1 12687dd9 2023-08-04 jrmu ;; The first three lines of this file were inserted by DrScheme. They record metadata
 2 12687dd9 2023-08-04 jrmu ;; about the language level of this file in a form that our tools can easily process.
 3 12687dd9 2023-08-04 jrmu #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 12687dd9 2023-08-04 jrmu ;; mini : nelon  ->  number
 5 12687dd9 2023-08-04 jrmu ;; to determine the smallest number
 6 12687dd9 2023-08-04 jrmu ;; on alon
 7 12687dd9 2023-08-04 jrmu (define (mini alon)
 8 12687dd9 2023-08-04 jrmu   (cond
 9 12687dd9 2023-08-04 jrmu     [(empty? (rest alon)) (first alon)]
10 12687dd9 2023-08-04 jrmu     [else (cond
11 12687dd9 2023-08-04 jrmu             [(< (first alon) 
12 12687dd9 2023-08-04 jrmu                 (mini (rest alon)))
13 12687dd9 2023-08-04 jrmu              (first alon)]
14 12687dd9 2023-08-04 jrmu             [else
15 12687dd9 2023-08-04 jrmu              (mini (rest alon))])]))
16 12687dd9 2023-08-04 jrmu 
17 12687dd9 2023-08-04 jrmu ;; maxi : nelon  ->  number
18 12687dd9 2023-08-04 jrmu ;; to determine the largest number
19 12687dd9 2023-08-04 jrmu ;; on alon
20 12687dd9 2023-08-04 jrmu (define (maxi alon)
21 12687dd9 2023-08-04 jrmu   (cond
22 12687dd9 2023-08-04 jrmu     [(empty? (rest alon)) (first alon)]
23 12687dd9 2023-08-04 jrmu     [else (cond
24 12687dd9 2023-08-04 jrmu             [(> (first alon)
25 12687dd9 2023-08-04 jrmu                 (maxi (rest alon)))
26 12687dd9 2023-08-04 jrmu              (first alon)]
27 12687dd9 2023-08-04 jrmu             [else
28 12687dd9 2023-08-04 jrmu              (maxi (rest alon))])]))
29 12687dd9 2023-08-04 jrmu 
30 12687dd9 2023-08-04 jrmu ;A non-empty-list-of-numbers (nelon) is
31 12687dd9 2023-08-04 jrmu ;1. (cons n empty)
32 12687dd9 2023-08-04 jrmu ;2. (cons n ne)
33 12687dd9 2023-08-04 jrmu ;where n is a number and ne is a non-empty-list-of-numbers (nelon).
34 12687dd9 2023-08-04 jrmu ;
35 12687dd9 2023-08-04 jrmu ;extrema : predicate nelon -> number
36 12687dd9 2023-08-04 jrmu ;Given predicate and a-lon, return the extreme value depending on the predicate.
37 12687dd9 2023-08-04 jrmu 
38 12687dd9 2023-08-04 jrmu ;pick-interesting : predicate list-of-numbers
39 12687dd9 2023-08-04 jrmu ;Given predicate and a-lon, pick the interesting (extreme) number.
40 12687dd9 2023-08-04 jrmu 
41 12687dd9 2023-08-04 jrmu (define (extrema predicate a-lon)
42 12687dd9 2023-08-04 jrmu   (cond
43 12687dd9 2023-08-04 jrmu     [(empty? (rest a-lon)) (first a-lon)]
44 12687dd9 2023-08-04 jrmu     [else (local ((define extrema-recursion (extrema predicate (rest a-lon)))
45 12687dd9 2023-08-04 jrmu                   (define (pick-interesting predicate a-lon)
46 12687dd9 2023-08-04 jrmu                     (cond
47 12687dd9 2023-08-04 jrmu                       [(predicate (first a-lon) extrema-recursion) (first a-lon)]
48 12687dd9 2023-08-04 jrmu                       [else extrema-recursion])))
49 12687dd9 2023-08-04 jrmu             (pick-interesting predicate a-lon))]))
50 12687dd9 2023-08-04 jrmu 
51 12687dd9 2023-08-04 jrmu ;mini1 : nelon -> number
52 12687dd9 2023-08-04 jrmu ;Given a-lon, returns the minimum value.
53 12687dd9 2023-08-04 jrmu (define (mini1 a-lon)
54 12687dd9 2023-08-04 jrmu   (extrema < a-lon))
55 12687dd9 2023-08-04 jrmu 
56 12687dd9 2023-08-04 jrmu ;maxi1 : nelon -> number
57 12687dd9 2023-08-04 jrmu ;Given a-lon, returns the maximum value.
58 12687dd9 2023-08-04 jrmu (define (maxi1 a-lon)
59 12687dd9 2023-08-04 jrmu   (extrema > a-lon))
60 12687dd9 2023-08-04 jrmu 
61 12687dd9 2023-08-04 jrmu ;(time (mini1 (list 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1)))
62 12687dd9 2023-08-04 jrmu ;(time (maxi1 (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)))
63 12687dd9 2023-08-04 jrmu 
64 12687dd9 2023-08-04 jrmu ;; sort : list-of-numbers predicate ->  list-of-numbers
65 12687dd9 2023-08-04 jrmu ;; to construct a list with all items from alon in ascending or descending order
66 12687dd9 2023-08-04 jrmu (define (sort1 alon predicate)
67 12687dd9 2023-08-04 jrmu   (local ((define (sort alon)
68 12687dd9 2023-08-04 jrmu 	    (cond
69 12687dd9 2023-08-04 jrmu 	      [(empty? alon) empty]
70 12687dd9 2023-08-04 jrmu 	      [else (insert (first alon) (sort (rest alon)))]))
71 12687dd9 2023-08-04 jrmu 	  (define (insert an alon)
72 12687dd9 2023-08-04 jrmu 	    (cond
73 12687dd9 2023-08-04 jrmu 	      [(empty? alon) (list an)]
74 12687dd9 2023-08-04 jrmu 	      [else (cond
75 12687dd9 2023-08-04 jrmu 		      [(predicate an (first alon)) (cons an alon)]
76 12687dd9 2023-08-04 jrmu 		      [else (cons (first alon) (insert an (rest alon)))])])))
77 12687dd9 2023-08-04 jrmu     (sort alon)))
78 12687dd9 2023-08-04 jrmu 
79 12687dd9 2023-08-04 jrmu ;sort-ascend : list-of-numbers
80 12687dd9 2023-08-04 jrmu ;Given a-lon, return a list-of-numbers sorted in ascending order.
81 12687dd9 2023-08-04 jrmu (define (sort-ascend alon)
82 12687dd9 2023-08-04 jrmu   (sort1 alon <))
83 12687dd9 2023-08-04 jrmu 
84 12687dd9 2023-08-04 jrmu ;sort-descend : list-of-numbers
85 12687dd9 2023-08-04 jrmu ;Given a-lon, return a list-of-numbers sorted in descending order.
86 12687dd9 2023-08-04 jrmu (define (sort-ascend alon)
87 12687dd9 2023-08-04 jrmu   (sort1 alon >))