![]() The objective is to fill 9 x 9 grid with digits so that each column, each row, and each of the 3 x 3 subgrids that compose the grid contains all of the digits from 1 to 9. Sudoku is a logic-based, combinatorial number-placement puzzle. Text1 = font1.Recently, I am learning about linear optimization using python. # Draw lines horizontally and verticallyto form grid # Fill grid with default numbers specified # Fill blue color in already numbered grid # Function to draw required lines for making Sudoku grid _caption("SUDOKU SOLVER USING BACKTRACKING")įont1 = ("comicsans", 40)įont2 = ("comicsans", 20) Should be a 5 x 5 for the inputs as followsĪlso, I had a buddy who helped me convert my algorithm into this python code for my amateur Sudoku project. ]Īlso, please remember that you need to know multiplication to output a properly mapped n^2 x n^2. #Manipulation of Elements to prepare valid gridįor grids larger than 9 x 9 please use additonal brackets for readablity. ![]() X = input('Enter mapping valid Sudoku eg. #Input required to map out valid n x m or n^2 x n^2 Sudoku Grid #Provide a list of non-repeating n-elements to output a valid sudoku grid. Poly-time is what you want for larger n^2 x n^2 Sudoku Latin-Squares. ![]() Guaranteeing one solution requires some backtracking. To create a puzzle, you may have to remove elements manually. Works on any of n^2 x n^2 (boards) in poly-time. If your goal is to create 9 x 9 Sudoku, then why not a simpler program? Print 'process took',total_tries,'tries in', round(amt_of_time,2), 'secs' ![]() Return_dict, total_tries, amt_of_time = sudoku(9) Print 'success found', len(mydict), 'row' Modtestlists = (testlist.index(t1) / 3) % 3ĭtestlists = ĭcombindedlists = v2ĭcombindedlists = dtestlists Modsavedlists = (savedlist.index(v1) / 3) % 3ĭsavedlists = 80% or more) will have a good chance of producing a more difficult puzzle within a reasonable timeframe. Starting out with more empty spaces (e.g. Choosing the minimum set of numbers to add back-in would require a layered or backtracking approach which would be a bit more complex and much slower to run. Note that this will work in a reasonable time for 9x9 sudoku boards but you will need a much better/faster solver function for larger boardsĪlso note that this will often produce "easy" puzzles as it will add in more numbers than absolutely necessary in some cases. Solved = ĭiffPos = [(r,c) for r in range(9) for c in range(9) Starting with a solution variable with all numbers present and board variable containing the puzzle with 3/4 of numbers cleared, you can add numbers back to the board until there is only one way to solve it: solution=, Solution = for r in range(0,side*side,side)] Used = set().union(*(cover for p,n in enumerate(board) if n))īoard = next((n for n in range(board+1,side+1) if not cover&used),0) Here's a simple one: def shortSudokuSolve(board):īoard = īlanks = Ĭover = You can put back a number at a random position or select a position where the solutions differ (which will converge faster to a single solution puzzle)įirst write a solver that will generate all solutions that it finds (ideally as a generator because we only need the first 2). If there is more than one solution, put back a number and check again. The strategy I would suggest is to start with 75% (or more) of the numbers removed, then check that there is only one solution. In order to generate a sudoku puzzle with only one solution you will need a solver function that can tell you if there are more than one solution. See the duplicate 8 in the top left block, duplicate 7 below that, etc. The algorithm below will generate a NxN random sudoku solution board instantly for N 3): 0 \ -|ģ | group 0 -| -| r in shuffle(rBase)Ĥ | group 1 -| * -| r in shuffle(rBase)ħ | group 2 -| -| r in shuffle(rBase) Making sure that it has exactly one solution is a bit more challenging (hint: you must leave at least 17 numbers for a 9x9 sudoku) This will ensure that the puzzle always has a solution. You can generate a random sudoku solution board where all numbers are filled in and then remove some of them to create the puzzle.
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