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trying out better file extensions
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@Pluies
Pluies committed Mar 25, 2011
1 parent 8211a87 commit 45da3b1
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@@ -1,283 +1,3 @@
;-- 1.2
(/ (+ 5
4
(- 2 (- 3 (+ 6 (/ 4 5)))))
(* 3
(- 6 2)
(- 2 7)))

;-- 1.3
(define (sumSqu x y) (+ (* x x) (* y y)))
(define (sumTwoBiggers a b c)
(cond ((> a b) (cond ((> b c) (sumSqu a b))
(else (sumSqu a c))))
(else (cond ((> a c) (sumSqu b a))
(else (sumSqu b c))))))


;-- 1.9 fibo
(define (fibo n)
(cond ((= n 0) 0)
((= n 1) 1)
(else (+ (fibo (- n 1)) (fibo (- n 2))))))

(define (fib n)
(fib-iter 0 1 n))
(define (fib-iter a b count)
(if (= count 0)
b
(fib-iter b (+ a b) (- count 1))))

;-- 1.11
(define (f n)
(if (< n 3)
n
(+ (f (- n 1))
(* 2 (f (- n 2)))
(* 3 (f (- n 3))))))

(define (f n)
(iter_f 0 1 2 3 n))

(define (iter_f a b c n)
(if (= n 0)
a
(iter_f (+ a (* 2 b) (* 3 c)) a b (- n 1))))

;-- 1.12
(define (pascal line col)
(cond ((= col 0) 1)
((< line 1) 0)
(else (+ (pascal (- line 1) col)
(pascal (- line 1) (- col 1))))))

;-- 1.17
(define (fast-mult a b)
(cond ((= b 1) a)
((even? b) (fast-mult (double a) (halve b)))
(else (+ a (fast-mult a (- b 1))))))

;-- 1.30
(define (sum term a next b)
(define (iter a result)
(if (> a b)
result
(iter (next a) (+ result (term a)))))
(iter a 0))

;-- 1.31
; a.
(define (product term a next b)
(define (iter a result)
(if (> a b)
result
(iter (next a) (* result (term a)))))
(iter a 1))

(define (identity x) x)
(define (addone x) (+ x 1))
(define (factorial x)
(product identity 1 addone x))

(define (littlepi n)
(if (even? n)
(/ (+ 2 n) (+ 1 n))
(/ (+ 1 n) (+ 2 n))))
(define (pi_approx precision)
(* 4 (product littlepi 1 addone precision)))


; b.
(define (product term a next b)
(if (> a b)
1
(* (term a) (product term (next a) next b))))

;-- 1.32
(define (accumulate combiner null-value term a next b)
(if (> a b)
null-value
(combiner (term a) (accumulate combiner null-value term (next a) next b))))

;-- 1.33
(define (filtered-accumulate combiner null-value filter term a next b)
(if (> a b)
null-value
(combiner (if (filter a)
(term a)
null-value)
(filtered-accumulate combiner null-value filter term (next a) next b))))

a.
(define (square x) (* x x))
(define (next x) (+ 1 x))
(define (smsqa a b)
(filtered-accumulate + 0 prime? square a next b))

b.
(define (exb n)
(define (filter x)
(= (gcd x n) 1))
(filter-accumulate * 1 filter identity 1 next n))

;-- 1.34
(define (f g)
(g 2))
;(f f) -> (f 2)
;(2 2)
;error

;-- 1.35
; Golden Number: x when x² = x + 1
; i.e. x = 1 + 1/x
(define phi
(fixed-point (lambda (x) (average x (+ 1 (/ 1 x))))
1.0))

Helpers:
(define (average x y) (/ (+ x y) 2))
(define tolerance 0.00001)
(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))

;-- 1.36
(define tolerance 0.00001)
(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(display guess)
(newline)
(if (close-enough? guess next)
next
(try next))))
(try first-guess))

(define xxth
(fixed-point (lambda (x) (/ (log 1000) (log x)))
2.0))
(define xxth_av
(fixed-point (lambda (x) (average x (/ (log 1000) (log x))))
2.0))

The average version uses far less iterations.

;-- 1.37
; Computes the k-term finite continued fraction N / D + N'
; Recursive process :
(define (cont-frac n d k)
(if (= k 0)
0
(/ (n k) (+ (d k) (cont-frac n d (- k 1))))))

; Iterative process :
(define (cont-frac n d k)
(define (loop result term)
(if (= term 0)
result
(loop (/ (n term) (+ (d term) result))
(- term 1))))
(loop 0 k))

;-- 1.38
(define (n x)
(cond ((= x 1) 1)
((= x 2) 2)
(else (if (= 2 (remainder x 3))
(* 2 (+ 1 (/ (- x 2) 3)))
1))))

(define e
(+ 2.0 (cont-frac (lambda (x) 1)
(lambda (x) (cond ((= x 0) 1)
((= x 1) 1)
((= x 2) 2)
(else (if (= 0 (remainder (- x 2) 3))
(* 2 (+ 1 (/ (- x 2) 3)))
1))))
50)))

;-- 1.39
(define (tan-cf x k)
(cont-frac (lambda (z) (if (= 1 z)
x
(- (* x x))))
(lambda (z) (- (* 2 z) 1))
k))

;-- 1.40

;-- 1.41
(define (double fun)
(lambda (x) (fun (fun x))))

(((double (double double)) inc) 5) ; gives 21

;-- 1.42
(define (compose f g)
(lambda (x) (f (g x))))

;-- 1.43
(define (square x) (* x x ))

(define (repeated fun n)
(if (= n 0)
(lambda (x) x)
(compose fun (repeated fun (- n 1)))))

; Or without using compose:
(define (repeated fun n)
(if (= n 0)
(lambda (x) x)
(lambda (x) (fun ((repeated fun (- n 1)) x)))))

;-- 1.44
(define (smooth f)
(define dx 0.001)
(lambda (x) (/ (+ (f (- x dx))
(f x)
(f (+ x dx)))
3)))

(define (nfoldsmooth f n)
((repeated smooth n) f))

;-- 1.45

;-- 1.46
(define (average x y) (/ (+ x y) 2))

(define (iterative-improve good-enough? improve)
(lambda (guess) (if (good-enough? guess)
guess
((iterative-improve good-enough? improve)(improve guess)))))

(define (sqrt-ii n)
((iterative-improve (lambda (guess)
(< (abs (- (square guess) n)) 0.001))
(lambda (guess)
(average guess (/ n guess))))
1.0))

(define (fixed-point-ii f)
((iterative-improve (lambda (guess)
(< (abs (- guess (f guess))) 0.00001))
(lambda (guess)
(f guess)))
1.0))



;; ¿¿ Part 2 ¿¿ ;;

;-- 2.1
(define (make-rat n d)
(let ((g (gcd n d)))
Expand Down Expand Up @@ -822,7 +542,7 @@ The average version uses far less iterations.


;-- 2.43
;Way longer, Louis is a n00b.
; Way longer, Louis is not skilled.

;-- 2.44
(define (up-split painter n)
Expand Down

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