diff -r 40657f9a4e4a -r 663c2a9108d1 pre_testing3/postfix2.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pre_testing3/postfix2.scala	Sun Nov 01 01:21:31 2020 +0000
@@ -0,0 +1,100 @@
+// Shunting Yard Algorithm 
+// including Associativity for Operators 
+// =====================================
+
+object CW8b { 
+
+// type of tokens
+type Toks = List[String]
+
+// 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
+
+// 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)
+
+// the operations in the basic version of the algorithm
+val ops = List("+", "-", "*", "/", "^")
+
+// (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 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)
+}
+
+def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = (toks, st, out) match {
+  case (Nil, _, _) => out.reverse ::: st
+  case (num::in, st, out) if (num.forall(_.isDigit)) => 
+    syard(in, st, num :: out)
+  case (op1::in, op2::st, out) if (is_op(op1) && is_op(op2) && prec(op1, op2)) =>
+    syard(op1::in, st, op2 :: out) 
+  case (op1::in, st, out) if (is_op(op1)) => syard(in, op1::st, out)
+  case ("("::in, st, out) => syard(in, "("::st, out)
+  case (")"::in, op2::st, out) =>
+    if (op2 == "(") syard(in, st, out) else syard(")"::in, st, op2 :: out)
+  case (in, st, out) => {
+    println(s"in: ${in}   st: ${st}   out: ${out.reverse}")
+    Nil
+  }  
+} 
+
+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)  
+}
+
+
+
+
+//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
+
+//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"))) // 3
+
+//compute(syard(split("( 3 + 1 ) ^ 2 ^ 3")))   // 65536
+
+
+
+}