Solution to Exercise 2.3:
; rectangle procedures
(define (perimeter-rect r)
(+ (* 2 (width-rect r))
(* 2 (height-rect r))))
(define (area-rect r)
(* (width-rect r) (height-rect r)))
; first representation (as a diagonal line segment)
(define (make-rect x1 y1 x2 y2)
(make-segment (make-point x1 y1)
(make-point x2 y2)))
(define (width-rect r)
(abs (- (x-point (start-segment r))
(x-point (end-segment r)))))
(define (height-rect r)
(abs (- (y-point (start-segment r))
(y-point (end-segment r)))))
; second representation (as corner point and dimensions)
(define (make-rect x1 y1 x2 y2)
(cons (make-point x1 y1) ; corner point
(cons (- x2 x1) ; relative width
(- y2 y1)))) ; relative height
(define (width-rect r)
(abs (car (cdr r))))
(define (height-rect r)
(abs (cdr (cdr r))))
Posted by Ken Dyck as Programming at 7:27 AM EDT
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Solution to Exercise 2.3:
; rectangle procedures
(define (perimeter-rect r)
(+ (* 2 (width-rect r))
(* 2 (height-rect r))))
(define (area-rect r)
(* (width-rect r) (height-rect r)))
; first representation (as a diagonal line segment)
(define (make-rect x1 y1 x2 y2)
(make-segment (make-point x1 y1)
(make-point x2 y2)))
(define (width-rect r)
(abs (- (x-point (start-segment r))
(x-point (end-segment r)))))
(define (height-rect r)
(abs (- (y-point (start-segment r))
(y-point (end-segment r)))))
; second representation (as corner point and dimensions)
(define (make-rect x1 y1 x2 y2)
(cons (make-point x1 y1) ; corner point
(cons (- x2 x1) ; relative width
(- y2 y1)))) ; relative height
(define (width-rect r)
(abs (car (cdr r))))
(define (height-rect r)
(abs (cdr (cdr r))))
Posted by Ken Dyck as Programming at 7:26 AM EDT
4 Comments »
Solution to Exercise 2.2:
(define (make-segment start end)
(cons start end))
(define (start-segment s)
(car s))
(define (end-segment s)
(cdr s))
(define (make-point x y)
(cons x y))
(define (x-point p)
(car p))
(define (y-point p)
(cdr p))
(define (avg a b)
(/ (+ a b) 2))
(define (midpoint-segment s)
(let ((start (start-segment s))
(end (end-segment s)))
(make-point (avg (x-point start) (x-point end))
(avg (y-point start) (y-point end)))))
Posted by Ken Dyck as Programming at 8:09 PM EDT
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Solution to Exercise 2.1:
(define (make-rat n d)
(let ((new-n (if (negative? d) (- n) n))
(new-d (abs d)))
(let ((g (gcd new-n new-d)))
(cons (/ new-n g) (/ new-d g)))))
Posted by Ken Dyck as Programming at 7:46 PM EDT
3 Comments »
Solution to Exercise 1.46:
(define (iterative-improve good-enough? improve)
(define (iter initial-guess)
(if (good-enough? initial-guess)
initial-guess
(iter (improve initial-guess))))
iter)
Posted by Ken Dyck as Programming at 6:42 PM EDT
3 Comments »
Solution to Exercise 1.44:
(define (average-3 a b c)
(/ (+ a b c) 3))
(define (smooth f dx)
(lambda (x) (average-3 (f (- x dx))
(f x)
(f (+ x dx)))))
(define (n-fold-smooth f dx n)
(repeated (lambda (g) (smooth g dx)) n) f)
Posted by Ken Dyck as Programming at 7:17 PM EDT
3 Comments »
Solution to Exercise 1.43:
(define (compose f g)
(lambda (x) (f (g x))))
(define (inc i) (+ i 1))
(define (repeated f n)
(define (iter i result)
(if (= i n)
result
(iter (inc i) (compose f result))))
(iter 1 f))
Posted by Ken Dyck as Programming at 6:34 PM EDT
1 Comment »
Solution to Exercise 1.42:
(define (compose f g)
(lambda (x) (f (g x))))
Posted by Ken Dyck as Programming at 6:23 PM EDT
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Solution to Exercise 1.41:
(define (double f)
(lambda (x) (f (f x))))
Output:
> (define (inc x) (+ x 1))
> (((double (double double)) inc) 5)
21
Posted by Ken Dyck as Programming at 5:31 AM EDT
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Solution to Exercise 1.40:
(define (cubic a b c)
(lambda (x) (+ (* x x x)
(* a x x)
(* b x)
c)))
Posted by Ken Dyck as Programming at 5:21 AM EDT
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