Racket 如何使用抽象列表函数在球拍中生成斐波那契序列

我正在尝试编写一个racket程序，该程序不使用递归，只使用抽象列表函数（so-map、builld-list、foldr、foldl）计算fibonacci序列中前n个项的和。我可以使用助手函数。 我被困在如何不使用递归就列出斐波那契数的问题上。我想我可以使用lambda函数：

(lambda (lst) (+ (list-ref lst (- (length lst) 1)) (list-ref lst (- (length lst 2)))))

但我不知道如何生成输入列表/如何将其添加到函数中。 一旦我有了斐波那契序列，我就知道我可以用（foldl+（carlst）（cdrlst））来求和。 谁能给我解释一下如何制作斐波那契序列/给我一个提示

; This is how I figure out
#|
(1 2 3 4 (0 1))
-> (1 2 3 (1 1))
-> (1 2 (1 2))
-> (1 (2 3))
-> (3 5)
|#

(define (fib n)
  (cond
    [(= n 0) 0]
    [(= n 1) 1]
    [(> n 1)
     (second
      (foldr (λ (no-use ls) (list (second ls) (+ (first ls) (second ls))))
             '(0 1)
             (build-list (- n 1) (λ (x) x))))]))

(fib 10)
(build-list 10 fib)

升级版本2

(define (fib-v2 n)
  (first
   (foldr (λ (no-use ls) (list (second ls) (+ (first ls) (second ls))))
          '(0 1)
          (build-list n (λ (x) x)))))


(build-list 10 fib-v2)

---

fib-seq

生成前n个fibonacci数的列表，

fib-sum

生成前n个fibonacci数的和

; Number -> [List-of Number]
(define (fib-seq n)
  (cond [(= n 0) '()]
        [(= n 1) '(0)]
        [else (reverse
               (for/fold ([lon '(1 0)]) ([_ (in-range (- n 2))])
                 (cons (apply + (take lon 2)) lon)))]))

; Number -> Number
(define (fib-sum n)
  (if (= n 0) 0 (add1 (apply + (take (fib-seq n) (sub1 n))))))

注：

fib-sum

等同于以下递归版本：

(define (fib0 n)
  (if (< n 2) n (+ (fib0 (- n 1)) (fib0 (- n 2)))))

(define (fib1 n)
  (let loop ((cnt 0) (a 0) (b 1))
    (if (= n cnt) a (loop (+ cnt 1) b (+ a b)))))

(define (fib2 n (a 0) (b 1))
  (if (= n 0) 0 (if (< n 2) 1 (+ a (fib2 (- n 1) b (+ a b))))))

测试：

(require rackunit)
(check-true
 (let* ([l (build-list 20 identity)]
        [fl (list fib0 fib1 fib2 fib3 fib-sum)]
        [ll (make-list (length fl) l)])
   (andmap (λ (x) (equal? (map fib0 l) x))
           (map (λ (x y) (map x y)) fl ll))))

---

我认为至少有10种方法建立斐波那契数。

(require rackunit)
(check-true
 (let* ([l (build-list 20 identity)]
        [fl (list fib0 fib1 fib2 fib3 fib-sum)]
        [ll (make-list (length fl) l)])
   (andmap (λ (x) (equal? (map fib0 l) x))
           (map (λ (x y) (map x y)) fl ll))))