1 ;; The first three lines of this file were inserted by DrScheme. They record metadata
2 ;; about the language level of this file in a form that our tools can easily process.
3 #reader(lib "htdp-intermediate-reader.ss" "lang")((modname 19.1.5) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp")))))
4 ;; mini : nelon  ->  number
5 ;; to determine the smallest number
6 ;; on alon
7 (define (mini alon)
8   (cond
9     [(empty? (rest alon)) (first alon)]
10     [else (cond
11             [(< (first alon) 
12                 (mini (rest alon)))
13              (first alon)]
14             [else
15              (mini (rest alon))])]))
16 
17 ;; maxi : nelon  ->  number
18 ;; to determine the largest number
19 ;; on alon
20 (define (maxi alon)
21   (cond
22     [(empty? (rest alon)) (first alon)]
23     [else (cond
24             [(> (first alon)
25                 (maxi (rest alon)))
26              (first alon)]
27             [else
28              (maxi (rest alon))])]))
29 
30 ;A non-empty-list-of-numbers (nelon) is
31 ;1. (cons n empty)
32 ;2. (cons n ne)
33 ;where n is a number and ne is a non-empty-list-of-numbers (nelon).
34 ;
35 ;extrema : predicate nelon -> number
36 ;Given predicate and a-lon, return the extreme value depending on the predicate.
37 
38 ;pick-interesting : predicate list-of-numbers
39 ;Given predicate and a-lon, pick the interesting (extreme) number.
40 
41 (define (extrema predicate a-lon)
42   (cond
43     [(empty? (rest a-lon)) (first a-lon)]
44     [else (local ((define extrema-recursion (extrema predicate (rest a-lon)))
45                   (define (pick-interesting predicate a-lon)
46                     (cond
47                       [(predicate (first a-lon) extrema-recursion) (first a-lon)]
48                       [else extrema-recursion])))
49             (pick-interesting predicate a-lon))]))
50 
51 ;mini1 : nelon -> number
52 ;Given a-lon, returns the minimum value.
53 (define (mini1 a-lon)
54   (extrema < a-lon))
55 
56 ;maxi1 : nelon -> number
57 ;Given a-lon, returns the maximum value.
58 (define (maxi1 a-lon)
59   (extrema > a-lon))
60 
61 ;(time (mini1 (list 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1)))
62 ;(time (maxi1 (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)))
63 
64 ;; sort : list-of-numbers predicate ->  list-of-numbers
65 ;; to construct a list with all items from alon in ascending or descending order
66 (define (sort1 alon predicate)
67   (local ((define (sort alon)
68 	    (cond
69 	      [(empty? alon) empty]
70 	      [else (insert (first alon) (sort (rest alon)))]))
71 	  (define (insert an alon)
72 	    (cond
73 	      [(empty? alon) (list an)]
74 	      [else (cond
75 		      [(predicate an (first alon)) (cons an alon)]
76 		      [else (cons (first alon) (insert an (rest alon)))])])))
77     (sort alon)))
78 
79 ;sort-ascend : list-of-numbers
80 ;Given a-lon, return a list-of-numbers sorted in ascending order.
81 (define (sort-ascend alon)
82   (sort1 alon <))
83 
84 ;sort-descend : list-of-numbers
85 ;Given a-lon, return a list-of-numbers sorted in descending order.
86 (define (sort-ascend alon)
87   (sort1 alon >))