;;; TREES
;;; Procedures for operating on trees

;;; define a couple of trees for testing

(define tree1 (cons (list 1 2) (list 3 4)))

(define tree2 (list (list 1 2)
		    (list 3
			  (list 4 5 6))
		    (list 7 8)))

;;; procedure to count the leaves of a tree

(define (count-leaves tree)
  (cond ((null? tree) 0)
	((not (pair? tree)) 1)
	(else (+ (count-leaves (car tree))
		 (count-leaves (cdr tree))))))

;;; fringe returns a list of the leaves of the tree

(define (fringe tree)
  (cond ((null? tree) nil)
	((not (pair? tree)) (list tree))
	(else (append (fringe (car tree))
		      (fringe (cdr tree))))))

;;; sum-fringe returns the sum of the leaves of a tree

(define (sum-fringe tree)
  (cond ((null? tree) 0)
	((number? tree) tree)
	(else (+ (sum-fringe (car tree))
		 (sum-fringe (cdr tree))))))

;;; map-tree applies a procedure to each leaf of the tree

(define (map-tree tree op)
  (cond ((null? tree) nil)
	((number? tree) (op tree))
	(else (cons (map-tree (car tree) op)
		    (map-tree (cdr tree) op)))))

;;; write scale-tree using map-tree

(define (scale-tree tree factor)
  (map-tree tree (lambda (x) (* x factor))))


;;; write increment-tree using map-tree

(define (increment-tree tree)
  (map-tree tree inc))