object SudokuSolver extends Application {
// 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]] = List.tabulate( 9, (x:int) => Console.readLine.toArray).toArray;
// For printing m, a method print is defined
def print = {Console.println(""); m map (carr=>Console.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 = Pair(x, y) match {
case Pair(9, y) => search(0, y+1, f, accu) // next row
case Pair(0, 9) => f(accu) // found a solution
case Pair(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
Console.println("\n"+search(0,0,i => {print; i+1},0)+" solution(s)")
}
