diff --git a/trees/main.rkt~ b/trees/main.rkt~ new file mode 100644 index 0000000..0dccaa1 --- /dev/null +++ b/trees/main.rkt~ @@ -0,0 +1,74 @@ +#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))) + +#| +; A MaybeTree is one of +; - (make-tree [Number MaybeTree MaybeTree]) +(define-struct tree [n left right]) +; - 'end + +(define sprout (make-tree 0 'end 'end)) +(define seedling (make-tree 5 sprout (make-tree 6 'end 'end))) +(define sapling (make-tree 10 + (make-tree 6 sprout 'end) + (make-tree 12 'end 'end))) +(define good-tree (make-tree 50 sapling (make-tree 100 'end 'end))) +(define broke-tree (make-tree 5 good-tree good-tree)) + +; Tree t -> Bool +; Determines whether a Tree is a binary search tree. +(define (bst? t) + (local [; Tree t -> Bool + ; Recursively checks left and right. + (define (recurse t) + (or (and (symbol? t) (symbol=? t 'end)) + (and (acc-right (tree-right t) (tree-n t)) + (acc-left (tree-left t) (tree-n t))))) + + ; Tree t, Number n -> Bool + ; Accumulates the current number to check left. + (define (acc-left t n) + (or (and (symbol? t) (symbol=? t 'end)) + (and (< (tree-n t) n) (recurse t)))) + + ; Tree t, Number n -> Bool + ; Accumulates the current number to check right. + (define (acc-right t n) + (or (and (symbol? t) (symbol=? t 'end)) + (and (> (tree-n t) n) (recurse t))))] + (recurse t))) + +(check-expect (bst? sprout) #t) +(check-expect (bst? sapling) #t) +(check-expect (bst? good-tree) #t) +(check-expect (bst? broke-tree) #f) +|# + +; A Trie is a [Node] + +; A Node is a +; (make-node [String c Boolean e [Node] l]) +; and represents a prefix tree. 'c' represents the node character, 'e' is a +; flag for if the node marks the end of a word in the tree, and 'l' is the list +; of child nodes. +(define-struct node [c e l]) + +(define example-trie + '((make-node "a" #t + ((make-node "n" #t ((make-node "d" #t ()) (make-node "t" #t ()))))) + (make-node "b" #f + ((make-node "e" #t ((make-node "e" #t ()) + (make-node "t" #t ((make-node "t" #f ((make-node "e" #f ((make-node "r" #t ()))))))))))) + (make-node "c" #f ((make-node "a" #f ((make-node "t" #t ()))))))) + +; String w, Trie t -> Boolean +; Determines whether the given word is in the given Trie. +(define (in-trie? w t) + (local [; [String]) + +(check-expect (in-trie? "cat" example-trie) #t) +(check-expect (in-trie? "ca" example-trie) #f) +(check-expect (in-trie? "catch" example-trie) #f) +(check-expect (in-trie? "better" example-trie) #t) +(check-expect (in-trie? "bee" example-trie) #t) +(check-expect (in-trie? "beee" example-trie) #f) +