6.090 IAP '05 - Optional Homework 5 Solutions

Problem 1:

(define square-list
  (lambda (lst)
    (if (null? lst)
	nil
	(cons (* (car lst) (car lst))
	      (square-list (cdr lst))))))

Problem 2:

(define stutter-list
  (lambda (lst)
    (if (null? lst)
	nil
	(cons (car lst)
	      (cons (car lst)
		    (stutter-list (cdr lst)))))))

Problem 3:

(define only-even
  (lambda (lst)
    (if (null? lst)
	nil
	(if (even? (car lst))
	    (cons (car lst)
		  (only-even (cdr lst)))
	    (only-even (cdr lst))))))

Problem 4:

(define add-lists
  (lambda (l1 l2)
    (if (null? l1)
	nil
	(cons (+ (car l1) (car l2))
	      (add-lists (cdr l1) (cdr l2))))))

Problem 5:

(define palindrome-list
  (lambda (lst)
    (append lst (reverse (cdr lst)))))

or

(define palindrome-list
  (lambda (lst)
    (if (or (null? lst) (null? (cdr lst)))
	lst
	(cons (car lst) (append (palindrome-list (cdr lst))
				(list (car lst)))))))

Problem 6:

(define replace-elem
  (lambda (lst f r)
    (if (null? lst)
	nil
	(if (= (car lst) f)
	    (cons r 
		  (replace-elem (cdr lst) f r))
	    (cons (car lst)
		  (replace-elem (cdr lst) f r))))))

Problem 7:

(define list-average
  (lambda (lst)
    (/ (sum-list lst) (length lst))))