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tree.scm
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tree.scm
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;; представяне: списък с три елемента (<корен> <ляво-поддърво> <дясно-поддърво>)
(define (tree? x)
(or (null? x)
(and (list? x) (= (length x) 3) (tree? (cadr x)) (tree? (caddr x)))))
(define empty-tree '())
(define (make-tree x l r) (list x l r))
(define root-tree car)
(define left-tree cadr)
(define right-tree caddr)
(define empty-tree? null?)
(define (make-leaf x) (make-tree x empty-tree empty-tree))
(define t (make-tree 1 (make-leaf 2) (make-tree 3 (make-leaf 4) (make-leaf 5))))
(define (depth-tree t)
(if (empty-tree? t) 0
(+ 1 (max (depth-tree (left-tree t)) (depth-tree (right-tree t))))))
(define (memv-tree x t)
(cond ((empty-tree? t) #f)
((eqv? x (root-tree t)) t)
(else (or (memv-tree x (left-tree t)) (memv-tree x (right-tree t))))))
(define (memv-tree x t)
(and (not (empty-tree? t))
(or (and (eqv? x (root-tree t)) t)
(memv-tree x (left-tree t))
(memv-tree x (right-tree t)))))
(define (path-tree x t)
(cond ((empty-tree? t) #f)
((eqv? x (root-tree t)) (list x))
(else (cons#f (root-tree t)
(or (path-tree x (left-tree t))
(path-tree x (right-tree t)))))))
(define (cons#f h t)
(if t (cons h t) #f))
(define (cons#f h t)
(and t (cons h t)))