// Shunting Yard Algorithm// by Edsger Dijkstra// ========================object CW8a {// type of tokenstype Toks = List[String]// the operations in the basic version of the algorithmval 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// (1) 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 = ???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 + +// (2) 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 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}