Sudoku solver in Java, using backtracking and recursion

Question

I am programming a Sudoku solver in Java for a 9x9 grid.

I have methods for:

• printing the grid

• initializing the board with given val

Answer 1

Firstly, a suggestion for optimization: While checking whether, the number you're going to put in a cell, is already present in the same row, column or minigrid, you don't have to run a loop or something like that. You can perform an instant check by array indexing.

Consider 3 9x9 boolean double dimensional arrays:

boolean row[9][9], col[9][9], minigrid[9][9]

We'll be using the first array for checking whether a number is present in the same row, the second array for checking if a number is present in the same column, and the third for the mini grid.

Supposing you want to put a number n in your cell i, j. You will check if row[i][n-1] is true. If yes, then i^th row already contains n. Similarly, you will check if col[j][n-1] and minigrid[gridnum][n-1] is true.

Here gridnum is the index of mini grid, where the cell you want to insert a number, lies in. To calculate mini grid number for cell i,j, divide i & j by 3, multiply the integral part of former with 3, and add it to the integral part of the latter.

This how it looks:

gridnum = (i/3)*3 + j/3

By looking at values of i/3 and j/3 for all i and j, you will get an idea of how this works. Also, if you put a number in a cell, update the arrays too. E.g. row[i][n-1] = true

If there is a part you don't understand, post a comment and I'll edit my answer to explain it.

Secondly, using recursion & backtracking to solve this is pretty easy.

boolean F( i, j) // invoke this function with i = j = 0
{
If i > 8: return true // solved

for n in 1..9
 {
 check if n exists in row, column, or mini grid by the method I described

 if it does: pass ( skip this iteration )

 if it doesn't
  {
   grid[i][j] = n
   update row[][], col[][], minigrid[][]

   if F( if j is 8 then i+1 else i, if j is 8 then 0 else j+1 ) return true // solved
  }
 }
 return false // no number could be entered in cell i,j
}