Trees exercise #1.

trees/main.rkt

@@ -0,0 +1,41 @@
+#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 -> Bool
+; Determines whether a Tree is a binary search tree.
+(define (bst? t)
+  (local [; Tree Number -> 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 Number -> 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 Number -> 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)
+