Scala Sudoku Solver

SudokuSolver.scala

import scala.collection.immutable.{Vector => $}

/**
  * This is highly inspired by https://gist.github.com/pathikrit/a32e17832296befd6b94
  * Actually only main recurssion block is changed for better readability
  *
  * See also excellent Computerphile video https://www.youtube.com/watch?v=G_UYXzGuqvM
  */
object Solver {
  val n = 9
  val s = Math.sqrt(n).toInt
  type Board = Vector[Vector[Int]]

  private def possibleDigits(board: Board, r: Int, c: Int): Seq[Int] = {
    def cells(i: Int) = Seq(board(r)(i), board(i)(c), board(s * (r / s) + i / s)(s * (c / s) + i % s))
    val used = board.indices.flatMap(cells)
    (1 to 9).diff(used)
  }

  def solve(board: Board, cell: Int = 0): Option[Board] = (cell % n, cell / n) match {
    case (0, 9) => Some(board) //cell=81 board is solved
    case (r, c) if board(r)(c) > 0 => solve(board, cell + 1) //cell is already filled, go to next
    case (r, c) =>
      possibleDigits(board, r, c)
        .flatMap(n => solve(board.updated(r, board(r).updated(c, n)))) //find next solution for each digit
        .headOption //return first non-empty element (the ultimate solution) otherwise None
  }

  def print(board: Board): Unit = println(board.map(_.mkString(" ")).mkString("\n"))
}

object SudokuSolver extends App {
  val board = $(
    $(8, 0, 0, 0, 0, 7, 0, 9, 0),
    $(0, 7, 0, 0, 2, 0, 0, 0, 8),
    $(0, 0, 9, 6, 0, 0, 5, 0, 0),
    $(0, 0, 5, 3, 0, 0, 9, 0, 0),
    $(0, 1, 0, 0, 8, 0, 0, 0, 2),
    $(6, 0, 0, 0, 0, 4, 0, 0, 0),
    $(3, 0, 0, 0, 0, 0, 0, 1, 0),
    $(0, 4, 0, 0, 0, 0, 0, 0, 7),
    $(0, 0, 7, 0, 0, 0, 3, 0, 0)
  )
  Solver.solve(board).map(Solver.print)
}