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// Shunting Yard Algorithm
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// including Associativity for Operators
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// =====================================
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401
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object C3b {
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249
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// type of tokens
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type Toks = List[String]
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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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// left- and right-associativity
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abstract class Assoc
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case object LA extends Assoc
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case object RA extends Assoc
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// power is right-associative,
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// everything else is left-associative
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def assoc(s: String) : Assoc = s match {
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case "^" => RA
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case _ => LA
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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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"^" -> 4)
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// the operations in the basic version of the algorithm
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val ops = List("+", "-", "*", "/", "^")
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// (8) Implement the extended version of the shunting yard algorithm.
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// This version should properly account for the fact that the power
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// operation is right-associative. Apart from the extension to include
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// the power operation, you can make the same assumptions as in
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// basic version.
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def is_op(op: String) : Boolean = ops.contains(op)
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def prec(op1: String, op2: String) : Boolean = assoc(op1) match {
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case LA => precs(op1) <= precs(op2)
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case RA => precs(op1) < precs(op2)
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}
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def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = (toks, st, out) match {
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case (Nil, _, _) => out.reverse ::: st
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case (num::in, st, out) if (num.forall(_.isDigit)) =>
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syard(in, st, num :: out)
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case (op1::in, op2::st, out) if (is_op(op1) && is_op(op2) && prec(op1, op2)) =>
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syard(op1::in, st, op2 :: out)
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case (op1::in, st, out) if (is_op(op1)) => syard(in, op1::st, out)
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case ("("::in, st, out) => syard(in, "("::st, out)
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case (")"::in, op2::st, out) =>
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if (op2 == "(") syard(in, st, out) else syard(")"::in, st, op2 :: out)
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case (in, st, out) => {
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println(s"in: ${in} st: ${st} out: ${out.reverse}")
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Nil
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}
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}
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401
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def op_comp(s: String, n1: Int, n2: Int) = s match {
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case "+" => n2 + n1
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case "-" => n2 - n1
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case "*" => n2 * n1
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case "/" => n2 / n1
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case "^" => BigInt(n2).pow(n1).toInt
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}
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401
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def compute(toks: Toks, st: List[Int] = Nil) : Int = (toks, st) match {
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case (Nil, st) => st.head
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case (op::in, n1::n2::st) if (is_op(op)) => compute(in, op_comp(op, n1, n2)::st)
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case (num::in, st) => compute(in, num.toInt::st)
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}
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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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//compute(syard(split("4 ^ 3 ^ 2"))) // 262144
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//compute(syard(split("4 ^ ( 3 ^ 2 )"))) // 262144
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//compute(syard(split("( 4 ^ 3 ) ^ 2"))) // 4096
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//compute(syard(split("( 3 + 1 ) ^ 2 ^ 3"))) // 65536
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//syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3")) // 3 4 8 * 5 1 - 2 3 ^ ^ / +
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//compute(syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3"))) // 3
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//compute(syard(split("( 3 + 1 ) ^ 2 ^ 3"))) // 65536
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300
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}
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