用球拍实现扩展功能

Question

我似乎想不出怎么写这个函数。我正在尝试编写的是一个函数expand，它接受一个列表lst作为'(a (2 b) (3 c))形式的参数，并被计算为'(a b b c c c)

Answer 1

这看起来像家庭作业，所以我不会给你一个直接的答案。相反，我将在正确的方向上给你一些建议。最有用的提示是，您应该将问题分成两个过程，一个用于处理“外部”列表，另一个用于生成内部子列表中编码的重复项。

请注意，这两个过程都是相互递归的(例如，它们相互调用)。expand过程在列表上递归，而repeat过程在重复次数上递归。这是建议的解决方案的一般结构，请在空白处填写：

; input:  lst - list to be processed
; output: list in the format requested
(define (expand lst)
  (cond ((null? lst)             ; if the list is null
         '())                    ; then return null
        ((not (pair? (car lst))) ; if the first element of the list is an atom
         (cons <???> <???>))     ; cons the atom and advance the recursion
        (else                    ; if the first element of the list is a list
         <???>)))                ; call `repeat` with the right params


; input: n   - number of repetitions for the first element in the list
;        lst - list, its first element is of the form (number atom)
; output: n repetitions of the atom in the first element of lst
(define (repeat n lst)
  (if (zero? n)          ; if the number of repetitions is zero
      (expand (cdr lst)) ; continue with expand's recursion
      (cons <???>        ; else cons the atom in the first element and
            <???>)))     ; advance the recursion with one less repetition

Answer 2

因为这个问题是在三年前回答的，所以我不认为我是在帮助做作业。我只想指出，这两个函数真的不能互相递归( need )。由于replicate是一个相当常见的函数，因此我建议：

(define (replicate what n)
  (if (zero? n)
      (list)
      (cons what (replicate what (- n 1)))))

(define (my-expand xs)
  (if (empty? xs)
      (list)
      (let ((x (first xs)))
        (if (list? x)
            (let ((the-number (first x))
                  (the-symbol (cadr x)))
              (flatten (cons (replicate the-symbol the-number)
                    (my-expand (rest xs)))))
            (cons x (my-expand (rest xs)))))))

当然，最好使用两个列表，并在最后执行展平，如下所示：

(define (my-expand xs)
  (define (inner-expander xs ys)
    (if (empty? xs) (flatten (reverse ys))
        (let ((x (first xs)))
        (if (list? x)
            (let ((the-number (first x))
                  (the-symbol (cadr x)))
              (inner-expander (rest xs) (cons (replicate the-symbol the-number) ys)))                    
            (inner-expander (rest xs) (cons x ys))))))
  (inner-expander xs (list)))