A brute force algorithm visits the empty cells in some order, filling in digits sequentially, or backtracking when the number is found to be not valid. This is repeated until the allowed value in the last (81st) cell is discovered. The animation shows how a Sudoku is solved with this method.
What is the formula for solving Sudoku?
For the second Sudoku, we have the following 10 equations: m+n=a. g+n+f=g+c⟹n+f=c. g+d=n….Sudoku 2.
| Letter | Number |
|---|---|
| f | 2 |
| g | 3 |
| m | 5 |
| n | 4 |
Can a Sudoku puzzle be constructed to work against backtracking?
A Sudoku can be constructed to work against backtracking. Assuming the solver works from top to bottom (as in the animation), a puzzle with few clues (17), no clues in the top row, and has a solution “987654321” for the first row, would work in opposition to the algorithm.
Is there a way to solve Sudoku one by one?
Try every configuration one by one until the correct configuration is found. Like all other Backtracking problems, we can solve Sudoku by one by one assigning numbers to empty cells. Before assigning a number, we check whether it is safe to assign.
How is the naive algorithm used to solve Sudoku?
The Naive Algorithm is to generate all possible configurations of numbers from 1 to 9 to fill the empty cells. Try every configuration one by one until the correct configuration is found. Like all other Backtracking problems, we can solve Sudoku by one by one assigning numbers to empty cells.
Is it possible to Express Sudoku as an integer linear programming problem?
It is also possible to express a Sudoku as an integer linear programming problem. Such approaches get close to a solution quickly, and can then use branching towards the end. The simplex algorithm is able to solve proper Sudokus, indicating if the Sudoku is not valid (no solution).
