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#lang racket
;; implements convential interfaces on sets represented as binary trees
(provide
entry
left-branch
right-branch
make-entry
element-of-set?
adjoin-set
tree->list
list->tree
union-set
intersection-set)
(define (entry tree) (car tree))
(define (left-branch tree) (cadr tree))
(define (right-branch tree) (caddr tree))
(define (make-entry entry left right)
(list entry left right))
(define (element-of-set? x mset)
(cond ((null? mset) false)
((= x (entry mset)) true)
((> x (entry mset))
(element-of-set? (right-branch mset)))
((< x (entry mset))
(element-of-set? (left-branch mset)))))
(define (adjoin-set x mset)
(cond ((null? mset) (make-entry x '() '()))
((= x (entry mset)) mset)
((< x (entry mset))
(make-entry
(entry mset)
(adjoin-set x (left-branch mset))
(right-branch mset)))
((> x (entry mset))
(make-entry
(entry mset)
(left-branch mset)
(adjoin-set x (right-branch mset))))))
(define (tree->list tree)
(define (copy-to-list t result-list)
(if (null? t)
result-list
(copy-to-list (left-branch t)
(cons (entry t)
(copy-to-list (right-branch t)
result-list)))))
(copy-to-list tree '()))
(define (list->tree elements)
(car (partial-tree elements (length elements))))
(define (partial-tree elts n)
(if (= n 0)
(cons '() elts)
(let ((left-size (quotient (- n 1) 2)))
(let ((left-result (partial-tree elts left-size)))
(let ((left-tree (car left-result))
(non-left-elts (cdr left-result))
(right-size (- n (+ left-size 1))))
(let ((this-entry (car non-left-elts))
(right-result (partial-tree (cdr non-left-elts)
right-size)))
(let ((right-tree (car right-result))
(remaining-elts (cdr right-result)))
(cons (make-entry this-entry left-tree right-tree)
remaining-elts))))))))
;; 2*O(n) + O(n) + O(n)
(define (union-set s1 s2)
(define (ordered-list-union-set set1 set2)
(cond
((and (null? set1) (null? set2)) '())
((null? set1) (cons (car set2) (ordered-list-union-set set1 (cdr set2))))
((null? set2) (cons (car set1) (ordered-list-union-set (cdr set1) set2)))
((= (car set1) (car set2)) (cons (car set2) (ordered-list-union-set (cdr set1) (cdr set2))))
((> (car set1) (car set2)) (cons (car set2) (ordered-list-union-set set1 (cdr set2))))
((< (car set1) (car set2)) (cons (car set1) (ordered-list-union-set (cdr set1) set2)))))
(list->tree
(ordered-list-union-set (tree->list s1) (tree->list s2))))
;; 2*O(n) + O(n) + O(n)
(define (intersection-set set1 set2)
(define (ordered-list-intersection-set s1 s2)
(if (or (null? s1) (null? s2))
'()
(let ((x1 (car s1)) (x2 (car s2)))
(cond ((= x1 x2)
(cons x1
(ordered-list-intersection-set
(cdr s1)
(cdr s2))))
((< x1 x2)
(ordered-list-intersection-set
(cdr s1)
s2))
((> x1 x2)
(ordered-list-intersection-set
s1
(cdr s2)))))))
(list->tree
(ordered-list-intersection-set
(tree->list set1) (tree->list set2))))
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