create a sudoku solver in matlab

main.m
function X = sudoku_solver(Y)
% Y is a 9x9 matrix representing the Sudoku puzzle to be solved.
% X is the solution to the Sudoku puzzle.

% Initialization
X = Y;
rows = [1, 2, 3, 4, 5, 6, 7, 8, 9];
cols = [1, 2, 3, 4, 5, 6, 7, 8, 9];
subs = [1, 2, 3, 10, 11, 12, 19, 20, 21];

% Check if the Sudoku puzzle is valid
if ~sudoku_check(Y)
    error('Invalid Sudoku puzzle');
end

% Solve the Sudoku puzzle
[X, ~, ~] = sudoku_helper(X, rows, cols, subs);

end

function [X, row, col] = sudoku_helper(X, rows, cols, subs)
% Recursive helper function to solve the Sudoku puzzle.

% Find the first empty cell
idx = find(X == 0, 1);
if isempty(idx)
    % If there are no empty cells, the Sudoku puzzle is solved.
    row = 0;
    col = 0;
    return;
else
    % Compute the row and column of the empty cell
    [row, col] = ind2sub([9, 9], idx);
end

% Compute the possible values for the empty cell
used = [X(row, :), X(:, col)', X(subs((row-1) \ 3 + 1) + (cols((col-1) \ 3 + 1)-1) * 9)];
possible = setdiff(1:9, used);

% Try all possible values recursively
for i = 1:length(possible)
    X(row, col) = possible(i);
    [X, row, col] = sudoku_helper(X, rows, cols, subs);
    if row == 0 && col == 0
        % If the Sudoku puzzle is solved, return
        return; 
    end
end

% If no solution is found, backtrack
X(row, col) = 0;

end

function valid = sudoku_check(X)
% Check if the Sudoku puzzle is valid.

% Check rows
valid = all(ismember(X, 1:9), 2);

% Check columns
valid = valid && all(ismember(X, 1:9), 1);

% Check subgrids
for i = 1:3
    for j = 1:3
        valid = valid && ismember([1:9], X(subs(i,:) + (subs(j,:) - 1) * 9));
    end
end

end
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