// Shunting Yard Algorithm+
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// by Edsger Dijkstra+
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// ========================+
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object CW9a {+
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+
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// type of tokens+
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type Toks = List[String]+
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+
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// the operations in the basic version of the algorithm+
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val ops = List("+", "-", "*", "/")+
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+
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// the precedences of the operators+
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val precs = Map("+" -> 1,+
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		"-" -> 1,+
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		"*" -> 2,+
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		"/" -> 2)+
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+
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// helper function for splitting strings into tokens+
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def split(s: String) : Toks = s.split(" ").toList+
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+
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+
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// (1) Implement below the shunting yard algorithm. The most+
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// convenient way to this in Scala is to implement a recursive +
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// function and to heavily use pattern matching. The function syard +
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// takes some input tokens as first argument. The second and third +
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// arguments represent the stack and the output of the shunting yard +
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// algorithm.+
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//+
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// In the marking, you can assume the function is called only with +
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// an empty stack and an empty output list. You can also assume the+
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// input os  only properly formatted (infix) arithmetic expressions+
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// (all parentheses will be well-nested, the input only contains +
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// operators and numbers).+
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+
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// You can implement any additional helper function you need. I found +
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// it helpful to implement two auxiliary functions for the pattern matching:  +
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// +
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// def is_op(op: String) : Boolean = ...+
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// def prec(op1: String, op2: String) : Boolean = ...+
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+
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+
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// def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = ...+
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+
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+
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// test cases+
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//syard(split("3 + 4 * ( 2 - 1 )"))  // 3 4 2 1 - * ++
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//syard(split("10 + 12 * 33"))       // 10 12 33 * ++
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//syard(split("( 5 + 7 ) * 2"))      // 5 7 + 2 *+
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//syard(split("5 + 7 / 2"))          // 5 7 2 / ++
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//syard(split("5 * 7 / 2"))          // 5 7 * 2 /+
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//syard(split("9 + 24 / ( 7 - 3 )")) // 9 24 7 3 - / ++
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+
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//syard(split("3 + 4 + 5"))           // 3 4 + 5 ++
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//syard(split("( ( 3 + 4 ) + 5 )"))    // 3 4 + 5 ++
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//syard(split("( 3 + ( 4 + 5 ) )"))    // 3 4 5 + ++
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//syard(split("( ( ( 3 ) ) + ( ( 4 + ( 5 ) ) ) )")) // 3 4 5 + ++
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+
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 +
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// (2) Implement a compute function that evaluates an input list+
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// in postfix notation. This function takes a list of tokens+
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// and a stack as argumenta. The function should produce the +
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// result as an integer using the stack. You can assume +
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// this function will be only called with proper postfix +
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// expressions.    +
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+
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// def compute(toks: Toks, st: List[Int] = Nil) : Int = ...+
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+
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+
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// test cases+
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// compute(syard(split("3 + 4 * ( 2 - 1 )")))  // 7+
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// compute(syard(split("10 + 12 * 33")))       // 406+
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// compute(syard(split("( 5 + 7 ) * 2")))      // 24+
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// compute(syard(split("5 + 7 / 2")))          // 8+
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// compute(syard(split("5 * 7 / 2")))          // 17+
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// compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15+
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+
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}+
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