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1 // Shunting Yard Algorithm |
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2 // including Associativity for Operators |
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3 // ===================================== |
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4 |
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5 object C3b { |
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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 // helper function for splitting strings into tokens |
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11 def split(s: String) : Toks = s.split(" ").toList |
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12 |
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13 // left- and right-associativity |
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14 abstract class Assoc |
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15 case object LA extends Assoc |
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16 case object RA extends Assoc |
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17 |
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18 // power is right-associative, |
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19 // everything else is left-associative |
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20 def assoc(s: String) : Assoc = s match { |
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21 case "^" => RA |
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22 case _ => LA |
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23 } |
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24 |
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25 // the precedences of the operators |
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26 val precs = Map("+" -> 1, |
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27 "-" -> 1, |
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28 "*" -> 2, |
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29 "/" -> 2, |
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30 "^" -> 4) |
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31 |
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32 // the operations in the basic version of the algorithm |
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33 val ops = List("+", "-", "*", "/", "^") |
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34 |
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35 // (8) Implement the extended version of the shunting yard algorithm. |
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36 // This version should properly account for the fact that the power |
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37 // operation is right-associative. Apart from the extension to include |
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38 // the power operation, you can make the same assumptions as in |
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39 // basic version. |
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40 |
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41 def is_op(op: String) : Boolean = ops.contains(op) |
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42 |
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43 def prec(op1: String, op2: String) : Boolean = assoc(op1) match { |
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44 case LA => precs(op1) <= precs(op2) |
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45 case RA => precs(op1) < precs(op2) |
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46 } |
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47 |
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48 def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = (toks, st, out) match { |
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49 case (Nil, _, _) => out.reverse ::: st |
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50 case (num::in, st, out) if (num.forall(_.isDigit)) => |
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51 syard(in, st, num :: out) |
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52 case (op1::in, op2::st, out) if (is_op(op1) && is_op(op2) && prec(op1, op2)) => |
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53 syard(op1::in, st, op2 :: out) |
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54 case (op1::in, st, out) if (is_op(op1)) => syard(in, op1::st, out) |
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55 case ("("::in, st, out) => syard(in, "("::st, out) |
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56 case (")"::in, op2::st, out) => |
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57 if (op2 == "(") syard(in, st, out) else syard(")"::in, st, op2 :: out) |
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58 case (in, st, out) => { |
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59 println(s"in: ${in} st: ${st} out: ${out.reverse}") |
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60 Nil |
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61 } |
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62 } |
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63 |
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64 def op_comp(s: String, n1: Int, n2: Int) = s match { |
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65 case "+" => n2 + n1 |
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66 case "-" => n2 - n1 |
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67 case "*" => n2 * n1 |
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68 case "/" => n2 / n1 |
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69 case "^" => BigInt(n2).pow(n1).toInt |
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70 } |
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71 |
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72 def compute(toks: Toks, st: List[Int] = Nil) : Int = (toks, st) match { |
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73 case (Nil, st) => st.head |
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74 case (op::in, n1::n2::st) if (is_op(op)) => compute(in, op_comp(op, n1, n2)::st) |
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75 case (num::in, st) => compute(in, num.toInt::st) |
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76 } |
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77 |
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78 |
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79 |
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80 |
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81 //compute(syard(split("3 + 4 * ( 2 - 1 )"))) // 7 |
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82 //compute(syard(split("10 + 12 * 33"))) // 406 |
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83 //compute(syard(split("( 5 + 7 ) * 2"))) // 24 |
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84 //compute(syard(split("5 + 7 / 2"))) // 8 |
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85 //compute(syard(split("5 * 7 / 2"))) // 17 |
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86 //compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15 |
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87 |
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88 //compute(syard(split("4 ^ 3 ^ 2"))) // 262144 |
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89 //compute(syard(split("4 ^ ( 3 ^ 2 )"))) // 262144 |
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90 //compute(syard(split("( 4 ^ 3 ) ^ 2"))) // 4096 |
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91 //compute(syard(split("( 3 + 1 ) ^ 2 ^ 3"))) // 65536 |
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92 |
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93 //syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3")) // 3 4 8 * 5 1 - 2 3 ^ ^ / + |
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94 //compute(syard(split("3 + 4 * 8 / ( 5 - 1 ) ^ 2 ^ 3"))) // 3 |
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95 |
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96 //compute(syard(split("( 3 + 1 ) ^ 2 ^ 3"))) // 65536 |
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97 |
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98 |
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99 |
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100 } |