object SudokuSolver extends App {
// The board is represented by an array of strings (arrays of chars),
// held in a global variable m. The program begins by reading 9 lines
// of input to fill the board
var m: Array[Array[Char]] = Array.tabulate(9)((x: Int) => readLine.toArray)
// For printing m, a method print is defined
def print = { println(""); m map (carr => println(new String(carr))) }
// The test for validity is performed by looping over i=0..8 and
// testing the row, column and 3x3 square containing the given
// coordinate
def invalid(i: Int, x: Int, y: Int, n: Char): Boolean =
i<9 && (m(y)(i) == n || m(i)(x) == n ||
m(y/3*3 + i/3)(x/3*3 + i % 3) == n || invalid(i+1, x, y, n))
// Looping over a half-closed range of consecutive integers [l..u)
// is factored out into a higher-order function
def fold(f: (Int, Int) => Int, accu: Int, l: Int, u: Int): Int =
if(l==u) accu else fold(f, f(accu, l), l+1, u)
// The search function examines each position on the board in turn,
// trying the numbers 1..9 in each unfilled position
// The function is itself a higher-order fold, accumulating the value
// accu by applying the given function f to it whenever a solution m
// is found
def search(x:Int, y:Int, f: (Int) => Int, accu: Int): Int = (x, y) match {
case (9, y) => search(0, y+1, f, accu) // next row
case (0, 9) => f(accu) // found a solution
case (x, y) => if (m(y)(x) != '0') search(x+1, y, f, accu) else
fold((accu: Int, n: Int) =>
if (invalid(0, x, y, (n + 48).toChar)) accu else {
m(y)(x) = (n + 48).toChar;
val newaccu = search(x+1, y, f, accu);
m(y)(x) = '0';
newaccu}, accu, 1, 10)}
// The main part of the program uses the search function to accumulate
// the total number of solutions
println("\n"+search(0,0,i => {print; i+1},0)+" solution(s)")
}
