6.090 IAP '05 - Lecture 7 Solutions

hypothetical cons abstraction

(define (cons a b)
  (lambda (x)
    (if x
        a
        b)))

(define (car p)
  (p #t))

(define (cdr p)
  (p #f))


list sorting

(define (min x y)
  (if (< x y)
      x
      y))

(define (min-list lst)
  (if (null? (cdr lst))
      (car lst)
      (min (car lst) (min-list (cdr lst)))))

(define (without-n lst n)
  (if (null? lst)
      nil
      (if (= (car lst) n)
          (cdr lst)
          (cons (car lst)
                (without-n (cdr lst) n)))))

(define (sort-list lst)
  (if (or (null? lst) (null? (cdr lst)))
      lst
      (let ((least (min-list lst)))
         (cons least
               (sort-list (without-n lst least))))))

(define (insert elem lst)
  (if (null? lst)
      (list elem)
      (if (< elem (car lst))
          (cons elem lst)
          (cons (car lst)
                (insert elem (cdr lst))))))

(define (insert-sort lst)
  (if (or (null? lst) (null? cdr lst))
      lst
      (insert (car lst)
              (insert-sort (cdr lst)))))