Workshop › Sudoku › Step 19 of 28

The solver

What we are doing

The solver tries each option in the easiest cell and then solves the rest of the board with itself: a function that calls itself is recursive. When a guess leads nowhere, it undoes it and tries the next one: backtracking. It also counts how many solutions there are, up to a limit.

```js
// Backtracking: fill a cell with each digit that fits and try to solve the rest; undo when stuck.
// Counts solutions up to `limit`.
function countSolutions(board, limit = 2) {
  const cell = bestCell(board)
  if (!cell) return 1 // no empty cell left: solved
  const { r, c, options } = cell
  let count = 0
  for (const d of options) {
    board[r][c] = d
    count += countSolutions(board, limit - count)
    if (count >= limit) return count // keep the board as it is: that is the solution
    board[r][c] = 0
  }
  return count
}
```

What it means

Your turn

Under bestCell, write the comments and countSolutions.

Skills: Functions

All steps

  1. Nine by nine
  2. Lines and boxes
  3. A puzzle from a string
  4. The puzzle's own digits
  5. Keep drawing
  6. The selected cell
  7. Light up row, column and box
  8. The same digit everywhere
  9. Click to select
  10. Move with the arrows
  11. Write digits
  12. The three rules in one loop
  13. Show mistakes
  14. Solved!
  15. A clock
  16. The solved message
  17. Play again
  18. The easiest cell
  19. The solver
  20. Random order
  21. Invent a puzzle
  22. A new puzzle every game
  23. Hints
  24. Best time
  25. N for a new puzzle
  26. A number pad
  27. Tap the pad
  28. Build it yourself: undo