// Shunting Yard Algorithm + −
// including Associativity for Operators + −
// =====================================+ −
+ −
object CW9b {+ −
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// type of tokens+ −
type Toks = List[String]+ −
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// helper function for splitting strings into tokens+ −
def split(s: String) : Toks = s.split(" ").toList+ −
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// left- and right-associativity+ −
abstract class Assoc+ −
case object LA extends Assoc+ −
case object RA extends Assoc+ −
+ −
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// power is right-associative,+ −
// everything else is left-associative+ −
def assoc(s: String) : Assoc = s match {+ −
case "^" => RA+ −
case _ => LA+ −
}+ −
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// the precedences of the operators+ −
val precs = Map("+" -> 1,+ −
"-" -> 1,+ −
"*" -> 2,+ −
"/" -> 2,+ −
"^" -> 4)+ −
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// the operations in the basic version of the algorithm+ −
val ops = List("+", "-", "*", "/", "^")+ −
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// (3) 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.+ −
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// def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = ...+ −
+ −
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// test cases+ −
// syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3")) // 3 4 8 * 5 1 - 2 3 ^ ^ / ++ −
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// (4) Implement a compute function that produces a Long(!) for an+ −
// input list of tokens in postfix notation.+ −
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//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+ −
+ −
}+ −