Question

我将稀疏多项式表示为（系数，对）的列表。例如：

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

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

但是，格式化单个术语时会出现某些显示问题。例如，以下内容应该都是真的：

(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)

我想知道是否有办法在没有大量if或cond宏的情况下执行此操作 - 只需使用单个format模式执行此操作。一切都有效但是“美化”这些术语（FormatPolynomialHelper3中的最后一行应该这样做）。

(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：正确已声明输出不应包含逻辑。也许我对问题的要求过于具体。这是正确格式化多项式的逻辑 - 但我正在寻找更清晰，更可读和更具口味的东西（这只是我写作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))))))

Answer 1

<强>答案：

我不会将此逻辑放入FORMAT语句中。仅当您要加密代码或为自己创建更多维护工作时。好的Lisp代码是自我记录的。 FORMAT语句永远不会自我记录。

在打印之前，我首先简化多项式。例如，删除每个乘以零的项。

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

然后，如果乘数为1，则可以在正常COND或CASE语句中进行测试。

另外，请确保从不使用自制数据结构CAR，CDR，FIRST，SECOND。多项式的组件应该主要通过隐藏大部分实现细节的自记录函数来访问。

我会在没有FORMAT的情况下写出来：

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)))

使用示例：

CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2

Lisp格式化多项式

1 个答案: