Exercise 2.32. We can represent a set as a list of distinct elements, and we can represent the set of all subsets of the set as a list of lists. For example, if the set is (1 2 3), then the set of all subsets is (() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)). Complete the following definition of a procedure that generates the set of subsets of a set and give a clear explanation of why it works:
(define (subsets s)
(if (null? s)
(list nil)
(let ((rest (subsets (cdr s))))
(append rest (map <??> rest)))))
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| (define nil '()) | |
| (define (subsets s) | |
| (if (null? s) | |
| (list nil) | |
| (let ((rest (subsets (cdr s)))) | |
| (append | |
| rest | |
| (map | |
| (lambda (x) (cons (car s) x)) | |
| rest))))) | |
| (subsets (list 1 2 3 4 5 6)) | |
| (length (subsets (list 1 2 3 4 5 6 7 8))) | |
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