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ex331.lisp
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; Answers for 3-3-1
(defun set-cdr! (x y)
(setf (cdr x) y))
(defun set-car! (x y)
(setf (car x) y))
(defun append! (x y)
(let nil
(set-cdr! (last-pair x) y)
x))
(defun last-pair (x)
(if (null (cdr x))
x
(last-pair (cdr x))))
; Exercise 3.12
(defvar x '(a b))
(defvar y '(c d))
(defvar z (append x y))
; (cdr x) at this point will be '(b), as we used the non-destructive append.
; +---+---+ +---+---+
; x -->| * | *-+----->| * | / |
; +-|-+---+ +-|-+---+
; v v
; +---+ +---+
; | a | | b |
; +---+ +---+
;
; +---+---+ +---+---+
; z -->| * | *-+----->| * | * +----+
; +-|-+---+ +-|-+---+ |
; v v |
; +---+ +---+ |
; | a | | b | |
; +---+ +---+ |
; +-------------------------+
; v
; +---+---+ +---+---+
; y -->| * | *-+----->| * | / |
; +-|-+---+ +-|-+---+
; v v
; +---+ +---+
; | c | | d |
; +---+ +---+
;
(defvar w (append! x y))
; (cdr x) at this point will be '(b c d) as we used the destructive append.
; w
; |
; v
; +---+---+ +---+---+
; x -->| * | *-+----->| * | * +----+
; +-|-+---+ +-|-+---+ |
; v v |
; +---+ +---+ |
; | a | | b | |
; +---+ +---+ |
; +-------------------------+
; v
; +---+---+ +---+---+
; y -->| * | *-+----->| * | / |
; +-|-+---+ +-|-+---+
; v v
; +---+ +---+
; | c | | d |
; +---+ +---+
;
; Exercise 3.13
; +-----------------------------------------+
; | |
; v |
; +---+---+ +---+---+ +---+---+ |
; z --> | * | *-+----->| * | *-+----->| * | *-+-----+
; +-|-+---+ +-|-+---+ +-|-+---+
; v v v
; +---+ +---+ +---+
; | a | | b | | c |
; +---+ +---+ +---+
;
; The program crashes - infinite loop.
; Exercise 3.14
(defun mystery (x)
(labels ((iter (x y)
(if (null x)
y
(let ((temp (cdr x)))
(set-cdr! x y)
(iter temp x)))))
(iter x '())))
; Reverses a list in place. You need to reset the variable, however, as it
; will still point to what was the first element in the list and is now the last.
; Before:
; +---+---+ +---+---+ +---+---+ +---+---+
; v --> | * | *-+----->| * | *-+----->| * | *-+----->| * | / |
; +-|-+---+ +-|-+---+ +-|-+---+ +-|-+---+
; v v v v
; +---+ +---+ +---+ +---+
; | a | | b | | c | | d |
; +---+ +---+ +---+ +---+
; After:
; v
;
; |
; v
; +---+---+ +---+---+ +---+---+ +---+---+
; w --> | * | *-+----->| * | *-+----->| * | *-+----->| * | / |
; +-|-+---+ +-|-+---+ +-|-+---+ +-|-+---+
; v v v v
; +---+ +---+ +---+ +---+
; | d | | c | | b | | a |
; +---+ +---+ +---+ +---+
; Exercise 3.15
(defun set-to-wow! (x)
(set-car! (car x) 'wow)
x)
;; GRRR MORE BOX POINTER DIAGRAMS!
; +---+---+
; z1 -->| * | * |
; +-|-+-|-+
; V V
; +---+---+ +---+---+
; x -->| * | *-+---->| * | / |
; +-|-+---+ +-|-+---+
; V V
; +---+ +---+
; | a | | b |
; +---+ +---+
; becomes ...
; +---+---+
; z1 -->| * | * |
; +-|-+-|-+
; V V
; +---+---+ +---+---+
; x -->| * | *-+---->| * | / |
; +-|-+---+ +-|-+---+
; V V
; +-----+ +---+
; | wow | | b |
; +-----+ +---+
; +---+---+ +---+---+ +---+---+
; z2 -->| * | *-+---->| * | *-+---->| * | / |
; +-|-+---+ +-|-+---+ +-|-+---+
; | V V
; | +---+ +---+
; | | a | | b |
; | +---+ +---+
; | ^ ^
; | | |
; | +-|-+---+ +-|-+---+
; +---------->| * | *-+---->| * | / |
; +---+---+ +---+---+
; becomes ...
; +---+---+ +---+---+ +---+---+
; z2 -->| * | *-+---->| * | *-+---->| * | / |
; +-|-+---+ +-|-+---+ +-|-+---+
; | V V
; | +---+ +---+
; | | a | | b |
; | +---+ +---+
; | ^
; | |
; | +---+---+ +-|-+---+
; +---------->| * | *-+---->| * | / |
; +-|-+---+ +---+---+
; |
; v
; +-----+
; | wow |
; +-----+
; Exercise 3.16
(defun count-pairs (x)
(if (or (not (listp x))
(null x))
0
(+ (count-pairs (car x))
(count-pairs (cdr x))
1)))
; 3:
;
; +---+---+ +---+---+ +---+---+
; -->| | *-+-->| | *-+-->| | / |
; +---+---+ +---+---+ +---+---+
;
(defparameter count-3 '(a b c))
; 4:
;
; +---+---+ +---+---+ +---+---+
; -->| | *-+-->| * | *-+-->| | / |
; +---+---+ +-|-+---+ +---+---+
; | ^
; | |
; +-----------+
;
(defparameter count-4 '(a b c))
(setf (cadr count-4)
(cddr count-4))
;
; 7:
;
; +-----------+
; | |
; | v
; +-|-+---+ +---+---+ +---+---+
; -->| * | *-+-->| * | *-+-->| | / |
; +---+---+ +-|-+---+ +---+---+
; | ^
; | |
; +-----------+
(defparameter count-7 '(a b c))
(setf (cadr count-7)
(cddr count-7))
(setf (car count-7)
(cdr count-7))
;
; never:
;
; +---------------------------+
; v |
; +---+---+ +---+---+ +---+-|-+
; -->| | *-+-->| | *-+-->| | * |
; +---+---+ +---+---+ +---+---+
(defparameter count-infinity '(a b c))
(setf (cdr (last-pair count-infinity))
count-infinity)
; Exercise 3.17
(defun make-set ()
'())
(defun add-to-set (x set)
(cons x set))
(defun element-of-set (x set)
(not (null (find x set :test #'eq))))
; Let's make a functional version ...
(defun count-distinct-pairs (x)
(labels ((iter (seq seen)
(if (or (not (listp seq))
(null seq)
(element-of-set seq seen))
0
(let ((seen (add-to-set seq seen)))
(+ 1
(iter (car seq) seen)
(iter (cdr seq) seen))))))
(iter x (make-set))))
; Exercise 3.18
(defun contains-cycle (seq)
(labels ((iter (seq seen)
(cond ((null seq) nil)
((element-of-set seq seen) t)
(t (iter (cdr seq) (add-to-set seq seen))))))
(iter seq (make-set))))
; Exercise 3.19
(defun contains-cycle-2 (front)
(labels ((iter (seq)
(cond ((null seq) nil)
((eq seq front) t)
(t (iter (cdr seq))))))
(iter (cdr front))))
; Have since realized this doesn't work for all cases, as a cycle could occur
; without containing the first element of the list.
; You could do it like this,
(defun contains-cycle-3 (front)
(labels ((position-of (x seq &optional (acc 0))
(if (eq x seq)
acc
(position-of x (cdr seq) (1+ acc))))
(iter (seq n)
(cond ((null seq) nil)
((/= (position-of seq front) n) t)
(t (iter (cdr seq) (1+ n))))))
(iter front 0)))
; but although it only uses constant space, it's not very efficient.
; So there's probably something I'm missing.
; Yes - there is. Although SICP didn't specify the algorithm still had to run
; in linear time, I think they were probably referring to Floyd's
; cycle-finding algorithm. Wikipedia has an interesting article on it - very
; elegant!
; Exercise 3.20
; +------------------------------------------------------------------+
; global --> | cons -+ cdr set-car! -+ x
; env | car | set-cdr! | z
; +-------|--------^---------------------------|--------^------------+
; | | | |
; | | | |
; v | v |
; +---+---+ | +---+---+ |
; | 0 | 0 +----+ | 0 | 0 +----+
; +-|-+---+ +-|-+---+
; | |
; v v
; parameters: x y parameters: z new-value
; body: (define (set-x! v) ... ) body: ((z 'set-cdr!) new-value)
; (define (set-y! v) ... )
; (define (dispatch m) ... )
; dispatch
; (etc. not going to list every method
; definition)
;
;
; global env
; --------------------------------------------------------------------------------------
;
;
; -----------------^---------------------^------------------------------------^---------
; | | | (cdr z)
; +---------------+ +--------------------+ +---------+----------+
;(cons 1 2) | x: 1 | | x: (E1's dispatch) | (cons x x) | z: (E2's dispatch) | <- E3
; | y: 2 | | y: (E1's dispatch) | +--------------------+
; E1 --> | set-x! | | set-x! | <-- E2
; | set-y! | | set-y! |
; +----->| dispatch | | dispatch |
; | +----|-------^--+ +--------------------+
; | | | ^ ^
; | v | | | (z 'cdr)
; | +---+---+ | | +-----+------+
; | | 0 | 0-+---+ | | m: 'cdr |<-- E4
; | +-|-+---+ | +------------+
; | v |
; | parameters: m | +-------------+
; | body: ... +----| m: 'set-car!|<-- E6
; | | +-------------+
; +-------------+ | (z 'set-car!)
; | v: 17 |<--- E7 +-------+
; +-------------+ |
; ((z 'set-car!) new-value) | (z 'car)
; | +---------+
; +----| m: car |<--- E9
; +---------+
;
;
; --------------------------------------------------------------------------------------
;
;
; -----------^-----------------------------------^--------------------------------------
; | |
; | (set-car! (cdr z) 17) | (car x)
; +---------------------+ +--------------------+
; | z: (E1's dispatch) | | z: (E1's dispatch) |<--- E8
; | new-value: 17 | <- E5 +--------------------+
; +---------------------+
;