42 lines
1.5 KiB
Racket
42 lines
1.5 KiB
Racket
#reader(lib "htdp-intermediate-reader.ss" "lang")((modname main) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))
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; A MaybeTree is one of
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; - (make-tree [Number MaybeTree MaybeTree])
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(define-struct tree [n left right])
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; - 'end
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(define sprout (make-tree 0 'end 'end))
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(define seedling (make-tree 5 sprout (make-tree 6 'end 'end)))
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(define sapling (make-tree 10 (make-tree 6 sprout 'end) (make-tree 12 'end 'end)))
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(define good-tree (make-tree 50 sapling (make-tree 100 'end 'end)))
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(define broke-tree (make-tree 5 good-tree good-tree))
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; Tree -> Bool
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; Determines whether a Tree is a binary search tree.
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(define (bst? t)
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(local [; Tree Number -> Bool
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; Recursively checks left and right.
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(define (recurse t)
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(or (and (symbol? t) (symbol=? t 'end))
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(and (acc-right (tree-right t) (tree-n t))
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(acc-left (tree-left t) (tree-n t)))))
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; Tree Number -> Bool
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; Accumulates the current number to check left.
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(define (acc-left t n)
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(or (and (symbol? t) (symbol=? t 'end))
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(and (< (tree-n t) n) (recurse t))))
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; Tree Number -> Bool
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; Accumulates the current number to check right.
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(define (acc-right t n)
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(or (and (symbol? t) (symbol=? t 'end))
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(and (> (tree-n t) n) (recurse t))))]
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(recurse t)))
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(check-expect (bst? sprout) #t)
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(check-expect (bst? sapling) #t)
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(check-expect (bst? good-tree) #t)
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(check-expect (bst? broke-tree) #f)
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