Brute force Algorithm for creation of Sudoku Board

Question

What I am developing is that initially the entire sudoku board is empty. One of the random cells(out of 81) is filled with a random value(1-9).

Now I want to fill all

Answer 1

This simple random walk algorithm should work too (but is inefficient- use at your own risk!!!):

EDIT: - added fix for unresolvable solutions.

For each empty cell in grid
    array = Get_Legal_Numbers_for_cell(row,col);
    If (array is empty) {
        Clear_All_cells()
    } else {
        number = Random_number_from(array);
        Put_Number_in_Cell(number);
    }

EDIT 2

If someone are interested here are described methods for solving sudoku with random-based search.