// Shunting Yard Algorithm 

// including Associativity for Operators 

// =====================================

// 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 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 ^ ^ / +

// (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 = ...

// 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