--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pre_templates3/postfix.scala	Sun Nov 01 01:21:31 2020 +0000
@@ -0,0 +1,81 @@
+// Shunting Yard Algorithm
+// by Edsger Dijkstra
+// ========================
+
+object CW8a {
+
+// type of tokens
+type Toks = List[String]
+
+// the operations in the basic version of the algorithm
+val ops = List("+", "-", "*", "/")
+
+// the precedences of the operators
+val precs = Map("+" -> 1,
+		"-" -> 1,
+		"*" -> 2,
+		"/" -> 2)
+
+// helper function for splitting strings into tokens
+def split(s: String) : Toks = s.split(" ").toList
+
+
+// (1) Implement below the shunting yard algorithm. The most
+// convenient way to this in Scala is to implement a recursive 
+// function and to heavily use pattern matching. The function syard 
+// takes some input tokens as first argument. The second and third 
+// arguments represent the stack and the output of the shunting yard 
+// algorithm.
+//
+// In the marking, you can assume the function is called only with 
+// an empty stack and an empty output list. You can also assume the
+// input os  only properly formatted (infix) arithmetic expressions
+// (all parentheses will be well-nested, the input only contains 
+// operators and numbers).
+
+// You can implement any additional helper function you need. I found 
+// it helpful to implement two auxiliary functions for the pattern matching:  
+// 
+
+def is_op(op: String) : Boolean = ???
+def prec(op1: String, op2: String) : Boolean = ???
+
+
+def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = ???
+
+
+// test cases
+//syard(split("3 + 4 * ( 2 - 1 )"))  // 3 4 2 1 - * +
+//syard(split("10 + 12 * 33"))       // 10 12 33 * +
+//syard(split("( 5 + 7 ) * 2"))      // 5 7 + 2 *
+//syard(split("5 + 7 / 2"))          // 5 7 2 / +
+//syard(split("5 * 7 / 2"))          // 5 7 * 2 /
+//syard(split("9 + 24 / ( 7 - 3 )")) // 9 24 7 3 - / +
+
+//syard(split("3 + 4 + 5"))           // 3 4 + 5 +
+//syard(split("( ( 3 + 4 ) + 5 )"))    // 3 4 + 5 +
+//syard(split("( 3 + ( 4 + 5 ) )"))    // 3 4 5 + +
+//syard(split("( ( ( 3 ) ) + ( ( 4 + ( 5 ) ) ) )")) // 3 4 5 + +
+
+ 
+// (2) Implement a compute function that evaluates an input list
+// in postfix notation. This function takes a list of tokens
+// and a stack as argumenta. The function should produce the 
+// result as an integer using the stack. You can assume 
+// this function will be only called with proper postfix 
+// expressions.    
+
+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
+
+}
+
+