Question

Sudoku backtrack method

int xx = (pos.getX() / 3) * 3;          
int yy = (pos.getY() / 3) * 3;           
for (int y = 0; y < 3; y++) {              
    for (int x = 0; x < 3; x++) {               
        if ((xx + x != pos.getX()) && (yy + y != pos.getY())) {            
            possible[work[xx + x][yy + y]] = false;           

where x and y =

private byte x;
private byte y;

Could someone explain why do we divide by three and multiply by three?

(pos.getY() / 3) * 3;                      
(pos.getX() / 3) * 3;

Answer 1

The division is integer division so it will remove the remainder. Doing the integer division following by a multiplication will give the you the first cell index of the correct 3×3 block.

E.g.

pos    0    1    2    3    4    5    6    7    8
/3     0    0    0    1    1    1    2    2    2
*3     0    0    0    3    3    3    6    6    6