--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pre_templates3/postfix2.scala	Sun Nov 01 01:21:31 2020 +0000
@@ -0,0 +1,69 @@
+// 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("+", "-", "*", "/", "^")
+
+// (3) 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, out: Toks = Nil) : Toks = ???
+
+
+// test cases
+// syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3"))  // 3 4 8 * 5 1 - 2 3 ^ ^ / +
+
+
+// (4) Implement a compute function that produces an Int for an
+// input list of tokens in postfix notation.
+
+def compute(toks: Toks, st: List[Int] = Nil) : Int = ???
+
+
+// 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
+
+}