Sudoku.scala

/*
 *  @author Daniel Strebel
 *
 *  Copyright 2011 University of Zurich
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 */

package com.signalcollect.examples

import scala.collection.mutable.HashMap
import scala.collection.mutable.ListMap
import com.signalcollect._
import java.util.concurrent.ConcurrentHashMap
import scala.collection.JavaConversions._

/**
 * Represents all associated Sudoku cells that have to be taken into account to determine
 * the value of a cell
 *
 */
class SudokuAssociation(t: Any) extends OptionalSignalEdge(t) {
  def signal = source.state
}

/**
 * Cell in a Sudoku grid.
 *
 * @param id identifier of the cell, where top left cell has id=0 top right has id of 8 and bottom right has id 80
 *
 */
class SudokuCell(id: Int, initialState: Option[Int] = None) extends DataGraphVertex(id, initialState) {

  type Signal = Int

  var possibleValues = SudokuHelper.legalNumbers
  if (initialState.isDefined) possibleValues = Set(initialState.get)

  def collect = {

    //make a list of all possible values
    possibleValues = possibleValues -- signals.toSet

    //If own value is determined i.e. if only one possible value is left choose own value
    if (possibleValues.size == 1) {
      Some(possibleValues.head)
    } else {
      state
    }
  }
}

object Sudoku extends App {
  //Setting the values that are given, rest has default value 'None'

  //Very simple Sudoku
  val sudoku1 = Map(
    (4, 9), (5, 6), (8, 5), (10, 9), (11, 4), (13, 2), (14, 1), (15, 8),
    (16, 6), (19, 1), (21, 4), (24, 3), (25, 2), (29, 3), (31, 4), (34, 7),
    (36, 1), (38, 6), (42, 4), (44, 2), (46, 4), (49, 6), (51, 5), (55, 5),
    (56, 2), (59, 4), (61, 1), (64, 6), (65, 1), (66, 2), (67, 3), (69, 7),
    (70, 8), (72, 4), (75, 8), (76, 1))

  //bad-ass Sudoku Puzzle
  val sudoku2 = Map(
    (0, 9), (8, 4), (11, 5), (13, 3), (15, 8), (16, 9),
    (21, 6), (24, 2), (28, 9), (31, 8), (33, 3), (35, 7),
    (38, 1), (42, 4), (45, 7), (47, 3), (49, 2), (52, 8),
    (56, 9), (59, 6), (64, 7), (65, 8), (67, 5), (69, 1),
    (72, 6), (80, 3))

  //select a sudoku puzzle
  val initialSeed = sudoku1

  var graph = computeGraphFactory(initialSeed)

  //print initial Sudoku
  var seed = new HashMap[Int, Option[Int]]()
  graph.foreachVertex { v => seed += Tuple2(v.id.asInstanceOf[Int], v.state.asInstanceOf[Option[Int]]) }
  SudokuHelper.printSudoku(seed)

  val stats = graph.execute
  println(stats)

  //If simple constraint propagation did not solve the problem apply a depth first search algorithm to find a suitable solution
  if (!isDone(graph)) {
    graph = tryPossibilities(graph)
    if (graph == null) {
      println()
      println("Sorry this Sudoku is not solvable")
      sys.exit(5)
    }
  }
  println()

  var result = new ConcurrentHashMap[Int, Option[Int]]
  graph.foreachVertex { v => result += Tuple2(v.id.asInstanceOf[Int], v.state.asInstanceOf[Option[Int]]) }
  graph.shutdown
  SudokuHelper.printSudoku(result)

  /**
   * Check if all cells have a value assigned to it
   */
  def isDone(graph: Graph[_, _]): Boolean = {
    var isDone = true
    graph.foreachVertex(v => if (v.state.asInstanceOf[Option[Int]] == None) isDone = false)
    isDone
  }

  /**
   * Recursive depth first search for possible values
   */
  def tryPossibilities(graph: Graph[Any, Any]): Graph[Any, Any] = {

    val possibleValues = new ListMap[Int, Set[Int]]()
    graph.foreachVertex(v => possibleValues.put(v.id.asInstanceOf[Int], v.asInstanceOf[SudokuCell].possibleValues))
    graph.shutdown

    var solutionFound = false

    // Try different values for the cell with the highest probability for each possible value i.e. the one with
    // the smallest number of alternatives.
    def mostConstrainedCell(possibilites: ListMap[Int, Set[Int]]): Option[(Int, Set[Int])] = {
      val mostConstrained = possibilites.toList.filter(_._2.size > 1).sortBy(_._2.size) // Just selects the smallest set of possible values among the cells
      if (mostConstrained.size == 0) {
        None //dead end
      } else {
        Some(mostConstrained.head)
      }
    }

    val candidate = mostConstrainedCell(possibleValues)

    if (candidate != None) {
      val iterator = candidate.get._2.iterator
      while (iterator.hasNext && !solutionFound) {
        var determinedValues = possibleValues.filter(_._2.size == 1).map(x => (x._1, x._2.head)).toMap[Int, Int]
        determinedValues += ((candidate.get._1, iterator.next))
        var graphTry = computeGraphFactory(determinedValues)
        graphTry.execute
        if (isDone(graphTry)) {
          solutionFound = true
          return graphTry
        } else {
          val nextTryResult = tryPossibilities(graphTry)
          if (nextTryResult != null) {
            return nextTryResult
          }
        }
      }
    }
    null
  }

  def computeGraphFactory(seed: Map[Int, Int]): Graph[Any, Any] = {
    val graph = GraphBuilder.build

    //Add all Cells for Sudoku
    for (index <- 0 to 80) {
      val seedValue = seed.get(index)
      graph.addVertex(new SudokuCell(index, seedValue))
    }

    //Determine neighboring cells for each cell and draw the edges between them
    for (index <- 0 to 80) {
      SudokuHelper.cellsToConsider(index).foreach({ i =>
        graph.addEdge(i, new SudokuAssociation(index))
      })
    }
    graph
  }

}

/**
 * Provides useful utilites for dealing with sudoku grids
 *
 */
object SudokuHelper {
  //All possible numbers for a cell
  val legalNumbers = {
    var numbers = (1 to 9).toSet
    numbers
  }

  //Get Rows, Columns and Blocks from ID
  def getRow(id: Int) = id / 9
  def getColumn(id: Int) = id % 9
  def getBlock(id: Int) = getRow(id) * 3 + getColumn(id)

  /**
   * Returns all the neighboring cells that influence a cell's value
   */
  def cellsToConsider(id: Int): List[Int] = {
    var neighborhood = List[Int]()

    //Same row
    for (col <- 0 to 8) {
      val otherID = getRow(id) * 9 + col
      if (otherID != id) {
        neighborhood = otherID :: neighborhood
      }
    }

    //Same column
    for (row <- 0 to 8) {
      val otherID = row * 9 + getColumn(id)
      if (otherID != id) {
        neighborhood = otherID :: neighborhood
      }
    }

    //Same block
    val topLeftRow = (getRow(id) / 3) * 3
    val topLeftColumn = (getColumn(id) / 3) * 3

    for (row <- topLeftRow to (topLeftRow + 2)) {
      for (column <- topLeftColumn to (topLeftColumn + 2)) {
        val otherID = row * 9 + column

        if (otherID != id && !neighborhood.contains(otherID)) {
          neighborhood = otherID :: neighborhood
        }
      }
    }

    neighborhood
  }

  /**
   * Formats the data in a classical sudoku layout
   */
  def printSudoku(data: collection.mutable.Map[Int, Option[Int]]) = {

    println()
    println("Sudoku")
    println("======")
    println()
    println("=========================================")

    for (i <- 0 to 8) {
      val j = i * 9
      print("II")
      for (k <- j to j + 8) {
        data.get(k) match {
          case Some(Some(v)) => print(" " + v + " ")
          case v => print("   ") //Empty or Error
        }
        if (k % 3 == 2) {
          print("II")
        } else {
          print("|")
        }
      }
      println()
      if (i % 3 == 2) {
        println("=========================================")
      }
    }
  }
}