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This way you can generate any possible sudoku board as well as any other nxn sudoku board. as for how efficient this algorithm is , it took 3.6 secs to generate a million boards in java & 3.5 sec in golang. Find any filled board of sudoku. (use trivial ones will not affect final result) int[][] board = new int[][] {.
import random, math, time class Sudoku: def __init__( self, _g=[] ): self._input_grid = [] # store a copy of the original input grid for later use self.grid = [] # this is the main grid that will be iterated for i in _g: # copy the nested lists by value, otherwise Python keeps the reference for the nested lists self._input_grid.append( i ...
This process is varies from 15 seconds to 2 minutes. Usually 30 seconds to get a sudoku puzzle. Third, if you don't want to wait 30 seconds to 2 minutes for each sudoku puzzle, you may apply some mutations to the above sudoku. This includes switching rows and columns, rotating. You may also remap the numbers.
So having thought about it, there aren't many things in a backtracking brute force algorithm that can be optimized (happy to be proven wrong here). The two real improvements that can be made are: first, the method by which the next blank cell is chosen and second, the method by which the next possible digit is chosen.
I've been working on a Sudoku Solver, my current solver uses the backtracking algorithm but it still takes too long. I'm hoping to get it down to less than a second for most cases. As such, I've decided to rewrite it with the dancing links algorithm, understanding it is one of the better bruteforce methods that works well especially with a ...
when the sum of each row/column/box equals n*(n+1)/2. and the product equals n! with n = number of rows or columns. this suffices the rules of a sudoku. Because that would allow for an algorithm of O (n^2), summing and multiplying the correct cells. Looking at n = 9, the sums should be 45, the products 362880.
5. Adding another answer for generating a sudoku of desired difficulty on-the-fly. This means that unlike other approaches the algorithm runs only once and returns a sudoku configuration matching the desired difficulty (with high probability within a range or with probability=1) Various solutions for generating (and rating) a sudoku difficulty ...
Apply your generic graph search algorithm (1) to the Sudoku state graph (2-4) (optional) If you do choose to use A* graph search, you can also define a heuristic on your Sudoku state space to potentially drastically increase performance how to design the heuristic is another whole problem, that's more of an art than a science; Current Approach
4. Try to find two solutions. The simplest algorithm is a brute force recursive algorithm with backtracking. Once you have found the first solution, backtrack and look for a second. This is slow but (unlike algorithms that rely on logic alone) it is guaranteed to be able to find all the solutions eventually.
First, randomly create a completed sudoku solution. This part require to have a sudoku solver. From the sudoku solution, constantly remove numbers at random locations. For each removal, check if the sudoku is still valid. That is, the sudoku has a unique solution. This part needs to find out if there is more than one solution.