// 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 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

}