sicp 习题 2.26 ~ 2.30

最新推荐文章于 2023-03-06 16:24:38 发布

最新推荐文章于 2023-03-06 16:24:38 发布 · 235 阅读

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本文解析了Scheme编程语言中几个经典习题的实现方法，包括列表操作、树结构处理及复杂数据结构的递归操作。通过具体例子展示了如何利用递归进行列表反转、深反转以及树形结构的平方操作。

2.26


(define x (list 1 2 3))
(define y (list 4 5 6))
(append x y)
(cons x y)
(list x y)

(define z (list x y))

(car z)
(cdr z)

2.27


(define nil '())

(define (my-reverse x)
  (if (null? x)
      nil
      (append (my-reverse (cdr x)) (list (car x)))))

(define (deep-reverse lst)
  (define (iter lst result)
    (cond ((null? lst) result)
          ((not (pair? (car lst))) (iter (cdr lst) (cons (car lst) result)))
          (else (iter (cdr lst) (cons (deep-reverse (car lst)) result)))))
  (iter lst nil))

(define x (list (list 1 2) (list 3 4 5) (list 6 7) 8))
(define y (list 1 2))
(my-reverse x)
(deep-reverse x)

2.28


(define nil '())

(define x (list (list 1 2) (list 3 4)))

(define y (list x x))

(define (fringe x)
  (define iter (lambda (x)
                 (append (fringe (car x)) (fringe (cdr x)))))

  (cond ((null? x) nil)
        ((not (pair? x)) (list x))
        (else (iter x))))

(fringe x)

(newline)

(fringe y)

2.29


(define (make-mobile left right)
  (list left right))

(define (make-branch length structure)
  (list length structure))

(define (left-branch m)
  (car m))

(define (right-branch m)
  (car (cdr m)))

(define (branch-length b)
  (car b))

(define (branch-structure b)
  (car (cdr b)))

(define l-branch (make-branch (make-branch 2 2) (make-branch 2 2)))

(define r-branch (make-branch (make-branch 2 2) (make-branch 2 2)))

(define mobile (make-mobile l-branch r-branch))

(left-branch mobile)

(right-branch mobile)

(define (is-mobile? m)
  (and (pair? m)
       (pair? (left-branch m))
       (pair? (right-branch m))))

(define (total-weight m)
  (if (is-mobile? m)
      (+ (total-weight (left-branch m)) (total-weight (right-branch m)))
      (branch-structure m)))

(define (total-moment m)
  (if (is-mobile? m)
      (+ (total-moment (left-branch m)) (total-moment (right-branch m)))
      (* (branch-length m) (branch-structure m))))

(total-weight mobile)

(total-moment mobile)

(define (is-mobile-deep-than-2-level? m)
  (and (pair? m)
       (pair? (left-branch m))
       (pair? (right-branch m))
       (pair? (left-branch (left-branch m)))
       (pair? (right-branch (left-branch m)))
       (pair? (left-branch (right-branch m)))
       (pair? (right-branch (right-branch m)))))

(is-mobile-deep-than-2-level? mobile)

(define (is-banlanced? m)
  (if (is-mobile-deep-than-2-level? m) 
      (and (is-banlanced? (left-branch m)) (is-banlanced? (right-branch m)))
      (= (total-moment (left-branch m)) (total-moment (right-branch m)))))

2.29 cons


(define (make-mobile left right)
  (cons left right))

(define (make-branch length structure)
  (cons length structure))

(define (left-branch m)
  (car m))

(define (right-branch m)
  (cdr m))

(define (branch-length b)
  (car b))

(define (branch-structure b)
  (cdr b))

(define l-branch (make-branch (make-branch 2 2) (make-branch 2 2)))

(define r-branch (make-branch (make-branch 2 2) (make-branch 2 2)))

(define mobile (make-mobile l-branch r-branch))

(left-branch mobile)

(right-branch mobile)

(define (is-mobile? m)
  (and (pair? m)
       (pair? (left-branch m))
       (pair? (right-branch m))))

(define (total-weight m)
  (if (is-mobile? m)
      (+ (total-weight (left-branch m)) (total-weight (right-branch m)))
      (branch-structure m)))

(define (total-moment m)
  (if (is-mobile? m)
      (+ (total-moment (left-branch m)) (total-moment (right-branch m)))
      (* (branch-length m) (branch-structure m))))

(total-weight mobile)

(total-moment mobile)

(define (is-mobile-deep-than-2-level? m)
  (and (pair? m)
       (pair? (left-branch m))
       (pair? (right-branch m))
       (pair? (left-branch (left-branch m)))
       (pair? (right-branch (left-branch m)))
       (pair? (left-branch (right-branch m)))
       (pair? (right-branch (right-branch m)))))

(is-mobile-deep-than-2-level? mobile)

(define (is-banlanced? m)
  (if (is-mobile-deep-than-2-level? m) 
      (and (is-banlanced? (left-branch m)) (is-banlanced? (right-branch m)))
      (= (total-moment (left-branch m)) (total-moment (right-branch m)))))

2.30


(define nil '())

(define (square x)
  (* x x))

(define (square-tree tree)
  (cond ((null? tree) nil)
        ((not (pair? tree)) (square tree))
        (else (cons (square-tree (car tree)) (square-tree (cdr tree))))))

(define (square-tree-map tree)
  (map (lambda (sub-tree)
         (if (pair? sub-tree)
             (square-tree-map sub-tree)
             (square sub-tree)))
       tree))

(square-tree (list 1 (list 2 (list 3 4) 5) (list 6 7)))

(square-tree-map (list 1 (list 2 (list 3 4) 5) (list 6 7)))