c6) AND (col2.c5 <> col2.c6) AND (col2.c5 <> col3.c4) AND (col2.c5 <> col3.c6) AND (col2.c6 <> col3.c4) AND (col2.c6 <> col3.c5) AND (col2.c7 <> col2.c8) AND
(col2.c7 <> col2.c9) AND (col2.c7 <> col3.c8) AND (col2.c7 <> col3.c9) AND (col2.c8 <> col2.c9) AND (col2.c8 <> col3.c7) AND (col2.c8 <> col3.c9) AND (col2.c9 <> col3.c7) AND (col2.c9 <> col3.c8) AND (col3.c1 <> col3.c2) AND (col3.c1 <> col3.c3) AND (col3.c2 <> col3.c3) AND (col3.c4 <> col3.c5) AND (col3.c4 <> col3.c6) AND (col3.c5 <> col3.c6) AND (col3.c7 <> col3.c8) AND (col3.c7 <> col3.c9) AND (col3.c8 <> col3.c9) AND (col4.c1 <> col4.c2) AND (col4.c1 <> col4.c3) AND (col4.c1 <> col5.c2) AND (col4.c1 <> col5.c3) AND (col4.c1 <> col6.c2) AND (col4.c1 <> col6.c3) AND (col4.c2 <> col4.c3) AND (col4.c2 <> col5.c1) AND (col4.c2 <> col5.c3) AND (col4.c2 <> col6.c1) AND (col4.c2 <> col6.c3) AND (col4.c3 <> col5.c1) AND (col4.c3 <> col5.c2) AND (col4.c3 <> col6.c1) AND (col4.c3 <> col6.c2) AND
(col4.c4 <> col4.c5) AND (col4.c4 <> col4.c6) AND (col4.c4 <> col5.c5) AND (col4.c4 <> col5.c6) AND (col4.c4 <> col6.c5) AND (col4.c4 <> col6.c6) AND (col4.c5 <> col4.c6) AND (col4.c5 <> col5.c4) AND (col4.c5 <> col5.c6) AND (col4.c5 <> col6.c4) AND (col4.c5 <> col6.c6) AND (col4.c6 <> col5.c4) AND (col4.c6 <> col5.c5) AND (col4.c6 <> col6.c4) AND (col4.c6 <> col6.c5) AND (col4.c7 <> col4.c8) AND (col4.c7 <> col4.c9) AND (col4.c7 <> col5.c8) AND (col4.c7 <> col5.c9) AND (col4.c7 <> col6.c8) AND (col4.c7 <> col6.c9) AND (col4.c8 <> col4.c9) AND (col4.c8 <> col5.c7) AND (col4.c8 <> col5.c9) AND (col4.c8 <> col6.c7) AND (col4.c8 <> col6.c9) AND (col4.c9 <> col5.c7) AND (col4.c9 <> col5.c8) AND (col4.c9 <> col6.c7) AND (col4.c9 <> col6.c8) AND (col5.c1 <> col5.c2) AND (col5.c1 <> col5.c3) AND
(col5.c1 <> col6.c2) AND (col5.c1 <> col6.c3) AND (col5.c2 <> col5.c3) AND (col5.c2 <> col6.c1) AND (col5.c2 <> col6.c3) AND (col5.c3 <> col6.c1) AND (col5.c3 <> col6.c2) AND (col5.c4 <> col5.c5) AND (col5.c4 <> col5.c6) AND (col5.c4 <> col6.c5) AND (col5.c4 <> col6.c6) AND (col5.c5 <> col5.c6) AND (col5.c5 <> col6.c4) AND (col5.c5 <> col6.c6) AND (col5.c6 <> col6.c4) AND (col5.c6 <> col6.c5) AND (col5.c7 <> col5.c8) AND (col5.c7 <> col5.c9) AND (col5.c7 <> col6.c8) AND (col5.c7 <> col6.c9) AND (col5.c8 <> col5.c9) AND (col5.c8 <> col6.c7) AND (col5.c8 <> col6.c9) AND (col5.c9 <> col6.c7) AND (col5.c9 <> col6.c8) AND (col6.c1 <> col6.c2) AND (col6.c1 <> col6.c3) AND (col6.c2 <> col6.c3) AND (col6.c4 <> col6.c5) AND (col6.c4 <> col6.c6) AND (col6.c5 <> col6.c6) AND (col6.c7 <> col6.c8) AND
(col6.c7 <> col6.c9) AND (col6.c8 <> col6.c9) AND (col7.c1 <> col7.c2) AND (col7.c1 <> col7.c3) AND (col7.c1 <> col8.c2) AND (col7.c1 <> col8.c3) AND (col7.c1 <> col9.c2) AND (col7.c1 <> col9.c3) AND (col7.c2 <> col7.c3) AND (col7.c2 <> col8.c1) AND (col7.c2 <> col8.c3) AND (col7.c2 <> col9.c1) AND (col7.c2 <> col9.c3) AND (col7.c3 <> col8.c1) AND (col7.c3 <> col8.c2) AND (col7.c3 <> col9.c1) AND (col7.c3 <> col9.c2) AND (col7.c4 <> col7.c5) AND (col7.c4 <> col7.c6) AND (col7.c4 <> col8.c5) AND (col7.c4 <> col8.c6) AND (col7.c4 <> col9.c5) AND (col7.c4 <> col9.c6) AND (col7.c5 <> col7.c6) AND (col7.c5 <> col8.c4) AND (col7.c5 <> col8.c6) AND (col7.c5 <> col9.c4) AND (col7.c5 <> col9.c6) AND (col7.c6 <> col8.c4) AND (col7.c6 <> col8.c5) AND (col7.c6 <> col9.c4) AND (col7.c6 <> col9.c5) AND
(col7.c7 <> col7.c8) AND (col7.c7 <> col7.c9) AND (col7.c7 <> col8.c8) AND (col7.c7 <> col8.c9) AND (col7.c7 <> col9.c8) AND (col7.c7 <> col9.c9) AND (col7.c8 <> col7.c9) AND (col7.c8 <> col8.c7) AND (col7.c8 <> col8.c9) AND (col7.c8 <> col9.c7) AND (col7.c8 <> col9.c9) AND (col7.c9 <> col8.c7) AND (col7.c9 <> col8.c8) AND (col7.c9 <> col9.c7) AND (col7.c9 <> col9.c8) AND (col8.c1 <> col8.c2) AND (col8.c1 <> col8.c3) AND (col8.c1 <> col9.c2) AND (col8.c1 <> col9.c3) AND (col8.c2 <> col8.c3) AND (col8.c2 <> col9.c1) AND (col8.c2 <> col9.c3) AND (col8.c3 <> col9.c1) AND (col8.c3 <> col9.c2) AND (col8.c4 <> col8.c5) AND (col8.c4 <> col8.c6) AND (col8.c4 <> col9.c5) AND (col8.c4 <> col9.c6) AND (col8.c5 <> col8.c6) AND (col8.c5 <> col9.c4) AND (col8.c5 <> col9.c6) AND (col8.c6 <> col9.c4) AND
(col8.c6 <> col9.c5) AND (col8.c7 <> col8.c8) AND (col8.c7 <> col8.c9) AND (col8.c7 <> col9.c8) AND (col8.c7 <> col9.c9) AND (col8.c8 <> col8.c9) AND (col8.c8 <> col9.c7) AND (col8.c8 <> col9.c9) AND (col8.c9 <> col9.c7) AND (col8.c9 <> col9.c8) AND (col9.c1 <> col9.c2) AND (col9.c1 <> col9.c3) AND (col9.c2 <> col9.c3) AND (col9.c4 <> col9.c5) AND (col9.c4 <> col9.c6) AND (col9.c5 <> col9.c6) AND (col9.c7 <> col9.c8) AND (col9.c7 <> col9.c9) AND (col9.c8 <> col9.c9);

Finalement, la vue combinée.

USE sudoku;

DROP VIEW IF EXISTS sudoku_memory_combined_view;
CREATE VIEW sudoku_memory_combined_view AS
SELECT t1.*
FROM sudoku_memory_rows_view t1
INNER JOIN sudoku_memory_columns_view t2
ON

-- Jointures entre représentation-colonnes et représentation-rangées
(t1.r1c1 = t2.r1c1) AND (t1.r1c2 = t2.r1c2) AND (t1.r1c3 = t2.r1c3) AND (t1.r1c4 = t2.r1c4) AND
(t1.r1c5 = t2.r1c5) AND (t1.r1c6 = t2.r1c6) AND (t1.r1c7 = t2.r1c7) AND (t1.r1c8 = t2.r1c8) AND
(t1.r1c9 = t2.r1c9) AND (t1.r2c1 = t2.r2c1) AND (t1.r2c2 = t2.r2c2) AND (t1.r2c3 = t2.r2c3) AND
(t1.r2c4 = t2.r2c4) AND (t1.r2c5 = t2.r2c5) AND (t1.r2c6 = t2.r2c6) AND (t1.r2c7 = t2.r2c7) AND
(t1.r2c8 = t2.r2c8) AND (t1.r2c9 = t2.r2c9) AND (t1.r3c1 = t2.r3c1) AND (t1.r3c2 = t2.r3c2) AND
(t1.r3c3 = t2.r3c3) AND (t1.r3c4 = t2.r3c4) AND (t1.r3c5 = t2.r3c5) AND (t1.r3c6 = t2.r3c6) AND
(t1.r3c7 = t2.r3c7) AND (t1.r3c8 = t2.r3c8) AND (t1.r3c9 = t2.r3c9) AND (t1.r4c1 = t2.r4c1) AND
(t1.r4c2 = t2.r4c2) AND (t1.r4c3 = t2.r4c3) AND (t1.r4c4 = t2.r4c4) AND (t1.r4c5 = t2.r4c5) AND
(t1.r4c6 = t2.r4c6) AND (t1.r4c7 = t2.r4c7) AND (t1.r4c8 = t2.r4c8) AND (t1.r4c9 = t2.r4c9) AND
(t1.r5c1 = t2.r5c1) AND (t1.r5c2 = t2.r5c2) AND (t1.r5c3 = t2.r5c3) AND (t1.r5c4 = t2.r5c4) AND
(t1.r5c5 = t2.r5c5) AND (t1.r5c6 = t2.r5c6) AND (t1.r5c7 = t2.r5c7) AND (t1.r5c8 = t2.r5c8) AND
(t1.r5c9 = t2.r5c9) AND (t1.r6c1 = t2.r6c1) AND (t1.r6c2 = t2.r6c2) AND (t1.r6c3 = t2.r6c3) AND
(t1.r6c4 = t2.r6c4) AND (t1.r6c5 = t2.r6c5) AND (t1.r6c6 = t2.r6c6) AND (t1.r6c7 = t2.r6c7) AND
(t1.r6c8 = t2.r6c8) AND (t1.r6c9 = t2.r6c9) AND (t1.r7c1 = t2.r7c1) AND (t1.r7c2 = t2.r7c2) AND
(t1.r7c3 = t2.r7c3) AND (t1.r7c4 = t2.r7c4) AND (t1.r7c5 = t2.r7c5) AND (t1.r7c6 = t2.r7c6) AND
(t1.r7c7 = t2.r7c7) AND (t1.r7c8 = t2.r7c8) AND (t1.r7c9 = t2.r7c9) AND (t1.r8c1 = t2.r8c1) AND
(t1.r8c2 = t2.r8c2) AND (t1.r8c3 = t2.r8c3) AND (t1.r8c4 = t2.r8c4) AND (t1.r8c5 = t2.r8c5) AND
(t1.r8c6 = t2.r8c6) AND (t1.r8c7 = t2.r8c7) AND (t1.r8c8 = t2.r8c8) AND (t1.r8c9 = t2.r8c9) AND
(t1.r9c1 = t2.r9c1) AND (t1.r9c2 = t2.r9c2) AND (t1.r9c3 = t2.r9c3) AND (t1.r9c4 = t2.r9c4) AND
(t1.r9c5 = t2.r9c5) AND (t1.r9c6 = t2.r9c6) AND (t1.r9c7 = t2.r9c7) AND (t1.r9c8 = t2.r9c8) AND
(t1.r9c9 = t2.r9c9);

Réessayons l’exemple du début de cet article pour comparer :


mysql> SELECT *
 -> FROM sudoku_memory_combined_view
 -> WHERE
 -> (r2c2 = 3) AND (r2c3 = 4) AND (r2c4 = 8) AND (r2c5 = 2) AND
 -> (r2c6 = 5) AND (r2c7 = 6) AND (r2c8 = 9) AND (r3c2 = 5) AND
 -> (r3c3 = 9) AND (r3c4 = 3) AND (r3c5 = 6) AND (r3c6 = 4) AND
 -> (r3c7 = 1) AND (r3c8 = 8) AND (r4c2 = 9) AND (r4c3 = 7) AND
 -> (r4c4 = 1) AND (r4c5 = 8) AND (r4c6 = 2) AND (r4c7 = 5) AND
 -> (r4c8 = 6) AND (r6c2 = 8) AND (r6c3 = 1) AND (r6c4 = 4) AND
 -> (r6c5 = 7) AND (r6c6 = 6) AND (r6c7 = 2) AND (r6c8 = 3) AND
 -> (r7c2 = 2) AND (r7c3 = 5) AND (r7c4 = 6) AND (r7c5 = 4) AND
 -> (r7c6 = 1) AND (r7c7 = 9) AND (r7c8 = 7) AND (r8c2 = 7) AND
 -> (r8c3 = 6) AND (r8c4 = 5) AND (r8c5 = 3) AND (r8c6 = 8) AND
 -> (r8c7 = 4) AND (r8c8 = 2);
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| r1c1 | r1c2 | r1c3 | r1c4 | r1c5 | r1c6 | r1c7 | r1c8 | r1c9 | r2c1 | r2c2 | r2c3 | r2c4 | r2c5 | r2c6 | r2c7 | r2c8 | r2c9 | r3c1 | r3c2 | r3c3 | r3c4 | r3c5 | r3c6 | r3c7 | r3c8 | r3c9 | r4c1 | r4c2 | r4c3 | r4c4 | r4c5 | r4c6 | r4c7 | r4c8 | r4c9 | r5c1 | r5c2 | r5c3 | r5c4 | r5c5 | r5c6 | r5c7 | r5c8 | r5c9 | r6c1 | r6c2 | r6c3 | r6c4 | r6c5 | r6c6 | r6c7 | r6c8 | r6c9 | r7c1 | r7c2 | r7c3 | r7c4 | r7c5 | r7c6 | r7c7 | r7c8 | r7c9 | r8c1 | r8c2 | r8c3 | r8c4 | r8c5 | r8c6 | r8c7 | r8c8 | r8c9 | r9c1 | r9c2 | r9c3 | r9c4 | r9c5 | r9c6 | r9c7 | r9c8 | r9c9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
|   2  |   6  |   8  |   7  |   1  |   9  |   3  |   4  |   5  |   1  |   3  |   4  |   8  |   2  |   5  |   6  |   9  |   7  |   7  |   5  |   9  |   3  |   6  |   4  |   1  |   8  |   2  |   3  |   9  |   7  |   1  |   8  |   2  |   5  |   6  |   4  |   6  |   4  |   2  |   9  |   5  |   3  |   7  |   1  |   8  |   5  |   8  |   1  |   4  |   7  |   6  |   2  |   3  |   9  |   8  |   2  |   5  |   6  |   4  |   1  |   9  |   7  |   3  |   9  |   7  |   6  |   5  |   3  |   8  |   4  |   2  |   1  |   4  |   1  |   3  |   2  |   9  |   7  |   8  |   5  |   6  |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
1 row in set (0.55 sec)

Wow! Nous sommes passés de 1.5 à 0.55 seconde! Maintenant, qu’en est-il de notre grille à 17 révélés ?

mysql> SELECT *
-> FROM sudoku_memory_combined_view
-> WHERE
-> (r1c8 = 1) AND
-> (r2c1 = 4) AND
-> (r3c2 = 2) AND
-> (r4c5 = 5) AND
-> (r4c7 = 4) AND
-> (r4c9 = 7) AND
-> (r5c3 = 8) AND
-> (r5c7 = 3) AND
-> (r6c3 = 1) AND
-> (r6c5 = 9) AND
-> (r7c1 = 3) AND
-> (r7c4 = 4) AND
-> (r7c7 = 2) AND
-> (r8c2 = 5) AND
-> (r8c4 = 1) AND
-> (r9c4 = 8) AND
-> (r9c6 = 6);
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| r1c1 | r1c2 | r1c3 | r1c4 | r1c5 | r1c6 | r1c7 | r1c8 | r1c9 | r2c1 | r2c2 | r2c3 | r2c4 | r2c5 | r2c6 | r2c7 | r2c8 | r2c9 | r3c1 | r3c2 | r3c3 | r3c4 | r3c5 | r3c6 | r3c7 | r3c8 | r3c9 | r4c1 | r4c2 | r4c3 | r4c4 | r4c5 | r4c6 | r4c7 | r4c8 | r4c9 | r5c1 | r5c2 | r5c3 | r5c4 | r5c5 | r5c6 | r5c7 | r5c8 | r5c9 | r6c1 | r6c2 | r6c3 | r6c4 | r6c5 | r6c6 | r6c7 | r6c8 | r6c9 | r7c1 | r7c2 | r7c3 | r7c4 | r7c5 | r7c6 | r7c7 | r7c8 | r7c9 | r8c1 | r8c2 | r8c3 | r8c4 | r8c5 | r8c6 | r8c7 | r8c8 | r8c9 | r9c1 | r9c2 | r9c3 | r9c4 | r9c5 | r9c6 | r9c7 | r9c8 | r9c9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
|    6 |    9 |    3 |    7 |    8 |    4 |    5 |    1 |    2 |    4 |    8 |    7 |    5 |    1 |    2 |    9 |    3 |    6 |    1 |    2 |    5 |    9 |    6 |    3 |    8 |    7 |    4 |    9 |    3 |    2 |    6 |    5 |    1 |    4 |    8 |    7 |    5 |    6 |    8 |    2 |    4 |    7 |    3 |    9 |    1 |    7 |    4 |    1 |    3 |    9 |    8 |    6 |    2 |    5 |    3 |    1 |    9 |    4 |    7 |    5 |    2 |    6 |    8 |    8 |    5 |    6 |    1 |    2 |    9 |    7 |    4 |    3 |    2 |    7 |    4 |    8 |    3 |    6 |    1 |    5 |    9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
1 row in set (7.41 sec)

sudoku17clues

Fantastique!  Nous sommes passés de 20 minutes à 7 secondes!  Mais il y a encore place à amélioration!

5. Presser encore plus fort

Maintenant que nous sommes en mesure d’obtenir des résultats dans des temps raisonnables en utilisant une table de type MEMORY, nous pouvons regarder du côté des variables système pour essayer de les optimiser.

Mais avant de se lancer dans cette entreprise, il importe d’avoir un jeu d’essai afin d’effectuer des tests reproduisibles et mesurables pour vérifier l’impact de chacun des changements sur ces variables.

Nous allons tout d’abord créer une table qui nous permettra de sauvegarder le temps d’exécution de toutes les grilles de notre jeu d’essai.

DROP TABLE IF EXISTS tests;

CREATE TABLE tests (
debut DATETIME,
fin DATETIME
) ENGINE=MYISAM;

Maintenant, nous allons créer notre jeu d’essai.  Évidemment notre échantillon de grilles est varié de façon à être représentatif afin  de mesurer chaque option de façon précise.

USE sudoku;
TRUNCATE tests;
INSERT INTO tests(debut, fin) VALUES (NOW(), NULL);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 1) AND (r1c3 = 3) AND (r1c4 = 7) AND (r1c9 = 5) AND (r2c4 = 6) AND (r2c6 = 4) AND (r3c1 = 8) AND (r4c4 = 8) AND (r4c5 = 1) AND (r5c2 = 9) AND (r5c7 = 7) AND (r6c2 = 6) AND (r6c8 = 9) AND (r7c2 = 2) AND (r7c7 = 4) AND (r8c1 = 5) AND (r8c5 = 3) AND (r9c8 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 8) AND (r1c4 = 3) AND (r1c6 = 7) AND (r2c3 = 9) AND (r3c1 = 2) AND (r3c2 = 7) AND (r3c5 = 4) AND (r4c2 = 3) AND (r4c5 = 1) AND (r5c1 = 4) AND (r5c4 = 9) AND (r5c7 = 2) AND (r5c8 = 8) AND (r6c4 = 6) AND (r6c6 = 2) AND (r6c7 = 4) AND (r6c8 = 3) AND (r7c1 = 3) AND (r7c2 = 1) AND (r7c6 = 6) AND (r8c1 = 6) AND (r8c3 = 8) AND (r8c4 = 1) AND (r8c9 = 7) AND (r9c5 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 3) AND (r3c5 = 5) AND (r4c4 = 4) AND (r4c8 = 6) AND (r5c3 = 2) AND (r5c7 = 9) AND (r6c2 = 5) AND (r6c6 = 8) AND (r7c5 = 3) AND (r7c7 = 5) AND (r8c1 = 7) AND (r8c2 = 9) AND (r8c4 = 1) AND (r9c2 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c2 = 8) AND (r3c5 = 5) AND (r3c6 = 3) AND (r3c8 = 8) AND (r3c9 = 9) AND (r4c2 = 2) AND (r4c3 = 4) AND (r4c6 = 9) AND (r5c5 = 1) AND (r5c9 = 5) AND (r6c2 = 1) AND (r6c6 = 7) AND (r7c3 = 2) AND (r7c4 = 1) AND (r7c7 = 3) AND (r8c1 = 9) AND (r8c6 = 5) AND (r8c9 = 7) AND (r9c1 = 5) AND (r9c5 = 8) AND (r9c8 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 5) AND (r1c6 = 8) AND (r1c7 = 6) AND (r2c6 = 6) AND (r2c7 = 2) AND (r2c8 = 7) AND (r3c2 = 1) AND (r4c1 = 9) AND (r4c4 = 7) AND (r4c5 = 6) AND (r4c6 = 2) AND (r5c1 = 7) AND (r6c3 = 8) AND (r7c1 = 2) AND (r7c3 = 3) AND (r7c7 = 8) AND (r8c4 = 1) AND (r8c5 = 9) AND (r8c9 = 5) AND (r9c3 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c4 = 8) AND (r1c5 = 3) AND (r2c7 = 7) AND (r2c8 = 1) AND (r3c2 = 3) AND (r4c1 = 7) AND (r4c4 = 4) AND (r4c7 = 8) AND (r5c1 = 1) AND (r5c3 = 2) AND (r7c2 = 8) AND (r7c4 = 6) AND (r7c7 = 4) AND (r8c1 = 9) AND (r8c6 = 2) AND (r9c5 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 7) AND (r1c9 = 5) AND (r2c2 = 3) AND (r2c8 = 7) AND (r3c1 = 2) AND (r3c3 = 5) AND (r3c8 = 3) AND (r3c9 = 8) AND (r4c8 = 8) AND (r4c9 = 9) AND (r5c1 = 5) AND (r5c3 = 8) AND (r5c4 = 2) AND (r5c6 = 9) AND (r5c7 = 7) AND (r5c9 = 4) AND (r6c1 = 3) AND (r7c1 = 6) AND (r7c3 = 4) AND (r7c4 = 9) AND (r7c5 = 8) AND (r7c6 = 7) AND (r7c7 = 5) AND (r8c1 = 9) AND (r8c4 = 5) AND (r9c4 = 4) AND (r9c6 = 6) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c2 = 6) AND (r1c3 = 8) AND (r1c7 = 1) AND (r2c2 = 7) AND (r2c4 = 4) AND (r2c6 = 8) AND (r2c8 = 5) AND (r3c4 = 6) AND (r4c3 = 6) AND (r4c4 = 1) AND (r4c5 = 8) AND (r4c6 = 3) AND (r4c9 = 7) AND (r5c3 = 7) AND (r6c1 = 3) AND (r6c5 = 5) AND (r6c7 = 2) AND (r6c9 = 1) AND (r7c6 = 7) AND (r8c4 = 8) AND (r8c6 = 2) AND (r8c7 = 5) AND (r9c6 = 5) AND (r9c7 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 5) AND (r3c5 = 6) AND (r4c4 = 3) AND (r4c8 = 7) AND (r5c3 = 2) AND (r5c7 = 6) AND (r6c2 = 1) AND (r6c6 = 5) AND (r7c5 = 8) AND (r7c7 = 2) AND (r8c1 = 7) AND (r8c2 = 3) AND (r8c4 = 9) AND (r9c2 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 7) AND (r1c9 = 2) AND (r2c5 = 4) AND (r2c6 = 5) AND (r2c8 = 7) AND (r3c3 = 9) AND (r4c1 = 3) AND (r4c5 = 5) AND (r4c7 = 8) AND (r5c1 = 4) AND (r5c2 = 8) AND (r5c4 = 9) AND (r5c6 = 1) AND (r5c9 = 7) AND (r6c3 = 7) AND (r6c6 = 4) AND (r6c7 = 2) AND (r6c9 = 9) AND (r7c5 = 1) AND (r7c7 = 3) AND (r8c8 = 5) AND (r9c2 = 3) AND (r9c4 = 8) AND (r9c5 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 9) AND (r1c8 = 7) AND (r2c8 = 2) AND (r2c9 = 4) AND (r3c1 = 1) AND (r4c2 = 2) AND (r4c3 = 9) AND (r4c9 = 5) AND (r5c6 = 1) AND (r5c7 = 6) AND (r6c2 = 4) AND (r6c5 = 8) AND (r7c4 = 4) AND (r7c5 = 3) AND (r8c1 = 5) AND (r8c7 = 8) AND (r9c4 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c2 = 9) AND (r2c3 = 3) AND (r3c2 = 7) AND (r3c8 = 3) AND (r4c3 = 9) AND (r4c5 = 6) AND (r4c8 = 7) AND (r4c9 = 4) AND (r5c3 = 6) AND (r5c5 = 7) AND (r5c7 = 3) AND (r5c8 = 9) AND (r6c2 = 3) AND (r6c4 = 5) AND (r6c7 = 6) AND (r6c8 = 8) AND (r7c1 = 9) AND (r7c5 = 8) AND (r7c6 = 2) AND (r7c7 = 4) AND (r8c2 = 8) AND (r8c3 = 2) AND (r8c5 = 3) AND (r8c8 = 5) AND (r8c9 = 7) AND (r9c2 = 6) AND (r9c3 = 4) AND (r9c4 = 7) AND (r9c5 = 5) AND (r9c8 = 2) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c5 = 5) AND (r1c8 = 6) AND (r1c9 = 9) AND (r2c1 = 6) AND (r2c8 = 4) AND (r3c2 = 1) AND (r3c5 = 8) AND (r3c6 = 9) AND (r3c9 = 3) AND (r4c4 = 1) AND (r5c4 = 3) AND (r6c2 = 8) AND (r6c8 = 9) AND (r7c1 = 4) AND (r7c2 = 6) AND (r8c3 = 7) AND (r8c6 = 3) AND (r8c9 = 8) AND (r9c2 = 5) AND (r9c3 = 8) AND (r9c4 = 7) AND (r9c6 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 7) AND (r1c5 = 9) AND (r1c6 = 4) AND (r2c2 = 1) AND (r2c6 = 7) AND (r3c3 = 9) AND (r3c4 = 2) AND (r3c5 = 1) AND (r4c1 = 2) AND (r4c4 = 5) AND (r4c6 = 9) AND (r5c3 = 8) AND (r5c4 = 6) AND (r6c1 = 9) AND (r6c2 = 5) AND (r6c6 = 1) AND (r6c8 = 2) AND (r6c9 = 7) AND (r7c1 = 8) AND (r7c6 = 2) AND (r7c7 = 6) AND (r8c1 = 1) AND (r8c5 = 5) AND (r8c6 = 8) AND (r8c9 = 2) AND (r9c4 = 7) AND (r9c5 = 4) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 1) AND (r1c4 = 6) AND (r1c5 = 2) AND (r2c1 = 5) AND (r2c8 = 4) AND (r2c9 = 3) AND (r3c5 = 9) AND (r4c1 = 7) AND (r4c8 = 8) AND (r5c3 = 5) AND (r5c9 = 4) AND (r6c4 = 1) AND (r7c6 = 3) AND (r7c7 = 6) AND (r8c2 = 9) AND (r8c7 = 2) AND (r9c1 = 8) AND (r9c6 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c3 = 8) AND (r1c6 = 6) AND (r1c7 = 3) AND (r1c8 = 2) AND (r1c9 = 4) AND (r2c1 = 9) AND (r2c2 = 2) AND (r2c3 = 3) AND (r2c6 = 8) AND (r2c7 = 5) AND (r2c8 = 6) AND (r3c5 = 5) AND (r4c9 = 8) AND (r5c2 = 8) AND (r5c3 = 7) AND (r5c6 = 9) AND (r7c2 = 4) AND (r7c4 = 6) AND (r7c6 = 7) AND (r7c8 = 5) AND (r8c1 = 3) AND (r8c5 = 9) AND (r8c6 = 5) AND (r8c8 = 8) AND (r8c9 = 2) AND (r9c2 = 9) AND (r9c3 = 5) AND (r9c5 = 8) AND (r9c7 = 6) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c5 = 7) AND (r1c7 = 8) AND (r2c4 = 4) AND (r2c6 = 3) AND (r3c1 = 2) AND (r3c4 = 5) AND (r3c5 = 6) AND (r3c6 = 8) AND (r3c9 = 3) AND (r4c2 = 6) AND (r4c3 = 2) AND (r4c7 = 5) AND (r4c8 = 3) AND (r5c1 = 1) AND (r5c3 = 5) AND (r5c7 = 9) AND (r5c9 = 4) AND (r6c2 = 3) AND (r6c3 = 9) AND (r6c7 = 2) AND (r6c8 = 1) AND (r7c1 = 3) AND (r7c4 = 6) AND (r7c5 = 2) AND (r7c6 = 7) AND (r7c9 = 5) AND (r8c4 = 9) AND (r8c6 = 5) AND (r9c3 = 7) AND (r9c5 = 8) AND (r9c7 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 3) AND (r1c3 = 8) AND (r2c1 = 7) AND (r2c6 = 8) AND (r3c1 = 6) AND (r3c2 = 4) AND (r3c3 = 9) AND (r3c4 = 3) AND (r3c5 = 1) AND (r3c6 = 7) AND (r3c8 = 2) AND (r4c1 = 1) AND (r4c2 = 7) AND (r4c5 = 3) AND (r4c6 = 6) AND (r4c8 = 8) AND (r4c9 = 2) AND (r5c1 = 3) AND (r5c3 = 6) AND (r5c4 = 2) AND (r5c6 = 1) AND (r5c8 = 7) AND (r5c9 = 9) AND (r6c5 = 7) AND (r7c1 = 4) AND (r7c2 = 9) AND (r7c8 = 1) AND (r8c2 = 6) AND (r8c3 = 1) AND (r8c5 = 9) AND (r8c8 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 5) AND (r1c8 = 8) AND (r2c2 = 1) AND (r2c6 = 3) AND (r3c1 = 3) AND (r3c3 = 7) AND (r3c4 = 6) AND (r4c2 = 9) AND (r4c4 = 1) AND (r4c5 = 7) AND (r4c6 = 6) AND (r4c7 = 3) AND (r5c4 = 9) AND (r5c6 = 8) AND (r5c8 = 1) AND (r6c1 = 2) AND (r7c2 = 6) AND (r8c2 = 8) AND (r8c6 = 1) AND (r8c8 = 6) AND (r9c2 = 3) AND (r9c4 = 2) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 8) AND (r1c7 = 4) AND (r1c9 = 3) AND (r2c1 = 9) AND (r2c4 = 3) AND (r2c7 = 7) AND (r3c2 = 1) AND (r3c3 = 5) AND (r3c6 = 2) AND (r4c1 = 6) AND (r4c8 = 9) AND (r4c9 = 5) AND (r5c2 = 3) AND (r5c3 = 7) AND (r6c4 = 8) AND (r7c7 = 8) AND (r7c8 = 3) AND (r7c9 = 2) AND (r8c2 = 2) AND (r8c5 = 9) AND (r9c1 = 8) AND (r9c4 = 7) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c4 = 2) AND (r1c6 = 4) AND (r1c8 = 5) AND (r2c2 = 4) AND (r2c9 = 2) AND (r3c2 = 2) AND (r3c5 = 8) AND (r3c9 = 6) AND (r4c3 = 7) AND (r4c9 = 5) AND (r5c1 = 8) AND (r5c4 = 5) AND (r6c1 = 6) AND (r6c3 = 3) AND (r6c8 = 7) AND (r7c3 = 9) AND (r7c4 = 7) AND (r8c1 = 3) AND (r8c3 = 2) AND (r8c5 = 5) AND (r8c8 = 6) AND (r9c3 = 5) AND (r9c4 = 3) AND (r9c7 = 9) AND (r9c8 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 8) AND (r1c8 = 7) AND (r2c1 = 2) AND (r2c2 = 6) AND (r3c2 = 4) AND (r3c5 = 6) AND (r3c6 = 5) AND (r4c3 = 7) AND (r5c6 = 2) AND (r5c8 = 3) AND (r6c6 = 3) AND (r6c8 = 4) AND (r6c9 = 5) AND (r7c4 = 3) AND (r8c3 = 2) AND (r8c4 = 8) AND (r8c5 = 9) AND (r8c6 = 7) AND (r9c2 = 5) AND (r9c9 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c5 = 8) AND (r1c8 = 7) AND (r1c9 = 1) AND (r2c2 = 6) AND (r2c3 = 7) AND (r3c1 = 8) AND (r5c1 = 7) AND (r5c2 = 2) AND (r5c3 = 9) AND (r5c5 = 3) AND (r5c6 = 1) AND (r5c8 = 6) AND (r5c9 = 4) AND (r6c1 = 3) AND (r6c2 = 8) AND (r6c3 = 1) AND (r7c3 = 8) AND (r7c5 = 1) AND (r7c7 = 7) AND (r7c8 = 4) AND (r8c2 = 1) AND (r8c3 = 2) AND (r8c4 = 6) AND (r8c8 = 8) AND (r8c9 = 3) AND (r9c1 = 6) AND (r9c4 = 3) AND (r9c5 = 4) AND (r9c8 = 1) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c8 = 4) AND (r2c5 = 8) AND (r2c9 = 7) AND (r3c4 = 1) AND (r3c5 = 4) AND (r3c6 = 6) AND (r3c7 = 9) AND (r3c9 = 8) AND (r4c1 = 2) AND (r4c5 = 6) AND (r4c9 = 3) AND (r5c3 = 1) AND (r5c5 = 9) AND (r5c9 = 6) AND (r6c2 = 8) AND (r6c3 = 6) AND (r6c4 = 3) AND (r6c5 = 7) AND (r6c7 = 4) AND (r7c5 = 1) AND (r7c7 = 7) AND (r8c1 = 9) AND (r8c2 = 4) AND (r8c8 = 3) AND (r8c9 = 1) AND (r9c6 = 7) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c5 = 2) AND (r1c6 = 6) AND (r2c7 = 4) AND (r2c9 = 1) AND (r3c1 = 5) AND (r4c1 = 2) AND (r4c8 = 6) AND (r5c6 = 5) AND (r5c8 = 3) AND (r6c2 = 4) AND (r6c4 = 1) AND (r7c4 = 4) AND (r7c5 = 1) AND (r7c7 = 7) AND (r8c4 = 8) AND (r9c1 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 4) AND (r1c7 = 8) AND (r1c8 = 1) AND (r2c1 = 9) AND (r2c4 = 6) AND (r2c6 = 7) AND (r3c3 = 8) AND (r3c6 = 2) AND (r3c8 = 6) AND (r4c6 = 1) AND (r4c8 = 4) AND (r4c9 = 2) AND (r5c2 = 3) AND (r6c1 = 6) AND (r6c2 = 4) AND (r7c1 = 8) AND (r7c2 = 1) AND (r8c7 = 4) AND (r8c8 = 3) AND (r9c3 = 7) AND (r9c4 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 3) AND (r1c3 = 4) AND (r1c6 = 5) AND (r1c8 = 8) AND (r2c2 = 5) AND (r2c5 = 9) AND (r2c8 = 4) AND (r2c9 = 3) AND (r3c1 = 9) AND (r3c2 = 8) AND (r3c4 = 2) AND (r3c9 = 5) AND (r4c1 = 3) AND (r4c5 = 7) AND (r4c9 = 8) AND (r5c2 = 4) AND (r5c6 = 3) AND (r5c7 = 6) AND (r5c8 = 9) AND (r6c2 = 9) AND (r6c5 = 6) AND (r6c7 = 2) AND (r7c1 = 6) AND (r7c5 = 5) AND (r7c6 = 7) AND (r8c5 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r1c5 = 5) AND (r1c6 = 4) AND (r1c7 = 3) AND (r1c8 = 6) AND (r1c9 = 1) AND (r2c4 = 2) AND (r3c5 = 1) AND (r3c6 = 9) AND (r4c4 = 4) AND (r4c6 = 8) AND (r5c2 = 4) AND (r5c4 = 3) AND (r5c5 = 2) AND (r5c6 = 5) AND (r5c7 = 1) AND (r5c8 = 8) AND (r6c5 = 6) AND (r6c8 = 9) AND (r6c9 = 4) AND (r7c1 = 3) AND (r7c4 = 1) AND (r7c6 = 2) AND (r7c9 = 5) AND (r8c9 = 3) AND (r9c6 = 6) AND (r9c7 = 2) AND (r9c8 = 1) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 1) AND (r1c5 = 6) AND (r2c2 = 3) AND (r2c7 = 5) AND (r2c9 = 4) AND (r3c5 = 2) AND (r4c8 = 7) AND (r4c9 = 2) AND (r5c3 = 1) AND (r5c4 = 5) AND (r5c5 = 7) AND (r5c7 = 9) AND (r6c2 = 4) AND (r6c8 = 1) AND (r7c2 = 9) AND (r7c3 = 2) AND (r8c4 = 7) AND (r8c7 = 6) AND (r8c8 = 3) AND (r9c8 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c3 = 5) AND (r1c9 = 2) AND (r2c4 = 9) AND (r2c6 = 1) AND (r3c1 = 3) AND (r4c2 = 6) AND (r4c4 = 7) AND (r4c7 = 4) AND (r5c1 = 2) AND (r5c5 = 5) AND (r6c8 = 6) AND (r7c4 = 3) AND (r7c5 = 8) AND (r8c2 = 1) AND (r8c7 = 7) AND (r9c2 = 4) AND (r9c8 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c2 = 7) AND (r2c7 = 8) AND (r2c9 = 4) AND (r3c5 = 9) AND (r3c6 = 8) AND (r3c7 = 3) AND (r3c9 = 2) AND (r4c1 = 6) AND (r4c4 = 1) AND (r4c7 = 9) AND (r5c3 = 7) AND (r5c8 = 3) AND (r6c1 = 2) AND (r6c2 = 8) AND (r6c6 = 3) AND (r6c7 = 6) AND (r7c2 = 3) AND (r7c4 = 9) AND (r7c5 = 4) AND (r7c6 = 6) AND (r7c9 = 8) AND (r8c2 = 2) AND (r9c1 = 1) AND (r9c3 = 4) AND (r9c4 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 6) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 2) AND (r3c5 = 5) AND (r4c4 = 6) AND (r4c8 = 7) AND (r5c3 = 8) AND (r5c7 = 9) AND (r6c2 = 5) AND (r6c6 = 3) AND (r7c5 = 6) AND (r7c7 = 5) AND (r8c1 = 7) AND (r8c2 = 1) AND (r8c4 = 9) AND (r9c2 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c3 = 3) AND (r1c7 = 6) AND (r1c8 = 4) AND (r2c1 = 1) AND (r2c2 = 2) AND (r2c5 = 6) AND (r2c7 = 5) AND (r3c1 = 5) AND (r3c4 = 8) AND (r3c5 = 9) AND (r3c6 = 3) AND (r3c8 = 2) AND (r3c9 = 1) AND (r4c5 = 3) AND (r5c2 = 6) AND (r5c5 = 2) AND (r5c6 = 5) AND (r5c8 = 1) AND (r5c9 = 3) AND (r6c2 = 1) AND (r6c6 = 9) AND (r6c8 = 5) AND (r7c1 = 4) AND (r7c4 = 3) AND (r7c6 = 1) AND (r8c2 = 5) AND (r9c4 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 5) AND (r1c3 = 3) AND (r1c5 = 9) AND (r2c7 = 8) AND (r2c9 = 1) AND (r3c1 = 2) AND (r4c1 = 4) AND (r4c5 = 2) AND (r4c8 = 5) AND (r5c2 = 1) AND (r5c4 = 8) AND (r6c2 = 6) AND (r6c4 = 7) AND (r7c4 = 4) AND (r7c6 = 7) AND (r7c7 = 6) AND (r8c8 = 3) AND (r9c1 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 1) AND (r1c4 = 7) AND (r1c7 = 2) AND (r1c9 = 5) AND (r2c8 = 6) AND (r2c9 = 3) AND (r3c3 = 3) AND (r3c5 = 6) AND (r4c1 = 5) AND (r4c4 = 3) AND (r4c9 = 7) AND (r6c3 = 8) AND (r6c4 = 2) AND (r6c6 = 7) AND (r6c7 = 3) AND (r6c8 = 9) AND (r7c8 = 7) AND (r8c1 = 2) AND (r8c4 = 5) AND (r8c7 = 1) AND (r9c2 = 6) AND (r9c4 = 8) AND (r9c5 = 3) AND (r9c6 = 1) AND (r9c7 = 5) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 9) AND (r1c4 = 5) AND (r1c6 = 6) AND (r1c7 = 4) AND (r1c8 = 2) AND (r2c1 = 2) AND (r2c2 = 3) AND (r2c7 = 8) AND (r2c9 = 5) AND (r3c2 = 5) AND (r3c3 = 4) AND (r3c5 = 3) AND (r3c8 = 6) AND (r3c9 = 9) AND (r4c3 = 8) AND (r4c4 = 6) AND (r4c5 = 7) AND (r4c6 = 5) AND (r6c4 = 3) AND (r6c5 = 2) AND (r6c6 = 9) AND (r6c9 = 6) AND (r7c2 = 4) AND (r7c3 = 2) AND (r7c5 = 9) AND (r7c6 = 3) AND (r7c7 = 6) AND (r8c4 = 4) AND (r8c5 = 6) AND (r9c1 = 3) AND (r9c4 = 2) AND (r9c6 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c5 = 5) AND (r2c3 = 9) AND (r2c7 = 1) AND (r3c6 = 9) AND (r3c9 = 6) AND (r4c4 = 8) AND (r4c9 = 5) AND (r5c5 = 1) AND (r5c7 = 8) AND (r5c8 = 3) AND (r6c2 = 3) AND (r6c3 = 2) AND (r6c8 = 7) AND (r7c1 = 1) AND (r7c2 = 8) AND (r7c7 = 3) AND (r8c3 = 7) AND (r8c8 = 2) AND (r9c2 = 5) AND (r9c7 = 7) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 6) AND (r1c7 = 8) AND (r1c9 = 7) AND (r2c3 = 3) AND (r2c8 = 4) AND (r3c1 = 2) AND (r3c2 = 9) AND (r3c5 = 7) AND (r3c9 = 6) AND (r4c4 = 9) AND (r4c7 = 2) AND (r4c9 = 3) AND (r5c4 = 2) AND (r5c5 = 6) AND (r5c9 = 9) AND (r7c1 = 3) AND (r7c2 = 8) AND (r7c5 = 2) AND (r8c3 = 7) AND (r8c7 = 1) AND (r8c9 = 4) AND (r9c4 = 1) AND (r9c8 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c8 = 1) AND (r2c6 = 1) AND (r2c8 = 2) AND (r2c9 = 3) AND (r3c5 = 5) AND (r4c4 = 6) AND (r4c8 = 4) AND (r5c3 = 3) AND (r5c7 = 5) AND (r6c2 = 7) AND (r6c6 = 2) AND (r7c5 = 4) AND (r7c7 = 8) AND (r8c1 = 2) AND (r8c2 = 1) AND (r8c4 = 8) AND (r8c8 = 7) AND (r9c2 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 5) AND (r1c5 = 7) AND (r1c7 = 4) AND (r1c8 = 1) AND (r2c3 = 7) AND (r2c4 = 2) AND (r2c7 = 3) AND (r2c9 = 9) AND (r3c5 = 4) AND (r3c7 = 7) AND (r3c9 = 2) AND (r4c3 = 8) AND (r4c6 = 2) AND (r5c4 = 3) AND (r5c5 = 9) AND (r5c7 = 2) AND (r5c8 = 4) AND (r6c2 = 3) AND (r6c4 = 4) AND (r6c9 = 5) AND (r7c4 = 9) AND (r7c5 = 2) AND (r7c7 = 5) AND (r8c4 = 8) AND (r8c5 = 1) AND (r8c6 = 4) AND (r8c9 = 7) AND (r9c1 = 8) AND (r9c6 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c2 = 7) AND (r2c4 = 6) AND (r2c5 = 3) AND (r3c3 = 9) AND (r3c4 = 8) AND (r3c8 = 6) AND (r4c7 = 7) AND (r4c8 = 3) AND (r5c3 = 2) AND (r5c4 = 3) AND (r5c7 = 5) AND (r5c9 = 9) AND (r6c3 = 6) AND (r6c5 = 1) AND (r6c7 = 2) AND (r7c1 = 2) AND (r7c3 = 3) AND (r7c6 = 1) AND (r8c1 = 9) AND (r8c5 = 6) AND (r8c9 = 8) AND (r9c2 = 8) AND (r9c3 = 1) AND (r9c4 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 9) AND (r2c4 = 3) AND (r2c5 = 6) AND (r2c7 = 1) AND (r3c5 = 1) AND (r3c6 = 9) AND (r3c7 = 5) AND (r4c1 = 5) AND (r4c8 = 9) AND (r4c9 = 2) AND (r5c5 = 7) AND (r6c4 = 6) AND (r6c9 = 3) AND (r7c4 = 9) AND (r7c7 = 7) AND (r7c8 = 5) AND (r8c5 = 5) AND (r8c6 = 1) AND (r8c8 = 2) AND (r9c2 = 6) AND (r9c5 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 3) AND (r1c3 = 7) AND (r2c1 = 9) AND (r2c2 = 4) AND (r2c3 = 6) AND (r2c9 = 3) AND (r3c1 = 1) AND (r3c4 = 7) AND (r4c1 = 2) AND (r4c2 = 8) AND (r4c3 = 1) AND (r4c4 = 4) AND (r5c3 = 3) AND (r5c6 = 6) AND (r6c1 = 4) AND (r7c5 = 1) AND (r7c7 = 9) AND (r7c9 = 2) AND (r8c3 = 2) AND (r8c4 = 9) AND (r8c6 = 4) AND (r8c9 = 6) AND (r9c1 = 3) AND (r9c2 = 1) AND (r9c5 = 8) AND (r9c8 = 4) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c1 = 4) AND (r2c2 = 2) AND (r2c3 = 9) AND (r2c5 = 8) AND (r2c6 = 3) AND (r3c2 = 8) AND (r3c4 = 5) AND (r3c6 = 4) AND (r4c5 = 2) AND (r4c7 = 4) AND (r4c8 = 7) AND (r5c2 = 4) AND (r5c4 = 8) AND (r5c6 = 9) AND (r5c8 = 5) AND (r6c3 = 2) AND (r6c4 = 1) AND (r6c7 = 3) AND (r6c9 = 8) AND (r7c2 = 9) AND (r8c1 = 8) AND (r8c5 = 7) AND (r8c6 = 2) AND (r8c9 = 4) AND (r9c4 = 9) AND (r9c5 = 1) AND (r9c6 = 8) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 2) AND (r1c7 = 4) AND (r1c9 = 9) AND (r2c2 = 4) AND (r2c8 = 5) AND (r2c9 = 2) AND (r3c3 = 5) AND (r3c7 = 8) AND (r3c8 = 7) AND (r4c2 = 8) AND (r4c8 = 9) AND (r4c9 = 6) AND (r5c3 = 7) AND (r5c6 = 9) AND (r5c7 = 2) AND (r5c8 = 3) AND (r6c3 = 2) AND (r6c5 = 3) AND (r6c7 = 7) AND (r6c9 = 8) AND (r7c2 = 5) AND (r7c5 = 8) AND (r7c7 = 9) AND (r8c1 = 2) AND (r8c3 = 6) AND (r9c3 = 8) AND (r9c4 = 5) AND (r9c6 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c5 = 6) AND (r2c3 = 2) AND (r2c7 = 6) AND (r3c2 = 1) AND (r3c6 = 9) AND (r3c7 = 5) AND (r3c9 = 3) AND (r4c2 = 7) AND (r4c7 = 8) AND (r5c1 = 1) AND (r5c8 = 3) AND (r6c3 = 9) AND (r6c9 = 5) AND (r7c2 = 8) AND (r7c6 = 3) AND (r7c9 = 9) AND (r8c1 = 7) AND (r8c3 = 5) AND (r8c6 = 2) AND (r8c7 = 1) AND (r8c9 = 6) AND (r9c1 = 6) AND (r9c8 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 3) AND (r1c8 = 1) AND (r2c1 = 7) AND (r2c4 = 5) AND (r3c1 = 2) AND (r3c5 = 4) AND (r4c2 = 3) AND (r4c3 = 9) AND (r4c6 = 8) AND (r5c8 = 6) AND (r5c9 = 2) AND (r6c2 = 1) AND (r7c1 = 5) AND (r7c4 = 6) AND (r7c9 = 7) AND (r8c2 = 8) AND (r8c7 = 9) AND (r9c5 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c3 = 1) AND (r1c5 = 7) AND (r1c8 = 6) AND (r1c9 = 3) AND (r2c2 = 6) AND (r2c8 = 2) AND (r3c2 = 2) AND (r3c3 = 3) AND (r3c5 = 6) AND (r3c7 = 7) AND (r3c8 = 9) AND (r5c2 = 1) AND (r5c7 = 3) AND (r5c8 = 5) AND (r6c3 = 9) AND (r6c8 = 4) AND (r7c1 = 6) AND (r7c4 = 4) AND (r7c6 = 9) AND (r7c7 = 5) AND (r8c1 = 5) AND (r8c2 = 9) AND (r8c4 = 6) AND (r8c5 = 3) AND (r8c8 = 7) AND (r8c9 = 4) AND (r9c3 = 4) AND (r9c4 = 7) AND (r9c5 = 5) AND (r9c8 = 3) AND (r9c9 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c8 = 9) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 2) AND (r3c5 = 5) AND (r4c4 = 4) AND (r4c8 = 2) AND (r5c3 = 6) AND (r5c7 = 7) AND (r6c2 = 5) AND (r6c6 = 3) AND (r7c5 = 6) AND (r7c7 = 5) AND (r8c1 = 8) AND (r8c2 = 1) AND (r8c4 = 9) AND (r9c2 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 1) AND (r1c8 = 8) AND (r2c6 = 1) AND (r2c8 = 2) AND (r2c9 = 3) AND (r3c3 = 4) AND (r3c5 = 5) AND (r4c4 = 2) AND (r4c8 = 6) AND (r5c3 = 7) AND (r5c7 = 8) AND (r6c2 = 5) AND (r6c6 = 9) AND (r7c5 = 7) AND (r7c7 = 5) AND (r8c1 = 6) AND (r8c2 = 3) AND (r8c4 = 8) AND (r9c2 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r1c3 = 7) AND (r1c5 = 3) AND (r1c6 = 4) AND (r1c8 = 6) AND (r1c9 = 5) AND (r2c6 = 8) AND (r2c9 = 2) AND (r3c3 = 4) AND (r3c7 = 7) AND (r4c1 = 4) AND (r4c9 = 3) AND (r5c1 = 8) AND (r5c3 = 2) AND (r5c7 = 6) AND (r5c8 = 4) AND (r6c2 = 7) AND (r6c9 = 8) AND (r7c2 = 2) AND (r7c3 = 1) AND (r7c5 = 8) AND (r7c8 = 5) AND (r8c1 = 6) AND (r8c2 = 4) AND (r8c5 = 2) AND (r8c6 = 5) AND (r8c7 = 3) AND (r9c1 = 5) AND (r9c6 = 7) AND (r9c9 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c8 = 8) AND (r2c1 = 3) AND (r2c4 = 5) AND (r2c6 = 7) AND (r2c7 = 1) AND (r3c6 = 1) AND (r3c8 = 6) AND (r3c9 = 3) AND (r4c3 = 2) AND (r5c1 = 8) AND (r5c3 = 7) AND (r5c7 = 2) AND (r5c8 = 3) AND (r6c1 = 5) AND (r6c5 = 7) AND (r7c2 = 8) AND (r7c5 = 4) AND (r7c6 = 3) AND (r7c8 = 2) AND (r7c9 = 1) AND (r8c1 = 1) AND (r8c3 = 5) AND (r8c9 = 6) AND (r9c1 = 4) AND (r9c2 = 3) AND (r9c7 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 5) AND (r3c5 = 7) AND (r4c4 = 4) AND (r4c8 = 5) AND (r5c3 = 7) AND (r5c7 = 6) AND (r6c2 = 8) AND (r6c6 = 1) AND (r7c5 = 5) AND (r7c7 = 8) AND (r8c1 = 1) AND (r8c2 = 2) AND (r8c4 = 3) AND (r9c2 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c5 = 3) AND (r1c6 = 1) AND (r2c1 = 3) AND (r2c4 = 4) AND (r2c5 = 2) AND (r2c8 = 6) AND (r3c4 = 6) AND (r3c6 = 9) AND (r4c5 = 7) AND (r4c6 = 3) AND (r4c7 = 4) AND (r5c2 = 7) AND (r5c4 = 1) AND (r5c6 = 2) AND (r5c7 = 5) AND (r5c8 = 3) AND (r6c4 = 5) AND (r6c5 = 4) AND (r6c8 = 1) AND (r7c2 = 1) AND (r7c7 = 3) AND (r8c1 = 5) AND (r8c2 = 3) AND (r8c7 = 6) AND (r8c8 = 9) AND (r9c2 = 6) AND (r9c3 = 9) AND (r9c5 = 1) AND (r9c6 = 4) AND (r9c7 = 2) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 8) AND (r1c7 = 4) AND (r2c2 = 2) AND (r2c6 = 1) AND (r2c8 = 9) AND (r3c5 = 7) AND (r3c9 = 5) AND (r4c4 = 4) AND (r4c7 = 8) AND (r5c5 = 5) AND (r5c9 = 7) AND (r6c1 = 1) AND (r6c6 = 9) AND (r6c8 = 2) AND (r7c1 = 9) AND (r7c6 = 6) AND (r7c7 = 1) AND (r7c8 = 3) AND (r8c1 = 2) AND (r9c1 = 6) AND (r9c3 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 3) AND (r1c3 = 4) AND (r1c4 = 6) AND (r1c7 = 9) AND (r1c8 = 2) AND (r1c9 = 1) AND (r2c1 = 2) AND (r3c2 = 1) AND (r3c3 = 9) AND (r3c9 = 5) AND (r4c2 = 4) AND (r4c3 = 2) AND (r4c9 = 9) AND (r5c2 = 9) AND (r5c3 = 6) AND (r6c1 = 3) AND (r6c4 = 9) AND (r6c8 = 6) AND (r7c2 = 2) AND (r7c3 = 1) AND (r7c5 = 4) AND (r7c6 = 9) AND (r7c8 = 5) AND (r8c4 = 5) AND (r8c6 = 6) AND (r8c8 = 1) AND (r9c4 = 2) AND (r9c5 = 1) AND (r9c7 = 7) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c9 = 4) AND (r2c2 = 3) AND (r2c3 = 1) AND (r2c6 = 9) AND (r2c9 = 7) AND (r3c1 = 2) AND (r3c2 = 9) AND (r3c6 = 1) AND (r4c2 = 7) AND (r4c6 = 6) AND (r5c6 = 2) AND (r5c9 = 9) AND (r6c4 = 7) AND (r6c5 = 4) AND (r7c1 = 5) AND (r7c5 = 1) AND (r7c8 = 2) AND (r8c2 = 6) AND (r8c5 = 9) AND (r8c8 = 7) AND (r8c9 = 3) AND (r9c3 = 3) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 4) AND (r1c6 = 2) AND (r1c7 = 5) AND (r1c8 = 6) AND (r2c4 = 7) AND (r2c9 = 3) AND (r3c2 = 1) AND (r4c1 = 6) AND (r4c5 = 9) AND (r4c6 = 8) AND (r5c5 = 1) AND (r6c9 = 4) AND (r7c7 = 1) AND (r7c8 = 8) AND (r8c1 = 4) AND (r8c4 = 3) AND (r9c1 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c4 = 4) AND (r1c5 = 2) AND (r1c6 = 6) AND (r1c7 = 1) AND (r2c2 = 4) AND (r2c4 = 3) AND (r2c5 = 7) AND (r2c8 = 2) AND (r3c3 = 6) AND (r3c5 = 1) AND (r3c6 = 5) AND (r3c8 = 7) AND (r4c1 = 6) AND (r5c2 = 8) AND (r5c4 = 5) AND (r6c1 = 4) AND (r6c2 = 5) AND (r6c3 = 2) AND (r6c5 = 6) AND (r6c6 = 3) AND (r7c1 = 5) AND (r7c4 = 7) AND (r7c9 = 2) AND (r8c1 = 7) AND (r8c9 = 1) AND (r9c1 = 3) AND (r9c3 = 4) AND (r9c4 = 6) AND (r9c5 = 5) AND (r9c6 = 2) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 9) AND (r1c7 = 3) AND (r1c9 = 6) AND (r2c1 = 7) AND (r2c4 = 6) AND (r2c6 = 4) AND (r2c7 = 8) AND (r3c1 = 6) AND (r3c2 = 1) AND (r3c5 = 3) AND (r3c9 = 7) AND (r4c1 = 1) AND (r4c2 = 6) AND (r4c7 = 4) AND (r4c9 = 3) AND (r5c6 = 1) AND (r5c7 = 7) AND (r6c2 = 8) AND (r6c4 = 4) AND (r6c5 = 9) AND (r6c8 = 1) AND (r7c2 = 9) AND (r7c5 = 4) AND (r8c9 = 4) AND (r9c1 = 2) AND (r9c2 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c2 = 3) AND (r1c5 = 7) AND (r1c6 = 6) AND (r1c7 = 5) AND (r1c8 = 9) AND (r2c2 = 6) AND (r2c3 = 5) AND (r2c5 = 4) AND (r3c4 = 5) AND (r3c5 = 9) AND (r3c7 = 3) AND (r4c2 = 1) AND (r4c6 = 8) AND (r4c7 = 4) AND (r4c8 = 5) AND (r5c1 = 3) AND (r5c2 = 7) AND (r5c4 = 6) AND (r5c6 = 4) AND (r5c7 = 1) AND (r5c9 = 9) AND (r6c5 = 1) AND (r6c6 = 9) AND (r6c8 = 7) AND (r6c9 = 3) AND (r7c2 = 9) AND (r7c5 = 8) AND (r8c2 = 5) AND (r8c5 = 6) AND (r8c6 = 7) AND (r8c7 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c2 = 4) AND (r1c6 = 6) AND (r1c8 = 2) AND (r2c3 = 6) AND (r2c9 = 9) AND (r3c7 = 1) AND (r4c5 = 9) AND (r4c8 = 3) AND (r5c1 = 3) AND (r5c2 = 6) AND (r5c7 = 9) AND (r6c3 = 2) AND (r6c4 = 8) AND (r7c2 = 9) AND (r7c7 = 4) AND (r7c8 = 7) AND (r8c2 = 7) AND (r8c3 = 1) AND (r8c5 = 4) AND (r8c7 = 6) AND (r8c9 = 8) AND (r9c1 = 2) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 2) AND (r1c4 = 3) AND (r1c6 = 8) AND (r1c8 = 6) AND (r2c1 = 8) AND (r2c5 = 7) AND (r2c9 = 2) AND (r3c3 = 6) AND (r3c4 = 5) AND (r3c6 = 2) AND (r3c7 = 8) AND (r4c1 = 6) AND (r4c3 = 2) AND (r4c7 = 7) AND (r4c9 = 3) AND (r5c2 = 9) AND (r5c8 = 2) AND (r6c1 = 3) AND (r6c3 = 5) AND (r6c7 = 9) AND (r6c9 = 4) AND (r7c3 = 7) AND (r7c4 = 2) AND (r7c6 = 1) AND (r7c7 = 6) AND (r8c1 = 5) AND (r8c5 = 6) AND (r8c9 = 1) AND (r9c2 = 6) AND (r9c4 = 4) AND (r9c6 = 5) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 2) AND (r1c3 = 4) AND (r1c8 = 3) AND (r1c9 = 1) AND (r2c1 = 9) AND (r2c3 = 6) AND (r2c4 = 4) AND (r2c5 = 5) AND (r3c3 = 3) AND (r3c5 = 7) AND (r3c8 = 6) AND (r5c1 = 4) AND (r5c8 = 7) AND (r5c9 = 9) AND (r6c4 = 5) AND (r6c5 = 6) AND (r7c1 = 1) AND (r7c4 = 2) AND (r8c1 = 6) AND (r8c2 = 7) AND (r8c5 = 4) AND (r9c5 = 9) AND (r9c6 = 7) AND (r9c8 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 6) AND (r1c7 = 4) AND (r2c1 = 9) AND (r2c3 = 3) AND (r3c4 = 4) AND (r3c8 = 2) AND (r4c9 = 9) AND (r5c1 = 2) AND (r5c7 = 3) AND (r6c5 = 3) AND (r6c6 = 1) AND (r6c7 = 7) AND (r7c1 = 5) AND (r7c2 = 9) AND (r7c3 = 7) AND (r8c1 = 4) AND (r8c4 = 9) AND (r9c2 = 2) AND (r9c7 = 6) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c4 = 7) AND (r1c8 = 3) AND (r2c2 = 8) AND (r2c6 = 9) AND (r2c9 = 5) AND (r3c4 = 1) AND (r3c7 = 6) AND (r3c9 = 2) AND (r4c8 = 9) AND (r5c5 = 6) AND (r6c4 = 3) AND (r6c6 = 1) AND (r7c2 = 7) AND (r7c8 = 8) AND (r8c1 = 6) AND (r8c4 = 2) AND (r8c5 = 8) AND (r8c7 = 3) AND (r9c1 = 1) AND (r9c2 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 7) AND (r2c2 = 4) AND (r2c7 = 1) AND (r2c9 = 3) AND (r3c6 = 9) AND (r3c8 = 6) AND (r3c9 = 5) AND (r4c3 = 4) AND (r5c2 = 3) AND (r5c3 = 7) AND (r5c4 = 2) AND (r5c8 = 9) AND (r6c4 = 1) AND (r7c1 = 7) AND (r7c5 = 1) AND (r7c7 = 6) AND (r8c3 = 5) AND (r8c6 = 7) AND (r8c7 = 2) AND (r9c5 = 6) AND (r9c6 = 5) AND (r9c8 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 2) AND (r1c5 = 3) AND (r1c8 = 5) AND (r2c2 = 8) AND (r2c9 = 1) AND (r3c2 = 9) AND (r4c1 = 5) AND (r4c6 = 1) AND (r4c8 = 3) AND (r5c5 = 8) AND (r5c7 = 9) AND (r6c1 = 2) AND (r7c2 = 4) AND (r7c4 = 6) AND (r7c7 = 8) AND (r8c1 = 7) AND (r8c4 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 6) AND (r1c5 = 4) AND (r1c6 = 1) AND (r1c7 = 8) AND (r1c9 = 5) AND (r2c3 = 8) AND (r2c6 = 2) AND (r2c7 = 4) AND (r2c9 = 1) AND (r3c1 = 1) AND (r3c3 = 4) AND (r3c4 = 5) AND (r3c5 = 8) AND (r3c8 = 6) AND (r4c3 = 1) AND (r4c5 = 3) AND (r4c9 = 4) AND (r6c6 = 9) AND (r6c9 = 3) AND (r7c2 = 2) AND (r7c3 = 6) AND (r8c1 = 5) AND (r8c3 = 9) AND (r8c5 = 1) AND (r8c6 = 4) AND (r8c8 = 2) AND (r8c9 = 6) AND (r9c1 = 4) AND (r9c5 = 6) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c4 = 2) AND (r2c1 = 5) AND (r2c5 = 8) AND (r2c7 = 6) AND (r2c9 = 4) AND (r3c9 = 9) AND (r4c1 = 3) AND (r4c4 = 4) AND (r4c5 = 5) AND (r5c3 = 8) AND (r5c4 = 1) AND (r5c5 = 9) AND (r5c6 = 6) AND (r6c1 = 4) AND (r6c5 = 3) AND (r6c7 = 1) AND (r6c9 = 6) AND (r7c1 = 1) AND (r7c4 = 6) AND (r7c7 = 9) AND (r7c8 = 5) AND (r7c9 = 8) AND (r8c4 = 5) AND (r9c1 = 8) AND (r9c2 = 6) AND (r9c7 = 4) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 6) AND (r1c3 = 4) AND (r1c4 = 3) AND (r1c5 = 1) AND (r1c9 = 5) AND (r2c2 = 2) AND (r2c5 = 5) AND (r2c7 = 6) AND (r2c9 = 4) AND (r3c3 = 8) AND (r3c5 = 6) AND (r3c6 = 4) AND (r3c8 = 2) AND (r4c3 = 1) AND (r4c7 = 9) AND (r4c9 = 2) AND (r5c2 = 3) AND (r6c1 = 8) AND (r6c5 = 2) AND (r6c6 = 6) AND (r6c9 = 1) AND (r7c4 = 5) AND (r7c5 = 9) AND (r8c1 = 3) AND (r8c6 = 8) AND (r9c1 = 9) AND (r9c5 = 4) AND (r9c6 = 3) AND (r9c8 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 1) AND (r1c8 = 7) AND (r1c9 = 3) AND (r2c4 = 5) AND (r2c5 = 6) AND (r2c7 = 8) AND (r2c8 = 4) AND (r3c4 = 3) AND (r3c6 = 8) AND (r3c7 = 6) AND (r4c5 = 5) AND (r4c6 = 2) AND (r4c7 = 7) AND (r4c9 = 6) AND (r5c4 = 7) AND (r5c5 = 1) AND (r5c8 = 3) AND (r7c1 = 2) AND (r7c2 = 7) AND (r7c8 = 6) AND (r7c9 = 8) AND (r8c2 = 4) AND (r8c3 = 5) AND (r8c4 = 1) AND (r9c1 = 6) AND (r9c2 = 8) AND (r9c3 = 3) AND (r9c6 = 7) AND (r9c9 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c5 = 5) AND (r1c8 = 1) AND (r2c1 = 5) AND (r2c2 = 8) AND (r3c5 = 7) AND (r4c4 = 7) AND (r4c5 = 2) AND (r4c6 = 4) AND (r4c7 = 1) AND (r4c8 = 8) AND (r5c1 = 1) AND (r5c5 = 8) AND (r5c9 = 9) AND (r6c2 = 7) AND (r6c4 = 1) AND (r6c5 = 3) AND (r6c8 = 4) AND (r7c1 = 3) AND (r7c3 = 2) AND (r7c5 = 9) AND (r7c7 = 8) AND (r7c8 = 5) AND (r7c9 = 4) AND (r8c2 = 9) AND (r8c3 = 7) AND (r8c7 = 2) AND (r9c1 = 8) AND (r9c3 = 5) AND (r9c6 = 2) AND (r9c8 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c6 = 7) AND (r1c9 = 2) AND (r2c1 = 5) AND (r2c2 = 2) AND (r2c4 = 9) AND (r2c5 = 3) AND (r2c7 = 4) AND (r3c4 = 5) AND (r3c9 = 7) AND (r4c1 = 9) AND (r4c2 = 3) AND (r4c9 = 4) AND (r5c9 = 1) AND (r6c6 = 1) AND (r6c7 = 3) AND (r7c3 = 4) AND (r7c5 = 2) AND (r8c1 = 2) AND (r8c2 = 9) AND (r8c5 = 7) AND (r9c1 = 1) AND (r9c5 = 8) AND (r9c6 = 5) AND (r9c8 = 2) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c7 = 7) AND (r1c8 = 5) AND (r1c9 = 3) AND (r2c2 = 7) AND (r2c3 = 9) AND (r2c6 = 3) AND (r2c7 = 2) AND (r2c8 = 1) AND (r3c3 = 5) AND (r4c5 = 2) AND (r5c3 = 4) AND (r5c5 = 3) AND (r5c7 = 1) AND (r5c9 = 7) AND (r6c1 = 3) AND (r6c3 = 6) AND (r6c4 = 1) AND (r6c7 = 4) AND (r6c8 = 2) AND (r7c1 = 2) AND (r7c3 = 3) AND (r7c6 = 6) AND (r7c7 = 5) AND (r7c9 = 1) AND (r8c2 = 6) AND (r8c3 = 7) AND (r8c5 = 1) AND (r8c8 = 4) AND (r8c9 = 2) AND (r9c7 = 6) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c3 = 7) AND (r1c8 = 5) AND (r2c3 = 9) AND (r2c5 = 6) AND (r2c8 = 1) AND (r3c6 = 1) AND (r3c7 = 3) AND (r4c2 = 7) AND (r5c3 = 1) AND (r5c4 = 2) AND (r5c6 = 7) AND (r5c9 = 5) AND (r6c5 = 3) AND (r6c7 = 8) AND (r6c9 = 6) AND (r7c6 = 3) AND (r8c4 = 7) AND (r8c5 = 8) AND (r9c1 = 6) AND (r9c8 = 9) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c7 = 5) AND (r1c8 = 9) AND (r2c2 = 5) AND (r2c3 = 1) AND (r2c5 = 6) AND (r2c6 = 3) AND (r3c3 = 9) AND (r3c5 = 2) AND (r5c2 = 7) AND (r5c3 = 3) AND (r5c5 = 5) AND (r5c8 = 2) AND (r6c3 = 2) AND (r6c7 = 1) AND (r6c8 = 7) AND (r7c2 = 9) AND (r7c4 = 7) AND (r7c6 = 6) AND (r7c7 = 3) AND (r7c8 = 5) AND (r8c1 = 7) AND (r8c2 = 8) AND (r9c5 = 8) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r2c4 = 4) AND (r2c8 = 5) AND (r3c1 = 8) AND (r3c2 = 5) AND (r3c3 = 9) AND (r3c4 = 2) AND (r4c3 = 3) AND (r4c4 = 5) AND (r4c7 = 4) AND (r4c8 = 9) AND (r5c7 = 5) AND (r5c9 = 6) AND (r6c3 = 7) AND (r6c4 = 9) AND (r6c5 = 2) AND (r6c6 = 4) AND (r6c8 = 3) AND (r6c9 = 8) AND (r7c6 = 2) AND (r7c8 = 8) AND (r8c1 = 7) AND (r8c4 = 8) AND (r8c5 = 5) AND (r8c7 = 9) AND (r8c8 = 4) AND (r9c2 = 3) AND (r9c4 = 7) AND (r9c5 = 4) AND (r9c8 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 9) AND (r1c7 = 6) AND (r2c1 = 8) AND (r2c3 = 6) AND (r2c4 = 7) AND (r2c5 = 4) AND (r2c6 = 5) AND (r2c8 = 2) AND (r2c9 = 9) AND (r3c3 = 4) AND (r3c6 = 3) AND (r3c8 = 7) AND (r3c9 = 5) AND (r4c1 = 4) AND (r4c4 = 3) AND (r4c5 = 7) AND (r4c6 = 9) AND (r4c8 = 6) AND (r5c6 = 4) AND (r6c1 = 7) AND (r6c5 = 8) AND (r6c8 = 5) AND (r7c3 = 8) AND (r7c4 = 4) AND (r7c6 = 6) AND (r8c1 = 3) AND (r8c5 = 5) AND (r8c6 = 8) AND (r9c4 = 2) AND (r9c5 = 3) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c5 = 7) AND (r3c3 = 3) AND (r3c5 = 2) AND (r3c8 = 5) AND (r4c2 = 6) AND (r4c5 = 4) AND (r4c9 = 2) AND (r5c3 = 8) AND (r5c4 = 5) AND (r5c6 = 9) AND (r6c4 = 6) AND (r7c1 = 6) AND (r7c8 = 9) AND (r8c3 = 2) AND (r8c5 = 3) AND (r8c9 = 4) AND (r9c1 = 4) AND (r9c2 = 7) AND (r9c4 = 8) AND (r9c7 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 3) AND (r1c4 = 4) AND (r1c6 = 6) AND (r2c2 = 9) AND (r2c7 = 7) AND (r4c1 = 6) AND (r4c3 = 4) AND (r4c4 = 1) AND (r5c5 = 7) AND (r5c7 = 2) AND (r5c9 = 9) AND (r6c7 = 5) AND (r7c5 = 3) AND (r7c8 = 8) AND (r8c1 = 5) AND (r8c2 = 2) AND (r9c4 = 8) AND (r9c8 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 7) AND (r1c5 = 2) AND (r2c2 = 8) AND (r2c6 = 6) AND (r3c6 = 3) AND (r3c9 = 6) AND (r4c3 = 3) AND (r4c5 = 4) AND (r4c7 = 7) AND (r4c8 = 8) AND (r5c1 = 2) AND (r5c5 = 1) AND (r6c2 = 6) AND (r6c9 = 5) AND (r7c4 = 1) AND (r7c7 = 3) AND (r7c8 = 7) AND (r8c5 = 5) AND (r9c3 = 8) AND (r9c6 = 7) AND (r9c8 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c8 = 8) AND (r2c1 = 3) AND (r2c2 = 5) AND (r2c3 = 1) AND (r2c5 = 7) AND (r3c6 = 9) AND (r3c7 = 7) AND (r3c9 = 3) AND (r4c3 = 7) AND (r4c4 = 1) AND (r4c6 = 8) AND (r4c7 = 5) AND (r5c5 = 3) AND (r5c7 = 2) AND (r6c2 = 8) AND (r6c6 = 5) AND (r6c8 = 9) AND (r7c7 = 1) AND (r7c8 = 5) AND (r7c9 = 2) AND (r8c3 = 3) AND (r8c4 = 4) AND (r8c6 = 1) AND (r9c4 = 9) AND (r9c5 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 3) AND (r1c9 = 8) AND (r2c1 = 7) AND (r2c2 = 2) AND (r2c4 = 9) AND (r2c9 = 6) AND (r3c4 = 1) AND (r4c2 = 8) AND (r4c6 = 6) AND (r5c3 = 7) AND (r5c5 = 5) AND (r5c8 = 6) AND (r6c1 = 3) AND (r6c5 = 2) AND (r7c1 = 5) AND (r7c3 = 8) AND (r7c4 = 7) AND (r7c5 = 1) AND (r8c6 = 9) AND (r9c1 = 2) AND (r9c3 = 6) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c3 = 2) AND (r1c4 = 9) AND (r2c7 = 8) AND (r3c8 = 4) AND (r3c9 = 6) AND (r4c2 = 1) AND (r4c6 = 2) AND (r4c9 = 3) AND (r5c1 = 3) AND (r5c2 = 7) AND (r6c6 = 4) AND (r7c8 = 7) AND (r8c1 = 6) AND (r8c4 = 5) AND (r8c6 = 1) AND (r9c1 = 4) AND (r9c4 = 3) AND (r9c6 = 9) AND (r9c7 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c5 = 6) AND (r1c6 = 4) AND (r1c8 = 2) AND (r1c9 = 5) AND (r2c2 = 5) AND (r2c6 = 9) AND (r2c9 = 1) AND (r3c5 = 2) AND (r3c8 = 4) AND (r3c9 = 9) AND (r4c1 = 5) AND (r4c3 = 6) AND (r4c6 = 3) AND (r4c8 = 1) AND (r5c1 = 4) AND (r5c3 = 2) AND (r6c2 = 1) AND (r7c1 = 3) AND (r7c2 = 6) AND (r7c3 = 9) AND (r7c4 = 4) AND (r7c8 = 5) AND (r8c3 = 5) AND (r8c6 = 6) AND (r9c1 = 7) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c5 = 6) AND (r1c6 = 5) AND (r1c9 = 7) AND (r2c1 = 5) AND (r2c6 = 3) AND (r2c8 = 6) AND (r2c9 = 8) AND (r3c3 = 8) AND (r3c4 = 4) AND (r3c9 = 9) AND (r4c3 = 2) AND (r5c5 = 5) AND (r5c9 = 3) AND (r6c3 = 6) AND (r6c6 = 7) AND (r7c5 = 9) AND (r7c7 = 2) AND (r8c4 = 3) AND (r8c7 = 4) AND (r9c1 = 6) AND (r9c8 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c4 = 3) AND (r1c8 = 6) AND (r2c5 = 8) AND (r2c7 = 5) AND (r3c2 = 1) AND (r4c1 = 8) AND (r4c3 = 9) AND (r4c4 = 6) AND (r4c7 = 4) AND (r5c4 = 1) AND (r5c6 = 2) AND (r6c1 = 5) AND (r7c4 = 7) AND (r7c8 = 3) AND (r7c9 = 2) AND (r8c1 = 4) AND (r8c5 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 4) AND (r1c8 = 6) AND (r2c4 = 1) AND (r2c5 = 2) AND (r2c6 = 9) AND (r2c8 = 8) AND (r2c9 = 4) AND (r3c3 = 2) AND (r4c3 = 5) AND (r4c7 = 4) AND (r5c2 = 2) AND (r5c4 = 4) AND (r5c5 = 1) AND (r5c7 = 8) AND (r5c8 = 5) AND (r6c2 = 6) AND (r6c4 = 5) AND (r6c6 = 8) AND (r6c8 = 2) AND (r7c1 = 2) AND (r7c2 = 1) AND (r7c3 = 6) AND (r7c6 = 5) AND (r8c2 = 8) AND (r8c4 = 2) AND (r8c5 = 3) AND (r9c2 = 3) AND (r9c3 = 4) AND (r9c4 = 8) AND (r9c6 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 8) AND (r1c7 = 1) AND (r1c9 = 4) AND (r2c1 = 7) AND (r2c2 = 3) AND (r4c5 = 7) AND (r4c6 = 2) AND (r4c7 = 6) AND (r5c2 = 1) AND (r5c3 = 3) AND (r7c3 = 4) AND (r7c4 = 3) AND (r7c5 = 1) AND (r8c1 = 2) AND (r8c7 = 5) AND (r8c8 = 7) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 9) AND (r1c5 = 4) AND (r1c8 = 8) AND (r2c2 = 4) AND (r2c9 = 7) AND (r3c4 = 6) AND (r3c9 = 2) AND (r4c3 = 5) AND (r4c7 = 7) AND (r4c8 = 4) AND (r5c1 = 9) AND (r5c2 = 6) AND (r5c7 = 5) AND (r6c4 = 2) AND (r7c2 = 5) AND (r7c5 = 2) AND (r7c9 = 8) AND (r8c3 = 4) AND (r8c5 = 8) AND (r8c6 = 3) AND (r9c2 = 8) AND (r9c4 = 9) AND (r9c5 = 7) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 2) AND (r1c5 = 6) AND (r1c8 = 8) AND (r2c1 = 9) AND (r2c3 = 4) AND (r4c2 = 8) AND (r4c4 = 5) AND (r4c8 = 6) AND (r5c1 = 7) AND (r5c6 = 9) AND (r6c9 = 1) AND (r7c2 = 2) AND (r7c4 = 6) AND (r8c5 = 3) AND (r8c7 = 9) AND (r9c1 = 1) AND (r9c7 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 4) AND (r1c3 = 8) AND (r1c4 = 9) AND (r1c6 = 7) AND (r1c7 = 1) AND (r3c4 = 4) AND (r3c5 = 3) AND (r3c6 = 1) AND (r4c6 = 4) AND (r5c5 = 9) AND (r5c7 = 7) AND (r6c1 = 6) AND (r6c5 = 2) AND (r6c6 = 3) AND (r7c2 = 7) AND (r7c6 = 8) AND (r7c7 = 3) AND (r7c9 = 9) AND (r8c1 = 1) AND (r8c3 = 3) AND (r8c5 = 7) AND (r8c6 = 2) AND (r8c7 = 8) AND (r8c9 = 4) AND (r9c2 = 8) AND (r9c3 = 4) AND (r9c7 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c3 = 5) AND (r1c7 = 8) AND (r1c8 = 2) AND (r2c1 = 2) AND (r2c2 = 9) AND (r2c3 = 8) AND (r2c4 = 7) AND (r3c1 = 4) AND (r3c2 = 3) AND (r3c8 = 5) AND (r3c9 = 9) AND (r4c1 = 8) AND (r4c4 = 3) AND (r4c5 = 4) AND (r4c6 = 6) AND (r5c4 = 2) AND (r5c7 = 3) AND (r6c5 = 5) AND (r6c6 = 7) AND (r7c5 = 6) AND (r7c6 = 4) AND (r8c4 = 8) AND (r8c6 = 9) AND (r8c8 = 4) AND (r9c4 = 5) AND (r9c5 = 3) AND (r9c7 = 6) AND (r9c8 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 1) AND (r1c8 = 8) AND (r2c8 = 6) AND (r3c3 = 8) AND (r3c4 = 4) AND (r3c7 = 1) AND (r4c1 = 5) AND (r4c3 = 6) AND (r4c7 = 4) AND (r5c5 = 9) AND (r5c8 = 5) AND (r5c9 = 7) AND (r6c5 = 8) AND (r6c6 = 4) AND (r7c4 = 8) AND (r7c6 = 7) AND (r7c7 = 2) AND (r8c2 = 2) AND (r8c3 = 7) AND (r8c5 = 1) AND (r9c2 = 5) AND (r9c4 = 6) AND (r9c6 = 2) AND (r9c7 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 6) AND (r1c4 = 3) AND (r1c6 = 1) AND (r2c5 = 8) AND (r2c9 = 1) AND (r3c2 = 8) AND (r3c4 = 9) AND (r3c5 = 5) AND (r3c6 = 7) AND (r3c8 = 3) AND (r4c1 = 9) AND (r4c3 = 8) AND (r4c5 = 3) AND (r4c6 = 4) AND (r4c8 = 6) AND (r5c6 = 9) AND (r6c4 = 1) AND (r6c5 = 7) AND (r6c6 = 8) AND (r6c8 = 9) AND (r6c9 = 5) AND (r7c1 = 8) AND (r7c2 = 6) AND (r7c6 = 5) AND (r7c7 = 7) AND (r7c8 = 1) AND (r8c1 = 7) AND (r8c3 = 1) AND (r8c6 = 3) AND (r8c7 = 5) AND (r8c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c8 = 4) AND (r2c1 = 6) AND (r2c4 = 3) AND (r2c5 = 8) AND (r2c9 = 7) AND (r3c4 = 7) AND (r3c5 = 9) AND (r3c6 = 6) AND (r4c4 = 6) AND (r4c8 = 3) AND (r5c5 = 1) AND (r6c3 = 7) AND (r6c4 = 4) AND (r6c9 = 2) AND (r7c2 = 4) AND (r7c4 = 8) AND (r7c9 = 6) AND (r8c1 = 3) AND (r8c2 = 1) AND (r9c2 = 9) AND (r9c7 = 2) AND (r9c8 = 1) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 1) AND (r1c7 = 6) AND (r2c2 = 4) AND (r2c3 = 3) AND (r2c8 = 8) AND (r2c9 = 5) AND (r3c1 = 6) AND (r3c4 = 5) AND (r3c9 = 2) AND (r4c6 = 3) AND (r4c7 = 2) AND (r5c3 = 5) AND (r5c5 = 1) AND (r5c6 = 7) AND (r5c8 = 6) AND (r5c9 = 8) AND (r6c4 = 8) AND (r6c6 = 5) AND (r6c9 = 1) AND (r7c3 = 2) AND (r7c6 = 6) AND (r7c7 = 1) AND (r7c8 = 3) AND (r7c9 = 4) AND (r8c1 = 4) AND (r8c6 = 1) AND (r8c8 = 2) AND (r8c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c5 = 2) AND (r1c6 = 9) AND (r1c7 = 3) AND (r1c8 = 6) AND (r2c1 = 3) AND (r2c2 = 8) AND (r2c4 = 1) AND (r2c5 = 4) AND (r2c8 = 2) AND (r3c2 = 9) AND (r4c2 = 1) AND (r4c3 = 9) AND (r4c4 = 8) AND (r4c7 = 4) AND (r5c4 = 4) AND (r5c5 = 9) AND (r5c9 = 7) AND (r6c6 = 3) AND (r7c1 = 8) AND (r7c3 = 6) AND (r8c3 = 7) AND (r8c7 = 8) AND (r9c6 = 2) AND (r9c8 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 1) AND (r1c8 = 6) AND (r2c1 = 6) AND (r2c5 = 7) AND (r2c6 = 2) AND (r3c9 = 9) AND (r4c1 = 1) AND (r4c2 = 8) AND (r4c4 = 2) AND (r4c7 = 5) AND (r6c6 = 5) AND (r6c8 = 9) AND (r6c9 = 4) AND (r7c1 = 7) AND (r7c2 = 5) AND (r7c7 = 9) AND (r8c1 = 4) AND (r8c6 = 6) AND (r8c7 = 8) AND (r8c8 = 5) AND (r9c3 = 6) AND (r9c5 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 6) AND (r1c6 = 7) AND (r1c7 = 5) AND (r2c5 = 5) AND (r2c8 = 6) AND (r2c9 = 4) AND (r3c2 = 5) AND (r3c5 = 6) AND (r3c7 = 9) AND (r3c8 = 8) AND (r3c9 = 1) AND (r4c1 = 1) AND (r5c3 = 7) AND (r5c4 = 9) AND (r5c9 = 2) AND (r6c2 = 9) AND (r6c7 = 1) AND (r7c3 = 4) AND (r7c5 = 1) AND (r7c6 = 5) AND (r7c9 = 9) AND (r8c1 = 8) AND (r8c5 = 7) AND (r8c9 = 6) AND (r9c6 = 2) AND (r9c8 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c5 = 6) AND (r2c2 = 2) AND (r2c3 = 7) AND (r2c5 = 9) AND (r2c6 = 1) AND (r2c9 = 5) AND (r3c3 = 3) AND (r3c4 = 7) AND (r3c6 = 8) AND (r4c8 = 3) AND (r5c1 = 5) AND (r5c3 = 6) AND (r5c5 = 2) AND (r5c6 = 9) AND (r5c7 = 7) AND (r6c1 = 2) AND (r6c3 = 1) AND (r6c6 = 7) AND (r7c1 = 3) AND (r7c3 = 9) AND (r7c6 = 6) AND (r7c7 = 1) AND (r7c8 = 2) AND (r8c2 = 6) AND (r8c3 = 5) AND (r8c5 = 1) AND (r8c6 = 2) AND (r9c1 = 1) AND (r9c4 = 9) AND (r9c5 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c7 = 7) AND (r1c8 = 6) AND (r2c1 = 8) AND (r2c5 = 2) AND (r2c6 = 6) AND (r2c8 = 5) AND (r3c1 = 4) AND (r3c2 = 5) AND (r4c8 = 1) AND (r5c3 = 2) AND (r5c4 = 8) AND (r5c6 = 5) AND (r5c8 = 3) AND (r5c9 = 7) AND (r6c9 = 8) AND (r7c1 = 2) AND (r7c3 = 8) AND (r7c4 = 6) AND (r8c2 = 3) AND (r8c4 = 5) AND (r8c7 = 6) AND (r8c8 = 2) AND (r9c3 = 7) AND (r9c6 = 2) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r2c2 = 1) AND (r2c5 = 8) AND (r2c6 = 6) AND (r2c7 = 4) AND (r3c2 = 4) AND (r4c3 = 8) AND (r4c7 = 1) AND (r4c8 = 3) AND (r5c1 = 5) AND (r5c2 = 3) AND (r6c2 = 7) AND (r6c3 = 1) AND (r6c5 = 3) AND (r6c7 = 5) AND (r7c3 = 7) AND (r7c4 = 4) AND (r7c8 = 1) AND (r8c2 = 5) AND (r8c3 = 4) AND (r8c4 = 7) AND (r8c5 = 9) AND (r8c7 = 6) AND (r8c9 = 8) AND (r9c2 = 6) AND (r9c3 = 9) AND (r9c4 = 8) AND (r9c5 = 5) AND (r9c6 = 1) AND (r9c7 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c3 = 8) AND (r1c5 = 2) AND (r2c8 = 9) AND (r2c9 = 1) AND (r3c1 = 3) AND (r4c2 = 4) AND (r4c3 = 6) AND (r5c5 = 3) AND (r5c7 = 7) AND (r6c4 = 5) AND (r7c2 = 5) AND (r7c4 = 9) AND (r7c6 = 6) AND (r8c4 = 4) AND (r8c8 = 1) AND (r9c1 = 2) AND (r9c7 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 3) AND (r1c9 = 2) AND (r2c3 = 8) AND (r3c5 = 5) AND (r4c9 = 4) AND (r5c2 = 5) AND (r5c5 = 7) AND (r5c8 = 2) AND (r6c2 = 7) AND (r6c4 = 3) AND (r6c5 = 8) AND (r6c6 = 4) AND (r6c8 = 5) AND (r7c2 = 9) AND (r7c3 = 7) AND (r7c6 = 8) AND (r7c9 = 5) AND (r8c2 = 8) AND (r8c3 = 2) AND (r8c5 = 1) AND (r8c6 = 7) AND (r8c8 = 4) AND (r9c2 = 1) AND (r9c3 = 5) AND (r9c4 = 4) AND (r9c5 = 2) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 7) AND (r1c6 = 5) AND (r2c1 = 6) AND (r2c9 = 4) AND (r3c1 = 8) AND (r3c2 = 5) AND (r3c6 = 7) AND (r4c6 = 8) AND (r4c9 = 6) AND (r5c1 = 9) AND (r5c2 = 6) AND (r5c5 = 4) AND (r5c7 = 5) AND (r6c3 = 1) AND (r6c6 = 3) AND (r6c7 = 8) AND (r7c3 = 4) AND (r7c5 = 7) AND (r8c1 = 3) AND (r8c4 = 8) AND (r8c7 = 9) AND (r8c9 = 7) AND (r9c2 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 8) AND (r1c5 = 7) AND (r1c8 = 2) AND (r2c7 = 6) AND (r2c9 = 4) AND (r3c3 = 6) AND (r3c4 = 9) AND (r3c6 = 5) AND (r3c7 = 3) AND (r4c4 = 5) AND (r4c6 = 7) AND (r5c5 = 9) AND (r5c8 = 8) AND (r5c9 = 2) AND (r6c7 = 5) AND (r7c1 = 2) AND (r7c2 = 3) AND (r7c6 = 4) AND (r7c9 = 9) AND (r8c1 = 4) AND (r8c4 = 7) AND (r8c5 = 6) AND (r8c9 = 5) AND (r9c1 = 5) AND (r9c5 = 3) AND (r9c6 = 9) AND (r9c8 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 6) AND (r1c4 = 8) AND (r1c6 = 9) AND (r1c9 = 5) AND (r2c1 = 5) AND (r2c6 = 4) AND (r3c1 = 9) AND (r3c2 = 2) AND (r3c7 = 6) AND (r4c3 = 1) AND (r4c7 = 3) AND (r5c3 = 3) AND (r5c5 = 8) AND (r5c9 = 6) AND (r6c1 = 6) AND (r6c4 = 1) AND (r6c5 = 9) AND (r6c8 = 5) AND (r6c9 = 8) AND (r7c9 = 3) AND (r8c6 = 2) AND (r9c4 = 6) AND (r9c7 = 1) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 6) AND (r1c9 = 7) AND (r2c4 = 7) AND (r2c5 = 9) AND (r2c8 = 8) AND (r2c9 = 3) AND (r3c5 = 8) AND (r3c7 = 5) AND (r3c8 = 4) AND (r4c2 = 4) AND (r4c3 = 3) AND (r4c5 = 1) AND (r4c9 = 5) AND (r5c3 = 5) AND (r5c8 = 6) AND (r6c2 = 6) AND (r6c5 = 3) AND (r6c7 = 4) AND (r7c1 = 6) AND (r7c4 = 3) AND (r7c6 = 9) AND (r7c7 = 8) AND (r8c6 = 5) AND (r8c8 = 9) AND (r9c1 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 2) AND (r2c2 = 4) AND (r2c6 = 6) AND (r2c8 = 7) AND (r2c9 = 1) AND (r3c3 = 9) AND (r3c4 = 3) AND (r3c7 = 4) AND (r4c4 = 9) AND (r4c5 = 4) AND (r5c3 = 6) AND (r5c6 = 1) AND (r5c9 = 7) AND (r6c3 = 1) AND (r6c5 = 2) AND (r6c6 = 7) AND (r7c1 = 7) AND (r7c3 = 4) AND (r7c4 = 1) AND (r7c5 = 6) AND (r7c8 = 9) AND (r7c9 = 5) AND (r8c1 = 9) AND (r9c1 = 6) AND (r9c2 = 1) AND (r9c5 = 5) AND (r9c8 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c6 = 1) AND (r1c8 = 4) AND (r2c1 = 8) AND (r2c3 = 9) AND (r2c4 = 2) AND (r2c8 = 1) AND (r3c4 = 8) AND (r3c6 = 7) AND (r3c7 = 2) AND (r3c9 = 5) AND (r4c1 = 5) AND (r5c3 = 4) AND (r5c4 = 6) AND (r5c8 = 8) AND (r6c3 = 7) AND (r6c4 = 4) AND (r7c4 = 9) AND (r7c8 = 6) AND (r7c9 = 8) AND (r8c1 = 9) AND (r8c3 = 5) AND (r8c4 = 1) AND (r8c6 = 8) AND (r8c7 = 4) AND (r8c8 = 7) AND (r9c1 = 4) AND (r9c3 = 8) AND (r9c5 = 2) AND (r9c8 = 5) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c3 = 8) AND (r1c9 = 4) AND (r2c1 = 6) AND (r2c3 = 2) AND (r2c7 = 5) AND (r2c8 = 8) AND (r3c1 = 5) AND (r3c2 = 4) AND (r3c5 = 2) AND (r3c7 = 1) AND (r3c8 = 6) AND (r3c9 = 7) AND (r4c7 = 8) AND (r4c8 = 4) AND (r5c1 = 2) AND (r5c7 = 7) AND (r5c9 = 5) AND (r6c1 = 4) AND (r6c2 = 8) AND (r6c3 = 5) AND (r6c6 = 1) AND (r6c8 = 2) AND (r7c1 = 7) AND (r7c4 = 3) AND (r7c6 = 4) AND (r8c9 = 2) AND (r9c1 = 8) AND (r9c2 = 5) AND (r9c6 = 6) AND (r9c7 = 4) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 5) AND (r1c9 = 3) AND (r2c3 = 6) AND (r2c6 = 1) AND (r2c8 = 8) AND (r3c4 = 4) AND (r3c7 = 6) AND (r3c9 = 2) AND (r4c9 = 1) AND (r5c4 = 9) AND (r5c6 = 8) AND (r5c7 = 5) AND (r6c5 = 3) AND (r6c6 = 6) AND (r6c7 = 8) AND (r7c1 = 4) AND (r7c7 = 1) AND (r7c8 = 9) AND (r8c1 = 8) AND (r8c3 = 5) AND (r8c5 = 1) AND (r8c8 = 4) AND (r9c4 = 6) AND (r9c6 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c5 = 3) AND (r2c3 = 6) AND (r2c4 = 2) AND (r2c6 = 8) AND (r3c4 = 9) AND (r3c5 = 7) AND (r3c9 = 5) AND (r5c1 = 2) AND (r5c3 = 9) AND (r5c4 = 8) AND (r5c6 = 3) AND (r6c4 = 6) AND (r6c6 = 7) AND (r6c9 = 9) AND (r7c1 = 7) AND (r7c2 = 5) AND (r7c8 = 8) AND (r7c9 = 4) AND (r8c2 = 4) AND (r8c3 = 8) AND (r8c5 = 5) AND (r8c7 = 6) AND (r8c9 = 3) AND (r9c3 = 2) AND (r9c8 = 5) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 1) AND (r1c5 = 2) AND (r2c4 = 1) AND (r2c9 = 8) AND (r3c2 = 8) AND (r3c4 = 3) AND (r3c6 = 7) AND (r3c8 = 1) AND (r4c2 = 5) AND (r4c3 = 7) AND (r4c8 = 3) AND (r5c3 = 2) AND (r5c7 = 6) AND (r6c1 = 8) AND (r6c7 = 5) AND (r6c8 = 7) AND (r6c9 = 4) AND (r7c2 = 7) AND (r7c9 = 3) AND (r8c3 = 4) AND (r8c4 = 7) AND (r8c7 = 1) AND (r8c8 = 2) AND (r9c1 = 2) AND (r9c3 = 5) AND (r9c7 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c2 = 1) AND (r1c6 = 3) AND (r1c7 = 9) AND (r2c2 = 6) AND (r2c8 = 8) AND (r2c9 = 2) AND (r3c1 = 2) AND (r3c4 = 7) AND (r3c7 = 3) AND (r4c2 = 8) AND (r4c5 = 3) AND (r4c6 = 6) AND (r5c2 = 9) AND (r5c5 = 1) AND (r5c7 = 4) AND (r5c8 = 3) AND (r6c3 = 6) AND (r6c6 = 9) AND (r7c3 = 2) AND (r8c5 = 8) AND (r8c8 = 7) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c5 = 8) AND (r1c7 = 4) AND (r2c1 = 3) AND (r2c9 = 2) AND (r4c1 = 1) AND (r4c3 = 6) AND (r4c4 = 3) AND (r5c7 = 8) AND (r5c8 = 5) AND (r6c1 = 2) AND (r7c2 = 8) AND (r7c3 = 4) AND (r7c8 = 3) AND (r8c4 = 2) AND (r8c6 = 1) AND (r9c5 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 4) AND (r1c3 = 9) AND (r2c6 = 7) AND (r3c2 = 6) AND (r3c7 = 4) AND (r4c1 = 9) AND (r4c2 = 1) AND (r4c4 = 7) AND (r4c8 = 3) AND (r4c9 = 6) AND (r5c4 = 3) AND (r5c5 = 5) AND (r5c7 = 1) AND (r5c8 = 4) AND (r6c1 = 2) AND (r7c4 = 5) AND (r7c8 = 7) AND (r8c2 = 3) AND (r8c3 = 6) AND (r8c5 = 2) AND (r9c2 = 2) AND (r9c4 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c5 = 5) AND (r1c8 = 4) AND (r1c9 = 6) AND (r2c6 = 1) AND (r2c8 = 7) AND (r3c1 = 3) AND (r3c3 = 6) AND (r3c6 = 9) AND (r3c7 = 5) AND (r3c9 = 1) AND (r4c2 = 5) AND (r4c5 = 9) AND (r4c6 = 4) AND (r5c4 = 2) AND (r6c1 = 9) AND (r6c5 = 7) AND (r6c9 = 3) AND (r7c1 = 4) AND (r7c5 = 6) AND (r7c6 = 7) AND (r7c8 = 2) AND (r7c9 = 5) AND (r9c1 = 6) AND (r9c4 = 5) AND (r9c5 = 1) AND (r9c6 = 3) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c4 = 2) AND (r1c6 = 4) AND (r1c8 = 1) AND (r2c1 = 4) AND (r2c2 = 9) AND (r2c4 = 1) AND (r2c6 = 7) AND (r2c8 = 5) AND (r2c9 = 2) AND (r3c5 = 5) AND (r4c1 = 1) AND (r4c2 = 3) AND (r4c8 = 9) AND (r4c9 = 7) AND (r5c3 = 9) AND (r5c7 = 2) AND (r6c1 = 5) AND (r6c2 = 4) AND (r6c8 = 6) AND (r6c9 = 3) AND (r7c5 = 2) AND (r8c1 = 2) AND (r8c2 = 5) AND (r8c4 = 7) AND (r8c6 = 1) AND (r8c8 = 8) AND (r8c9 = 6) AND (r9c2 = 1) AND (r9c4 = 6) AND (r9c6 = 3) AND (r9c8 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 5) AND (r1c6 = 2) AND (r1c9 = 4) AND (r2c1 = 7) AND (r2c3 = 2) AND (r2c6 = 4) AND (r2c7 = 3) AND (r2c8 = 5) AND (r3c2 = 1) AND (r3c6 = 3) AND (r3c7 = 9) AND (r4c1 = 3) AND (r4c3 = 7) AND (r4c4 = 5) AND (r4c6 = 8) AND (r4c7 = 2) AND (r6c7 = 7) AND (r6c9 = 8) AND (r7c2 = 7) AND (r7c3 = 1) AND (r7c5 = 8) AND (r7c6 = 5) AND (r7c7 = 4) AND (r8c1 = 4) AND (r8c3 = 3) AND (r8c9 = 2) AND (r9c1 = 2) AND (r9c3 = 8) AND (r9c5 = 3) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 2) AND (r3c5 = 5) AND (r4c4 = 4) AND (r4c8 = 6) AND (r5c3 = 7) AND (r5c7 = 8) AND (r6c2 = 5) AND (r7c5 = 7) AND (r7c7 = 5) AND (r8c1 = 9) AND (r8c2 = 4) AND (r8c4 = 1) AND (r9c2 = 6) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c9 = 1) AND (r2c6 = 4) AND (r2c8 = 8) AND (r3c2 = 4) AND (r3c4 = 6) AND (r3c6 = 1) AND (r3c8 = 2) AND (r4c1 = 5) AND (r4c2 = 6) AND (r4c3 = 2) AND (r4c5 = 7) AND (r4c7 = 3) AND (r4c8 = 4) AND (r5c1 = 1) AND (r5c3 = 7) AND (r5c6 = 3) AND (r5c9 = 2) AND (r6c1 = 4) AND (r6c2 = 3) AND (r6c5 = 6) AND (r6c8 = 7) AND (r7c9 = 7) AND (r8c6 = 6) AND (r8c7 = 8) AND (r8c9 = 4) AND (r9c1 = 3) AND (r9c4 = 8) AND (r9c6 = 7) AND (r9c7 = 2) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 3) AND (r2c1 = 7) AND (r2c7 = 8) AND (r2c8 = 5) AND (r3c2 = 8) AND (r3c4 = 4) AND (r3c5 = 9) AND (r3c8 = 7) AND (r4c3 = 4) AND (r5c2 = 3) AND (r5c4 = 1) AND (r5c5 = 8) AND (r6c1 = 6) AND (r6c3 = 9) AND (r6c9 = 4) AND (r8c3 = 6) AND (r8c5 = 5) AND (r8c9 = 3) AND (r9c5 = 6) AND (r9c9 = 1);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c6 = 4) AND (r1c8 = 8) AND (r1c9 = 6) AND (r2c3 = 6) AND (r2c4 = 3) AND (r2c7 = 7) AND (r3c2 = 4) AND (r3c3 = 8) AND (r3c8 = 3) AND (r3c9 = 5) AND (r4c2 = 9) AND (r4c4 = 4) AND (r5c3 = 1) AND (r6c1 = 4) AND (r6c3 = 5) AND (r6c4 = 9) AND (r6c6 = 6) AND (r7c1 = 7) AND (r7c2 = 8) AND (r7c3 = 4) AND (r7c5 = 6) AND (r7c6 = 9) AND (r7c9 = 3) AND (r8c6 = 3) AND (r9c1 = 6) AND (r9c4 = 1) AND (r9c5 = 4) AND (r9c6 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 5) AND (r1c4 = 9) AND (r1c7 = 1) AND (r2c4 = 4) AND (r2c7 = 9) AND (r3c1 = 6) AND (r3c2 = 3) AND (r3c5 = 2) AND (r3c7 = 5) AND (r4c1 = 4) AND (r4c9 = 6) AND (r5c3 = 1) AND (r5c5 = 3) AND (r6c8 = 3) AND (r6c9 = 4) AND (r7c1 = 7) AND (r7c2 = 2) AND (r7c4 = 6) AND (r8c4 = 7) AND (r9c8 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r1c5 = 1) AND (r1c7 = 4) AND (r2c3 = 3) AND (r2c5 = 9) AND (r2c7 = 2) AND (r2c8 = 5) AND (r3c1 = 7) AND (r3c3 = 5) AND (r4c4 = 9) AND (r4c7 = 6) AND (r4c9 = 3) AND (r5c1 = 9) AND (r6c3 = 2) AND (r6c6 = 5) AND (r7c5 = 2) AND (r7c8 = 4) AND (r8c6 = 9) AND (r8c8 = 2) AND (r8c9 = 7) AND (r9c3 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c6 = 5) AND (r2c1 = 4) AND (r2c4 = 8) AND (r2c5 = 6) AND (r2c6 = 9) AND (r2c9 = 5) AND (r3c1 = 8) AND (r4c3 = 9) AND (r4c6 = 2) AND (r4c8 = 5) AND (r4c9 = 6) AND (r5c1 = 1) AND (r5c3 = 2) AND (r5c8 = 3) AND (r6c1 = 6) AND (r6c2 = 8) AND (r6c4 = 9) AND (r6c5 = 3) AND (r6c8 = 2) AND (r6c9 = 4) AND (r7c2 = 3) AND (r7c3 = 8) AND (r7c4 = 6) AND (r7c9 = 9) AND (r8c1 = 5) AND (r9c3 = 6) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c9 = 1) AND (r2c3 = 2) AND (r2c4 = 9) AND (r2c8 = 5) AND (r3c1 = 8) AND (r3c7 = 4) AND (r4c3 = 6) AND (r4c4 = 2) AND (r4c5 = 5) AND (r5c6 = 7) AND (r6c4 = 3) AND (r6c6 = 6) AND (r6c8 = 9) AND (r7c1 = 4) AND (r7c7 = 7) AND (r8c2 = 1) AND (r8c9 = 8) AND (r9c3 = 5) AND (r9c5 = 3) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 3) AND (r1c4 = 5) AND (r1c8 = 8) AND (r2c1 = 7) AND (r2c5 = 2) AND (r3c3 = 9) AND (r3c6 = 7) AND (r4c4 = 2) AND (r4c6 = 1) AND (r5c1 = 5) AND (r5c2 = 2) AND (r6c2 = 4) AND (r6c5 = 8) AND (r6c7 = 7) AND (r7c4 = 3) AND (r7c8 = 2) AND (r8c5 = 9) AND (r8c6 = 8) AND (r8c7 = 3) AND (r9c2 = 1) AND (r9c3 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c2 = 1) AND (r1c3 = 2) AND (r1c5 = 3) AND (r2c1 = 4) AND (r2c7 = 5) AND (r3c4 = 7) AND (r3c7 = 2) AND (r3c8 = 3) AND (r4c1 = 2) AND (r4c4 = 8) AND (r4c5 = 5) AND (r5c1 = 3) AND (r5c4 = 1) AND (r5c5 = 6) AND (r5c6 = 7) AND (r5c7 = 8) AND (r5c9 = 5) AND (r6c4 = 4) AND (r6c8 = 7) AND (r6c9 = 6) AND (r7c1 = 1) AND (r7c5 = 7) AND (r8c2 = 6) AND (r8c3 = 5) AND (r8c9 = 8) AND (r9c9 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c7 = 8) AND (r2c1 = 2) AND (r2c2 = 8) AND (r2c3 = 3) AND (r2c7 = 4) AND (r2c8 = 1) AND (r3c4 = 2) AND (r4c3 = 1) AND (r4c4 = 3) AND (r4c9 = 6) AND (r5c3 = 2) AND (r5c4 = 1) AND (r5c6 = 6) AND (r5c8 = 5) AND (r5c9 = 4) AND (r6c6 = 5) AND (r6c8 = 7) AND (r7c1 = 1) AND (r7c3 = 5) AND (r8c4 = 4) AND (r8c8 = 3) AND (r8c9 = 1) AND (r9c1 = 3) AND (r9c3 = 8) AND (r9c6 = 1) AND (r9c7 = 6) AND (r9c8 = 2) AND (r9c9 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c6 = 5) AND (r1c9 = 1) AND (r2c2 = 6) AND (r2c5 = 7) AND (r2c7 = 2) AND (r3c2 = 1) AND (r3c3 = 7) AND (r4c3 = 3) AND (r4c4 = 5) AND (r4c5 = 2) AND (r5c4 = 8) AND (r5c5 = 3) AND (r5c7 = 1) AND (r5c9 = 4) AND (r7c4 = 7) AND (r7c9 = 5) AND (r8c3 = 2) AND (r8c6 = 1) AND (r8c9 = 3) AND (r9c1 = 3) AND (r9c2 = 4) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 7) AND (r1c4 = 5) AND (r1c6 = 8) AND (r1c8 = 6) AND (r2c1 = 8) AND (r2c5 = 1) AND (r2c9 = 7) AND (r3c2 = 9) AND (r3c8 = 8) AND (r4c3 = 8) AND (r4c4 = 6) AND (r4c6 = 9) AND (r4c7 = 7) AND (r5c2 = 5) AND (r5c3 = 9) AND (r5c4 = 2) AND (r5c6 = 7) AND (r5c7 = 8) AND (r5c8 = 1) AND (r6c3 = 7) AND (r6c4 = 1) AND (r6c6 = 3) AND (r6c7 = 5) AND (r7c2 = 3) AND (r7c8 = 4) AND (r8c1 = 7) AND (r8c5 = 6) AND (r8c9 = 2) AND (r9c2 = 6) AND (r9c4 = 8) AND (r9c6 = 4) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 8) AND (r1c7 = 7) AND (r1c8 = 4) AND (r2c1 = 5) AND (r2c3 = 1) AND (r3c1 = 3) AND (r3c8 = 9) AND (r4c2 = 9) AND (r4c4 = 2) AND (r4c7 = 5) AND (r5c4 = 6) AND (r5c5 = 8) AND (r6c7 = 3) AND (r7c5 = 3) AND (r7c6 = 1) AND (r8c2 = 2) AND (r8c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 3) AND (r1c7 = 5) AND (r1c9 = 9) AND (r2c1 = 9) AND (r2c2 = 8) AND (r2c3 = 6) AND (r2c5 = 2) AND (r2c7 = 3) AND (r3c3 = 2) AND (r3c9 = 1) AND (r4c7 = 1) AND (r4c8 = 7) AND (r5c4 = 5) AND (r5c6 = 7) AND (r7c1 = 7) AND (r7c6 = 3) AND (r7c7 = 8) AND (r7c8 = 6) AND (r8c3 = 8) AND (r8c4 = 2) AND (r8c5 = 6) AND (r9c2 = 5) AND (r9c9 = 3);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 4) AND (r1c9 = 3) AND (r2c2 = 2) AND (r2c5 = 5) AND (r2c9 = 9) AND (r3c2 = 9) AND (r3c3 = 5) AND (r3c5 = 3) AND (r3c8 = 8) AND (r4c4 = 4) AND (r6c1 = 6) AND (r6c6 = 9) AND (r6c7 = 7) AND (r7c1 = 4) AND (r7c4 = 7) AND (r7c7 = 6) AND (r7c8 = 2) AND (r8c4 = 6) AND (r8c9 = 5) AND (r9c1 = 3) AND (r9c4 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 9) AND (r2c5 = 6) AND (r2c8 = 1) AND (r3c6 = 5) AND (r4c2 = 1) AND (r4c6 = 9) AND (r5c1 = 8) AND (r5c5 = 4) AND (r6c1 = 4) AND (r6c2 = 2) AND (r6c4 = 8) AND (r6c8 = 3) AND (r7c4 = 9) AND (r7c7 = 5) AND (r7c9 = 3) AND (r8c2 = 8) AND (r8c3 = 5) AND (r8c4 = 3) AND (r8c9 = 1) AND (r9c4 = 1) AND (r9c6 = 2) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c8 = 1) AND (r2c1 = 3) AND (r2c2 = 2) AND (r2c4 = 9) AND (r2c9 = 5) AND (r3c2 = 8) AND (r3c4 = 4) AND (r3c5 = 5) AND (r4c3 = 2) AND (r4c4 = 5) AND (r4c6 = 3) AND (r5c8 = 5) AND (r5c9 = 9) AND (r6c1 = 7) AND (r6c9 = 3) AND (r7c3 = 7) AND (r8c1 = 5) AND (r8c5 = 4) AND (r8c7 = 1) AND (r9c2 = 9) AND (r9c3 = 1) AND (r9c4 = 3) AND (r9c7 = 5) AND (r9c8 = 2) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c4 = 5) AND (r1c8 = 4) AND (r2c1 = 5) AND (r2c4 = 3) AND (r2c6 = 8) AND (r3c1 = 2) AND (r3c7 = 9) AND (r4c2 = 6) AND (r4c5 = 7) AND (r5c1 = 4) AND (r5c2 = 3) AND (r5c7 = 6) AND (r6c3 = 5) AND (r6c5 = 8) AND (r7c3 = 9) AND (r7c9 = 6) AND (r8c1 = 7) AND (r8c7 = 5) AND (r9c2 = 8) AND (r9c4 = 4) AND (r9c6 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 9) AND (r1c4 = 3) AND (r1c6 = 5) AND (r1c7 = 7) AND (r2c2 = 3) AND (r2c4 = 8) AND (r2c9 = 2) AND (r3c3 = 8) AND (r3c5 = 2) AND (r3c7 = 6) AND (r4c3 = 2) AND (r4c8 = 9) AND (r4c9 = 7) AND (r5c2 = 7) AND (r5c3 = 6) AND (r5c5 = 5) AND (r5c7 = 1) AND (r6c2 = 8) AND (r6c7 = 3) AND (r7c4 = 9) AND (r7c9 = 1) AND (r8c6 = 1) AND (r9c8 = 6);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 1) AND (r1c6 = 6) AND (r1c9 = 7) AND (r2c2 = 2) AND (r2c4 = 5) AND (r2c7 = 8) AND (r3c3 = 9) AND (r3c4 = 7) AND (r3c9 = 6) AND (r4c1 = 7) AND (r4c3 = 5) AND (r5c3 = 1) AND (r5c5 = 3) AND (r5c7 = 2) AND (r5c8 = 9) AND (r7c5 = 9) AND (r7c6 = 5) AND (r8c1 = 2) AND (r8c9 = 3) AND (r9c1 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r1c2 = 9) AND (r1c4 = 1) AND (r1c5 = 4) AND (r2c5 = 5) AND (r2c6 = 8) AND (r3c1 = 1) AND (r3c2 = 8) AND (r3c5 = 6) AND (r3c7 = 5) AND (r4c1 = 8) AND (r4c9 = 2) AND (r5c2 = 1) AND (r5c4 = 7) AND (r5c9 = 6) AND (r6c7 = 7) AND (r6c8 = 9) AND (r7c1 = 4) AND (r7c7 = 2) AND (r7c8 = 1) AND (r8c9 = 9) AND (r9c1 = 7) AND (r9c4 = 2) AND (r9c7 = 4) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 6) AND (r1c3 = 1) AND (r1c5 = 9) AND (r3c1 = 9) AND (r3c3 = 7) AND (r3c5 = 4) AND (r3c8 = 6) AND (r4c3 = 8) AND (r4c8 = 4) AND (r5c1 = 7) AND (r5c2 = 3) AND (r5c3 = 2) AND (r5c8 = 9) AND (r6c1 = 1) AND (r6c8 = 7) AND (r7c2 = 8) AND (r7c3 = 4) AND (r7c4 = 6) AND (r7c5 = 1) AND (r7c9 = 9) AND (r8c1 = 2) AND (r8c3 = 9) AND (r8c5 = 8) AND (r8c6 = 4) AND (r8c7 = 3) AND (r9c5 = 2) AND (r9c6 = 7) AND (r9c8 = 8) AND (r9c9 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 4) AND (r1c6 = 1) AND (r1c8 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 5) AND (r3c5 = 6) AND (r4c4 = 3) AND (r4c9 = 7) AND (r5c3 = 1) AND (r5c7 = 6) AND (r6c1 = 6) AND (r6c6 = 2) AND (r7c5 = 4) AND (r7c7 = 1) AND (r8c1 = 9) AND (r8c2 = 7) AND (r9c2 = 3) AND (r9c4 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c2 = 9) AND (r2c1 = 3) AND (r2c3 = 6) AND (r2c5 = 4) AND (r3c2 = 1) AND (r3c3 = 4) AND (r4c2 = 7) AND (r4c9 = 1) AND (r5c3 = 1) AND (r5c5 = 6) AND (r6c1 = 2) AND (r6c6 = 7) AND (r6c7 = 9) AND (r6c9 = 8) AND (r7c1 = 7) AND (r7c4 = 6) AND (r7c5 = 2) AND (r7c6 = 1) AND (r7c7 = 8) AND (r7c9 = 3) AND (r8c4 = 7) AND (r8c6 = 3) AND (r8c7 = 4) AND (r8c8 = 9) AND (r9c2 = 3) AND (r9c5 = 8) AND (r9c6 = 9) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 4) AND (r2c2 = 4) AND (r2c5 = 7) AND (r2c8 = 3) AND (r2c9 = 6) AND (r3c1 = 2) AND (r3c5 = 3) AND (r3c6 = 6) AND (r3c8 = 8) AND (r4c4 = 1) AND (r4c5 = 4) AND (r4c9 = 7) AND (r5c1 = 1) AND (r5c6 = 3) AND (r5c8 = 6) AND (r6c4 = 6) AND (r6c8 = 2) AND (r7c1 = 3) AND (r7c5 = 5) AND (r7c8 = 1) AND (r8c2 = 5) AND (r8c4 = 7) AND (r8c5 = 8) AND (r8c6 = 2) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c8 = 1) AND (r2c6 = 2) AND (r2c8 = 3) AND (r2c9 = 4) AND (r3c3 = 5) AND (r3c5 = 6) AND (r4c4 = 4) AND (r4c8 = 7) AND (r5c3 = 2) AND (r5c7 = 6) AND (r6c2 = 1) AND (r6c6 = 5) AND (r7c5 = 8) AND (r7c7 = 2) AND (r8c1 = 7) AND (r8c2 = 3) AND (r8c4 = 1) AND (r9c2 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 8) AND (r1c4 = 4) AND (r1c5 = 3) AND (r1c7 = 9) AND (r1c8 = 1) AND (r2c1 = 3) AND (r2c5 = 9) AND (r3c2 = 4) AND (r3c4 = 7) AND (r3c6 = 1) AND (r3c9 = 6) AND (r4c2 = 7) AND (r4c4 = 1) AND (r4c5 = 4) AND (r4c7 = 5) AND (r5c1 = 6) AND (r5c3 = 3) AND (r6c1 = 5) AND (r6c2 = 1) AND (r6c8 = 8) AND (r7c1 = 7) AND (r7c3 = 6) AND (r7c4 = 8) AND (r7c8 = 9) AND (r8c2 = 3) AND (r8c4 = 9) AND (r9c2 = 9) AND (r9c4 = 3) AND (r9c9 = 8);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 7) AND (r1c3 = 1) AND (r1c4 = 2) AND (r1c5 = 5) AND (r1c8 = 8) AND (r2c1 = 8) AND (r2c3 = 6) AND (r2c5 = 7) AND (r2c6 = 4) AND (r2c9 = 5) AND (r3c2 = 9) AND (r3c3 = 4) AND (r3c6 = 6) AND (r3c7 = 7) AND (r5c3 = 8) AND (r5c4 = 6) AND (r5c6 = 5) AND (r5c9 = 9) AND (r6c4 = 8) AND (r6c5 = 2) AND (r6c6 = 1) AND (r6c8 = 4) AND (r6c9 = 6) AND (r7c1 = 6) AND (r7c6 = 8) AND (r7c9 = 1) AND (r8c1 = 1) AND (r8c3 = 9) AND (r8c9 = 7) AND (r9c2 = 4);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 1) AND (r1c5 = 5) AND (r1c7 = 6) AND (r2c1 = 8) AND (r2c3 = 7) AND (r3c1 = 3) AND (r4c4 = 7) AND (r4c6 = 8) AND (r4c8 = 3) AND (r5c2 = 1) AND (r5c7 = 4) AND (r7c2 = 4) AND (r7c5 = 6) AND (r7c7 = 2) AND (r8c1 = 5) AND (r8c8 = 8) AND (r9c4 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 7) AND (r1c5 = 9) AND (r1c7 = 2) AND (r2c3 = 6) AND (r2c7 = 3) AND (r2c9 = 8) AND (r3c2 = 5) AND (r3c5 = 8) AND (r3c6 = 3) AND (r3c8 = 7) AND (r3c9 = 9) AND (r4c3 = 4) AND (r4c4 = 3) AND (r4c7 = 7) AND (r4c8 = 6) AND (r5c7 = 8) AND (r5c9 = 2) AND (r6c1 = 5) AND (r6c2 = 6) AND (r8c2 = 8) AND (r8c3 = 9) AND (r8c4 = 5) AND (r8c6 = 6) AND (r9c1 = 3) AND (r9c2 = 2) AND (r9c9 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c3 = 2) AND (r1c4 = 8) AND (r1c6 = 1) AND (r1c7 = 5) AND (r1c8 = 4) AND (r2c5 = 3) AND (r3c4 = 4) AND (r3c5 = 6) AND (r3c6 = 5) AND (r4c1 = 8) AND (r4c3 = 3) AND (r4c6 = 9) AND (r4c7 = 4) AND (r4c9 = 5) AND (r5c2 = 5) AND (r5c6 = 3) AND (r5c9 = 1) AND (r6c3 = 6) AND (r6c7 = 3) AND (r7c4 = 2) AND (r7c6 = 4) AND (r8c3 = 5) AND (r8c5 = 1) AND (r8c6 = 8) AND (r8c7 = 6) AND (r8c8 = 2) AND (r9c3 = 9) AND (r9c5 = 5);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c4 = 1) AND (r2c1 = 1) AND (r2c2 = 2) AND (r2c5 = 9) AND (r2c8 = 7) AND (r3c5 = 7) AND (r3c6 = 6) AND (r5c2 = 6) AND (r5c5 = 3) AND (r5c6 = 9) AND (r5c8 = 1) AND (r6c1 = 5) AND (r6c3 = 9) AND (r6c4 = 4) AND (r6c6 = 7) AND (r6c8 = 2) AND (r7c3 = 2) AND (r7c6 = 3) AND (r7c7 = 4) AND (r7c8 = 5) AND (r8c1 = 6) AND (r8c4 = 7) AND (r8c5 = 2) AND (r8c8 = 3) AND (r8c9 = 9) AND (r9c2 = 7) AND (r9c4 = 9) AND (r9c5 = 4) AND (r9c6 = 1) AND (r9c8 = 6) AND (r9c9 = 2);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 2) AND (r2c3 = 5) AND (r2c5 = 3) AND (r2c6 = 9) AND (r2c7 = 8) AND (r3c1 = 8) AND (r3c2 = 4) AND (r3c3 = 9) AND (r3c5 = 7) AND (r4c3 = 7) AND (r4c4 = 3) AND (r4c5 = 2) AND (r4c6 = 6) AND (r5c4 = 7) AND (r5c5 = 4) AND (r5c6 = 8) AND (r5c9 = 3) AND (r6c6 = 5) AND (r7c3 = 3) AND (r7c5 = 6) AND (r7c9 = 5) AND (r8c2 = 5) AND (r8c4 = 9) AND (r8c8 = 6) AND (r9c1 = 4) AND (r9c3 = 8) AND (r9c5 = 5) AND (r9c6 = 7) AND (r9c8 = 3) AND (r9c9 = 9);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 1) AND (r1c2 = 9) AND (r2c1 = 8) AND (r2c5 = 7) AND (r2c8 = 1) AND (r2c9 = 6) AND (r3c2 = 7) AND (r3c4 = 2) AND (r3c7 = 5) AND (r3c9 = 3) AND (r4c8 = 2) AND (r4c9 = 7) AND (r5c2 = 3) AND (r5c9 = 8) AND (r6c1 = 9) AND (r6c3 = 5) AND (r7c2 = 1) AND (r7c3 = 8) AND (r7c6 = 2) AND (r7c8 = 3) AND (r8c9 = 2) AND (r9c2 = 6) AND (r9c5 = 1) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c1 = 8) AND (r1c3 = 5) AND (r1c9 = 2) AND (r2c4 = 9) AND (r2c6 = 1) AND (r3c1 = 3) AND (r4c2 = 6) AND (r4c4 = 7) AND (r4c7 = 4) AND (r5c1 = 2) AND (r5c5 = 5) AND (r6c8 = 6) AND (r7c4 = 3) AND (r7c5 = 8) AND (r8c2 = 1) AND (r8c7 = 9) AND (r9c2 = 4) AND (r9c8 = 7);
SELECT * FROM sudoku_memory_combined_view WHERE (r1c2 = 8) AND (r2c1 = 1) AND (r2c3 = 7) AND (r2c7 = 8) AND (r2c9 = 3) AND (r3c6 = 6) AND (r3c9 = 1) AND (r4c2 = 2) AND (r5c1 = 3) AND (r5c5 = 1) AND (r6c3 = 8) AND (r6c4 = 5) AND (r6c7 = 6) AND (r6c8 = 9) AND (r7c5 = 3) AND (r7c6 = 7) AND (r7c7 = 9) AND (r8c6 = 1) AND (r9c1 = 5) AND (r9c2 = 9);
UPDATE tests SET fin = NOW() WHERE fin IS NULL;
SELECT TO_SECONDS(fin) - TO_SECONDS(debut) FROM tests;

6. Gosser à la main!

Maintenant que nous avons un échantillon représentatif et significatif et tout ce qu’il nous faut pour mesurer, de façon répétable et facile, chacun des changements que nous voulons effectuer, nous sommes en mesure de vérifier l’impact de 2 variables importantes : optimizer_search_depth et join_buffer_size.

Tout d’abord, la variable optimizer_search_depth dont voici les différents résultats :

optimizer_search_depth_table

Il est clair que cette variable a un impact majeur.  Nous savons maintenant que la valeur optimale de cette variable (dans notre cas précis) est 1.

optimizer_search_depth

On serait tenté de croire que la variable join_buffer_size pourrait avoir un impact non négligeable mais ce n’est pas le cas ici.

join_buffer_size_table

Les différences de temps (hormis pour la valeur 2Mb) ne sont pas assez significatives pour indiquer une tendance.  Malgré tout, théoriquement, cette variable devrait avoir un impact.  Pour les biens de la cause, autant avoir plus de mémoire que moins pour cette variable!  Je vous recommande donc 128Mb (plus, dans notre cas, serait un gaspillage de mémoire).

join_buffer_size

Finalement, pour mettre en valeur la différence entre une solution utilisant une table sur disque versus notre solution finale (une table en mémoire), l’histogramme suivant parle de lui-même!

engine_type

Voilà!  CQFD. En espérant que cette série d’articles vous aura permis de constater que parfois, il est nécessaire de penser out of the box et d’envisager des solutions saugrenues pour arriver à ses fins.

7. Ressources et outils

Quelques-unes des ressources et des outils utilisés dans le cadre de cette série d’articles:

setbb.com : des forums de discussion sur le sudoku (en anglais) pour les programmeurs

enjoysudoku.com : des forums de discussions (en anglais) variés et nombreux sur les sudokus

QQWing : un outil (en ligne de commande) permettant de solutionner et de générer des grilles de sudoku

SudoCue : une application permettant de solutionner et générer des sudokus

Sudoku Explainer : une application permettant de solutionner et générer des sudokus

R : langage de programmation et environnement mathématique utilisé pour le traitement de données et l’analyse statistique

db4free.net : un serveur MySQL vous permettant de créer une base de donnée gratuitement et d’expérimenter

Pharo : un environnement de développement Smalltalk


Comment presser un citron (deuxième partie)

8 janvier 2012

Dans le premier article, nous avons vu combien il était facile de solutionner des grilles de sudoku avec une seule requête SQL. Malheureusement, c’était trop beau pour être vrai…

Avant de poursuivre, voici un outil utile pour se faciliter la tâche.  Pour ceux qui utilisent Smalltalk, vous pouvez vous aider du script suivant :


| uneTableOuVue uneStringSudoku stream estLePremier |

uneTableOuVue := 'sudoku_rows_view'.
uneStringSudoku := '.........134825697759364182397182564.........581476239825641973976538421.........'.

stream := ReadWriteStream on: String new.
stream
nextPutAll: 'SELECT * '; cr;
nextPutAll: 'FROM ';
nextPutAll: uneTableOuVue;
space; cr;
nextPutAll: 'WHERE'; cr.

estLePremier := false.
1 to: 9 do: [:r |
1 to: 9 do: [:c | | i |
i := (r-1)*9 + c.
((uneStringSudoku at: i) ~= $. and: [(uneStringSudoku at: i) ~= 0])
ifTrue: [    estLePremier ifTrue: [stream nextPutAll: ' AND ';cr].
estLePremier := true.
stream
nextPutAll: '(r'; nextPutAll: r asString;
nextPutAll: 'c'; nextPutAll: c asString;
nextPutAll: ' = ';
nextPutAll: (uneStringSudoku at: i) asString;
nextPutAll: ')'.
].]].
Transcript cr;show: stream contents

Ce script génère  les requêtes SQL à partir d’une chaîne de caractères (uneStringSudoku) représentant une grille de sudoku pour une table/vue précise (uneTableOuVue) en affichant le résultat dans le Transcript.

1. Problème majeur

Il y a une faille majeure et évidente dans la solution telle que présentée : elle repose totalement sur la capacité de MySQL de faire correspondre les révélés (givens en anglais) de la grille à des lignes. Que se passerait-il si une ligne (ou pire encore, plusieurs lignes) dans le sudoku ne contenait pas de révélés (ou pas assez)? Sans index à utiliser, une lecture séquentielle de la table nous attend sans doute! Prenons, par exemple, la grille suivante:

Ce sudoku contient 54 révélés (la première grille n’en comptait que 30, près de la moitié de celle-ci) et 6 de ses lignes seront rapidement récupérées avec les index.  De plus, il y a suffisamment de révélés pour éliminer rapidement un bon nombre de lignes candidates avec les contraintes du puzzle incluses dans la vue sudoku_rows_view.

Cependant les lignes vides (1, 5 et 9) causeront probablement une lecture séquentielle (table scan) de la table.  Nous faisons face à un problème majeur avec les lignes 1, 5 et 9 étant vides! Examinons la requête pour ce sudoku :

EXPLAIN
SELECT *
FROM sudoku_rows_view
WHERE
(r2c1 = 1) AND (r2c2 = 3) AND (r2c3 = 4) AND (r2c4 = 8) AND
(r2c5 = 2) AND (r2c6 = 5) AND (r2c7 = 6) AND (r2c8 = 9) AND
(r2c9 = 7) AND (r3c1 = 7) AND (r3c2 = 5) AND (r3c3 = 9) AND
(r3c4 = 3) AND (r3c5 = 6) AND (r3c6 = 4) AND (r3c7 = 1) AND
(r3c8 = 8) AND (r3c9 = 2) AND (r4c1 = 3) AND (r4c2 = 9) AND
(r4c3 = 7) AND (r4c4 = 1) AND (r4c5 = 8) AND (r4c6 = 2) AND
(r4c7 = 5) AND (r4c8 = 6) AND (r4c9 = 4) AND (r6c1 = 5) AND
(r6c2 = 8) AND (r6c3 = 1) AND (r6c4 = 4) AND (r6c5 = 7) AND
(r6c6 = 6) AND (r6c7 = 2) AND (r6c8 = 3) AND (r6c9 = 9) AND
(r7c1 = 8) AND (r7c2 = 2) AND (r7c3 = 5) AND (r7c4 = 6) AND
(r7c5 = 4) AND (r7c6 = 1) AND (r7c7 = 9) AND (r7c8 = 7) AND
(r7c9 = 3) AND (r8c1 = 9) AND (r8c2 = 7) AND (r8c3 = 6) AND
(r8c4 = 5) AND (r8c5 = 3) AND (r8c6 = 8) AND (r8c7 = 4) AND
(r8c8 = 2) AND (r8c9 = 1);

Le résultat du EXPLAIN :

+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+--------+----------------------------------------------------------------------------------+
| id | select_type | table | type        | possible_keys                                                                                                                                      | key         | key_len | ref  | rows   | Extra                                                                            |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+--------+----------------------------------------------------------------------------------+
|  1 | SIMPLE      | r2    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i29     | 2,2     | NULL |     68 | Using intersect(i37,i29); Using where                                            |
|  1 | SIMPLE      | r3    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i28     | 2,2     | NULL |     68 | Using intersect(i37,i28); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r4    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i56,i29     | 2,2     | NULL |     68 | Using intersect(i56,i29); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r6    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12,i35     | 2,2     | NULL |     68 | Using intersect(i12,i35); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r7    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12,i68     | 2,2     | NULL |     68 | Using intersect(i12,i68); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r8    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i79,i38 | 2,2,2   | NULL |     78 | Using intersect(i37,i79,i38); Using where; Using join buffer (Block Nested Loop) |
|  1 | SIMPLE      | r1    | range       | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23         | 1       | NULL |  40012 | Using index condition; Using where; Using join buffer (Block Nested Loop)        |
|  1 | SIMPLE      | r5    | ALL         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | NULL        | NULL    | NULL | 362880 | Using where; Using join buffer (Block Nested Loop)                               |
|  1 | SIMPLE      | r9    | ALL         | NULL                                                                                                                                               | NULL        | NULL    | NULL | 362880 | Using where; Using join buffer (Block Nested Loop)                               |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+--------+----------------------------------------------------------------------------------+
9 rows in set (13.39 sec)

Les lignes vides (lignes 1, 5 et 9) nous feront payer très chèrement le fait que nous ne pouvons pas utiliser pleinement les index! Il n’y a qu’à constater le nombre de lignes à potentiellement examiner pour joindre les tables r1, r5 et r9 (40012 x 362880 x 362880 = 5268855958732800) ainsi que le type de jointure utilisé (range, ALL et ALL).

Vérifions en combien de temps la requête s’exécute :


+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| r1c1 | r1c2 | r1c3 | r1c4 | r1c5 | r1c6 | r1c7 | r1c8 | r1c9 | r2c1 | r2c2 | r2c3 | r2c4 | r2c5 | r2c6 | r2c7 | r2c8 | r2c9 | r3c1 | r3c2 | r3c3 | r3c4 | r3c5 | r3c6 | r3c7 | r3c8 | r3c9 | r4c1 | r4c2 | r4c3 | r4c4 | r4c5 | r4c6 | r4c7 | r4c8 | r4c9 | r5c1 | r5c2 | r5c3 | r5c4 | r5c5 | r5c6 | r5c7 | r5c8 | r5c9 | r6c1 | r6c2 | r6c3 | r6c4 | r6c5 | r6c6 | r6c7 | r6c8 | r6c9 | r7c1 | r7c2 | r7c3 | r7c4 | r7c5 | r7c6 | r7c7 | r7c8 | r7c9 | r8c1 | r8c2 | r8c3 | r8c4 | r8c5 | r8c6 | r8c7 | r8c8 | r8c9 | r9c1 | r9c2 | r9c3 | r9c4 | r9c5 | r9c6 | r9c7 | r9c8 | r9c9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
|    2 |    6 |    8 |    7 |    1 |    9 |    3 |    4 |    5 |    1 |    3 |    4 |    8 |    2 |    5 |    6 |    9 |    7 |    7 |    5 |    9 |    3 |    6 |    4 |    1 |    8 |    2 |    3 |    9 |    7 |    1 |    8 |    2 |    5 |    6 |    4 |    6 |    4 |    2 |    9 |    5 |    3 |    7 |    1 |    8 |    5 |    8 |    1 |    4 |    7 |    6 |    2 |    3 |    9 |    8 |    2 |    5 |    6 |    4 |    1 |    9 |    7 |    3 |    9 |    7 |    6 |    5 |    3 |    8 |    4 |    2 |    1 |    4 |    1 |    3 |    2 |    9 |    7 |    8 |    5 |    6 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
1 row in set (6.17 sec)

Ouf!  Nous sommes passés de 0.39 seconde (grille 01) à 6.17 secondes (grille 02) malgré le fait que la grille 02 comporte près de 2 fois plus de révélés que la grille 01!  Cet exemple démontre clairement que les choses peuvent rapidement mal tourner à un rythme alarmant (même exponentiel) quand nous sommes confrontés à une grille contenant des lignes vides ou presque vides!

2. Changer de point de vue!

Imaginons maintenant que nous faisons effectuer une rotation à notre grille et que les colonnes deviennent des lignes.  Dans ce cas, chaque nouvelle ligne pourrait dès lors bénéficier des index!

Voyons cette nouvelle grille :

La requête aurait désormais l’air de ceci :


SELECT *
FROM sudoku_rows_view
WHERE
(r1c2 = 1) AND (r1c3 = 7) AND (r1c4 = 3) AND (r1c6 = 5) AND
(r1c7 = 8) AND (r1c8 = 9) AND (r2c2 = 3) AND (r2c3 = 5) AND
(r2c4 = 9) AND (r2c6 = 8) AND (r2c7 = 2) AND (r2c8 = 7) AND
(r3c2 = 4) AND (r3c3 = 9) AND (r3c4 = 7) AND (r3c6 = 1) AND
(r3c7 = 5) AND (r3c8 = 6) AND (r4c2 = 8) AND (r4c3 = 3) AND
(r4c4 = 1) AND (r4c6 = 4) AND (r4c7 = 6) AND (r4c8 = 5) AND
(r5c2 = 2) AND (r5c3 = 6) AND (r5c4 = 8) AND (r5c6 = 7) AND
(r5c7 = 4) AND (r5c8 = 3) AND (r6c2 = 5) AND (r6c3 = 4) AND
(r6c4 = 2) AND (r6c6 = 6) AND (r6c7 = 1) AND (r6c8 = 8) AND
(r7c2 = 6) AND (r7c3 = 1) AND (r7c4 = 5) AND (r7c6 = 2) AND
(r7c7 = 9) AND (r7c8 = 4) AND (r8c2 = 9) AND (r8c3 = 8) AND
(r8c4 = 6) AND (r8c6 = 3) AND (r8c7 = 7) AND (r8c8 = 2) AND
(r9c2 = 7) AND (r9c3 = 2) AND (r9c4 = 4) AND (r9c6 = 9) AND
(r9c7 = 3) AND (r9c8 = 1);

Le résultat du EXPLAIN correspondant :


+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+------+----------------------------------------------------------------------------------+
| id | select_type | table | type        | possible_keys                                                                                                                                      | key         | key_len | ref  | rows | Extra                                                                            |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+------+----------------------------------------------------------------------------------+
|  1 | SIMPLE      | r3    | index_merge | i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i67,i68,i69,i78,i79,i89                                                    | i23,i38,i48 | 2,2,2   | NULL |   64 | Using intersect(i23,i38,i48); Using where                                        |
|  1 | SIMPLE      | r9    | index_merge | i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i67,i68,i69,i78,i79,i89                                                    | i78,i68,i48 | 2,2,2   | NULL |   65 | Using intersect(i78,i68,i48); Using where; Using join buffer (Block Nested Loop) |
|  1 | SIMPLE      | r1    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i67     | 2,2     | NULL |   68 | Using intersect(i23,i67); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r2    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL |   68 | Using intersect(i23,i68); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r4    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i46     | 2,2     | NULL |   68 | Using intersect(i78,i46); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r5    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL |   68 | Using intersect(i23,i68); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r6    | index_merge | i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i67,i68,i69,i78,i79,i89                                                    | i23,i67     | 2,2     | NULL |   68 | Using intersect(i23,i67); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r7    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL |   68 | Using intersect(i23,i68); Using where; Using join buffer (Block Nested Loop)     |
|  1 | SIMPLE      | r8    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i24     | 2,2     | NULL |   68 | Using intersect(i37,i24); Using where; Using join buffer (Block Nested Loop)     |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+------+------+----------------------------------------------------------------------------------+
9 rows in set (42.98 sec)

Et combien de temps la requête prendrait-elle à s’exécuter?

SELECT *
FROM sudoku_rows_view
WHERE
(r1c2 = 1) AND (r1c3 = 7) AND (r1c4 = 3) AND (r1c6 = 5) AND
(r1c7 = 8) AND (r1c8 = 9) AND (r2c2 = 3) AND (r2c3 = 5) AND
(r2c4 = 9) AND (r2c6 = 8) AND (r2c7 = 2) AND (r2c8 = 7) AND
(r3c2 = 4) AND (r3c3 = 9) AND (r3c4 = 7) AND (r3c6 = 1) AND
(r3c7 = 5) AND (r3c8 = 6) AND (r4c2 = 8) AND (r4c3 = 3) AND
(r4c4 = 1) AND (r4c6 = 4) AND (r4c7 = 6) AND (r4c8 = 5) AND
(r5c2 = 2) AND (r5c3 = 6) AND (r5c4 = 8) AND (r5c6 = 7) AND
(r5c7 = 4) AND (r5c8 = 3) AND (r6c2 = 5) AND (r6c3 = 4) AND
(r6c4 = 2) AND (r6c6 = 6) AND (r6c7 = 1) AND (r6c8 = 8) AND
(r7c2 = 6) AND (r7c3 = 1) AND (r7c4 = 5) AND (r7c6 = 2) AND
(r7c7 = 9) AND (r7c8 = 4) AND (r8c2 = 9) AND (r8c3 = 8) AND
(r8c4 = 6) AND (r8c6 = 3) AND (r8c7 = 7) AND (r8c8 = 2) AND
(r9c2 = 7) AND (r9c3 = 2) AND (r9c4 = 4) AND (r9c6 = 9) AND
(r9c7 = 3) AND (r9c8 = 1);
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| r1c1 | r1c2 | r1c3 | r1c4 | r1c5 | r1c6 | r1c7 | r1c8 | r1c9 | r2c1 | r2c2 | r2c3 | r2c4 | r2c5 | r2c6 | r2c7 | r2c8 | r2c9 | r3c1 | r3c2 | r3c3 | r3c4 | r3c5 | r3c6 | r3c7 | r3c8 | r3c9 | r4c1 | r4c2 | r4c3 | r4c4 | r4c5 | r4c6 | r4c7 | r4c8 | r4c9 | r5c1 | r5c2 | r5c3 | r5c4 | r5c5 | r5c6 | r5c7 | r5c8 | r5c9 | r6c1 | r6c2 | r6c3 | r6c4 | r6c5 | r6c6 | r6c7 | r6c8 | r6c9 | r7c1 | r7c2 | r7c3 | r7c4 | r7c5 | r7c6 | r7c7 | r7c8 | r7c9 | r8c1 | r8c2 | r8c3 | r8c4 | r8c5 | r8c6 | r8c7 | r8c8 | r8c9 | r9c1 | r9c2 | r9c3 | r9c4 | r9c5 | r9c6 | r9c7 | r9c8 | r9c9 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
|    2 |    1 |    7 |    3 |    6 |    5 |    8 |    9 |    4 |    6 |    3 |    5 |    9 |    4 |    8 |    2 |    7 |    1 |    8 |    4 |    9 |    7 |    2 |    1 |    5 |    6 |    3 |    7 |    8 |    3 |    1 |    9 |    4 |    6 |    5 |    2 |    1 |    2 |    6 |    8 |    5 |    7 |    4 |    3 |    9 |    9 |    5 |    4 |    2 |    3 |    6 |    1 |    8 |    7 |    3 |    6 |    1 |    5 |    7 |    2 |    9 |    4 |    8 |    4 |    9 |    8 |    6 |    1 |    3 |    7 |    2 |    5 |    5 |    7 |    2 |    4 |    8 |    9 |    3 |    1 |    6 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
1 row in set (0.22 sec)

Nous sommes passés de 6.17 secondes à 0.22 seconde! Un gain imposant!

3. Les vues combinées

Alors pourquoi ne tenterions-nous pas de résoudre nos sudokus en effectuant la recherche par ligne ET par colonne à la fois?

Nous allons donc construire une seconde vue (sudoku_columns_view) qui sera basée sur les colonnes de la grille.  Pour faire résoudre les sudokus, il nous faudra une troisième vue (sudoku_combined_view) qui combinera la vue par lignes (sudoku_rows_view) avec la vue par colonne (sudoku_columns_view).  De cette façon, nous serons à l’abri des grilles avec des lignes vides et des grilles avec des colonnes vides.  L’optimisateur de requête aura dorénavant tout le luxe de choisir la « méthode » la plus efficace!

Construisons la vue par colonnes en exécutant cette requête :

USE sudoku;

CREATE VIEW sudoku_columns_view AS
SELECT
col1.c1 as r1c1, col1.c2 as r2c1, col1.c3 as r3c1, col1.c4 as r4c1, col1.c5 as r5c1,col1.c6 as r6c1, col1.c7 as r7c1, col1.c8 as r8c1, col1.c9 as r9c1, col2.c1 as r1c2,
col2.c2 as r2c2, col2.c3 as r3c2, col2.c4 as r4c2, col2.c5 as r5c2, col2.c6 as r6c2,col2.c7 as r7c2, col2.c8 as r8c2, col2.c9 as r9c2, col3.c1 as r1c3, col3.c2 as r2c3,
col3.c3 as r3c3, col3.c4 as r4c3, col3.c5 as r5c3, col3.c6 as r6c3, col3.c7 as r7c3,col3.c8 as r8c3, col3.c9 as r9c3, col4.c1 as r1c4, col4.c2 as r2c4, col4.c3 as r3c4,
col4.c4 as r4c4, col4.c5 as r5c4, col4.c6 as r6c4, col4.c7 as r7c4, col4.c8 as r8c4,col4.c9 as r9c4, col5.c1 as r1c5, col5.c2 as r2c5, col5.c3 as r3c5, col5.c4 as r4c5,
col5.c5 as r5c5, col5.c6 as r6c5, col5.c7 as r7c5, col5.c8 as r8c5, col5.c9 as r9c5,col6.c1 as r1c6, col6.c2 as r2c6, col6.c3 as r3c6, col6.c4 as r4c6, col6.c5 as r5c6,
col6.c6 as r6c6, col6.c7 as r7c6, col6.c8 as r8c6, col6.c9 as r9c6, col7.c1 as r1c7,col7.c2 as r2c7, col7.c3 as r3c7, col7.c4 as r4c7, col7.c5 as r5c7, col7.c6 as r6c7,
col7.c7 as r7c7, col7.c8 as r8c7, col7.c9 as r9c7, col8.c1 as r1c8, col8.c2 as r2c8,col8.c3 as r3c8, col8.c4 as r4c8, col8.c5 as r5c8, col8.c6 as r6c8, col8.c7 as r7c8,
col8.c8 as r8c8, col8.c9 as r9c8, col9.c1 as r1c9, col9.c2 as r2c9, col9.c3 as r3c9,col9.c4 as r4c9, col9.c5 as r5c9, col9.c6 as r6c9, col9.c7 as r7c9, col9.c8 as r8c9,
col9.c9 as r9c9
FROM
positions col1, positions col2, positions col3,positions col4, positions col5, positions col6,positions col7, positions col8, positions col9
WHERE
-- Nombres uniques dans chaque rangee
(col1.c1 <> col2.c1) AND (col1.c1 <> col3.c1) AND (col1.c1 <> col4.c1) AND (col1.c1 <> col5.c1) AND (col1.c1 <> col6.c1) AND (col1.c1 <> col7.c1) AND (col1.c1 <> col8.c1) AND (col1.c1 <> col9.c1) AND (col1.c2 <> col2.c2) AND (col1.c2 <> col3.c2) AND (col1.c2 <> col4.c2) AND (col1.c2 <> col5.c2) AND (col1.c2 <> col6.c2) AND (col1.c2 <> col7.c2) AND (col1.c2 <> col8.c2) AND (col1.c2 <> col9.c2) AND (col1.c3 <> col2.c3) AND (col1.c3 <> col3.c3) AND (col1.c3 <> col4.c3) AND (col1.c3 <> col5.c3) AND (col1.c3 <> col6.c3) AND (col1.c3 <> col7.c3) AND (col1.c3 <> col8.c3) AND (col1.c3 <> col9.c3) AND (col1.c4 <> col2.c4) AND (col1.c4 <> col3.c4) AND (col1.c4 <> col4.c4) AND (col1.c4 <> col5.c4) AND (col1.c4 <> col6.c4) AND (col1.c4 <> col7.c4) AND (col1.c4 <> col8.c4) AND (col1.c4 <> col9.c4) AND
(col1.c5 <> col2.c5) AND (col1.c5 <> col3.c5) AND (col1.c5 <> col4.c5) AND (col1.c5 <> col5.c5) AND (col1.c5 <> col6.c5) AND (col1.c5 <> col7.c5) AND (col1.c5 <> col8.c5) AND (col1.c5 <> col9.c5) AND (col1.c6 <> col2.c6) AND (col1.c6 <> col3.c6) AND (col1.c6 <> col4.c6) AND (col1.c6 <> col5.c6) AND (col1.c6 <> col6.c6) AND (col1.c6 <> col7.c6) AND (col1.c6 <> col8.c6) AND (col1.c6 <> col9.c6) AND (col1.c7 <> col2.c7) AND (col1.c7 <> col3.c7) AND (col1.c7 <> col4.c7) AND (col1.c7 <> col5.c7) AND (col1.c7 <> col6.c7) AND (col1.c7 <> col7.c7) AND (col1.c7 <> col8.c7) AND (col1.c7 <> col9.c7) AND (col1.c8 <> col2.c8) AND (col1.c8 <> col3.c8) AND (col1.c8 <> col4.c8) AND (col1.c8 <> col5.c8) AND (col1.c8 <> col6.c8) AND (col1.c8 <> col7.c8) AND (col1.c8 <> col8.c8) AND (col1.c8 <> col9.c8) AND
(col1.c9 <> col2.c9) AND (col1.c9 <> col3.c9) AND (col1.c9 <> col4.c9) AND (col1.c9 <> col5.c9) AND (col1.c9 <> col6.c9) AND (col1.c9 <> col7.c9) AND (col1.c9 <> col8.c9) AND (col1.c9 <> col9.c9) AND (col2.c1 <> col3.c1) AND (col2.c1 <> col4.c1) AND (col2.c1 <> col5.c1) AND (col2.c1 <> col6.c1) AND (col2.c1 <> col7.c1) AND (col2.c1 <> col8.c1) AND (col2.c1 <> col9.c1) AND (col2.c2 <> col3.c2) AND (col2.c2 <> col4.c2) AND (col2.c2 <> col5.c2) AND (col2.c2 <> col6.c2) AND (col2.c2 <> col7.c2) AND (col2.c2 <> col8.c2) AND (col2.c2 <> col9.c2) AND (col2.c3 <> col3.c3) AND (col2.c3 <> col4.c3) AND (col2.c3 <> col5.c3) AND (col2.c3 <> col6.c3) AND (col2.c3 <> col7.c3) AND (col2.c3 <> col8.c3) AND (col2.c3 <> col9.c3) AND (col2.c4 <> col3.c4) AND (col2.c4 <> col4.c4) AND (col2.c4 <> col5.c4) AND
(col2.c4 <> col6.c4) AND (col2.c4 <> col7.c4) AND (col2.c4 <> col8.c4) AND (col2.c4 <> col9.c4) AND (col2.c5 <> col3.c5) AND (col2.c5 <> col4.c5) AND (col2.c5 <> col5.c5) AND (col2.c5 <> col6.c5) AND (col2.c5 <> col7.c5) AND (col2.c5 <> col8.c5) AND (col2.c5 <> col9.c5) AND (col2.c6 <> col3.c6) AND (col2.c6 <> col4.c6) AND (col2.c6 <> col5.c6) AND (col2.c6 <> col6.c6) AND (col2.c6 <> col7.c6) AND (col2.c6 <> col8.c6) AND (col2.c6 <> col9.c6) AND (col2.c7 <> col3.c7) AND (col2.c7 <> col4.c7) AND (col2.c7 <> col5.c7) AND (col2.c7 <> col6.c7) AND (col2.c7 <> col7.c7) AND (col2.c7 <> col8.c7) AND (col2.c7 <> col9.c7) AND (col2.c8 <> col3.c8) AND (col2.c8 <> col4.c8) AND (col2.c8 <> col5.c8) AND (col2.c8 <> col6.c8) AND (col2.c8 <> col7.c8) AND (col2.c8 <> col8.c8) AND (col2.c8 <> col9.c8) AND
(col2.c9 <> col3.c9) AND (col2.c9 <> col4.c9) AND (col2.c9 <> col5.c9) AND (col2.c9 <> col6.c9) AND (col2.c9 <> col7.c9) AND (col2.c9 <> col8.c9) AND (col2.c9 <> col9.c9) AND (col3.c1 <> col4.c1) AND (col3.c1 <> col5.c1) AND (col3.c1 <> col6.c1) AND (col3.c1 <> col7.c1) AND (col3.c1 <> col8.c1) AND (col3.c1 <> col9.c1) AND (col3.c2 <> col4.c2) AND (col3.c2 <> col5.c2) AND (col3.c2 <> col6.c2) AND (col3.c2 <> col7.c2) AND (col3.c2 <> col8.c2) AND (col3.c2 <> col9.c2) AND (col3.c3 <> col4.c3) AND (col3.c3 <> col5.c3) AND (col3.c3 <> col6.c3) AND (col3.c3 <> col7.c3) AND (col3.c3 <> col8.c3) AND (col3.c3 <> col9.c3) AND (col3.c4 <> col4.c4) AND (col3.c4 <> col5.c4) AND (col3.c4 <> col6.c4) AND (col3.c4 <> col7.c4) AND (col3.c4 <> col8.c4) AND (col3.c4 <> col9.c4) AND (col3.c5 <> col4.c5) AND
(col3.c5 <> col5.c5) AND (col3.c5 <> col6.c5) AND (col3.c5 <> col7.c5) AND (col3.c5 <> col8.c5) AND (col3.c5 <> col9.c5) AND (col3.c6 <> col4.c6) AND (col3.c6 <> col5.c6) AND (col3.c6 <> col6.c6) AND (col3.c6 <> col7.c6) AND (col3.c6 <> col8.c6) AND (col3.c6 <> col9.c6) AND (col3.c7 <> col4.c7) AND (col3.c7 <> col5.c7) AND (col3.c7 <> col6.c7) AND (col3.c7 <> col7.c7) AND (col3.c7 <> col8.c7) AND (col3.c7 <> col9.c7) AND (col3.c8 <> col4.c8) AND (col3.c8 <> col5.c8) AND (col3.c8 <> col6.c8) AND (col3.c8 <> col7.c8) AND (col3.c8 <> col8.c8) AND (col3.c8 <> col9.c8) AND (col3.c9 <> col4.c9) AND (col3.c9 <> col5.c9) AND (col3.c9 <> col6.c9) AND (col3.c9 <> col7.c9) AND (col3.c9 <> col8.c9) AND (col3.c9 <> col9.c9) AND (col4.c1 <> col5.c1) AND (col4.c1 <> col6.c1) AND (col4.c1 <> col7.c1) AND
(col4.c1 <> col8.c1) AND (col4.c1 <> col9.c1) AND (col4.c2 <> col5.c2) AND (col4.c2 <> col6.c2) AND (col4.c2 <> col7.c2) AND (col4.c2 <> col8.c2) AND (col4.c2 <> col9.c2) AND (col4.c3 <> col5.c3) AND (col4.c3 <> col6.c3) AND (col4.c3 <> col7.c3) AND (col4.c3 <> col8.c3) AND (col4.c3 <> col9.c3) AND (col4.c4 <> col5.c4) AND (col4.c4 <> col6.c4) AND (col4.c4 <> col7.c4) AND (col4.c4 <> col8.c4) AND (col4.c4 <> col9.c4) AND (col4.c5 <> col5.c5) AND (col4.c5 <> col6.c5) AND (col4.c5 <> col7.c5) AND (col4.c5 <> col8.c5) AND (col4.c5 <> col9.c5) AND (col4.c6 <> col5.c6) AND (col4.c6 <> col6.c6) AND (col4.c6 <> col7.c6) AND (col4.c6 <> col8.c6) AND (col4.c6 <> col9.c6) AND (col4.c7 <> col5.c7) AND (col4.c7 <> col6.c7) AND (col4.c7 <> col7.c7) AND (col4.c7 <> col8.c7) AND (col4.c7 <> col9.c7) AND
(col4.c8 <> col5.c8) AND (col4.c8 <> col6.c8) AND (col4.c8 <> col7.c8) AND (col4.c8 <> col8.c8) AND (col4.c8 <> col9.c8) AND (col4.c9 <> col5.c9) AND (col4.c9 <> col6.c9) AND (col4.c9 <> col7.c9) AND (col4.c9 <> col8.c9) AND (col4.c9 <> col9.c9) AND (col5.c1 <> col6.c1) AND (col5.c1 <> col7.c1) AND (col5.c1 <> col8.c1) AND (col5.c1 <> col9.c1) AND (col5.c2 <> col6.c2) AND (col5.c2 <> col7.c2) AND (col5.c2 <> col8.c2) AND (col5.c2 <> col9.c2) AND (col5.c3 <> col6.c3) AND (col5.c3 <> col7.c3) AND (col5.c3 <> col8.c3) AND (col5.c3 <> col9.c3) AND (col5.c4 <> col6.c4) AND (col5.c4 <> col7.c4) AND (col5.c4 <> col8.c4) AND (col5.c4 <> col9.c4) AND (col5.c5 <> col6.c5) AND (col5.c5 <> col7.c5) AND (col5.c5 <> col8.c5) AND (col5.c5 <> col9.c5) AND (col5.c6 <> col6.c6) AND (col5.c6 <> col7.c6) AND
(col5.c6 <> col8.c6) AND (col5.c6 <> col9.c6) AND (col5.c7 <> col6.c7) AND (col5.c7 <> col7.c7) AND (col5.c7 <> col8.c7) AND (col5.c7 <> col9.c7) AND (col5.c8 <> col6.c8) AND (col5.c8 <> col7.c8) AND (col5.c8 <> col8.c8) AND (col5.c8 <> col9.c8) AND (col5.c9 <> col6.c9) AND (col5.c9 <> col7.c9) AND (col5.c9 <> col8.c9) AND (col5.c9 <> col9.c9) AND (col6.c1 <> col7.c1) AND (col6.c1 <> col8.c1) AND (col6.c1 <> col9.c1) AND (col6.c2 <> col7.c2) AND (col6.c2 <> col8.c2) AND (col6.c2 <> col9.c2) AND (col6.c3 <> col7.c3) AND (col6.c3 <> col8.c3) AND (col6.c3 <> col9.c3) AND (col6.c4 <> col7.c4) AND (col6.c4 <> col8.c4) AND (col6.c4 <> col9.c4) AND (col6.c5 <> col7.c5) AND (col6.c5 <> col8.c5) AND (col6.c5 <> col9.c5) AND (col6.c6 <> col7.c6) AND (col6.c6 <> col8.c6) AND (col6.c6 <> col9.c6) AND
(col6.c7 <> col7.c7) AND (col6.c7 <> col8.c7) AND (col6.c7 <> col9.c7) AND (col6.c8 <> col7.c8) AND (col6.c8 <> col8.c8) AND (col6.c8 <> col9.c8) AND (col6.c9 <> col7.c9) AND (col6.c9 <> col8.c9) AND (col6.c9 <> col9.c9) AND (col7.c1 <> col8.c1) AND (col7.c1 <> col9.c1) AND (col7.c2 <> col8.c2) AND (col7.c2 <> col9.c2) AND (col7.c3 <> col8.c3) AND (col7.c3 <> col9.c3) AND (col7.c4 <> col8.c4) AND (col7.c4 <> col9.c4) AND (col7.c5 <> col8.c5) AND (col7.c5 <> col9.c5) AND (col7.c6 <> col8.c6) AND (col7.c6 <> col9.c6) AND (col7.c7 <> col8.c7) AND (col7.c7 <> col9.c7) AND (col7.c8 <> col8.c8) AND (col7.c8 <> col9.c8) AND (col7.c9 <> col8.c9) AND (col7.c9 <> col9.c9) AND (col8.c1 <> col9.c1) AND (col8.c2 <> col9.c2) AND (col8.c3 <> col9.c3) AND (col8.c4 <> col9.c4) AND (col8.c5 <> col9.c5) AND
(col8.c6 <> col9.c6) AND (col8.c7 <> col9.c7) AND (col8.c8 <> col9.c8) AND (col8.c9 <> col9.c9) AND
-- Nombres uniques dans chaque maison de 3x3
(col1.c1 <> col1.c2) AND (col1.c1 <> col1.c3) AND (col1.c1 <> col2.c2) AND (col1.c1 <> col2.c3) AND (col1.c1 <> col3.c2) AND (col1.c1 <> col3.c3) AND (col1.c2 <> col1.c3) AND (col1.c2 <> col2.c1) AND (col1.c2 <> col2.c3) AND (col1.c2 <> col3.c1) AND (col1.c2 <> col3.c3) AND (col1.c3 <> col2.c1) AND (col1.c3 <> col2.c2) AND (col1.c3 <> col3.c1) AND (col1.c3 <> col3.c2) AND (col1.c4 <> col1.c5) AND (col1.c4 <> col1.c6) AND (col1.c4 <> col2.c5) AND (col1.c4 <> col2.c6) AND (col1.c4 <> col3.c5) AND (col1.c4 <> col3.c6) AND (col1.c5 <> col1.c6) AND (col1.c5 <> col2.c4) AND (col1.c5 <> col2.c6) AND (col1.c5 <> col3.c4) AND (col1.c5 <> col3.c6) AND (col1.c6 <> col2.c4) AND (col1.c6 <> col2.c5) AND (col1.c6 <> col3.c4) AND (col1.c6 <> col3.c5) AND (col1.c7 <> col1.c8) AND (col1.c7 <> col1.c9) AND
(col1.c7 <> col2.c8) AND (col1.c7 <> col2.c9) AND (col1.c7 <> col3.c8) AND (col1.c7 <> col3.c9) AND (col1.c8 <> col1.c9) AND (col1.c8 <> col2.c7) AND (col1.c8 <> col2.c9) AND (col1.c8 <> col3.c7) AND (col1.c8 <> col3.c9) AND (col1.c9 <> col2.c7) AND (col1.c9 <> col2.c8) AND (col1.c9 <> col3.c7) AND (col1.c9 <> col3.c8) AND (col2.c1 <> col2.c2) AND (col2.c1 <> col2.c3) AND (col2.c1 <> col3.c2) AND (col2.c1 <> col3.c3) AND (col2.c2 <> col2.c3) AND (col2.c2 <> col3.c1) AND (col2.c2 <> col3.c3) AND (col2.c3 <> col3.c1) AND (col2.c3 <> col3.c2) AND (col2.c4 <> col2.c5) AND (col2.c4 <> col2.c6) AND (col2.c4 <> col3.c5) AND (col2.c4 <> col3.c6) AND (col2.c5 <> col2.c6) AND (col2.c5 <> col3.c4) AND (col2.c5 <> col3.c6) AND (col2.c6 <> col3.c4) AND (col2.c6 <> col3.c5) AND (col2.c7 <> col2.c8) AND
(col2.c7 <> col2.c9) AND (col2.c7 <> col3.c8) AND (col2.c7 <> col3.c9) AND (col2.c8 <> col2.c9) AND (col2.c8 <> col3.c7) AND (col2.c8 <> col3.c9) AND (col2.c9 <> col3.c7) AND (col2.c9 <> col3.c8) AND (col3.c1 <> col3.c2) AND (col3.c1 <> col3.c3) AND (col3.c2 <> col3.c3) AND (col3.c4 <> col3.c5) AND (col3.c4 <> col3.c6) AND (col3.c5 <> col3.c6) AND (col3.c7 <> col3.c8) AND (col3.c7 <> col3.c9) AND (col3.c8 <> col3.c9) AND (col4.c1 <> col4.c2) AND (col4.c1 <> col4.c3) AND (col4.c1 <> col5.c2) AND (col4.c1 <> col5.c3) AND (col4.c1 <> col6.c2) AND (col4.c1 <> col6.c3) AND (col4.c2 <> col4.c3) AND (col4.c2 <> col5.c1) AND (col4.c2 <> col5.c3) AND (col4.c2 <> col6.c1) AND (col4.c2 <> col6.c3) AND (col4.c3 <> col5.c1) AND (col4.c3 <> col5.c2) AND (col4.c3 <> col6.c1) AND (col4.c3 <> col6.c2) AND
(col4.c4 <> col4.c5) AND (col4.c4 <> col4.c6) AND (col4.c4 <> col5.c5) AND (col4.c4 <> col5.c6) AND (col4.c4 <> col6.c5) AND (col4.c4 <> col6.c6) AND (col4.c5 <> col4.c6) AND (col4.c5 <> col5.c4) AND (col4.c5 <> col5.c6) AND (col4.c5 <> col6.c4) AND (col4.c5 <> col6.c6) AND (col4.c6 <> col5.c4) AND (col4.c6 <> col5.c5) AND (col4.c6 <> col6.c4) AND (col4.c6 <> col6.c5) AND (col4.c7 <> col4.c8) AND (col4.c7 <> col4.c9) AND (col4.c7 <> col5.c8) AND (col4.c7 <> col5.c9) AND (col4.c7 <> col6.c8) AND (col4.c7 <> col6.c9) AND (col4.c8 <> col4.c9) AND (col4.c8 <> col5.c7) AND (col4.c8 <> col5.c9) AND (col4.c8 <> col6.c7) AND (col4.c8 <> col6.c9) AND (col4.c9 <> col5.c7) AND (col4.c9 <> col5.c8) AND (col4.c9 <> col6.c7) AND (col4.c9 <> col6.c8) AND (col5.c1 <> col5.c2) AND (col5.c1 <> col5.c3) AND
(col5.c1 <> col6.c2) AND (col5.c1 <> col6.c3) AND (col5.c2 <> col5.c3) AND (col5.c2 <> col6.c1) AND (col5.c2 <> col6.c3) AND (col5.c3 <> col6.c1) AND (col5.c3 <> col6.c2) AND (col5.c4 <> col5.c5) AND (col5.c4 <> col5.c6) AND (col5.c4 <> col6.c5) AND (col5.c4 <> col6.c6) AND (col5.c5 <> col5.c6) AND (col5.c5 <> col6.c4) AND (col5.c5 <> col6.c6) AND (col5.c6 <> col6.c4) AND (col5.c6 <> col6.c5) AND (col5.c7 <> col5.c8) AND (col5.c7 <> col5.c9) AND (col5.c7 <> col6.c8) AND (col5.c7 <> col6.c9) AND (col5.c8 <> col5.c9) AND (col5.c8 <> col6.c7) AND (col5.c8 <> col6.c9) AND (col5.c9 <> col6.c7) AND (col5.c9 <> col6.c8) AND (col6.c1 <> col6.c2) AND (col6.c1 <> col6.c3) AND (col6.c2 <> col6.c3) AND (col6.c4 <> col6.c5) AND (col6.c4 <> col6.c6) AND (col6.c5 <> col6.c6) AND (col6.c7 <> col6.c8) AND
(col6.c7 <> col6.c9) AND (col6.c8 <> col6.c9) AND (col7.c1 <> col7.c2) AND (col7.c1 <> col7.c3) AND (col7.c1 <> col8.c2) AND (col7.c1 <> col8.c3) AND (col7.c1 <> col9.c2) AND (col7.c1 <> col9.c3) AND (col7.c2 <> col7.c3) AND (col7.c2 <> col8.c1) AND (col7.c2 <> col8.c3) AND (col7.c2 <> col9.c1) AND (col7.c2 <> col9.c3) AND (col7.c3 <> col8.c1) AND (col7.c3 <> col8.c2) AND (col7.c3 <> col9.c1) AND (col7.c3 <> col9.c2) AND (col7.c4 <> col7.c5) AND (col7.c4 <> col7.c6) AND (col7.c4 <> col8.c5) AND (col7.c4 <> col8.c6) AND (col7.c4 <> col9.c5) AND (col7.c4 <> col9.c6) AND (col7.c5 <> col7.c6) AND (col7.c5 <> col8.c4) AND (col7.c5 <> col8.c6) AND (col7.c5 <> col9.c4) AND (col7.c5 <> col9.c6) AND (col7.c6 <> col8.c4) AND (col7.c6 <> col8.c5) AND (col7.c6 <> col9.c4) AND (col7.c6 <> col9.c5) AND
(col7.c7 <> col7.c8) AND (col7.c7 <> col7.c9) AND (col7.c7 <> col8.c8) AND (col7.c7 <> col8.c9) AND (col7.c7 <> col9.c8) AND (col7.c7 <> col9.c9) AND (col7.c8 <> col7.c9) AND (col7.c8 <> col8.c7) AND (col7.c8 <> col8.c9) AND (col7.c8 <> col9.c7) AND (col7.c8 <> col9.c9) AND (col7.c9 <> col8.c7) AND (col7.c9 <> col8.c8) AND (col7.c9 <> col9.c7) AND (col7.c9 <> col9.c8) AND (col8.c1 <> col8.c2) AND (col8.c1 <> col8.c3) AND (col8.c1 <> col9.c2) AND (col8.c1 <> col9.c3) AND (col8.c2 <> col8.c3) AND (col8.c2 <> col9.c1) AND (col8.c2 <> col9.c3) AND (col8.c3 <> col9.c1) AND (col8.c3 <> col9.c2) AND (col8.c4 <> col8.c5) AND (col8.c4 <> col8.c6) AND (col8.c4 <> col9.c5) AND (col8.c4 <> col9.c6) AND (col8.c5 <> col8.c6) AND (col8.c5 <> col9.c4) AND (col8.c5 <> col9.c6) AND (col8.c6 <> col9.c4) AND
(col8.c6 <> col9.c5) AND (col8.c7 <> col8.c8) AND (col8.c7 <> col8.c9) AND (col8.c7 <> col9.c8) AND (col8.c7 <> col9.c9) AND (col8.c8 <> col8.c9) AND (col8.c8 <> col9.c7) AND (col8.c8 <> col9.c9) AND (col8.c9 <> col9.c7) AND (col8.c9 <> col9.c8) AND (col9.c1 <> col9.c2) AND (col9.c1 <> col9.c3) AND (col9.c2 <> col9.c3) AND (col9.c4 <> col9.c5) AND (col9.c4 <> col9.c6) AND (col9.c5 <> col9.c6) AND (col9.c7 <> col9.c8) AND (col9.c7 <> col9.c9) AND (col9.c8 <> col9.c9);

Maintenant, chers lecteurs, patientez un peu!

ATTENTION : n’allez surtout pas essayer de solutionner une grille  avant de passer au prochain point!

Pour l’instant, contentez-vous seulement de créer la nouvelle vue sudoku_combined_view :

USE sudoku;

CREATE VIEW sudoku_combined_view AS
SELECT t1.*
FROM sudoku_rows_view t1
INNER JOIN sudoku_columns_view t2
ON

-- Jointures entre représentation-colonnes et représentation-rangées
(t1.r1c1 = t2.r1c1) AND (t1.r1c2 = t2.r1c2) AND (t1.r1c3 = t2.r1c3) AND (t1.r1c4 = t2.r1c4) AND
(t1.r1c5 = t2.r1c5) AND (t1.r1c6 = t2.r1c6) AND (t1.r1c7 = t2.r1c7) AND (t1.r1c8 = t2.r1c8) AND
(t1.r1c9 = t2.r1c9) AND (t1.r2c1 = t2.r2c1) AND (t1.r2c2 = t2.r2c2) AND (t1.r2c3 = t2.r2c3) AND
(t1.r2c4 = t2.r2c4) AND (t1.r2c5 = t2.r2c5) AND (t1.r2c6 = t2.r2c6) AND (t1.r2c7 = t2.r2c7) AND
(t1.r2c8 = t2.r2c8) AND (t1.r2c9 = t2.r2c9) AND (t1.r3c1 = t2.r3c1) AND (t1.r3c2 = t2.r3c2) AND
(t1.r3c3 = t2.r3c3) AND (t1.r3c4 = t2.r3c4) AND (t1.r3c5 = t2.r3c5) AND (t1.r3c6 = t2.r3c6) AND
(t1.r3c7 = t2.r3c7) AND (t1.r3c8 = t2.r3c8) AND (t1.r3c9 = t2.r3c9) AND (t1.r4c1 = t2.r4c1) AND
(t1.r4c2 = t2.r4c2) AND (t1.r4c3 = t2.r4c3) AND (t1.r4c4 = t2.r4c4) AND (t1.r4c5 = t2.r4c5) AND
(t1.r4c6 = t2.r4c6) AND (t1.r4c7 = t2.r4c7) AND (t1.r4c8 = t2.r4c8) AND (t1.r4c9 = t2.r4c9) AND
(t1.r5c1 = t2.r5c1) AND (t1.r5c2 = t2.r5c2) AND (t1.r5c3 = t2.r5c3) AND (t1.r5c4 = t2.r5c4) AND
(t1.r5c5 = t2.r5c5) AND (t1.r5c6 = t2.r5c6) AND (t1.r5c7 = t2.r5c7) AND (t1.r5c8 = t2.r5c8) AND
(t1.r5c9 = t2.r5c9) AND (t1.r6c1 = t2.r6c1) AND (t1.r6c2 = t2.r6c2) AND (t1.r6c3 = t2.r6c3) AND
(t1.r6c4 = t2.r6c4) AND (t1.r6c5 = t2.r6c5) AND (t1.r6c6 = t2.r6c6) AND (t1.r6c7 = t2.r6c7) AND
(t1.r6c8 = t2.r6c8) AND (t1.r6c9 = t2.r6c9) AND (t1.r7c1 = t2.r7c1) AND (t1.r7c2 = t2.r7c2) AND
(t1.r7c3 = t2.r7c3) AND (t1.r7c4 = t2.r7c4) AND (t1.r7c5 = t2.r7c5) AND (t1.r7c6 = t2.r7c6) AND
(t1.r7c7 = t2.r7c7) AND (t1.r7c8 = t2.r7c8) AND (t1.r7c9 = t2.r7c9) AND (t1.r8c1 = t2.r8c1) AND
(t1.r8c2 = t2.r8c2) AND (t1.r8c3 = t2.r8c3) AND (t1.r8c4 = t2.r8c4) AND (t1.r8c5 = t2.r8c5) AND
(t1.r8c6 = t2.r8c6) AND (t1.r8c7 = t2.r8c7) AND (t1.r8c8 = t2.r8c8) AND (t1.r8c9 = t2.r8c9) AND
(t1.r9c1 = t2.r9c1) AND (t1.r9c2 = t2.r9c2) AND (t1.r9c3 = t2.r9c3) AND (t1.r9c4 = t2.r9c4) AND
(t1.r9c5 = t2.r9c5) AND (t1.r9c6 = t2.r9c6) AND (t1.r9c7 = t2.r9c7) AND (t1.r9c8 = t2.r9c8) AND
(t1.r9c9 = t2.r9c9);

4. L’optimisateur de plan

Avant de tenter d’exécuter la requête de la grille présentée au point 1 de cet article, quelques explications sont de mise. Il appert que notre nouvelle façon de faire change radicalement les choses!

En effet, au lieu de joindre seulement 9 tables comme c’était le cas avec sudoku_rows_view, notre nouvelle solution joint 9 tables une première fois (sudoku_rows_view), encore une fois 9 tables (sudoku_columns_view) puis regroupe les résultats de ces 2 vues dans sudoku_combined_view.

Il faut savoir que l’optimisateur de requêtes de MySQL, par défaut, énumère toutes les jointures possibles pour déterminer le plan d’accès qu’il considère comme optimal. Dans le cas qui nous intéresse, l’optimisateur détecte donc 18 tables indirectement référencées par la vue sudoku_combined_view et aura donc à examiner 18! (18 factorielle) jointures possibles, c’est-à-dire un total de 6402373705728000 jointures! Si par malheur vous tentiez d’exécuter la requête sur la vue sudoku_combined_view, il vous faudrait attendre une éternité avant que MySQL détermine un plan d’accès!  Pour vérifier, j’ai laissé rouler une requête de EXPLAIN sur la vue sudoku_combined_view pendant 2 jours avant de l’arrêter…

Heureusement, il existe une variable système nous permettant de contrôler le zèle de l’optimisateur de requêtes!  Cette variable s’appelle optimizer_search_depth.  Elle détermine la profondeur d’analyse de l’optimisateur quand celui-ci essaie de trouver le plan d’accès optimal.  À quoi bon un plan d’accès optimal si celui-ci prend 3 semaines à être généré ?  En ce qui nous concerne, un plan d’accès non optimal mais généré rapidement, compte tenu des 18 tables, est ce que nous recherchons!

La variable optimizer_search_depth peut être changée dans les fichiers de configuration de MySQL ou dynamiquement au beau milieu d’une session.  Prenez garde toutefois!  Si vous changez cette variable dans une session et non au niveau des fichiers de configuration, la nouvelle valeur de la variable ne s’applique qu’à la session!

Réglons cette valeur à 3  pour l’instant (plus de détails quant à cette valeur dans le prochain article)  :


set @@optimizer_search_depth = 3;

Maintenant, nous pouvons exécuter notre requête :


SELECT *
FROM sudoku_combined_view
WHERE
(r2c1 = 1) AND (r2c2 = 3) AND (r2c3 = 4) AND (r2c4 = 8) AND
(r2c5 = 2) AND (r2c6 = 5) AND (r2c7 = 6) AND (r2c8 = 9) AND
(r2c9 = 7) AND (r3c1 = 7) AND (r3c2 = 5) AND (r3c3 = 9) AND
(r3c4 = 3) AND (r3c5 = 6) AND (r3c6 = 4) AND (r3c7 = 1) AND
(r3c8 = 8) AND (r3c9 = 2) AND (r4c1 = 3) AND (r4c2 = 9) AND
(r4c3 = 7) AND (r4c4 = 1) AND (r4c5 = 8) AND (r4c6 = 2) AND
(r4c7 = 5) AND (r4c8 = 6) AND (r4c9 = 4) AND (r6c1 = 5) AND
(r6c2 = 8) AND (r6c3 = 1) AND (r6c4 = 4) AND (r6c5 = 7) AND
(r6c6 = 6) AND (r6c7 = 2) AND (r6c8 = 3) AND (r6c9 = 9) AND
(r7c1 = 8) AND (r7c2 = 2) AND (r7c3 = 5) AND (r7c4 = 6) AND
(r7c5 = 4) AND (r7c6 = 1) AND (r7c7 = 9) AND (r7c8 = 7) AND
(r7c9 = 3) AND (r8c1 = 9) AND (r8c2 = 7) AND (r8c3 = 6) AND
(r8c4 = 5) AND (r8c5 = 3) AND (r8c6 = 8) AND (r8c7 = 4) AND
(r8c8 = 2) AND (r8c9 = 1);

Fantastique!  1.08 seconde!  Est-il possible d’extraire plus de jus de ce citron?

Voyons ce que le EXPLAIN a à nous dire :

+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+--------------------------------------------------------------+
| id | select_type | table | type        | possible_keys                                                                                                                                      | key         | key_len | ref                           | rows | Extra                                                        |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+--------------------------------------------------------------+
|  1 | SIMPLE      | col3  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i38,i48 | 2,2,2   | NULL                          |   64 | Using intersect(i23,i38,i48); Using where                    |
|  1 | SIMPLE      | col9  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i68,i48 | 2,2,2   | NULL                          |   65 | Using intersect(i78,i68,i48); Using where; Using join buffer |
|  1 | SIMPLE      | r2    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i29     | 2,2     | NULL                          |   68 | Using intersect(i37,i29); Using where; Using join buffer     |
|  1 | SIMPLE      | r3    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i28     | 2,2     | NULL                          |   68 | Using intersect(i37,i28); Using where; Using join buffer     |
|  1 | SIMPLE      | r4    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i56,i29     | 2,2     | NULL                          |   68 | Using intersect(i56,i29); Using where; Using join buffer     |
|  1 | SIMPLE      | r6    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12,i35     | 2,2     | NULL                          |   68 | Using intersect(i12,i35); Using where; Using join buffer     |
|  1 | SIMPLE      | r7    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12,i68     | 2,2     | NULL                          |   68 | Using intersect(i12,i68); Using where; Using join buffer     |
|  1 | SIMPLE      | col1  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i67     | 2,2     | NULL                          |   68 | Using intersect(i23,i67); Using where; Using join buffer     |
|  1 | SIMPLE      | col2  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer     |
|  1 | SIMPLE      | col4  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i78,i46     | 2,2     | NULL                          |   68 | Using intersect(i78,i46); Using where; Using join buffer     |
|  1 | SIMPLE      | col5  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer     |
|  1 | SIMPLE      | col6  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i67     | 2,2     | NULL                          |   68 | Using intersect(i23,i67); Using where; Using join buffer     |
|  1 | SIMPLE      | r8    | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i79,i38 | 2,2,2   | NULL                          |   78 | Using intersect(i37,i79,i38); Using where; Using join buffer |
|  1 | SIMPLE      | col8  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i37,i24     | 2,2     | NULL                          |   68 | Using intersect(i37,i24); Using where; Using join buffer     |
|  1 | SIMPLE      | col7  | index_merge | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i23,i68     | 2,2     | NULL                          |   68 | Using intersect(i23,i68); Using where; Using join buffer     |
|  1 | SIMPLE      | r1    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c1,sudoku.col2.c1 | 5040 | Using where                                                  |
|  1 | SIMPLE      | r5    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c5,sudoku.col2.c5 | 5040 | Using where                                                  |
|  1 | SIMPLE      | r9    | ref         | i12,i13,i14,i15,i16,i17,i18,i19,i23,i24,i25,i26,i27,i28,i29,i34,i35,i36,i37,i38,i39,i45,i46,i47,i48,i49,i56,i57,i58,i59,i67,i68,i69,i78,i79,i89,i9 | i12         | 2       | sudoku.col1.c9,sudoku.col2.c9 | 5040 | Using where                                                  |
+----+-------------+-------+-------------+----------------------------------------------------------------------------------------------------------------------------------------------------+-------------+---------+-------------------------------+------+--------------------------------------------------------------+
18 rows in set (0.28 sec)

5. Optimisation de la table

Il existe quelques trucs d’optimisation de table que nous avons omis de faire.  C’est peut-être le temps d’y songer pour extraire chaque milliseconde et chaque octet possible!

Bien que la table positions ne subisse jamais de UPDATE, de INSERT ou de DELETE, sommes-nous certains que les pages d’index sont triées ? Pour ce faire, nous pourrions exécuter un OPTIMIZE TABLE sur la table positions.  Ce serait inutile dans notre cas.  Pourquoi?  Parce que les permutations générées pour créer les requêtes d’insertion dans la table positions ont été générées dans l’ordre des index.

D’autre part, comme la table n’a connu aucune modification, un ANALYZE TABLE serait, lui aussi, totalement inutile!

Changer la définition de la table avec un ALTER TABLE pour y inclure AVG_ROW_LENGTH et MAX_ROWS ?  Pas plus utile.  Comme le format des lignes dans la table positions est Fixed et que la table est de format MyISAM, ces deux valeurs n’ont pas à être forcées puisque MySQL les détermine sans notre aide!

6. Impossible n’est pas français!

Est-ce possible de faire mieux?  En éternel optimiste et têtu que je suis, je répondrai « oui » !  Mais comment?

Seulement, avons-nous tout prévu?  Que faire avec une grille contenant des lignes vides et des colonnes vides comme la grille suivante :

Suite au prochain article!