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#lang scheme
;; NAME: hw04_bintree.scm
;; AUTHOR: Ben Burwell
;; DESC: CSI310 - Programming Languages - Homework 4 - Binary Tree
;; HISTORY: Created 2013-02-11
;; ========== PROCEDURE ==========
;; NAME: tree?
;; DESC: takes a parameter and returns true if it is a tree
;; and false otherwise
(define tree?
(λ (arg)
;; a tree has the following properties:
(and
;; it is a list
(list? arg)
;; it has three elements
(equal? (length arg) 3)
;; its first element is a number
(number? (car arg))
;; its second element has one of the following:
(or
;; it is an empty list...
(and (list? (cadr arg)) (equal? (length (cadr arg)) 0))
;; ...or it is a tree
(tree? (cadr arg)))
;; its third element also has one of the above conditions
(or
(and (list? (caddr arg)) (equal? (length (caddr arg)) 0))
(tree? (caddr arg)))
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (tree?) ==========================================================================")
(newline)
(display "Expected output: #t ")
(tree? '(1 () ()))
(display "Expected output: #t ")
(tree? '(5 (2 () ()) ()))
(display "Expected output: #f ")
(tree? '())
(display "Expected output: #f ")
(tree? 1)
(display "Expected output: #t ")
(tree? '( 14 (7 () (12 () ())) (26 (20 (17 () ()) ()) (31 () ()))))
;; ========== PROCEDURE ==========
;; NAME: make-tree
;; DESC: makes a tree from three parameters
(define make-tree
(λ (val lc rc)
(cond
[ (and (tree? lc) (tree? rc)) (list val lc rc) ]
[ (tree? lc) (list val lc '()) ]
[ (tree? rc) (list val '() rc) ]
[ else (list val '() '()) ]
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (make-tree) ======================================================================")
(newline)
(display "Expected output: (1 () ()) ")
(make-tree 1 '() '())
(display "Expected output: (5 (4 (3 (2 (1 () ()) ()) ()) ()) ()) ")
(make-tree 5 (make-tree 4 (make-tree 3 (make-tree 2 (make-tree 1 '() '()) '()) '()) '()) '())
;; ========== PROCEDURE ==========
;; NAME: get-value
;; DESC: returns the value of the root element of the
;; tree parameter, not-a-tree if the argument is
;; not a tree
(define get-value
(λ (tree)
(if (tree? tree)
(car tree)
'not-a-tree
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (get-value) ======================================================================")
(newline)
(display "Expected output: 1 ")
(get-value (make-tree 1 '() '()))
(display "Expected output: 5 ")
(get-value (make-tree 5 (make-tree 4 (make-tree 3 (make-tree 2 (make-tree 1 '() '()) '()) '()) '()) '()))
;; ========== PROCEDURE ==========
;; NAME: get-left
;; DESC: returns the left child of the tree parameter
;; or not-a-tree if the parameter is not a tree
(define get-left
(λ (tree)
(if (tree? tree)
(cadr tree)
'not-a-tree
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (get-left) =======================================================================")
(newline)
(display "Expected output: (1 () ()) ")
(get-left (make-tree 5 (make-tree 1 '() '()) '()))
;; ========== PROCEDURE ==========
;; NAME: get-right
;; DESC: returns the right child of the tree parameter
;; or not-a-tree if the parameter is not a tree
(define get-right
(λ (tree)
(if (tree? tree)
(caddr tree)
'not-a-tree
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (get-right) ======================================================================")
(newline)
(display "Expected output: (1 () ()) ")
(get-right (make-tree 5 '() (make-tree 1 '() '())))
;; ========== HELP FUNC ==========
;; takes a number to find in a bst as well as a path to append to
(define path-helper
(λ (n bst pth)
(cond
;; we have found the path
[ (equal? (get-value bst) n) pth ]
;; the element is not in the tree, return not-found
[ (and (not (tree? (get-left bst))) (not (tree? (get-right bst)))) 'not-found ]
;; n < value, we must go left
[ (< n (get-value bst)) (cons 'left (path-helper n (get-left bst) pth)) ]
;; n > value, we must go right
[ (> n (get-value bst)) (cons 'right (path-helper n (get-right bst) pth)) ]
)))
;; ========== PROCEDURE ==========
;; NAME: path
;; DESC: takes a number and a binary search tree in which
;; to find it and returns a list containing the
;; appropriate "left"s and "right"s to navigate from
;; the root of the tree to the element
;;
;; returns not-found if the needle is not in the
;; haystack.
(define path
(λ (n bst)
(cond
[ (not (tree? bst)) 'not-a-tree ]
[ else (path-helper n bst '()) ]
)))
;; ========== TEST CODE ==========
(newline)
(display "Testing (path) ===========================================================================")
(newline)
(display "Expected output: (right left left) ")
(path 17 '( 14 (7 () (12 () ())) (26 (20 (17 () ()) ()) (31 () ()))))
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