// Shunting Yard Algorithm

// by Edsger Dijkstra

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

// 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

// 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 + +

// 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