#include <SQLite.au3>
;~ #include <SQLite.dll.au3>	; download the most recent suitable DLL once and comment this out

Local $hDB


Local $aSudokus = [ _
	["Juvigy Med",    "29    8  85 4 137     3     3   2 56 4 397 1 12 5   3     1     649 8 23  7    85"], _
	["Juvigy Hard",   "       84 9  5   7     91    95   7  7 3 2 6  6   18    67     1   3  4 32       "], _
	["Juvigy Harder", "       934 2     7 3 1      4 2  6   7    9  5   63 4      7 6     4   8  1 8 2  "], _
	["MvGulik",       " 23 9 8  6 1 38   5  4     3     2 4  6   3  7 8     1     3  8   78 9 6  2 5 14 "], _
	["Easy",          "53  7    6  195    98    6 8   6   34  8 3  17   2   6 6    28    419  5    8  79"], _
	["Sqlite",        "1    7 9  3  2   8  96  5    53  9   1  8   26    4   3      1  4      7  7   3  "], _
	["Hard",          "     6    59     82    8    45        3        6  3 54   325  6                  "], _
	["Hola",          "4 2    3 1  6 5 299     1      42    8 9 1 5    85      3     861 5 4  2 4    5 7"], _
	["Hardest",       "8          36      7  9 2   5   7       457     1   3   1    68  85   1  9    4  "], _
	["EasterMonster", "1       2 9 4   5   6   7   5 9 3       7       85  4 7     6   3   9 8   2     1"] _
]

_SQLite_Startup()

$hDB = _SQLite_Open()
Local $sTempCreate = "" & _
"create temporary table i (" & _
	"i integer primary key, " & _
	"name char, " & _
	"word0, " & _
	"word1, " & _
	"peers0, " & _
	"peers1)" & _
";" & _
"insert into i " & _
	"select i, " & _
		"char(65+y)||(x+1) as name, " & _
		"case when iword=0 then 1<<ibit else 0 end AS word0, " & _
		"case when iword=1 then 1<<ibit else 0 end AS word1, " & _
		"CASE WHEN iword=0 THEN (512-1)<<(y*9) ELSE 0 END | " & _
			"((1+512*(1+512*(1+512*(1+512*(1+512)))))<<x) | " & _
			"CASE WHEN iword=0 THEN ((8-1)*(1+512*(1+512)))<<(y/3*3*9+x/3*3) ELSE 0 END AS peers0, " & _
		"CASE WHEN iword=1 THEN (512-1)<<((y%6)*9) ELSE 0 END | " & _
			"((1 + 512 * (1 + 512)) << x) | " & _
			"CASE WHEN iword=1 THEN ((8-1)*(1+512*(1+512)))<<((y%6)/3*3*9+x/3*3) ELSE 0 END AS peers1 " & _
	"from (" & _
		"with xy AS (SELECT 0 AS xy UNION ALL SELECT xy+1 FROM xy WHERE xy < 80) " & _
		"select  xy+1 AS i, " & _
				"xy%9 AS x, " & _
				"xy/9 AS y, " & _
				"xy/54 AS iword, " & _
				"xy%54 AS ibit " & _
		"from xy" & _
	")" & _
";"

_SQLite_Exec($hDB, $sTempCreate)

Local $sInsaneSolver = "" & _
"with   z AS (SELECT 1 AS z UNION ALL SELECT z+1 FROM z WHERE z < 9), " & _
		"input as (" & _
			"select  input, " & _
					"sud, " & _
					"ifnull (sum (word0), 0) as w0, " & _
					"ifnull (sum (word1), 0) as w1, " & _
					"ifnull (sum (case when z=1 then word0 end), 0) as w10, " & _
					"ifnull (sum (case when z=1 then word1 end), 0) as w11, " & _
					"ifnull (sum (case when z=2 then word0 end), 0) as w20, " & _
					"ifnull (sum (case when z=2 then word1 end), 0) as w21, " & _
					"ifnull (sum (case when z=3 then word0 end), 0) as w30, " & _
					"ifnull (sum (case when z=3 then word1 end), 0) as w31, " & _
					"ifnull (sum (case when z=4 then word0 end), 0) as w40, " & _
					"ifnull (sum (case when z=4 then word1 end), 0) as w41, " & _
					"ifnull (sum (case when z=5 then word0 end), 0) as w50, " & _
					"ifnull (sum (case when z=5 then word1 end), 0) as w51, " & _
					"ifnull (sum (case when z=6 then word0 end), 0) as w60, " & _
					"ifnull (sum (case when z=6 then word1 end), 0) as w61, " & _
					"ifnull (sum (case when z=7 then word0 end), 0) as w70, " & _
					"ifnull (sum (case when z=7 then word1 end), 0) as w71, " & _
					"ifnull (sum (case when z=8 then word0 end), 0) as w80, " & _
					"ifnull (sum (case when z=8 then word1 end), 0) as w81, " & _
					"ifnull (sum (case when z=9 then word0 end), 0) as w90, " & _
					"ifnull (sum (case when z=9 then word1 end), 0) as w91, " & _
					"count (*) as fixed, " & _
					"ifnull (sum (z=1), 0) as f1, " & _
					"ifnull (sum (z=2), 0) as f2, " & _
					"ifnull (sum (z=3), 0) as f3, " & _
					"ifnull (sum (z=4), 0) as f4, " & _
					"ifnull (sum (z=5), 0) as f5, " & _
					"ifnull (sum (z=6), 0) as f6, " & _
					"ifnull (sum (z=7), 0) as f7, " & _
					"ifnull (sum (z=8), 0) as f8, " & _
					"ifnull (sum (z=9), 0) as f9 " & _
			"from ( " & _
				"select '" & $aSudokus[0][0] & "' as input, " & _
				"'" & $aSudokus[0][1] & "' as sud " & _
			"union all " & _
				"select '" & $aSudokus[1][0] & "', " & _
				"'" & $aSudokus[1][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[2][0] & "', " & _
				"'" & $aSudokus[2][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[3][0] & "', " & _
				"'" & $aSudokus[3][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[4][0] & "', " & _
				"'" & $aSudokus[4][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[5][0] & "', " & _
				"'" & $aSudokus[5][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[6][0] & "', " & _
				"'" & $aSudokus[6][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[7][0] & "', " & _
				"'" & $aSudokus[7][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[8][0] & "', " & _
				"'" & $aSudokus[8][1] & "' " & _
			"union all " & _
				"select '" & $aSudokus[9][0] & "', " & _
				"'" & $aSudokus[9][1] & "' " & _
			") " & _
			"join i " & _
			"join z on z = cast (substr (sud, i.i, 1) as int) " & _
			"where input='#####' " & _
		") " & _
", " & _
"sudoku as (" & _
    "select " & _
		"'' as text, " & _
		"fixed, " & _
        "f1,f2,f3,f4,f5,f6,f7,f8,f9, " & _
        "0 as zfixed, " & _
        "0 as i0, " & _
        "w0, w1, " & _
        "w10, w11, " & _
        "w20, w21, " & _
        "w30, w31, " & _
        "w40, w41, " & _
        "w50, w51, " & _
        "w60, w61, " & _
        "w70, w71, " & _
        "w80, w81, " & _
        "w90, w91 " & _
    "from input " & _
    "union all " & _
    "select " & _
		"(fixed+1)||','|| " & _
			"name||','|| " & _
			"( " & _
				"(w10&peers0 or w11&peers1) + " & _
				"(w20&peers0 or w21&peers1) + " & _
				"(w30&peers0 or w31&peers1) + " & _
				"(w40&peers0 or w41&peers1) + " & _
				"(w50&peers0 or w51&peers1) + " & _
				"(w60&peers0 or w61&peers1) + " & _
				"(w70&peers0 or w71&peers1) + " & _
				"(w80&peers0 or w81&peers1) + " & _
				"(w90&peers0 or w91&peers1) " & _
			") ||','|| " & _
			"z||','|| " & _
			"'', " & _
		"fixed+1, " & _
		"f1+(z=1), " & _
		"f2+(z=2), " & _
		"f3+(z=3), " & _
		"f4+(z=4), " & _
		"f5+(z=5), " & _
		"f6+(z=6), " & _
		"f7+(z=7), " & _
		"f8+(z=8), " & _
		"f9+(z=9), " & _
		"case z " & _
			"when 1 then f1 " & _
			"when 2 then f2 " & _
			"when 3 then f3 " & _
			"when 4 then f4 " & _
			"when 5 then f5 " & _
			"when 6 then f6 " & _
			"when 7 then f7 " & _
			"when 8 then f8 " & _
			"when 9 then f9 " & _
		"end, " & _
		"i.i, " & _
		"w0+word0, " & _
		"w1+word1, " & _
		"case when z=1 then w10+word0 else w10 end, " & _
		"case when z=1 then w11+word1 else w11 end, " & _
		"case when z=2 then w20+word0 else w20 end, " & _
		"case when z=2 then w21+word1 else w21 end, " & _
		"case when z=3 then w30+word0 else w30 end, " & _
		"case when z=3 then w31+word1 else w31 end, " & _
		"case when z=4 then w40+word0 else w40 end, " & _
		"case when z=4 then w41+word1 else w41 end, " & _
		"case when z=5 then w50+word0 else w50 end, " & _
		"case when z=5 then w51+word1 else w51 end, " & _
		"case when z=6 then w60+word0 else w60 end, " & _
		"case when z=6 then w61+word1 else w61 end, " & _
		"case when z=7 then w70+word0 else w70 end, " & _
		"case when z=7 then w71+word1 else w71 end, " & _
		"case when z=8 then w80+word0 else w80 end, " & _
		"case when z=8 then w81+word1 else w81 end, " & _
		"case when z=9 then w90+word0 else w90 end, " & _
		"case when z=9 then w91+word1 else w91 end " & _
    "from sudoku " & _
    "join i " & _
		"on i = ifnull ( " & _
							"( " & _
								"select  i " & _
								"from    i " & _
								"where   i > i0 " & _
									"and     not (word0&w0 or word1&w1) " & _
									"and     ( " & _
												"(w10&peers0 or w11&peers1) + " & _
												"(w20&peers0 or w21&peers1) + " & _
												"(w30&peers0 or w31&peers1) + " & _
												"(w40&peers0 or w41&peers1) + " & _
												"(w50&peers0 or w51&peers1) + " & _
												"(w60&peers0 or w61&peers1) + " & _
												"(w70&peers0 or w71&peers1) + " & _
												"(w80&peers0 or w81&peers1) + " & _
												"(w90&peers0 or w91&peers1) " & _
											") = 8 " & _
								"limit 1 " & _
							") " & _
							", " & _
							"( " & _
								"select  i " & _
								"from    ( " & _
									"select  i, " & _
											"max ( " & _
													"(w10&peers0 or w11&peers1) + " & _
													"(w20&peers0 or w21&peers1) + " & _
													"(w30&peers0 or w31&peers1) + " & _
													"(w40&peers0 or w41&peers1) + " & _
													"(w50&peers0 or w51&peers1) + " & _
													"(w60&peers0 or w61&peers1) + " & _
													"(w70&peers0 or w71&peers1) + " & _
													"(w80&peers0 or w81&peers1) + " & _
													"(w90&peers0 or w91&peers1) " & _
											") as maxfixed " & _
									"from    i " & _
									"where   not (word0&w0 or word1&w1) " & _
								") " & _
								"where     maxfixed is not null " & _
						")) " & _
    "join    z " & _
    "on " & _
		"case z " & _
			"when 1 then not (w10&peers0 or w11&peers1) " & _
			"when 2 then not (w20&peers0 or w21&peers1) " & _
			"when 3 then not (w30&peers0 or w31&peers1) " & _
			"when 4 then not (w40&peers0 or w41&peers1) " & _
			"when 5 then not (w50&peers0 or w51&peers1) " & _
			"when 6 then not (w60&peers0 or w61&peers1) " & _
			"when 7 then not (w70&peers0 or w71&peers1) " & _
			"when 8 then not (w80&peers0 or w81&peers1) " & _
			"when 9 then not (w90&peers0 or w91&peers1) " & _
		"end " & _
    "order by fixed desc, " & _
            "zfixed desc " & _
") " & _
", " & _
"output as ( " & _
    "select  * " & _
    "from    ( " & _
        "select  1 as i, " & _
                "w10, w11, " & _
                "w20, w21, " & _
                "w30, w31, " & _
                "w40, w41, " & _
                "w50, w51, " & _
                "w60, w61, " & _
                "w70, w71, " & _
                "w80, w81, " & _
                "w90, w91, " & _
                "'' as sud " & _
        "from    sudoku " & _
        "where   fixed = 81 limit 1 " & _
	") " & _
    "union all " & _
    "select  nullif (output.i + 1, 82), " & _
            "w10, w11, " & _
            "w20, w21, " & _
            "w30, w31, " & _
            "w40, w41, " & _
            "w50, w51, " & _
            "w60, w61, " & _
            "w70, w71, " & _
            "w80, w81, " & _
            "w90, w91, " & _
            "sud || replace (cast ( " & _
                "case 1 " & _
                "when w10&word0 OR w11&word1 then 1 " & _
                "when w20&word0 OR w21&word1 then 2 " & _
                "when w30&word0 OR w31&word1 then 3 " & _
                "when w40&word0 OR w41&word1 then 4 " & _
                "when w50&word0 OR w51&word1 then 5 " & _
                "when w60&word0 OR w61&word1 then 6 " & _
                "when w70&word0 OR w71&word1 then 7 " & _
                "when w80&word0 OR w81&word1 then 8 " & _
                "when w90&word0 OR w91&word1 then 9 " & _
                "else 0 " & _
                "end " & _
                "as char), '0', ' ') " & _
    "from    output " & _
    "join    i on i.i = output.i " & _
") " & _
", " & _
"result as (select sud s from input union all select sud from output WHERE i is null) " & _
"SELECT " & _
       "'┏━━━┯━━━┯━━━┳━━━┯━━━┯━━━┳━━━┯━━━┯━━━┓' || x'0d0a' || " & _
       "'┃ ' || substr(s, 1,1) || ' │ ' || substr(s, 2,1) || ' │ ' || substr(s, 3,1) || ' ┃ ' || " & _
              "substr(s, 4,1) || ' │ ' || substr(s, 5,1) || ' │ ' || substr(s, 6,1) || ' ┃ ' || " & _
              "substr(s, 7,1) || ' │ ' || substr(s, 8,1) || ' │ ' || substr(s, 9,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,10,1) || ' │ ' || substr(s,11,1) || ' │ ' || substr(s,12,1) || ' ┃ ' || " & _
              "substr(s,13,1) || ' │ ' || substr(s,14,1) || ' │ ' || substr(s,15,1) || ' ┃ ' || " & _
              "substr(s,16,1) || ' │ ' || substr(s,17,1) || ' │ ' || substr(s,18,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,19,1) || ' │ ' || substr(s,20,1) || ' │ ' || substr(s,21,1) || ' ┃ ' || " & _
              "substr(s,22,1) || ' │ ' || substr(s,23,1) || ' │ ' || substr(s,24,1) || ' ┃ ' || " & _
              "substr(s,25,1) || ' │ ' || substr(s,26,1) || ' │ ' || substr(s,27,1) || ' ┃' || x'0d0a' || " & _
       "'┣━━━┿━━━┿━━━╋━━━┿━━━┿━━━╋━━━┿━━━┿━━━┫' || x'0d0a' || " & _
       "'┃ ' || substr(s,28,1) || ' │ ' || substr(s,29,1) || ' │ ' || substr(s,30,1) || ' ┃ ' || " & _
              "substr(s,31,1) || ' │ ' || substr(s,32,1) || ' │ ' || substr(s,33,1) || ' ┃ ' || " & _
              "substr(s,34,1) || ' │ ' || substr(s,35,1) || ' │ ' || substr(s,36,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,37,1) || ' │ ' || substr(s,38,1) || ' │ ' || substr(s,39,1) || ' ┃ ' || " & _
              "substr(s,40,1) || ' │ ' || substr(s,41,1) || ' │ ' || substr(s,42,1) || ' ┃ ' || " & _
              "substr(s,43,1) || ' │ ' || substr(s,44,1) || ' │ ' || substr(s,45,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,46,1) || ' │ ' || substr(s,47,1) || ' │ ' || substr(s,48,1) || ' ┃ ' || " & _
              "substr(s,49,1) || ' │ ' || substr(s,50,1) || ' │ ' || substr(s,51,1) || ' ┃ ' || " & _
              "substr(s,52,1) || ' │ ' || substr(s,53,1) || ' │ ' || substr(s,54,1) || ' ┃' || x'0d0a' || " & _
       "'┣━━━┿━━━┿━━━╋━━━┿━━━┿━━━╋━━━┿━━━┿━━━┫' || x'0d0a' || " & _
       "'┃ ' || substr(s,55,1) || ' │ ' || substr(s,56,1) || ' │ ' || substr(s,57,1) || ' ┃ ' || " & _
              "substr(s,58,1) || ' │ ' || substr(s,59,1) || ' │ ' || substr(s,60,1) || ' ┃ ' || " & _
              "substr(s,61,1) || ' │ ' || substr(s,62,1) || ' │ ' || substr(s,63,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,64,1) || ' │ ' || substr(s,65,1) || ' │ ' || substr(s,66,1) || ' ┃ ' || " & _
              "substr(s,67,1) || ' │ ' || substr(s,68,1) || ' │ ' || substr(s,69,1) || ' ┃ ' || " & _
              "substr(s,70,1) || ' │ ' || substr(s,71,1) || ' │ ' || substr(s,72,1) || ' ┃' || x'0d0a' || " & _
       "'┠───┼───┼───╂───┼───┼───╂───┼───┼───┨' || x'0d0a' || " & _
       "'┃ ' || substr(s,73,1) || ' │ ' || substr(s,74,1) || ' │ ' || substr(s,75,1) || ' ┃ ' || " & _
              "substr(s,76,1) || ' │ ' || substr(s,77,1) || ' │ ' || substr(s,78,1) || ' ┃ ' || " & _
              "substr(s,79,1) || ' │ ' || substr(s,80,1) || ' │ ' || substr(s,81,1) || ' ┃' || x'0d0a' || " & _
       "'┗━━━┷━━━┷━━━┻━━━┷━━━┷━━━┻━━━┷━━━┷━━━┛'" & _
"FROM result;"

Local $aRows, $iRows, $iCols
Local $sProblem
Local $iTime

For $n = 0 To UBound($aSudokus) - 1
	$iTime = TimerInit()
	$sProblem = StringReplace($sInsaneSolver, "#####", $aSudokus[$n][0])
	_SQLite_GetTable($hDB, $sProblem, $aRows,$iRows, $iCols)
	_ConsoleWrite($aSudokus[$n][0] & " problem" & @LF & $aRows[2] & @LF & @LF)
	_ConsoleWrite($aSudokus[$n][0] & " solution (" & Round(TimerDiff($iTime) / 1000, 3) & " s)" & @LF & $aRows[3] & @LF & @LF)
Next

Func _ConsoleWrite($s)
	ConsoleWrite(BinaryToString(StringToBinary($s, 4), 1))
EndFunc