How to find minimum and maximum of cartesian co-ordinates in Scala

Question

I am trying to solve GameOfLife in Scala where I have an infinte grid. I am trying to represent the grid as a Set of Cell(x,y). When I read from say String I start at (0,0). But because of the laws of GameOfLife and since I am considering Infinite Grid after having applied rules to my Generation class I want to print current generation.

Here I am not sure how to calculate the minimum position (read x,y iterators) from where to start iterating and printing either 'X' for alive cell and '-' for dead cell in GameOfLife for that Generation.I am supplying my naive solution of toString method of Generation class. But I am not at all happy with it. Can somebody suggest be a better succient solution?

override def toString:String = 
   {
        val output:StringBuilder = new StringBuilder();
        val minOfRowColumn = for
        {
          cell <- aliveCells
          row = cell.row
          column = cell.column
        } yield if( row < column ) row else column

        val min = minOfRowColumn.min

        val maxOfRowColumn = for
        {
          cell <- aliveCells
          row = cell.row
          column = cell.column
        } yield if( row > column ) row else column

        val max = maxOfRowColumn.max

        var row = min;
        var column = min;

        while(row <= max)
        {
          while(column <= max)
          {
            if(aliveCells.contains(Cell(row,column)))
            {
              output.append('X')
            }
            else
              output.append('-')
            column = column + 1
          }
          output.append("\n");
          column = min
          row = row + 1
        }


        //remove the last new line addded.
        val indexOfNewLine = output.lastIndexOf("\n");
        if( -1 != indexOfNewLine )
        output.delete(indexOfNewLine,output.length());

        return output.toString();
   }

aliveCells here is a Set[Cell] where Cell is Cell(x,y) a case class.

Answer 1

I propose the following code :

override def toString = {
  val min = aliveCells.iterator.flatMap(c => Seq(c.row, c.column)).min
  val max = aliveCells.iterator.flatMap(c => Seq(c.row, c.column)).max

  (min to max) map { row =>
    (min to max) map (col => if (aliveCells(Cell(row, col))) "X" else "-") mkString
  } mkString ("\n")
}

You may want to separate min/max column and row if you do not specifically want a squared grid:

val minC = aliveCells.iterator.map(_.column).min

and so on.