The New Sudoku Players' Forum

by **rjamil** » Wed Nov 22, 2017 6:52 pm

Hi,

I am trying to find a way to check whether two cells lying within same row or column or box or band or stack or not within 9x9 grid (as Pascal language has functions to manipulate union and intersection between arrays; and I am unaware of the same functions equivalent in either C or C++ languages).

I propose to add another 32 bit integer value in each cell's 20 peers array that will represent cell's band, stack, row, column and box respectively as follows:

Hidden Text: Show

Code: Select all: Cell Row Col Box Bnd Stk PBd PSk PRow PCol PBox Binary Peer 00 1 1 1 0 0 00 00 000000001 000000001 000000001 0000000000001000000001000000001 262657 01 1 2 1 0 0 00 00 000000001 000000010 000000001 0000000000001000000010000000001 263169 02 1 3 1 0 0 00 00 000000001 000000100 000000001 0000000000001000000100000000001 264193 03 1 4 2 0 1 00 01 000000001 000001000 000000010 0001000000001000001000000000010 134483970 04 1 5 2 0 1 00 01 000000001 000010000 000000010 0001000000001000010000000000010 134488066 05 1 6 2 0 1 00 01 000000001 000100000 000000010 0001000000001000100000000000010 134496258 06 1 7 3 0 2 00 10 000000001 001000000 000000100 0010000000001001000000000000100 268730372 07 1 8 3 0 2 00 10 000000001 010000000 000000100 0010000000001010000000000000100 268763140 08 1 9 3 0 2 00 10 000000001 100000000 000000100 0010000000001100000000000000100 268828676 09 2 1 1 0 0 00 00 000000010 000000001 000000001 0000000000010000000001000000001 524801 10 2 2 1 0 0 00 00 000000010 000000010 000000001 0000000000010000000010000000001 525313 11 2 3 1 0 0 00 00 000000010 000000100 000000001 0000000000010000000100000000001 526337 12 2 4 2 0 1 00 01 000000010 000001000 000000010 0001000000010000001000000000010 134746114 13 2 5 2 0 1 00 01 000000010 000010000 000000010 0001000000010000010000000000010 134750210 14 2 6 2 0 1 00 01 000000010 000100000 000000010 0001000000010000100000000000010 134758402 15 2 7 3 0 2 00 10 000000010 001000000 000000100 0010000000010001000000000000100 268992516 16 2 8 3 0 2 00 10 000000010 010000000 000000100 0010000000010010000000000000100 269025284 17 2 9 3 0 2 00 10 000000010 100000000 000000100 0010000000010100000000000000100 269090820 18 3 1 1 0 0 00 00 000000100 000000001 000000001 0000000000100000000001000000001 1049089 19 3 2 1 0 0 00 00 000000100 000000010 000000001 0000000000100000000010000000001 1049601 20 3 3 1 0 0 00 00 000000100 000000100 000000001 0000000000100000000100000000001 1050625 21 3 4 2 0 1 00 01 000000100 000001000 000000010 0001000000100000001000000000010 135270402 22 3 5 2 0 1 00 01 000000100 000010000 000000010 0001000000100000010000000000010 135274498 23 3 6 2 0 1 00 01 000000100 000100000 000000010 0001000000100000100000000000010 135282690 24 3 7 3 0 2 00 10 000000100 001000000 000000100 0010000000100001000000000000100 269516804 25 3 8 3 0 2 00 10 000000100 010000000 000000100 0010000000100010000000000000100 269549572 26 3 9 3 0 2 00 10 000000100 100000000 000000100 0010000000100100000000000000100 269615108 27 4 1 4 1 0 01 00 000001000 000000001 000001000 0100000001000000000001000001000 538968584 28 4 2 4 1 0 01 00 000001000 000000010 000001000 0100000001000000000010000001000 538969096 29 4 3 4 1 0 01 00 000001000 000000100 000001000 0100000001000000000100000001000 538970120 30 4 4 5 1 1 01 01 000001000 000001000 000010000 0101000001000000001000000010000 673189904 31 4 5 5 1 1 01 01 000001000 000010000 000010000 0101000001000000010000000010000 673194000 32 4 6 5 1 1 01 01 000001000 000100000 000010000 0101000001000000100000000010000 673202192 33 4 7 6 1 2 01 10 000001000 001000000 000100000 0110000001000001000000000100000 807436320 34 4 8 6 1 2 01 10 000001000 010000000 000100000 0110000001000010000000000100000 807469088 35 4 9 6 1 2 01 10 000001000 100000000 000100000 0110000001000100000000000100000 807534624 36 5 1 4 1 0 01 00 000010000 000000001 000001000 0100000010000000000001000001000 541065736 37 5 2 4 1 0 01 00 000010000 000000010 000001000 0100000010000000000010000001000 541066248 38 5 3 4 1 0 01 00 000010000 000000100 000001000 0100000010000000000100000001000 541067272 39 5 4 5 1 1 01 01 000010000 000001000 000010000 0101000010000000001000000010000 675287056 40 5 5 5 1 1 01 01 000010000 000010000 000010000 0101000010000000010000000010000 675291152 41 5 6 5 1 1 01 01 000010000 000100000 000010000 0101000010000000100000000010000 675299344 42 5 7 6 1 2 01 10 000010000 001000000 000100000 0110000010000001000000000100000 809533472 43 5 8 6 1 2 01 10 000010000 010000000 000100000 0110000010000010000000000100000 809566240 44 5 9 6 1 2 01 10 000010000 100000000 000100000 0110000010000100000000000100000 809631776 45 6 1 4 1 0 01 00 000100000 000000001 000001000 0100000100000000000001000001000 545260040 46 6 2 4 1 0 01 00 000100000 000000010 000001000 0100000100000000000010000001000 545260552 47 6 3 4 1 0 01 00 000100000 000000100 000001000 0100000100000000000100000001000 545261576 48 6 4 5 1 1 01 01 000100000 000001000 000010000 0101000100000000001000000010000 679481360 49 6 5 5 1 1 01 01 000100000 000010000 000010000 0101000100000000010000000010000 679485456 50 6 6 5 1 1 01 01 000100000 000100000 000010000 0101000100000000100000000010000 679493648 51 6 7 6 1 2 01 10 000100000 001000000 000100000 0110000100000001000000000100000 813727776 52 6 8 6 1 2 01 10 000100000 010000000 000100000 0110000100000010000000000100000 813760544 53 6 9 6 1 2 01 10 000100000 100000000 000100000 0110000100000100000000000100000 813826080 54 7 1 7 2 0 10 00 001000000 000000001 001000000 1000001000000000000001001000000 1090519616 55 7 2 7 2 0 10 00 001000000 000000010 001000000 1000001000000000000010001000000 1090520128 56 7 3 7 2 0 10 00 001000000 000000100 001000000 1000001000000000000100001000000 1090521152 57 7 4 8 2 1 10 01 001000000 000001000 010000000 1001001000000000001000010000000 1224740992 58 7 5 8 2 1 10 01 001000000 000010000 010000000 1001001000000000010000010000000 1224745088 59 7 6 8 2 1 10 01 001000000 000100000 010000000 1001001000000000100000010000000 1224753280 60 7 7 9 2 2 10 10 001000000 001000000 100000000 1010001000000001000000100000000 1358987520 61 7 8 9 2 2 10 10 001000000 010000000 100000000 1010001000000010000000100000000 1359020288 62 7 9 9 2 2 10 10 001000000 100000000 100000000 1010001000000100000000100000000 1359085824 63 8 1 7 2 0 10 00 010000000 000000001 001000000 1000010000000000000001001000000 1107296832 64 8 2 7 2 0 10 00 010000000 000000010 001000000 1000010000000000000010001000000 1107297344 65 8 3 7 2 0 10 00 010000000 000000100 001000000 1000010000000000000100001000000 1107298368 66 8 4 8 2 1 10 01 010000000 000001000 010000000 1001010000000000001000010000000 1241518208 67 8 5 8 2 1 10 01 010000000 000010000 010000000 1001010000000000010000010000000 1241522304 68 8 6 8 2 1 10 01 010000000 000100000 010000000 1001010000000000100000010000000 1241530496 69 8 7 9 2 2 10 10 010000000 001000000 100000000 1010010000000001000000100000000 1375764736 70 8 8 9 2 2 10 10 010000000 010000000 100000000 1010010000000010000000100000000 1375797504 71 8 9 9 2 2 10 10 010000000 100000000 100000000 1010010000000100000000100000000 1375863040 72 9 1 7 2 0 10 00 100000000 000000001 001000000 1000100000000000000001001000000 1140851264 73 9 2 7 2 0 10 00 100000000 000000010 001000000 1000100000000000000010001000000 1140851776 74 9 3 7 2 0 10 00 100000000 000000100 001000000 1000100000000000000100001000000 1140852800 75 9 4 8 2 1 10 01 100000000 000001000 010000000 1001100000000000001000010000000 1275072640 76 9 5 8 2 1 10 01 100000000 000010000 010000000 1001100000000000010000010000000 1275076736 77 9 6 8 2 1 10 01 100000000 000100000 010000000 1001100000000000100000010000000 1275084928 78 9 7 9 2 2 10 10 100000000 001000000 100000000 1010100000000001000000100000000 1409319168 79 9 8 9 2 2 10 10 100000000 010000000 100000000 1010100000000010000000100000000 1409351936 80 9 9 9 2 2 10 10 100000000 100000000 100000000 1010100000000100000000100000000 1409417472

How to check two cells lying either same band, stack, row, column and/or box, bit wise checking as follows:

Hidden Text: Show

R. Jamil

by **rjamil** » Wed Jul 04, 2018 5:00 pm

Hi StrmCkr,

I am trying to summarized BarnS=4 that are not covered in WXYZ-Wings strategy in different ways how to search step by step in exemplars form as follows:

Hidden Text: Show

Code: Select all: *A) WXYZ-Wings Type 5a (Row-Box-Column wise) *1st Wing within Apex Row but not Box 2nd Wing within Apex ER-Box --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . . . 02) 2 . 2 | . . . | . . . . A . | 1 1 1 | 1 1 1 . A . | . . . | . 1 . . . . | . . . | . . . 2 . 2 | . . . | . . . 06--------------+-------------+-----------04--------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *3rd Wing within either Apex or 1st or 2nd Wing Column but not Box --------------+-------------+----------- 03) . . . | . . . | . . . . A . | . . . | . 1 . . . 2 | . . . | . . . 18--------------+-------------+----------- . 3 3 | . . . | . 3 . . 3 3 | . . . | . 3 . . 3 3 | . . . | . 3 . --------------+-------------+----------- . 3 3 | . . . | . 3 . . 3 3 | . . . | . 3 . . 3 3 | . . . | . 3 . --------------+-------------+----------- *If Apex and 1st Wing contain digit Z If Apex and 2nd Wing contain digit Z --------------+-------------+----------- --------------+-------------+----------- 04) . . . | . . . | . . . 05)-Z -Z -Z | . . . | . . . -Z A -Z | -Z -Z -Z | -Z 1 -Z -Z A -Z | . . . | . 1 . . . 2 | . . . | . . . -Z -Z 2 | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . 3 | . . . | . . . . . 3 | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If Apex and 3rd Wing contain digit Z If 1st and 2nd Wings contain digit Z --------------+-------------+----------- --------------+-------------+----------- 06) . . -Z | . . . | . . . 07) . . . | . . . | . . . . A -Z | . . . | . 1 . -Z A -Z | . . . | . 1 . . . 2 | . . . | . . . . . 2 | . . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . -Z . | . . . | . . . . . . | . . . | . . . . -Z 3 | . . . | . . . . . 3 | . . . | . . . . -Z . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If 1st and 3rd Wings contain digit Z If 2nd and 3rd Wings contain digit Z --------------+-------------+----------- --------------+-------------+----------- 08) . . . | . . . | . . . 09) . . -Z | . . . | . . . . A -Z | . . . | . 1 . . A -Z | . . . | . 1 . . . 2 | . . . | . . . . . 2 | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . -Z | . . . | . . . . . . | . . . | . . . . . -Z | . . . | . . . . . . | . . . | . . . . . -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . -Z | . . . | . . . . . 3 | . . . | . -Z . . . 3 | . . . | . . . . . . | . . . | . . . . . -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *Else --------------+-------------+----------- 10) . . . | . . . | . . . . A -Z | . . . | . 1 . . . 2 | . . . | . . . --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- . . . | . . . | . . . . . 3 | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- *B) WXYZ-Wings Type 5b (Row-Column-Box wise) *1st Wing within Apex Row but not Box 2nd Wing within Apex Column but not Box --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . . . 02) . . . | . . . | . . . . A . | 1 1 1 | 1 1 1 . A . | . . . | . 1 . . . . | . . . | . . . . . . | . . . | . . . 06--------------+-------------+-----------06--------------+-------------+----------- . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *3rd Wing within either 1st or 2nd Wing Box *but not Apex Line --------------+-------------+----------- 03) . . . | . . . | 3 3 3 . A . | . . . | . 1 . . . . | . . . | 3 3 3 12--------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- 3 . 3 | . . . | . . . 3 2 3 | . . . | . . . 3 . 3 | . . . | . . . --------------+-------------+----------- *C) WXYZ-Wings Type 5c (Row-Column-Column wise) *1st Wing within Apex Row but not Box 2nd Wing within Apex Column --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . . . 02) . 2 . | . . . | . . . . A . | 1 1 1 | 1 1 1 . A . | . . . | . 1 . . . . | . . . | . . . . 2 . | . . . | . . . 06--------------+-------------+-----------08--------------+-------------+----------- . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . . . . | . . . | . . . . 2 . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *3rd Wing within 1st Wing Column but not Box --------------+-------------+----------- 03) . . . | . . . | . . . . A . | . . . | . 1 . . . . | . . . | . . . 06--------------+-------------+----------- . . . | . . . | . 3 . . . . | . . . | . 3 . . . . | . . . | . 3 . --------------+-------------+----------- . . . | . . . | . 3 . . 2 . | . . . | . 3 . . . . | . . . | . 3 . --------------+-------------+----------- *D) WXYZ-Wings Type 6a (Line-Box-Box wise) *1st Wing within Apex Line but not Apex Box 2nd Wing within Apex Box but not 1st Wing Line --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . . . 02) 2 2 2 | . . . | . . . . A . | 1 1 1 | 1 1 1 . A . | . . . | . 1 . . . . | . . . | . . . 2 2 2 | . . . | . . . 06--------------+-------------+-----------06--------------+-------------+----------- *3rd Wing within 1st Wing Box but not Apex Line --------------+-------------+----------- 03) . . 2 | . . . | 3 3 3 . A . | . . . | . 1 . . . . | . . . | 3 3 3 06--------------+-------------+----------- *If Apex and 1st Wing contain digit Z If Apex and 2nd Wing contain digit Z --------------+-------------+----------- --------------+-------------+----------- 04) . . 2 | . . . | . . . 05)-Z -Z 2 | . . . | . . . -Z A -Z | -Z -Z -Z | -Z 1 -Z -Z A -Z | . . . | . 1 . . . . | . . . | 3 . . -Z -Z -Z | . . . | 3 . . --------------+-------------+----------- --------------+-------------+----------- *If Apex and 3rd Wing contain digit Z If 1st and 2nd Wings contain digit Z --------------+-------------+----------- --------------+-------------+----------- 06) . . 2 | . . . | . . . 07) . . 2 | . . . | -Z -Z -Z . A . | . . . | -Z 1 -Z -Z A -Z | . . . | . 1 . -Z -Z -Z | . . . | 3 . . . . . | . . . | 3 . . --------------+-------------+----------- --------------+-------------+----------- *If 1st and 3rd Wings contain Z If 2nd and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 08) . . 2 | . . . | -Z -Z -Z 09) . . 2 | . . . | -Z -Z -Z . A . | . . . | -Z 1 -Z . A . | . . . | . 1 . . . . | . . . | 3 -Z -Z -Z -Z -Z | . . . | 3 . . --------------+-------------+----------- --------------+-------------+----------- *If Apex, 1st and 2nd Wings contain Z If Apex, 1st and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 10) . . 2 | . . . | . . . 11) . . 2 | . . . | . . . -Z A -Z | . . . | . 1 . . A . | . . . | -Z 1 -Z . . . | . . . | 3 . . . . . | . . . | 3 . . --------------+-------------+----------- --------------+-------------+----------- *If Apex, 2nd and 3rd Wings contain Z If 1st, 2nd and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 12) . . 2 | . . . | . . . 13) . . 2 | . . . | -Z -Z -Z . A . | . . . | . 1 . . A . | . . . | . 1 . -Z -Z -Z | . . . | 3 . . . . . | . . . | 3 . . --------------+-------------+----------- --------------+-------------+----------- *E) WXYZ-Wings Type 6b (Box-Line-Line wise) *1st Wing within Apex Line but not Apex Box 2nd Wing within Apex Box but not 1st Wing Line --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . . . 02) 2 2 2 | . . . | . . . . A . | 1 1 1 | 1 1 1 . A . | . . . | . 1 . . . . | . . . | . . . 2 2 2 | . . . | . . . 06--------------+-------------+-----------06--------------+-------------+----------- *3rd Wing within 2nd Wing Row but not 1st and 2nd Wings Box --------------+-------------+----------- 03) . . 2 | 3 3 3 | . . . . A . | . . . | . 1 . . . . | . . . | . . . 03--------------+-------------+----------- *If Apex and 1st Wing contain digit Z If Apex and 2nd Wing contain digit Z --------------+-------------+----------- --------------+-------------+----------- 04) . . 2 | 3 . . | . . . 05)-Z -Z 2 | 3 . . | . . . -Z A -Z | -Z -Z -Z | -Z 1 -Z -Z A -Z | . . . | . 1 . . . . | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If Apex and 3rd Wing contain digit Z If 1st and 2nd Wings contain digit Z --------------+-------------+----------- --------------+-------------+----------- 06)-Z -Z 2 | 3 . . | . . . 07) . . 2 | 3 . . | -Z -Z -Z . A . | -Z -Z -Z | . 1 . -Z A -Z | . . . | . 1 . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If 1st and 3rd Wings contain Z If 2nd and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 08) . . 2 | 3 . . | -Z -Z -Z 09)-Z -Z 2 | 3 -Z -Z | -Z -Z -Z . A . | -Z -Z -Z | . 1 . . A . | . . . | . 1 . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If Apex, 1st and 2nd Wings contain Z If Apex, 1st and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 10) . . 2 | 3 . . | . . . 11) . . 2 | 3 . . | . . . -Z A -Z | . . . | . 1 . . A . | -Z -Z -Z | . 1 . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- *If Apex, 2nd and 3rd Wings contain Z If 1st, 2nd and 3rd Wings contain Z --------------+-------------+----------- --------------+-------------+----------- 12)-Z -Z 2 | 3 . . | . . . 13) . . 2 | 3 . . | -Z -Z -Z . A . | . . . | . 1 . . A . | . . . | . 1 . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+-----------

Please look in to each step and correct me where necessary.

R. Jamil

Added more patterns as on 20180710. Hope now all patterns covered.

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