从这个网页看到一个用postgresql的自定义函数求解数独的程序，其实核心还是一个利用递归CTE的SQL。
然后把两个计算行列宫的临时表做成物理表。
对问题表中的每行执行上述标量函数，效率和单独的SQL差不多。难题耗时比较长。
postgres@b3490d8427cd:~$ psql
psql (17.7 (Debian 17.7-3.pgdg13+1))
Type "help" for help.
postgres=# table sudoku9_9;
postgres=# CREATE TABLE allnum AS
SELECT generate_series(1, 9) AS num
;
SELECT 9
postgres=# CREATE TABLE grid AS
SELECT
(i - 1) * 9 + j AS indexof
,i
,j
,(i - 1) / 3 * 3 + 1 + (j - 1) / 3 AS grp
FROM
allnum n1(i)
,allnum n2(j)
;
SELECT 81
postgres=# CREATE OR REPLACE FUNCTION sudoku(text)
RETURNS text LANGUAGE sql IMMUTABLE AS $$
WITH RECURSIVE _sudoku AS (
-- 初期値
SELECT $1 kekka
-- 再帰with句で追加されていく行
UNION ALL(
WITH latest AS (
SELECT
kekka
,(ROW_NUMBER() OVER())::int parallelid
FROM _sudoku
)
,gridnum AS (
SELECT
latest.parallelid
,indexof, i, j, grp
,substr(latest.kekka, indexof, 1) AS num
FROM latest, grid
)
,used AS (
SELECT
gridnums.parallelid
,gridnums.indexof
,array_agg(DISTINCT usednums.num :: int) usednumarray
FROM
gridnum usednums
,gridnum gridnums
WHERE
usednums.num <> ' '
AND
gridnums.num = ' '
AND
usednums.parallelid = gridnums.parallelid
AND(
usednums.i = gridnums.i
OR
usednums.j = gridnums.j
OR
usednums.grp = gridnums.grp
)
GROUP BY
gridnums.parallelid
,gridnums.indexof
)
,insertnum AS (
SELECT
parallelid
,indexof
,usednumarray
,DENSE_RANK() OVER(
PARTITION BY used.parallelid
ORDER BY ARRAY_LENGTH(used.usednumarray, 1) DESC, indexof
) AS insertorder
FROM used
)
SELECT
overlay(latest.kekka placing allnum.num::text FROM insertnum.indexof FOR 1) AS kekka
FROM
latest
,allnum
,insertnum
WHERE
latest.parallelid = insertnum.parallelid
AND
insertnum.insertorder = 1
AND
allnum.num <> ALL(insertnum.usednumarray)
)
)
SELECT kekka
FROM _sudoku
WHERE strpos(kekka, ' ') = 0;
$$ ;
CREATE FUNCTION
postgres=# CREATE TABLE sudoku_q AS
SELECT 1 id, ' 6 3 1 9 5 2 31 14 678 786529 34567 93 1891456372 24 875 9'::text as question
UNION SELECT 2, ' 7 3 6 9152 23 48 7418 65 7 9325 876 9341 9215 37 5 18296'
UNION SELECT 3, ' 3 1967 4 8 2 34157 2 62315 68 9 13 68 9 258479 6 2 9143857'
UNION SELECT 4, ' 9 8 7 42 6 3 7 1 2 5 836 992 651 475 63491831 8 7452 9521 63'
UNION SELECT 5, ' 5 3 6 824 7 1 2954167 1 86 2954 6 7 9312 39784 563241 7 9 5283'
;
SELECT 5
postgres=# SELECT * FROM sudoku_q ORDER BY id;
id | question
----+-----------------------------------------------------------------------------------
1 | 6 3 1 9 5 2 31 14 678 786529 34567 93 1891456372 24 875 9
2 | 7 3 6 9152 23 48 7418 65 7 9325 876 9341 9215 37 5 18296
3 | 3 1967 4 8 2 34157 2 62315 68 9 13 68 9 258479 6 2 9143857
4 | 9 8 7 42 6 3 7 1 2 5 836 992 651 475 63491831 8 7452 9521 63
5 | 5 3 6 824 7 1 2954167 1 86 2954 6 7 9312 39784 563241 7 9 5283
(5 rows)
postgres=# \timing
Timing is on.
postgres=# SELECT id, sudoku(question) FROM sudoku_q ORDER BY id;
id | sudoku
----+-----------------------------------------------------------------------------------
1 | 472931658635842917918765423259314786143678295786529134567293841891456372324187569
2 | 694857123387142659152639784235481967418976532769325841876293415921564378543718296
3 | 458326719672914385913857426341579268896231574725468193137685942584792631269143857
4 | 235976841178342596694158327867419235541283679923765184752634918316897452489521763
5 | 635217849741893526982456731329541678178632954564789312213978465856324197497165283
(5 rows)
Time: 35.973 ms
postgres=# insert into sudoku_q SELECT 8 AS id, E'8 36 7 9 2 5 7 457 1 3 1 68 85 1 9 4 ';
INSERT 0 1
Time: 3.909 ms
postgres=# SELECT id, sudoku(question) FROM sudoku_q ORDER BY id;
id | sudoku
----+-----------------------------------------------------------------------------------
1 | 472931658635842917918765423259314786143678295786529134567293841891456372324187569
2 | 694857123387142659152639784235481967418976532769325841876293415921564378543718296
3 | 458326719672914385913857426341579268896231574725468193137685942584792631269143857
4 | 235976841178342596694158327867419235541283679923765184752634918316897452489521763
5 | 635217849741893526982456731329541678178632954564789312213978465856324197497165283
8 | 812753649943682175675491283154237896369845721287169534521974368438526917796318452
(6 rows)
Time: 4808.878 ms (00:04.809)
postgres=#