Question

Can someone please help me understand this solution:

 Initialize 2D array with 81 empty grids (nx = 9, ny = 9)
 Fill in some empty grid with the known values
 Make an original copy of the array
 Start from top left grid (nx = 0, ny = 0), check if grid is empty
 if (grid is empty) {
   assign the empty grid with values (i)
   if (no numbers exists in same rows & same columns same as (i) & 3x3 zone (i) is currently in)
     fill in the number
   if (numbers exists in same rows & same columns same as (i) & 3x3 zone (i) is currently in)
     discard (i) and repick other values (i++)
 }
 else {
   while (nx < 9) {
     Proceed to next row grid(nx++, ny)
     if (nx equals 9) {
       reset nx = 1
       proceed to next column grid(nx,ny++)
       if (ny equals 9) {
         print solution
       }
     }
   }
 }

Answer 1

It’s a simple brute force solver. It starts from the top left, working left to right line by line, trying to place each possible number into each square, and continuing by using a recursive call. On failure it backtracks and tries a different alternative.

The function called safe determines whether it is currently legal to place the value n in a certain cell, by checking which values have already been placed in the row, column and box.

It’s one of the simplest (and slowest) ways to solve a Sudoku.