Zapiski #3 srečanja programerskega bralnega krožka SICP
Teme
Funkcije višjega reda
Vaje
1.29 Simpsonovo pravilo
(define(cube x) (* x x x)) (define(sum-integers a b) (if ( > a b) 0 (+ a (sum-integers (+ a 1) b)))) (define(sum-cubes a b) (if (> a b) 0 (+ (cube a) (sum-cubes(+ a 1) b)))) (define (sum term a next b) (if (> a b) 0 (+ (term a) (sum term (next a) next b)))) (define (integral f a b dx) (define (add-dx x) (+ x dx)) (* (sum f (+ a (/ dx 2.0)) add-dx b) dx)) (define (simpson f a b n) (define h (/ (- b a) n)) (define (add-hh a) (+ a h h)) (* (+ (- (f a)) (* 2 (sum f a add-hh b)) (* 4 (sum f (+ a h) add-hh b)) (- (f b))) (/ h 3.0))) (list (simpson cube 1 2 100) (simpson cube 1 2 1000))
3.7500000000000004 | 3.75 |
1.30 linearen sum
Rekurzivne procedure:
(define (sum term a next b) (if (> a b) 0 (+ (term a) (sum term (next a) next b)))) (define (cube n) (* n n n)) (define (inc n) (+ n 1)) (define (sum-cubes a b) (sum cube a inc b)) (sum-cubes 1 10)
3025
Iterativne procedure:
(define (sum-iter term a next b) (define (iter a result) (if (> a b) result (iter (next a) (+ result (term a))))) (iter a 0)) (define (cube n) (* n n n)) (define (inc n) (+ n 1)) (define (sum-cubes-iter a b) (sum-iter cube a inc b)) (sum-cubes-iter 1 10)
3025
1.31 Produkt višjega reda
(define (prod-iter term a next b) (define (iter a result) (if (> a b) result (iter (next a) (* result (term a))))) (iter a 0)) (define (piblizek n) (define (stevec n) (+ n 2)) (* 4 (/ (prod-iter (lambda (n) (* (- n 1) (+ n 1))) 3 stevec n) (prod-iter (lambda (n) (* n n)) 3 stevec n)))) (piblizek 10)
TODO popravi!