Pascal's triangle: Difference between revisions

Line 1,512:

<lang lisp>(defun pascal (n)

(genrow n '(1)))

(defun genrow (n l)

(when (< 0 n)

(print l)

(genrow (1- n) (cons 1 (newrow l)))))

(defun newrow (l)

(if (> 2 (length l))

'(1)

(cons (+ (car l) (cadr l)) (newrow (cdr l)))))</lang>

Line 1,527:

<lang lisp>(defun pascal-next-row (a)

(loop :for q :in a

:and p = 0 :then q

:as s = (list (+ p q))

:nconc s :into a

:finally (rplacd s (list 1))

(return a)))

(defun pascal (n)

(loop :for a = (list 1) :then (pascal-next-row a)

:repeat n

:collect a))</lang>

Another iterative solution, this time using pretty-printing to automatically print the triangle in the shape of a triangle in the terminal. The pascal-~~print~~ function ~~determines~~ the length of the ~~final~~ ~~row~~ ~~and uses it~~ to decide how wide the triangle should be.

Another iterative solution, this time using pretty-printing to automatically print the triangle in the shape of a triangle in the terminal. The print-pascal-triangle function computes and uses the length of the printed last row to decide how wide the triangle should be.

(defun next-pascal (l)

(defun next-pascal-triangle-row (list)

`(1

`(1 ,@(loop for i from 0 to (- (length l) 2)

~~collect (~~+ ~~(nth i l)~~ (~~nth (1+ i)~~ l)))

,.(mapcar #'+ list (rest list))

1))

(defun pascal-~~print~~ (r)

(defun pascal-triangle (number-of-rows)

(loop repeat number-of-rows

(let* ((pasc (loop with p = (list (list 1))

~~repeat~~ r do (~~nconc~~ p (~~list (apply #'~~next-pascal ~~(last p)))~~)

for row = '(1) then (next-pascal-triangle-row row)

~~finally~~ ~~(return~~ p)))

collect row))

(len (length (format nil "~A" (car (last pasc))))))

(defun print-pascal-triangle (number-of-rows)

⚫

~~(format~~ t (format nil "~~{~~~D:@<~~{~~A ~~}~~>~~%~~}" ~~len) pasc))~~)

(let* ((triangle (pascal-triangle number-of-rows))

(max-row-length (length (write-to-string (first (last triangle))))))

(format t

⚫

(format nil "~~{~~~D:@<~~{~~A ~~}~~>~~%~~}" max-row-length)

triangle)))

</lang>

For example:

<lang lisp>(pascal-~~print~~ 4)</lang>

<lang lisp>(print-pascal-triangle 4)</lang>

<lang>

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

</lang>

<lang lisp>(pascal-~~print~~ 8)</lang>

<lang lisp>(print-pascal-triangle 8)</lang>

<lang>

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

</lang>