why I have problem in my program

I make a program about the sudoku matrix. I wanted my program to execute any size such as 9x9, 16x16, 25x25, and 256 x 256.

I succeeded in executing the program for size 9x9 and 16x16, but when executing the size 25x25 and 256x256 is not implemented and the program remains in a busy situation. I hope you know the problem in the code to executed any size.

the code is an attachment

[Walter Roberson]

I do not see anything obviously wrong with your program. I would recommend that you change the interface slightly so that you only define p once and pass it to everywhere else that needs it, so that you do not have to edit so many locations to change the board size, but that does not affect your algorithm.

You are running a recursive routine, and the number of possibilities to examine goes up with the factorial of the board size or something like that, so it does not take much of an increase in board size to make it take a long time to execute.

[Walter Roberson]

candidates is your most expensive function. Your most expensive line is

            z(nonzeros(A(row_mod,col_mod))) = 0;

It is important to understand that that the containing loop for that will be executed many millions of times, so it is important to optimize the code. For example, you have

            row_mod = k*ceil(ii/k-1) + (1:k);
            col_mod = k*ceil(jj/k-1) + (1:k);

ii does not change within the for jj loop, so you should calculate row_mod in the for ii loop rather than in the for jj loop. You could probably also shave a little time by not doing

            z = 1:p;

inside the loop, and instead doing something like

  zp = 1:p;
  

before the loop, and at that point in the loop do

            z = zp;

Beyond that... it seems to me that if you were to increment all of the values by 1, so for example you would be filling in 1:17 instead of 1:16 for the 256 x 256 matrix, and you were to use 1 as your marker instead of 0, then you would not need all those nonzeros() calls:

            z(A(ii,:)) = 1;
            z(A(:,jj)) = 1;
            z(A(row_mod,col_mod)) = 1;

The nonzeros calls are there so that you do not index at 0, but if you bump everything up by 1 and ignore z(1) then it might be more efficient.

[noran ahmed]

Walter Roberson thank you for answer

I need a Sudoku matrix program in size 256x256 and also fast and I am very beginner in Matlab. For this, I need someone who can help me modify the program or suggest me a better program than this program.

[Walter Roberson]

I have never investigated sudoku solving algorithms. But see https://www.mathworks.com/help/optim/examples/solve-sudoku-puzzles-via-integer-programming.html and https://www.mathworks.com/matlabcentral/fileexchange/13846-solve-and-create-sudoku-puzzles-for-different-levels

Sudoku solving is not an algorithm for beginniners.

[noran ahmed]

Walter Roberson

I made the change according to what you said to me, but there is an error in the code. If you have tried the change, please attach the file.

[noran ahmed]

Image Analyst

Can you provide a solution to this problem, please.