调车场算法

Question

我正在努力在 Clojure 中实现一个中缀计算器，首先是我实现 Dijkstra 的分流场算法。我以为我已经把它写得很好了，但对我来说是个笑话，它似乎根本不能很好地处理操作员。调用(调车场“3 + 5”) => (\3)。就这样。有人可以告诉我这里对运算符字符的处理有什么问题吗？

(import '(java.lang.Character))

(defn operator? [sym]
  "Determines if a given token is a mathematical operator."
  (some #{sym} '(\+ \- \* \/ \% \^ \!)))

(defn associativity-of [operator]
  "Determines the associativity of a given mathematical operator."
  (if (some #{operator} '(\+ \- \* \/ \%))
    'left
    'right))

(defn precedence-of [operator]
  "Determines the precedence of a given mathematical operator."
  (case operator
        (\+ \-)    2
        (\* \/ \%) 3
        (\^ \!)    4
                   0))

(defn operator-actions [stmt stack]
  "Actions taken when the next token in the stmt is an operator."
  (let [token-prec  (precedence-of (first stmt))
        token-assoc (associativity-of (first stmt))
        stack-oper  (first stack)
        stack-prec  (precedence-of stack-oper)]
    (cond (or (and (= token-assoc 'left)
                   (<= token-prec stack-prec))
              (and (= token-assoc 'right)
                   (< token-prec stack-prec)))
          (cons stack-oper (shunt stmt (rest stack)))
          :else (shunt (rest stmt) (cons (first stmt) stack)))))

(defn stack-operations [stack]
  "Actions to take if (nil? stmt)"
  (comment "If a left paren is found on the stack, it means
           that there was no right paren to match it, and
           therefore the statement had unbalanced parentheses.")
  (cond (and (not (nil? stack))
             (= (first stack) \()) (print "Unbalanced parentheses.\n")
        (nil? stack) ()
        :else (cons (first stack) (stack-operations (rest stack)))))

(defn shunt [stmt stack]
  (cond (empty? stmt) (stack-operations stack)
        (Character/isDigit (first stmt)) (cons (first stmt)
                                               (shunt (rest stmt) stack))
        (operator? (first stmt)) (operator-actions stmt stack)
        (= (first stmt) \() (recur (rest stmt) (cons (first stmt) stack))
        (= (first stmt) \)) (if (= (first stack) \()
                              (recur (rest stmt) (rest stack))
                              (cons (first stack) (shunt stmt (rest stack))))))

(defn shunting-yard [stmt]
  (shunt stmt ()))

Answer 1

我实际上并不知道 Shunting-Yard 算法（刚才在维基百科上节省了 2 分钟），但我看到的一个问题是 shunt 不处理空格。因此它读取您的 \3、递归并退出，因为下一个字符是 \space。如果 stmt 没有空格，即 "3+5"，您会收到 StackOverflowError，但我想这就是进步。