Updated.
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# DrRacket.
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*.rkt~
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@@ -1,3 +0,0 @@
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;; The first three lines of this file were inserted by DrRacket. They record metadata
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;; about the language level of this file in a form that our tools can easily process.
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#reader(lib "htdp-beginner-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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+37
-31
@@ -13,30 +13,28 @@
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(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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(define deeply-broke-tree (make-tree 5 (make-tree 3 (make-tree 2 sprout sprout) 'end) (make-tree 10 (make-tree 7 'end 'end) 'end)))
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(define deeply-broke-tree
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(make-tree 10
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(make-tree 6 'end (make-tree 11 'end 'end))
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(make-tree 12 'end 'end)))
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; Tree t -> 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 t -> 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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(local [; Convenient form of greater than.
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(define (<2 a b c)
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(cond [(and (symbol? a) (symbol? c)) #t]
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[(symbol? a) (< (- b 1) b c)]
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[(symbol? c) (< a b (+ b 1))]
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[else (< a b c)]))
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; Tree t, Number n -> 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 t, Number n -> 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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; Recursively checks left & right with lower & upper bounds.
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(define (recurse t lower upper)
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(cond [(symbol? t) (symbol=? t 'end)]
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[else (and (<2 lower (tree-n t) upper)
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(recurse (tree-left t) lower (tree-n t))
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(recurse (tree-right t) (tree-n t) upper))]))]
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(recurse t 'quite-little 'very-big)))
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(check-expect (bst? sprout) #t)
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(check-expect (bst? sapling) #t)
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@@ -63,20 +61,27 @@
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; String w, Trie t -> Boolean
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; Determines whether the given word is in the given Trie.
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(define (in-trie? w t)
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(local [; [Node] l, String wsf -> Boolean
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; Basically ormap of in?h on list of nodes but no lambda so this exists.
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(define (childs? l wsf)
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(and (not (empty? l))
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(or (in?h (first l) wsf) (childs? (rest l) wsf))))
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(local [(define ln (string-length w))
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; Node n, String wsf -> Boolean
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; Helper for in?. Accumulates word so far.
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(define (in?h n wsf)
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(or (and (string=? (string-append wsf (node-c n)) w) (node-e n)) (childs? (node-l n) (string-append wsf (node-c n)))))
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; undernode?: l: [Node], i: [Index] → Bool
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; Whether it's in the node's list of nodes.
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(define (undernode? l i)
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(cond [(empty? l) #f]
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[else (or (atnode? (first l) i)
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(undernode? (rest l) i))]))
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; Node n -> Boolean
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; Determines whether word is in the node or child nodes.
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(define (in? n) (in?h n ""))] (ormap in? t)))
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; atnode?: n: Node, i: Index → Bool
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; Check if node has the character at index i in the word, and continue down if it does.
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(define (atnode? n i)
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(if (>= i ln)
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#f
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(if (string=? (node-c n) (substring w i (+ i 1)))
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(if (= (+ i 1) ln) ; If we've hit the end of the word.
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(node-e n)
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(undernode? (node-l n) (+ i 1)))
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#f)))]
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(undernode? t 0)))
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(check-expect (in-trie? "cat" example-trie) #t)
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(check-expect (in-trie? "ca" example-trie) #f)
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@@ -84,6 +89,7 @@
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(check-expect (in-trie? "better" example-trie) #t)
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(check-expect (in-trie? "bee" example-trie) #t)
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(check-expect (in-trie? "beee" example-trie) #f)
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(check-expect (in-trie? "" example-trie) #f)
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; [String] l -> Trie
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; Generates the trie for a list of strings.
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@@ -1,114 +0,0 @@
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;; The first three lines of this file were inserted by DrRacket. They record metadata
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;; about the language level of this file in a form that our tools can easily process.
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#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
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(make-tree 6 sprout 'end)
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(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 t -> 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 t -> 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 t, Number n -> 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 t, Number n -> 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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; A Trie is a [Node]
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; A Node is a
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; (make-node [String c Boolean e [Node] l])
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; and represents a prefix tree. 'c' represents the node character, 'e' is a
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; flag for if the node marks the end of a word in the tree, and 'l' is the list
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; of child nodes.
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(define-struct node [c e l])
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(define example-trie
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(list (make-node "a" #t
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(list (make-node "n" #t (list (make-node "d" #t '()) (make-node "t" #t '())))))
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(make-node "b" #f
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(list (make-node "e" #t (list (make-node "e" #t '()) (make-node "t" #t (list (make-node "t" #f (list (make-node "e" #f (list (make-node "r" #t '())))))))))))
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(make-node "c" #f (list (make-node "a" #f (list (make-node "t" #t '())))))))
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; String w, Trie t -> Boolean
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; Determines whether the given word is in the given Trie.
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(define (in-trie? w t)
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(local [; [Node] l, String wsf -> Boolean
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; Basically ormap of in?h on list of nodes but no lambda so this exists.
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(define (childs? l wsf)
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(and (not (empty? l))
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(or (in?h (first l) wsf) (childs? (rest l) wsf))))
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; Node n, String wsf -> Boolean
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; Helper for in?. Accumulates word so far.
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(define (in?h n wsf)
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(or (and (string=? (string-append wsf (node-c n)) w) (node-e n)) (childs? (node-l n) (string-append wsf (node-c n)))))
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; Node n -> Boolean
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; Determines whether word is in the node or child nodes.
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(define (in? n) (in?h n ""))] (ormap in? t)))
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(check-expect (in-trie? "cat" example-trie) #t)
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(check-expect (in-trie? "ca" example-trie) #f)
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(check-expect (in-trie? "catch" example-trie) #f)
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(check-expect (in-trie? "better" example-trie) #t)
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(check-expect (in-trie? "bee" example-trie) #t)
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(check-expect (in-trie? "beee" example-trie) #f)
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; [String] l -> Trie
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; Generates the trie for a list of strings.
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(define (strie l)
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(local [; String w, Trie t -> Trie
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; Adds word w to a Trie.
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(define (triadd w t)
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(local [; String c, String wrest, Trie t -> Trie
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; Helper function to insert a chacater (and the rest of the word) to the Trie.
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(define (insert-char c wrest t)
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(cond [(empty? t)
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(list (make-node c ; Node character.
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(string=? wrest "") ; Mark whether Node's a word end.
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(if (string=? wrest "") ; If more left in the word, recurse.
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'()
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(triadd wrest '()))))]
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[(string=? (node-c (first t)) c) ; Character matches -- return existing Trie Node + whatever added if necessary.
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(cons (make-node c
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(or (node-e (first t))
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(string=? wrest ""))
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(if (string=? wrest "")
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(node-l (first t))
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(triadd wrest (node-l (first t))))) ; Recurse.
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(rest t))]
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[else
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(cons (first t) (insert-char c wrest (rest t)))]))]
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(insert-char (substring w 0 1) (substring w 1) t)))]
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(foldl triadd '() l)))
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(check-expect (strie '("and" "bee" "cat" "an" "a" "ant" "better" "bet" "be")) example-trie)
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@@ -1,22 +0,0 @@
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;; The first three lines of this file were inserted by DrRacket. They record metadata
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;; about the language level of this file in a form that our tools can easily process.
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#reader(lib "htdp-intermediate-lambda-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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; foo: (bar: A → A) → (A → A)
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(define (foo bar)
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(local [(define (baz buzz)
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(bar (bar buzz)))] baz))
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(check-expect ((foo add1) 1) 3)
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; goodies: (good?: A → Boolean, l: [A]) → [Index]
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; Returns a list of indices considered "good."
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(define (goodies good? l)
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(local [; goodies/help: (good?: A → Boolean, l :[A], i: Int, a: [Index]) → [Index]
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(define (goodies/help l i a)
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(cond [(empty? l) (reverse a)]
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[(good? (first l)) (goodies/help (rest l) (add1 i) (cons i a))]
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[else (goodies/help (rest l) (add1 i) a)]))]
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(goodies/help l 0 '())))
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(check-expect (goodies even? '(1 2 3 4 5)) '(1 3))
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(check-expect (goodies even? '()) '())
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@@ -1,3 +0,0 @@
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;; The first three lines of this file were inserted by DrRacket. They record metadata
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;; about the language level of this file in a form that our tools can easily process.
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#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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