// Shunting Yard Algorithm

// by Edsger Dijkstra

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

object CW9a {

type Toks = List[String]

// the operations in the simple version

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

// (6) 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 = ops.contains(op)

def prec(op1: String, op2: String) : Boolean = 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

  }  

} 

// 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 + +

// (7) 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 op_comp(s: String, n1: Int, n2: Int) = s match {

  case "+" => n2 + n1

  case "-" => n2 - n1

  case "*" => n2 * n1

  case "/" => n2 / n1

} 

def compute(toks: Toks, st: List[Int] = Nil) : Int = (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)  

}

// 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

}