39 lines
1.6 KiB
Scheme
39 lines
1.6 KiB
Scheme
(load "displaylib.scm")
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(title "Exercise 2.60")
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(print "
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We specified that a set would be represented as a list with no duplicates. Now suppose we allow duplicates. For instance, the set {1,2,3} could be represented as the list (2 3 2 1 3 2 2). Design procedures element-of-set?, adjoin-set, union-set, and intersection-set that operate on this representation. How does the efficiency of each compare with the corresponding procedure for the non-duplicate representation? Are there applications for which you would use this representation in preference to the non-duplicate one?
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")
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; -- given lib --
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(define (element-of-set? x set)
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(cond ((null? set) false)
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((equal? x (car set)) true)
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(else (element-of-set? x (cdr set)))))
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(define (intersection-set set1 set2)
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(cond ((or (null? set1) (null? set2)) '())
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((element-of-set? (car set1) set2)
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(cons (car set1)
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(intersection-set (cdr set1) set2)))
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(else (intersection-set (cdr set1) set2))))
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(define (adjoin-set x set) (cons x set))
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; -- START --
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(define (union-set e f) (append e f))
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(define set1 '(a b c))
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(define set2 '(a x y))
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(display "set1 = '")(display set1)(newline)
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(display "set2 = '")(display set2)(newline)
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(display "(union-set set1 set2)")(newline)
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(display (union-set set1 set2))(newline)
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(display "(intersection-set set1 set2)")(newline)
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(display (intersection-set set1 set2))(newline)
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(display "(adjoin-set 'a set1)")(newline)
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(display (adjoin-set 'a set1))(newline)
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; Worse if you have to manage a lot of duplicate values.
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; Better if you have to manage very few duplicate values (sparse set).
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