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trees.scm
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trees.scm
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(define (tree? t)
(or (null? t)
(and (list? t) (= (length t) 3) (tree? (cadr t)) (tree? (caddr t)))))
(define (leaf x) (make-tree x empty-tree empty-tree))
(define empty-tree '())
(define (make-tree root left right) (list root left right))
(define root-tree car)
(define left-tree cadr)
(define right-tree caddr)
(define empty-tree? null?)
(define t (make-tree 1 (leaf 2) (make-tree 3 (leaf 4) (leaf 5))))
(define (depth t)
(if (empty-tree? t) 0
(+ 1 (max (depth (left-tree t)) (depth (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 (cons#f h t) (and t (cons h t)))
(define (path-tree x t)
(cond ((empty-tree? t) #f)
((eqv? x (root-tree t)) (list (root-tree t)))
(else (cons#f (root-tree t)
(or (path-tree x (left-tree t))
(path-tree x (right-tree t)))))))
(define (filter p? l)
(cond ((null? l) l)
((p? (car l)) (cons (car l) (filter p? (cdr l))))
(else (filter p? (cdr l)))))
(define (search p l)
(and (not (null? l))
(or (p (car l)) (search p (cdr l)))))
(define (exists? p? l)
(not (null? (filter p? l))))