initial commit a8.scm

a8.scm

@@ -0,0 +1,89 @@
+"problem 1."
+(define (has-duplicates? l)
+  (and (not (null? l))
+       (or (list? (member (car l) (cdr l)))
+           (has-duplicates? (cdr l)))))
+
+"problem 2."
+(define (num-zeroes l)
+  (define (loop rem acc)
+    (cond ((null? rem) acc)
+          ((list? (car rem)) (loop (cdr rem)
+                                   (+ acc (num-zeroes (car rem)))))
+          ((equal? (car rem) 0) (loop (cdr rem)
+                                      (+ acc 1)))
+          (else (loop (cdr rem)
+                      acc))))
+  (loop l 0))
+
+"problem 3. (a)"
+(define (insert item lst precedes)
+  (if (or (null? lst) (precedes item (car lst)))
+      (cons item lst)
+      (cons (car lst) (insert item (cdr lst) precedes))))
+
+(define (insert item lst precedes)
+  (define (iterate acc rem)
+    (cond ((or (null? rem) (precedes item (car rem)))
+           (append acc (list item) rem))
+          (else
+           (iterate (append acc (list (car rem))) (cdr rem)))))
+  (iterate '() lst))
+
+"problem 3. (b)"
+(define (insert-all lst precedes)
+  (define (loop rem acc)
+    (if (null? rem)
+        acc
+        (loop (cdr rem) (insert (car rem) acc precedes))))
+  (loop lst '()))
+
+"problem 4."
+(define (make-tree value left right)
+  (list value left right))
+(define (value tree)
+  (car tree))
+(define (left tree)
+  (cadr tree))
+(define (right tree)
+  (caddr tree))
+(define empty-tree?
+  null?)
+(define testtree
+  (make-tree 1
+             (make-tree 3
+                        (make-tree 7 '() '())
+                        (make-tree 9 '() '()))
+             (make-tree 5 '() '())))
+
+"problem 4. (a)"
+(define (tree-node-count t)
+  (if (empty-tree? t)
+      0
+      (+ 1
+         (tree-node-count (left t))
+         (tree-node-count (right t)))))
+
+"problem 4. (b)"
+(define (tree-node-sum t)
+  (if (empty-tree? t)
+      0
+      (+ (value t)
+         (tree-node-sum (left t))
+         (tree-node-sum (right t)))))
+
+"problem 4. (c)"
+(define (tree-height t)
+  (if (empty-tree? t)
+      -1
+      (+ 1
+         (max (tree-height (left t))
+              (tree-height (right t))))))
+
+"problem 4. (d)"
+(define (tree-map f t)
+  (if (empty-tree? t)
+      t
+      (make-tree (f (value t))
+                 (tree-map f (left t))
+                 (tree-map f (right t)))))