exam9.5.4

;; mht created on Nov 15, 2011

;; check-range1? : list-of-numbers -> boolean
;; to check whether all items in a-list-of-nums are in interval [5, 95]
(define (check-range1? a-list-of-nums)
  (cond
    [(empty? a-list-of-nums) true]
    [else
     (and
      (is-between-5-and-95? (first a-list-of-nums))
      (check-range1? (rest a-list-of-nums)))]))

;; is-between-5-and-95? : number -> boolean
(define (is-between-5-and-95? n)
  (and
   (< 5 n)
   (< n 95)))


;; test:
(check-range1? empty)
(check-range1? (cons 25 (cons 35 (cons 90 empty))))
(not (check-range1? (cons 25 (cons 95 (cons 23 empty)))))

;; generalized-check-range1? : list-of-numbers number number -> boolean
;; to check whether all items in a-list-of-nums are in interval[n1 n2]
(define (generalized-check-range1? a-list-of-nums n1 n2)
  (cond
    [(empty? a-list-of-nums) true]
    [else
     (and
      (is-between-interval? (first a-list-of-nums) n1 n2)
      (generalized-check-range1? (rest a-list-of-nums) n1 n2))]))

;; is-between-interval? : number number number -> boolean
;; to determine n is in [n1 n2]
(define (is-between-interval? n n1 n2)
  (and
   (< n1 n)
   (< n n2)))


;; test:
(generalized-check-range1? empty 5 95)
(generalized-check-range1? (cons 25 (cons 35 (cons 90 empty))) 5 95)
(not (generalized-check-range1? (cons 25 (cons 95 (cons 23 empty))) 5 95))