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我将稀疏多项式表示为（系数，对）列表。例如：

'((1 2) (3 6) (-20 48)) => x^2 + 3x^6 - 20x^48

我是 Lisp 格式的新手，但遇到了一些非常漂亮的工具，例如(format nil "~:[+~;-~]" (> 0 coefficient))将系数的符号作为文本获取（我知道，这可能不是惯用的）。

但是，在格式化单个术语时存在一定的显示问题。例如，以下都应该是正确的：

(1 0) => 1x^0 => 1    (reducible)
(1 1) => 1x^1 => x    (reducible)
(1 2) => 1x^2 => x^2  (reducible)
(2 0) => 2x^0 => 2    (reducible)
(2 1) => 2x^1 => 2x   (reducable)
(2 2) => 2x^2 => 2x^2 (this one is okay)

我想知道是否有一种方法可以在没有大量if或cond宏的情况下做到这一点 - 一种只用一个format模式来做到这一点的方法。一切正常，但“美化”条款（最后一行FormatPolynomialHelper3应该这样做）。

(defun FormatPolynomial (p)
    "Readably formats the polynomial p."
    ; The result of FormatPolynomialHelper1 is a list of the form (sign formatted),
    ; where 'sign' is the sign of the first term and 'formatted' is the rest of the
    ; formatted polynomial. We make this a special case so that we can print a sign
    ; attached to the first term if it is negative, and leave it out otherwise. So,
    ; we format the first term to be either '-7x^20' or '7x^20', rather than having
    ; the minus or plus sign separated by a space.
    (destructuring-bind (sign formatted-poly) (FormatPolynomialHelper1 p)
        (cond
            ((string= formatted-poly "") (format nil "0"))
            (t                           (format nil "~:[~;-~]~a" (string= sign "-") formatted-poly)))))

; Helpers

(defun FormatPolynomialHelper1 (p)
    (reduce #'FormatPolynomialHelper2 (mapcar #'FormatPolynomialHelper3 p) :initial-value '("" "")))

(defun FormatPolynomialHelper2 (t1 t2)
    ; Reduces ((sign-a term-a) (sign-b term-b)) => (sign-b "term-b sign-a term-a"). As
    ; noted, this accumulates the formatted term in the variable t2, beginning with an
    ; initial value of "", and stores the sign of the leading term in the variable t1.
    ; The sign of the leading term is placed directly before the accumulated formatted
    ; term, ensuring that the signs are placed correctly before their coefficient. The
    ; sign of the the leading term of the polynomial (the last term that is processed)
    ; is available to the caller for special-case formatting.
    (list
        (first t2)
        (format nil "~@{~a ~}" (second t2) (first t1) (second t1))))

(defun FormatPolynomialHelper3 (tm)
    ; Properly formats a term in the form "ax^b", excluding parts of the form if they
    ; evaluate to one. For example, 1x^3 => x^3, 2x^1 => 2x, and 3x^0 => 3). The list
    ; is in the form (sign formatted), denoting the sign of the term, and the form of
    ; the term state above (the coefficient have forced absolute value).
    (list
        (format nil "~:[+~;-~]" (> 0 (first tm)))
        (format nil "~a~@[x^~a~]" (abs (first tm)) (second tm))))

编辑：正确地指出输出不应包含逻辑。也许我对我的问题提出了一个过于具体的问题。这是正确格式化多项式的逻辑 - 但我正在寻找更清洁、更易读和更 lisp 惯用的东西（这只是我写 lisp 的第三天）。

(defun FormatPolynomialHelper3 (tm)
    ; Properly formats a term in the form "ax^b", excluding parts of the form if they
    ; evaluate to one. For example, 1x^3 => x^3, 2x^1 => 2x, and 3x^0 => 3). The list
    ; is in the form (sign formatted), denoting the sign of the term, and the form of
    ; the term state above (the coefficient have forced absolute value).
    (list
        (format nil "~:[+~;-~]"   (> 0 (first tm)))
        (cond
            ((= 0 (second tm))      (format nil "~a" (abs (first tm))))
            ((= 1 (abs (first tm))) (cond
                ((= 1 (second tm))  (format nil "x"))
                (t                  (format nil "x^~a" (second tm)))))
            ((= 1 (second tm))      (format nil "~ax" (abs (first tm))))
            (t                      (format nil "~ax^~a" (abs (first tm)) (second tm))))))
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1 回答 1

5

答案：

我不会把这个逻辑放到FORMAT语句中。仅当您想加密代码或为自己创建更多维护工作时。好的 Lisp 代码是自记录的。FORMAT陈述永远不会自我记录。

在打印之前，我将首先简化多项式。例如删除每个乘以零的术语。

((0 10) (1 2)) -> ((1 2))

然后如果乘数为 1 可以在正常的CONDorCASE语句中进行测试。

还要确保你永远不要使用自制的数据CAR结构。多项式的组成部分应该主要由隐藏大部分实现细节的自记录函数访问。CDRFIRSTSECOND

我会写它没有FORMAT：

示例代码：

(defun term-m (term)
  (first term))

(defun term-e (term)
  (second term))

(defun simplify-polynomial (p)
  (remove-if #'zerop (sort p #'> :key #'term-e)
             :key #'term-m))

(defun write-term (m e start-p stream)
  ; sign or operator
  (cond ((and (minusp m) start-p)
         (princ "-" stream))
        ((not start-p)
         (princ (if (plusp m) " + " " - ") stream)))
  ; m
  (cond ((not (= (abs m) 1))
         (princ (abs m) stream)))
  (princ "x" stream)
  ; e
  (cond ((not (= 1 e))
         (princ "^" stream)
         (princ e stream))))

(defun write-polynomial (p &optional (stream *standard-output*))
  (loop for (m e) in (simplify-polynomial p)
        for start-p = t then nil
        do (write-term m e start-p stream)))

示例使用：

CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2
于 2012-09-08T06:38:00.773 回答