Exercise 2.30 of SICP

2009-08-15

sicp

Exercise 2.30: Define a procedure square-tree analogous to the square-list procedure of exercise 2.21. That is, square-list should behave as follows:

(square-tree
 (list 1
       (list 2 (list 3 4) 5)
       (list 6 7)))
(1 (4 (9 16) 25) (36 49))

Define square-tree both directly (i.e., without using any higher-order procedures) and also by using map and recursion.

(define (map proc items)
  (if (null? items)
    '()
    (cons (proc (car items)) (map proc (cdr items)))))

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

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

(define (map-square-tree tree)
  (map (lambda (sub-tree)
           (if (not (pair? sub-tree))
             (square sub-tree)
             (map-square-tree sub-tree)))
         tree))

> (define t (list 1 (list 2 (list 3 4) 5) (list 6 7))) 
> t 
(1 (2 (3 4) 5) (6 7))
>(map-square-tree t) 
(1 (4 (9 16) 25) (36 49))
>(square-tree t)
(1 (4 (9 16) 25) (36 49))

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