25x25 sudoku

This is a discussion on 25x25 sudoku within the C++ Programming forums, part of the General Programming Boards category; We have already established that 9x9 sudoku is too easy for computers (hardest ones solved in milliseconds) - http://cboard.cprogramming.com/cplus...algorithm.html An ...

  1. #1
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    25x25 sudoku

    We have already established that 9x9 sudoku is too easy for computers (hardest ones solved in milliseconds) -
    Sudoku solution generator algorithm

    An easy way to increase difficulty is to make the board bigger. Like 25x25.

    This is one I found on a random website (of "extreme" difficulty). I transcribed it into this computer-parseable format -
    Code:
    0 0 12 6 0 0 7 0 18 0 5 24 0 10 1 0 0 4 0 0 0 0 0 0 0 
    2 0 19 0 13 0 0 0 10 0 0 0 0 0 0 0 0 18 5 0 0 0 0 0 1 
    0 0 0 0 0 0 0 22 0 0 0 0 3 0 2 0 0 14 12 0 16 8 25 0 0 
    0 16 0 0 0 2 23 0 0 13 12 22 0 0 0 21 15 19 3 0 0 0 0 14 0 
    23 0 24 0 0 0 0 0 25 8 4 0 16 19 21 0 0 7 0 0 0 3 12 0 9 
    0 4 0 2 0 0 0 0 0 0 0 10 0 24 12 17 16 0 0 0 5 0 0 0 0 
    0 0 9 0 0 6 25 0 0 0 8 0 5 3 0 0 0 0 0 0 20 0 0 18 19 
    15 0 10 11 0 0 0 18 12 19 0 0 0 0 0 0 0 23 0 0 7 0 0 4 0 
    0 0 0 0 0 0 0 14 0 22 0 0 18 16 20 0 6 11 13 0 0 0 0 0 0 
    0 22 0 25 0 0 1 17 5 4 7 0 0 14 0 8 3 21 0 0 11 0 0 0 6 
    0 20 13 15 0 0 0 0 0 0 9 0 0 2 0 25 0 1 8 0 0 5 0 21 0 
    0 1 0 0 0 0 16 10 0 7 0 0 4 20 0 0 9 0 0 14 0 24 0 17 0 
    25 2 5 0 0 0 0 0 13 0 0 0 0 0 22 0 0 0 0 0 19 1 8 0 0 
    0 0 7 21 0 0 12 0 2 17 0 0 0 18 6 16 0 0 15 0 0 13 0 10 0 
    8 10 18 12 16 9 0 0 0 5 0 0 0 0 19 0 0 17 0 21 0 15 0 0 22 
    0 8 0 0 15 0 3 0 6 0 21 0 0 7 0 18 14 5 0 1 0 0 0 0 0 
    0 0 0 19 0 1 0 16 11 0 0 0 10 22 25 15 0 0 0 0 0 0 21 0 0 
    0 3 1 0 21 0 0 4 0 0 0 0 2 0 13 0 24 25 0 0 14 0 0 6 0 
    0 0 0 0 0 0 0 15 0 12 14 0 6 17 24 0 0 0 0 0 0 0 13 0 0 
    0 5 23 16 4 0 13 24 7 2 0 9 0 0 15 3 0 22 0 0 0 0 0 0 8 
    0 0 25 20 2 0 19 0 0 0 0 1 0 0 0 0 21 3 0 0 12 0 0 0 0 
    16 12 0 5 0 11 21 0 23 0 0 15 0 0 0 0 19 9 0 0 0 0 0 25 10 
    0 0 0 0 9 20 22 7 4 0 3 0 14 25 18 0 11 0 0 0 0 0 1 0 15 
    24 0 6 0 22 8 0 25 14 0 10 11 0 9 0 20 1 16 0 7 0 23 0 0 13 
    14 13 21 1 0 0 5 0 0 0 6 0 22 0 23 10 0 0 0 2 0 0 18 7 11
    0 means blank, filled in values are 1-25.

    Or, in another format -
    Code:
    ..LF..G.R.EX.JA..D.......
    B.S.M...J........RE.....A
    .......V....C.B..NL.PHY..
    .P...BW..MLV...UOSC....N.
    W.X.....YHD.PSU..G...CL.I
    .D.B.......J.XLQP...E....
    ..I..FY...H.EC......T..RS
    O.JK...RLS.......W..G..D.
    .......N.V..RPT.FKM......
    .V.Y..AQEDG..N.HCU..K...F
    .TMO......I..B.Y.AH..E.U.
    .A....PJ.G..DT..I..N.X.Q.
    YBE.....M.....V.....SAH..
    ..GU..L.BQ...RFP..O..M.J.
    HJRLPI...E....S..Q.U.O..V
    .H..O.C.F.U..G.RNE.A.....
    ...S.A.PK...JVYO......U..
    .CA.U..D....B.M.XY..N..F.
    .......O.LN.FQX.......M..
    .EWPD.MXGB.I..OC.V......H
    ..YTB.S....A....UC..L....
    PL.E.KU.W..O....SI.....YJ
    ....ITVGD.C.NYR.K.....A.O
    X.F.VH.YN.JK.I.TAP.G.W..M
    NMUA..E...F.V.WJ...B..RGK
    Me and my friend have double checked it, so it should be correct. The "numbers" version is generated from the "letters" version with a simple program.

    I changed my "blazingly fast" 9x9 solution to work with 25x25 board, and, well, it has been running for half an hour now. No solution yet .

    Anyone else want to take a stab at it?

    It HAS to be possible, since the puzzle is meant to be solved by a human...

    Bragging only in this thread, please (for now) , don't spoil it for me, yet.

  2. #2
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    For a 9x9 board, there are 9 ^ 9 ^ 9 = 96627050475552913618075908526912116283103450944214 766927315415537966391196809 possibilities, from which exactly one should be right. For a 25x25 board, there are 25 ^ 25 ^ 25 = 88817841970012523233890533447265625 ^ 25 of them. That is about 875 digits. Good luck in calculating that. You gotta have a huge amount of chance for doing this.
    Last edited by Brafil; 06-20-2009 at 06:27 AM.

  3. #3
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    Yes, that's why we don't dumb brute-force it.

    A lot of the possibilities can be eliminated if you try them in a certain order, for example.

    My 9x9 solver solves any puzzle you throw at it in milliseconds. It only tries about 100000 configurations/s.

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    Well I have a sudoku solver- in C++ that finds one, many, or no solutions...bad thing is the input I would have to type in by hand...unless I read it in a text file....

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    Oh. Maybe I should take a look at the algorithm. But It will need some time. Anyway, what I meant is that either the program is buggy (probably not) or it always takes much time. The complexity increases greatly. But I think you'll do it. Great work, your solver.

  6. #6
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    When I do a sudoku on paper, I fill the blank spaces (in pencil so I can erase it later) with all the possible values that could go in there and usually do that to all the blank squares in a row or column. Then I see which numbers only appear once in that row, column or big square and that HAS to be the right number, so I erase the possible numbers in that square and fill in the real number. I also remove that number from all the other possible numbers in the large square... Rinse, Lather, Repeat until it's done.

    Maybe you can use this "caching" technique in your algorithm?
    "I am probably the laziest programmer on the planet, a fact with which anyone who has ever seen my code will agree." - esbo, 11/15/2008

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  7. #7
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    Quote Originally Posted by cpjust View Post
    When I do a sudoku on paper, I fill the blank spaces (in pencil so I can erase it later) with all the possible values that could go in there and usually do that to all the blank squares in a row or column. Then I see which numbers only appear once in that row, column or big square and that HAS to be the right number, so I erase the possible numbers in that square and fill in the real number. I also remove that number from all the other possible numbers in the large square... Rinse, Lather, Repeat until it's done.

    Maybe you can use this "caching" technique in your algorithm?
    I tried to make my sudoku program do that but it always ran into trouble when it encountered something along the line of
    Code:
    | 1 | 2 | 3 ||   |   |   ||   |   |   |
    |   |   |   || 1 | 2 | 3 ||   |   |   |
    |   |   |   ||   |   |   || 4 | 5 | 6 |
    Last edited by ಠ_ಠ; 06-20-2009 at 12:15 PM.
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  8. #8
    Algorithm Dissector iMalc's Avatar
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    I made the necessary modifications to mine also, and it is taking a long time as well. I think it has been around 15 minutes so far.
    Not sure I want to burn my processor at 100% for that much longer.

    Any idea how long 16x16 ones take to solve?
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    Well I have a sudoku solver- in C++ that finds one, many, or no solutions...bad thing is the input I would have to type in by hand...unless I read it in a text file....
    Just use redirection.
    Code:
    ./solver < input.txt
    Your code will get the input as if it was typed (from stdin).

    When I do a sudoku on paper, I fill the blank spaces (in pencil so I can erase it later) with all the possible values that could go in there and usually do that to all the blank squares in a row or column. Then I see which numbers only appear once in that row, column or big square and that HAS to be the right number, so I erase the possible numbers in that square and fill in the real number. I also remove that number from all the other possible numbers in the large square... Rinse, Lather, Repeat until it's done.

    Maybe you can use this "caching" technique in your algorithm?
    That is what I do with my program. It always tries the square with least possible fillers first, so if a puzzle (at any stage in the search) has a square with just one possible filler, the branching factor will be 1.

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    I made the necessary modifications to mine also, and it is taking a long time as well. I think it has been around 15 minutes so far.
    Not sure I want to burn my processor at 100% for that much longer.
    That surprised me, too, especially since this puzzle is meant to be solved by humans, and I THOUGHT my algorithm is pretty close to the one used by humans. Maybe we should go visit a human sudoku master and see how s/he does it .

    Code:
    real	688m38.768s
    user	685m27.038s
    sys	0m13.289s
    I SIGTERM'ed it.

  11. #11
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    Here is a puzzle my friend sent me (for 9x9)
    Code:
    3 6 2 0 0 0 0 0 7
    0 0 0 0 3 0 0 0 6
    0 0 0 5 0 0 0 0 0
    0 0 0 8 0 0 4 0 1
    0 1 0 6 0 3 0 7 0
    2 0 3 0 0 9 0 0 0
    0 0 0 0 0 7 0 0 0
    9 0 0 0 8 0 0 0 0
    4 0 0 0 0 0 1 5 9
    I'm not sure what's so special about it, but it takes my code 0.102s to solve it, by far the longest I have seen (everything else I found could be solved in milliseconds).

    [edit]uh, nvm. There was a bug in my code. 15ms now.[/edit]
    Last edited by cyberfish; 06-20-2009 at 06:36 PM.

  12. #12
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    There is an elaborate solver written in C# by somone at Microsoft which uses all of the human solving techniques as well as the backtrack-solving I use. I wonder how well that would do.
    I think it would take so long because the cost paid when you have to backtrack is about 2^n where n is how many levels you have to backtrack by. With far more many holes compared to a 9x9 board, it's clear that it would take many more levels of magnitude longer. Even backtracking by 40 levels compared to 20 is going to take about 1 million times longer, and it's probably way more than that because I accidentally blew the stack upon my first run before optimising the amount of stack space used per call.
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    But that is assuming a branching factor of 2 everywhere. Meaning the square with the least amount of fillers in each stage is 2. That would be impossible for humans to solve.

    Most 9x9 puzzles have a branching factor of 1 in most if not all stages.

  14. #14
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    A difficult 16x16 puzzle -
    Code:
    0 2 14 0 0 0 16 4 0 0 0 1 0 0 5 0 
    0 0 9 0 0 10 0 1 0 0 0 0 0 4 0 0 
    0 0 0 0 13 6 0 0 0 14 0 0 15 12 0 16 
    6 5 10 0 8 2 0 0 0 12 0 0 0 1 0 7 
    9 0 5 4 1 0 0 2 0 0 0 0 12 0 7 0 
    0 0 0 0 11 0 0 13 0 3 0 0 0 0 0 1 
    0 0 0 0 16 0 0 0 13 10 15 9 14 0 4 0 
    10 0 0 11 0 4 8 15 0 0 0 0 5 0 13 0 
    0 11 0 1 0 0 0 0 10 7 4 0 3 0 0 6 
    0 7 0 2 14 16 6 10 0 0 0 11 0 0 0 0 
    16 0 0 0 0 0 1 0 12 0 0 14 0 0 0 0 
    0 4 0 10 0 0 0 0 15 0 0 2 16 5 0 11 
    11 0 12 0 0 0 14 0 0 0 13 7 0 9 6 2 
    8 0 7 9 0 0 11 0 0 0 14 10 0 0 0 0 
    0 0 4 0 0 0 0 0 11 0 2 0 0 8 0 0 
    0 6 0 0 12 0 0 0 9 8 0 0 0 14 1 0
    Takes my code ~15s on a AMD crap.

  15. #15
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    Quote Originally Posted by cyberfish View Post
    But that is assuming a branching factor of 2 everywhere. Meaning the square with the least amount of fillers in each stage is 2. That would be impossible for humans to solve.

    Most 9x9 puzzles have a branching factor of 1 in most if not all stages.
    I don't know why you're saying that. I'll define "branching factor" to mean how many numbers have not yet been eliminated for the cell with the lowest number of non-eliminated values. The minimum of this will almost certainly often be two for a medium difficulty puzzle, sometimes 3 or maybe even 4 for a hard/expert human level puzzle. Consider the XY-wing for example. There are two possibilities until you apply the rule and solve the square. If every move were of that difficulty then it is most certainly human-solveable! I know I could do it.

    Only the simplest of rules (given in the definition of the game) are required to work out the value when there is only one possibility, such as when there is only one number left in a given row. My solver fills all of such cases in without even having to recurse.

    No the branching factor wont be 2 everywhere, but for a few 1's here and there, the odd 3 may approximately balance that out. Sure that probably classifies it as a hard level puzzle, but lets not claim that hard means that no expert can solve it.
    Even the hardest Sudoku has been solved by a human, and it surely has a "branching factor" of 5 or more for some of the puzzle.
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