--- a/templates4/postfix2.scala	Wed Nov 28 17:13:40 2018 +0000
+++ b/templates4/postfix2.scala	Wed Nov 28 23:26:47 2018 +0000
@@ -1,86 +1,65 @@
-// Shunting Yard Algorithm
-// Edsger Dijkstra
+// Shunting Yard Algorithm 
+// including Associativity for Operators 
+// =====================================
 
-
+// type of tokens
 type Toks = List[String]
 
-def split(s: String) = s.split(" ").toList
+// helper function for splitting strings into tokens
+def split(s: String) : Toks = s.split(" ").toList
+
+// left- and right-associativity
+abstract class Assoc
+case object LA extends Assoc
+case object RA extends Assoc
 
 
-abstract class Assoc
-case object RA extends Assoc
-case object LA extends Assoc
-
+// power is right-associative,
+// everything else is left-associative
 def assoc(s: String) : Assoc = s match {
   case "^" => RA
   case _ => LA
 }
 
 
+// the precedences of the operators
 val precs = Map("+" -> 1,
-  		 "-" -> 1,
-		 "*" -> 2,
-		 "/" -> 2,
-                 "^" -> 4)
+  		"-" -> 1,
+		"*" -> 2,
+		"/" -> 2,
+                "^" -> 4)
 
+// the operations in the basic version of the algorithm
 val ops = List("+", "-", "*", "/", "^")
 
-def is_op(op: String) : Boolean = ops.contains(op)
-
-def prec(op1: String, op2: String) : Boolean = assoc(op1) match {
-  case LA => precs(op1) <= precs(op2)
-  case RA => precs(op1) < precs(op2)
-}
+// (8) Implement the extended version of the shunting yard algorithm.
+// This version should properly account for the fact that the power 
+// operation is right-associative. Apart from the extension to include
+// the power operation, you can make the same assumptions as in 
+// basic version.
 
-def syard(toks: Toks, st: Toks = Nil, rout: Toks = Nil) : Toks = (toks, st, rout) match {
-  case (Nil, _, _) => rout.reverse ::: st
-  case (num::in, st, rout) if (num.forall(_.isDigit)) => 
-    syard(in, st, num :: rout)
-  case (op1::in, op2::st, rout)  if (is_op(op1) && is_op(op2) && prec(op1, op2)) =>
-    syard(op1::in, st, op2 :: rout) 
-  case (op1::in, st, rout) if (is_op(op1)) => syard(in, op1::st, rout)
-  case ("("::in, st, rout) => syard(in, "("::st, rout)
-  case (")"::in, op2::st, rout) =>
-    if (op2 == "(") syard(in, st, rout) else syard(")"::in, st, op2 :: rout)
-  case (in, st, rout) => {
-    println(s"in: ${in}   st: ${st}   rout: ${rout.reverse}")
-    Nil
-  }  
-} 
+// def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = ...
+
 
-def op_comp(s: String, n1: Long, n2: Long) = s match {
-  case "+" => n2 + n1
-  case "-" => n2 - n1
-  case "*" => n2 * n1
-  case "/" => n2 / n1
-  case "^" => Math.pow(n2, n1).toLong
-} 
-
-def compute(toks: Toks, st: List[Long] = Nil) : Long = (toks, st) match {
-  case (Nil, st) => st.head
-  case (op::in, n1::n2::st) if (is_op(op)) => compute(in, op_comp(op, n1, n2)::st)
-  case (num::in, st) => compute(in, num.toInt::st)  
-}
+// test cases
+// syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3"))  // 3 4 8 * 5 1 - 2 3 ^ ^ / +
 
 
+// (9) Implement a compute function that produces a Long(!) for an
+// input list of tokens in postfix notation.
+
+//def compute(toks: Toks, st: List[Long] = Nil) : Long = ...
 
 
-compute(syard(split("3 + 4 * ( 2 - 1 )")))   // 7
-compute(syard(split("10 + 12 * 33")))       // 406
-compute(syard(split("( 5 + 7 ) * 2")))      // 24
-compute(syard(split("5 + 7 / 2")))          // 8
-compute(syard(split("5 * 7 / 2")))          // 17
-compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15
+// test cases
+// compute(syard(split("3 + 4 * ( 2 - 1 )")))   // 7
+// compute(syard(split("10 + 12 * 33")))       // 406
+// compute(syard(split("( 5 + 7 ) * 2")))      // 24
+// compute(syard(split("5 + 7 / 2")))          // 8
+// compute(syard(split("5 * 7 / 2")))          // 17
+// compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15
+// compute(syard(split("4 ^ 3 ^ 2")))      // 262144
+// compute(syard(split("4 ^ ( 3 ^ 2 )")))  // 262144
+// compute(syard(split("( 4 ^ 3 ) ^ 2")))  // 4096
+// compute(syard(split("( 3 + 1 ) ^ 2 ^ 3")))   // 65536
 
-compute(syard(split("4 ^ 3 ^ 2")))      // 262144
-compute(syard(split("4 ^ ( 3 ^ 2 )")))  // 262144
-compute(syard(split("( 4 ^ 3 ) ^ 2")))  // 4096
-
-
-syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3"))  // 3 4 8 * 5 1 - 2 3 ^ ^ / +
-compute(syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3")))
-
-compute(syard(split("( 3 + 1 ) ^ 2 ^ 3")))   // 65536
-
-
-def pow(n1: Long, n2: Long) = Math.pow(n1, n2).toLong