Do Sudoku Solving Algorithms Work?

Angela McCainby:


Not all of us like having math as part of our entertainment activities. And for most people, Sudoku seems like some math problem they can never solve as it may involve intricate calculations. But on the contrary, Sudoku is simply a relaxing yet challenging puzzle that puts our logical abilities to the test.

A standard 81 cell grid having numbers 1 through 9 can also be replaced with symbols or pictures to form the puzzle. Producing Sudoku puzzles may undoubtedly require some level of arithmetic. But the question is, how can one play Sudoku? And do Sudoku solving computer algorithms really work?

Rules of Sudoku

A 9×9 standard grid comes pre-filled with some numerical clues to give the puzzle a head start. Your aim is to place the missing digits. Every row, column, and nonet (3×3 sub-square) must have numbers from 1 to 9 represented just once. No repetitions, no math, and no guessing.

Sudoku Solving Algorithms

There are numerous approaches to solving a Sudoku puzzle. Easier ones can be solved with more straightforward computer algorithms. But advanced problems need complex processes. And here we talk about a few of them:

  • Backtracking

One keeps trying for candidates to fit in empty spaces until there aren’t any possible ones left. Then you backtrack and do the same for previous slots. This is somewhat a depth-first strategy as you entirely examine one branch for a possible solution before moving to another. The advantage of using this brute force kind of algorithm is that a solution is guaranteed. Solving time may be much slower, but it’s the easiest algorithms of all.

  • Stochastic search method

The Stochastic search method unsystematically assigns numbers to blank cells on the grid. It shuffles the numbers placed to calculate the errors and reduce them to zero. This is how a solution is found. Tabu search, simulated annealing, and genetic algorithms are part of the shuffling techniques.

  • Optimization methods

For such processes, problems may necessarily not be logical. They can solve a wide range of puzzles pretty quickly. Integer linear programming and the simplex algorithm perform well to find a solution even to non-proper Sudoku that may have more than one unique answer.

  • Constraint programming

Modeling the puzzle as a constraint problem, several reasoning algorithms can be devised to reach a solution. Confident constraint solvers don’t even require a hundred line code, provided there’s strong reasoning as well as backtracking for more complex problems. A constraint algorithm clubbed with backtracking techniques solves just any Sudoku within no time.

  • Exact cover

Sudoku can also be presented as an exact cover problem. Using such an algorithm ensures a quick and efficient solution. However, the aim is to model the puzzle as an exact cover problem and solve it using an alternative algorithm to come to a solution in a few milliseconds.

So that’s a gist of a few Sudoku solving algorithms that work.

Such computer programs search for Sudoku solutions with particular properties. However, there are more cumbersome algorithms as well that programmers keep coming up with now and then.

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