1 // Shunting Yard Algorithm |
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2 // by Edsger Dijkstra |
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3 // ======================== |
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4 |
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5 object CW8a { |
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6 |
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7 type Toks = List[String] |
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8 |
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9 // the operations in the simple version |
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10 val ops = List("+", "-", "*", "/") |
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11 |
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12 // the precedences of the operators |
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13 val precs = Map("+" -> 1, |
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14 "-" -> 1, |
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15 "*" -> 2, |
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16 "/" -> 2) |
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17 |
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18 // helper function for splitting strings into tokens |
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19 def split(s: String) : Toks = s.split(" ").toList |
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20 |
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21 // (6) Implement below the shunting yard algorithm. The most |
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22 // convenient way to this in Scala is to implement a recursive |
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23 // function and to heavily use pattern matching. The function syard |
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24 // takes some input tokens as first argument. The second and third |
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25 // arguments represent the stack and the output of the shunting yard |
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26 // algorithm. |
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27 // |
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28 // In the marking, you can assume the function is called only with |
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29 // an empty stack and an empty output list. You can also assume the |
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30 // input os only properly formatted (infix) arithmetic expressions |
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31 // (all parentheses will be well-nested, the input only contains |
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32 // operators and numbers). |
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33 |
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34 // You can implement any additional helper function you need. I found |
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35 // it helpful to implement two auxiliary functions for the pattern matching: |
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36 // |
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37 |
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38 def is_op(op: String) : Boolean = ops.contains(op) |
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39 |
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40 def prec(op1: String, op2: String) : Boolean = precs(op1) <= precs(op2) |
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41 |
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42 |
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43 def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = (toks, st, out) match { |
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44 case (Nil, _, _) => out.reverse ::: st |
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45 case (num::in, st, out) if (num.forall(_.isDigit)) => |
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46 syard(in, st, num :: out) |
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47 case (op1::in, op2::st, out) if (is_op(op1) && is_op(op2) && prec(op1, op2)) => |
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48 syard(op1::in, st, op2 :: out) |
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49 case (op1::in, st, out) if (is_op(op1)) => syard(in, op1::st, out) |
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50 case ("("::in, st, out) => syard(in, "("::st, out) |
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51 case (")"::in, op2::st, out) => |
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52 if (op2 == "(") syard(in, st, out) else syard(")"::in, st, op2 :: out) |
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53 case (in, st, out) => { |
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54 println(s"in: ${in} st: ${st} out: ${out.reverse}") |
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55 Nil |
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56 } |
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57 } |
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58 |
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59 |
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60 // test cases |
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61 //syard(split("3 + 4 * ( 2 - 1 )")) // 3 4 2 1 - * + |
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62 //syard(split("10 + 12 * 33")) // 10 12 33 * + |
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63 //syard(split("( 5 + 7 ) * 2")) // 5 7 + 2 * |
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64 //syard(split("5 + 7 / 2")) // 5 7 2 / + |
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65 //syard(split("5 * 7 / 2")) // 5 7 * 2 / |
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66 //syard(split("9 + 24 / ( 7 - 3 )")) // 9 24 7 3 - / + |
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67 |
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68 //syard(split("3 + 4 + 5")) // 3 4 + 5 + |
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69 //syard(split("( ( 3 + 4 ) + 5 )")) // 3 4 + 5 + |
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70 //syard(split("( 3 + ( 4 + 5 ) )")) // 3 4 5 + + |
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71 //syard(split("( ( ( 3 ) ) + ( ( 4 + ( 5 ) ) ) )")) // 3 4 5 + + |
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72 |
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73 // (7) Implement a compute function that evaluates an input list |
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74 // in postfix notation. This function takes a list of tokens |
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75 // and a stack as argumenta. The function should produce the |
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76 // result as an integer using the stack. You can assume |
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77 // this function will be only called with proper postfix |
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78 // expressions. |
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79 |
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80 def op_comp(s: String, n1: Int, n2: Int) = s match { |
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81 case "+" => n2 + n1 |
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82 case "-" => n2 - n1 |
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83 case "*" => n2 * n1 |
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84 case "/" => n2 / n1 |
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85 } |
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86 |
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87 def compute(toks: Toks, st: List[Int] = Nil) : Int = (toks, st) match { |
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88 case (Nil, st) => st.head |
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89 case (op::in, n1::n2::st) if (is_op(op)) => compute(in, op_comp(op, n1, n2)::st) |
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90 case (num::in, st) => compute(in, num.toInt::st) |
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91 } |
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92 |
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93 // test cases |
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94 // compute(syard(split("3 + 4 * ( 2 - 1 )"))) // 7 |
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95 // compute(syard(split("10 + 12 * 33"))) // 406 |
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96 // compute(syard(split("( 5 + 7 ) * 2"))) // 24 |
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97 // compute(syard(split("5 + 7 / 2"))) // 8 |
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98 // compute(syard(split("5 * 7 / 2"))) // 17 |
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99 // compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15 |
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100 |
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101 } |
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102 |
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103 |
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