SICP Chapter 5.3

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Section 5.3

Notes

Exercises

Exercise 5.20

Draw the box-and-pointer representation and the memory-vector representation (as in Figure 5.14) of the list structure produced by

(define x (cons 1 2))
(define y (list x x))

with the free pointer initially p1. What is the final value of free? What pointers represent the values of x and y?

Solution

Exercise 5.21

Implement register machines for the following procedures. Assume that the list-structure memory operations are available as machine primitives.

1. Recursive count-leaves:

(define (count-leaves tree)
  (cond ((null? tree) 0)
        ((not (pair? tree)) 1)
        (else 
         (+ (count-leaves (car tree))
            (count-leaves (cdr tree))))))

2. Recursive count-leaves with explicit counter:

(define (count-leaves tree)
  (define (count-iter tree n)
    (cond ((null? tree) n)
          ((not (pair? tree)) (+ n 1))
          (else 
           (count-iter 
            (cdr tree)
            (count-iter (car tree) 
                        n)))))
  (count-iter tree 0))
Solution

Exercise 5.22

Exercise 3.12 of 3.3.1 presented an append procedure that appends two lists to form a new list and an append! procedure that splices two lists together. Design a register machine to implement each of these procedures. Assume that the list-structure memory operations are available as primitive operations.

Solution