I made an algorithm to generate sudokus, but it was terribly inefficient. Each puzzle took minutes to generate. So now I am trying to write it again in optimal way. But I am experiencing some problems I need help with.
There are two aproaches:
- Start with blank grid and add numbers, then check if it is solvable.
- Create full valid grid with all 81 numbers and then remove until we are happy with number of remaining numbers and it is still solvable.
First I used first approach but now I am going to use second because I think it is more effective (we are starting with valid puzzle which is guaranteed to be solvable). I am right that second approach is better?
When I am trying to generate full populated grid I am running into difficulties. My algorithm is:
- Set candidates for each cells. Initialy they are numbers 1 through 9.
- Pick random cell without value.
- Select random candidate from that cell and assign it as cell value. Other candidates are discarded.
- Now for each row, cell and square corresponding to assigned cell I remove value of cell from these candidates, so each number is unique in a row/column/square
- Repeat
This technique guarantees random grid without duplicate numbers. However, most of times, when I do not break any rules of placement a run to conflict – like empty cells where all candidates have been removed etc and I need to start over. Is there more elegant/efficient way to filling entire grid with numbers without breaking rules of placement and still random numbers?
Have you looked at existing algorithms and/or code?
Check out https://www.sudokuwiki.org/Sudoku_Creation_and_Grading.pdf for an algorithmic description, and Peter Norvig’s article at http://norvig.com/sudoku.html.
There are some implementations out there in Python. So far I’ve never seen a published C# solution.