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