A Takuzu/Binary puzzle solver in SQL (SQLite dialect)

takuzu.sql

WITH RECURSIVE
  input(puz) AS (
    VALUES ('....00.0....' ||
            '1....0....11' ||
            '.1......00..' ||
            '............' ||
            '.00...1.....' ||
            '.......0..0.' ||
            '.1.11...1...' ||
            '0......0....' ||
            '..1..1......' || 
            '.0..0....0..' ||
            '.......01.1.' ||
            '...1...0..1.')
  ),
  side_len(n) AS (
    SELECT CAST(sqrt(length(puz)) AS INT) FROM input
  ),
  bits(b) AS (
    VALUES ('0'), ('1')
  ),
  idx(i) AS (
    SELECT 0
    UNION ALL 
    SELECT i + 1 FROM idx, side_len WHERE i + 1 < n
  ),
  x(s, ind) AS (
    SELECT puz, instr(puz, '.') FROM input
    UNION ALL
    SELECT
      substr(s,1,ind-1) || b || substr(s,ind+1),
      instr(substr(s,1,ind-1) || b || substr(s,ind+1), '.')
    FROM x, bits, side_len
    WHERE ind > 0
      -- No row may contain three consecutive identical values
      AND substr(substr(s,1,ind-1) || b || substr(s,ind+1), ((ind-1)/n)*n + 1, n) NOT LIKE '%' || b || b || b || '%'
      -- No column may contain three consecutive identical values
      AND NOT EXISTS (
        SELECT 1
        FROM idx i
        WHERE i <= n-3
          AND substr(substr(s,1,ind-1) || b || substr(s,ind+1), i*n + ((ind-1)%n) + 1, 1) = b
          AND substr(substr(s,1,ind-1) || b || substr(s,ind+1), (i+1)*n + ((ind-1)%n) + 1, 1) = b
          AND substr(substr(s,1,ind-1) || b || substr(s,ind+1), (i+2)*n + ((ind-1)%n) + 1, 1) = b
      )
      -- Every row must contain exactly the same number of 0s and 1s.
      AND (
        SELECT count(*)
        FROM idx i
        WHERE substr(substr(s,1,ind-1) || b || substr(s,ind+1), ((ind-1)/n)*n + i + 1, 1) = b
      ) <= n/2
      -- Every column must contain exactly the same number of 0s and 1s.
      AND (
        SELECT count(*)
        FROM idx i
        WHERE substr(substr(s,1,ind-1) || b || substr(s,ind+1), i*n + ((ind-1)%n) + 1, 1) = b
      ) <= n/2
  )
SELECT x.s
FROM x, side_len
WHERE ind = 0
-- No two rows may be identical.
AND (SELECT count(*) = count(DISTINCT substr(x.s, i*n + 1, n)) FROM idx i)
-- No two columns may be identical.
AND (
  SELECT count(*) = count(DISTINCT 
    (SELECT group_concat(substr(x.s, r.i*n + c.i + 1, 1), '') FROM idx r)
  ) 
  FROM idx c
);