MatrixDSL.scala

## MatrixDSL.scala
/* This is a scala solution for a mini domain specific language (DSL)
 * defining instructions for populating an empty matrix.
 *
 * Input consists of a single string separated by spaces:
 * - the first number represents the size of the matrix, NxN
 * - the rest of the input consists of one or more strings defining
 *   the range of cells and how each of their populations will be
 *   incremented
 *
 * Increment pattern possibilities:
 *   x1:x2;y1:y2;+i -> add i to the current population in each cell defined by matrix(x, y) where x1 <= x <= x2 and y1 <= y <= y2
 *   x1:x2;y1:y2;*m -> multiply the current population in each cell by m
 *   x1:x2;y1:y2;^n -> raise the current population in each cell by a power of n
 *
 * Example input and expected outputs (input is a single string command-line argument):
 *
 * scala MatrixDSL "10 1:2;2:3;+1 2:2;3:3;+5 7:9;5:8;^3"
 * 9
 *
 * This solution is a pure functional approach, using curried increment
 * functions, regular expressions and scala's built-in pattern matching
 * to parse and process input correctly, even without resorting to
 * Option/Some or Try/Success/Failure constructs.
 *
 * @author Denis Papathanasiou (https://github.com/dpapathanasiou)
 * @license The MIT License (http://opensource.org/licenses/MIT)
 * Copyright (c) 2015 Denis Papathanasiou
 *
 */

object MatrixDSL {

  /* define the valid input patterns */

  val argsPattern     = """^(\d+)\s(.*)""".r
  val inputPattern    = """(\d+:\d+);(\d+:\d+);((\^|\+|\*)\d+)""".r
  val plusPattern     = """^(\+)(\d+)""".r
  val multiplyPattern = """^(\*)(\d+)""".r
  val raisePattern    = """^(\^)(\d+)""".r

  /* define the valid population increments as curried functions
   * b is the factor from the input pattern
   * a is the current population in a given matrix cell
   */

  def popPlus     (b: Long)(a: Long): Long = a + b
  def popRaise    (b: Long)(a: Long): Long = scala.math.pow(a, b).toLong
  def popMultiply (b: Long)(a: Long): Long = a * b

  /* Apply the increment function to the matrix
   * for the given ranges (Xi:Xj), (Yi:Yj)
   */

  def incrementPopulation (matrix: Array[Array[Long]], x: Array[Int], y: Array[Int], func:(Long) => Long): Array[Array[Long]] = {
    for( i <- x )
      for( j <- y )
        matrix(i)(j) = func(matrix(i)(j))
    matrix
  }

  /* Convert the Xi:Xj or Yi:Yj string into an array of ints
   * we can do this without error checking b/c this function
   * is not called unless the pattern regex matches
   */

  def parseInputRange (s: String): Array[Int] = {
    val ab = s.split(":").map(_.toInt)
    (ab(0) until ab(1)+1).toArray
  }

  /* Convert the (+|*|^)\d string to a curried function
   * to add, multiply, or raise to a power by the given number
   */

  def parseIncrementFunction (s: String): Long => Long =
    s match {
      case plusPattern(sign, value) => popPlus(value.toLong)
      case multiplyPattern(sign, value) => popMultiply(value.toLong)
      case raisePattern(sign, value) => popRaise(value.toLong)
      case _ => {
        println("Invalid increment pattern: %s".format(s)) // side effect (we could do without, but useful perhaps for feedback)
        popPlus(0) // an invalid pattern does not change the matrix
      }
    }

  /* Apply the input string to the matrix, updating the population,
   * but only if it matches the expected input pattern
   */

  def processInput (s: String, m: Array[Array[Long]]): Array[Array[Long]] =
    s match {
      case inputPattern(x, y, inc, op) => incrementPopulation(m, parseInputRange(x), parseInputRange(y), parseIncrementFunction(inc))
      case _ => {
        println("Invalid input pattern: %s".format(s)) // side effect (we could do without, but useful perhaps for feedback)
        m // return the matrix unchanged
      }
    }

  /* Create and return a two-dimensional array
   * with both dimensions the same size (n)
   */

  def createMatrix(n: Int): Array[Array[Long]] =
    Array.ofDim[Long](n, n)

  /* Create the two-dimensional array (nxn), apply each of the input strings
   * to increment the population if each input string pattern is valid,
   * and return the fully-populated two-dimensional array
   */

  def setPopulation (n: Int, inputs: Array[String]): Array[Array[Long]] = {
    @annotation.tailrec
    def calculate(m: Array[Array[Long]], inp: Array[String]): Array[Array[Long]] = {
      if( 0 == inp.length ) m
      else calculate(processInput(inp(0), m), inp.tail)
    }

    calculate(createMatrix(n), inputs)
  }

  /* Calculate the sum of the two-dimensional array */

  def getPopulation (matrix: Array[Array[Long]]): Long = {
    for {
      row  <- matrix
      cell <- row.filter(_ > 0)
    } yield cell
  }.sum

  def main(args: Array[String]): Unit = {
    if( args.length < 1 )
      println("Need an input argument (single string)")
    else {
      args(0) match {
        case argsPattern (n, rest) => println(getPopulation(setPopulation(n.toInt, rest.split(" "))))
        case _ => println("Invalid input")
      }
    }
  }

}