// Shunting Yard Algorithm// by Edsger Dijkstra// ========================object C3a {type Toks = List[String]// the operations in the simple versionval ops = List("+", "-", "*", "/")// the precedences of the operatorsval precs = Map("+" -> 1, "-" -> 1, "*" -> 2, "/" -> 2)// helper function for splitting strings into tokensdef 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}