Subversion Repositories programming

;Written By: Ira Snyder

;Due Date:   02-16-2005

;Homework #: hw08

;License: Public Domain

;ASSUMPTIONS: I chose to use the print format specified in the table

;             on the document that was handed out in class for hw08.

;             The difference is in the spaces between the coefficient

;             and the "x" that is printed. In the table there is a space

;             between the coefficient and the "x", whereas in the example

;             runs on the bottom of the page, there is not a space.

;             The change to make it the same as the example runs is to delete

;             the space between "~A" and "x" in the format statements on

;             lines 111 and 112 (the last two lines in the cond of WRITE-NUM).

;

;             Also, I was forced to assume that the last printed line on the

;             the hw08 handout is incorrect, since the terms are unsorted

;             and have un-combined coefficients with the same exponent.

;             Mine is correct and combines terms with the same exponent

;             and sorts the list from highest to lowest exponent.

;

;;; Given a list in unsorted, unreduced Polynomial

;;; Normal Form, and returns a list in perfect PNF

(defun PNF (L)

  (do ((L L (cdr L))

       (RET nil))

      ((null L) RET)

    (setf RET (INSERT (car L) RET))

    (setf RET (DEL-ZERO-COEF RET))

  )

)

;;; Given a pair of numbers (in a list) and a list of pairs

;;; this inserts the pair into the list in it's correct place

;;; including combining coefficients

(defun INSERT (PAIR LIST)

  (cond

    ((null LIST)                  (cons PAIR LIST))

    ((> (cadr PAIR) (cadar LIST)) (cons PAIR LIST))

    ((= (cadr PAIR) (cadar LIST)) (progn

                                    (setf (caar LIST) (+ (car PAIR) (caar LIST)))

                                    LIST

                                  ))

    (t                            (cons (car LIST ) (INSERT PAIR (cdr LIST))))

  )

)

;;; Deletes all of the pairs that have zero coefficients in

;;; a PNF list

(defun DEL-ZERO-COEF (L)

  (cond

    ((null L) nil)

    ((= 0 (caar L)) (DEL-ZERO-COEF (cdr L)))

    (t              (cons (car L) (DEL-ZERO-COEF (cdr L))))

  )

)

;;; This takes a non-negative integer, and returns a string

;;; containing the number of spaces specified by the integer

(defun SPACES (N)

  (do ((N N (1- N))

       (STR (format nil "")))

      ((zerop N) STR)

    (setf STR (concatenate 'string STR " "))

  )

)

;;; This checks if nil was passed. If it was, print a blank line, then

;;; a "0" line. Else pass the list off to the WRITE-POLY1 function.

(defun WRITE-POLY (L)

  (cond

    ((null L) (format t "~%0~%"))

    (t       (WRITE-POLY1 L))

  )

)

;;; Given a list in Polynomial Normal Form, this will print

;;; the human readable form of the list on two lines.

;;; Example:

;;;   INPUT:  ((1 1) (2 3) (-10 0) (3 2) (2 1))

;;;   OUTPUT:      3      2      

;;;   OUTPUT: + 2 x  + 3 x  + 3 x - 10

(defun WRITE-POLY1 (L)

  (do ((L (PNF L) (cdr L))

       (EXP  (format nil ""))

       (COEF (format nil "")))

      ((null L) (format t "~A~%~A~%" EXP COEF))

    (setf COEF (concatenate 'string COEF (WRITE-NUM (caar L) (cadar L))))

    (MAKE-EQUAL EXP COEF)

    (setf EXP  (concatenate 'string EXP  (WRITE-EXP (caar L) (cadar L))))

    (MAKE-EQUAL EXP COEF)

  )

)

;;; Given a coefficient and an exponent, output the correct expression

;;; to represent it.

;;; Examples:

;;; INPUT:  3 4

;;; OUTPUT: + 3 x

;;;

;;; INPUT:  3 0

;;; OUTPUT: + 3

;;;

;;; INPUT:  -3 0

;;; OUTPUT: - 3

(defun WRITE-NUM (NUM EXP)

  (cond

    ; don't output an x if we have a zero exponent

    ((zerop EXP) (if (plusp NUM) (format nil " + ~A" NUM) 

                                 (format nil " - ~A" (abs NUM))))

    ((plusp NUM) (format nil " + ~A x" NUM))

    (t           (format nil " - ~A x" (abs NUM)))

  )

)

;;; Given a coefficient and an exponent, output the exponent.

;;; NOTE: I chose to have the syntax of WRITE-EXP match the syntax of WRITE-NUM

;;;       even though I do not use the parameter NUM in the code. This was for

;;;       uniformity reasons.

(defun WRITE-EXP (NUM EXP)

  (cond

    ((zerop EXP) nil)

    ((= EXP 1)   nil)

    (t           (format nil "~A" EXP))

  )

)

;;; When called with two strings as arguments, this macro expands to

;;; make them the same length, regardless of which is longer.

(defmacro MAKE-EQUAL (S1 S2)

  `(cond

     ((> (length ,S1) (length ,S2)) (let ((DIFF (- (length ,S1) (length ,S2))))

                                    (setf ,S2 (concatenate 'string ,S2 (SPACES DIFF)))))

     ((< (length ,S1) (length ,S2)) (let ((DIFF (- (length ,S2) (length ,S1))))

                                    (setf ,S1 (concatenate 'string ,S1 (SPACES DIFF)))))

     (t                             nil)

   )

)