Last week I came across an interesting "coding kata" by Brett Schuchert on the Object Mentor blog. The trick of a kata is that you grow the program step-by-step using tests, just like a kata in karate is tought to a student. The problem of this kata was the Shunting Yard algorithm of Dijkstra. I wanted to see if I could implement this kata in Scala.

Instead of writing the algorithm as described, the trick in a coding kata is that you first write a test, and then make the test pass. And subsequently each time adding a test and keeping it all in the green. Brett described the test-cases in his blog entry.

The Shunting Yard algorithm is used to convert a mathematical function in infix notation to a reverse polish or postfix notation. For instance, it can convert an expression like 3+4 to 3 4 +.

In order to implement this algorithm, one needs to do string parsing to break up the infix string. Scala has the parser combinators that can do just this. Using a parser I build an Abstract Syntax Tree (AST) which is a representation of the formula in a tree form. An AST for 3 + 4 and (3 + 4) * 4 looks like:

The AST representation of the formula can then easily be printed in a reverse polish notation, as the code shows. The final Parser looks like this:

import scala.util.parsing.combinator.syntactical._

abstract class Expr {
  def rpn:String
}
case class BinaryOperator(lhs:Expr, op:String, rhs:Expr) extends Expr {
	def rpn:String = lhs.rpn + " " + rhs.rpn + " " + op
}
case class Number(v:String) extends Expr { def rpn:String = v }
case class Variable(v:String) extends Expr { def rpn:String = v }
case class Function(f:String, e:List[Expr]) extends Expr { def rpn:String = {
	var s = ""
	e.foreach { x => s += x.rpn + " " }
	s += f
	return s
  }
}
object ShuntingYard extends StandardTokenParsers {
    lexical.delimiters ++= List("+","-","*","/", "^","(",")",",")

    def value  arser[Expr] = numericLit ^^ { s => Number(s) }
    def variable:Parser[Expr] =  ident ^^ { s => Variable(s) }
    def parens:Parser[Expr] = "(" ~> expr <~ ")"

    def argument:Parser[Expr] = expr <~ (","?)
    def func:Parser[Expr] = ( ident ~ "(" ~ (argument+) ~ ")" ^^ { case f ~ _ ~ e ~ _ => Function(f, e) })

    def term = (value | parens | func | variable)

    // Needed to define recursive because ^ is right-associative
    def pow  arser[Expr] = ( term ~ "^" ~ pow ^^ {case left ~ _ ~ right => BinaryOperator(left, "^", right) }|
    			term)
    def factor = pow * ("*" ^^^ { (left:Expr, right:Expr) => BinaryOperator(left, "*", right) } |
                        "/" ^^^ { (left:Expr, right:Expr) => BinaryOperator(left, "/", right) } )
    def sum =  factor * ("+" ^^^ { (left:Expr, right:Expr) => BinaryOperator(left, "+", right) } |
    					"-" ^^^ { (left:Expr, right:Expr) => BinaryOperator(left, "-", right) } )
    def expr = ( sum | term )

    def parse(s:String) = {
        val tokens = new lexical.Scanner(s)
        phrase(expr)(tokens)
    }

    def shunt(exprstr: String) : String = exprstr match {
      case null => return ""
      case "" => return ""
      case _ =>
    	parse(exprstr) match {
            case Success(tree, _) =>
                println("Tree: "+tree)
                val v = tree.rpn
                println("RPN: "+v)
                return v
            case e: NoSuccess => Console.err.println(e)
            	return e.toString
        }
    }
}

Of course I tested this using the following unit test, of which I will show only a small part, one can easily complete this by looking at Brett's examples:

import org.junit.Test
import org.junit.Assert._

class ShuntingYardTest {
  @Test
  def test_11() {
    assertEquals("4 g f", ShuntingYard.shunt("f(g(4))"))
  }

  @Test
  def test_12() {
    assertEquals("3 4 19 f", ShuntingYard.shunt("f(3, 4, 19)"))
  }

  @Test
  def test_13() {
    assertEquals("3 4 2 * 1 5 - 2 3 ^ ^ / +", ShuntingYard.shunt("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"))
  }

  @Test
  def test_14 () {
    assertEquals("4 5 + 1 a 2 ^ + 8 b + 10 * f", ShuntingYard.shunt("f(4+5,1+a^2,(8+b)*10)"))
  }
}

Of all the tests that Brett defined, only one doesn't pass, can you spot which one? Of course as this is one of my first exercises in Scala, it probably isn't optimal yet, any improvements are welcome in the comments!

Tags: Functional Programming, kata, Scala, shunting, yard
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