2.64.rkt

#lang sicp
;; Exercise 2.64:
;; The following procedure list->tree converts an ordered list to a balanced binary tree.
;; The helper procedure partial-tree takes as arguments an integer n and list of at least
;; n elements and constructs a balanced tree containing the first n elements of the list.
;; The result returned by partial-tree is a pair (formed with cons) whose car is the constructed tree and
;; whose cdr is the list of elements not included in the tree. 

(define (entry tree) (car tree))
(define (left-branch tree) (cadr tree))
(define (right-branch tree) (caddr tree))
(define (make-tree entry left right)
  (list entry left right))

(define (list->tree elements)
  (car (partial-tree 
        elements (length elements))))

(define (partial-tree elts n)
  (if (= n 0)
      (cons '() elts)
      (let ((left-size 
             (quotient (- n 1) 2)))
        (let ((left-result 
               (partial-tree 
                elts left-size)))
          (let ((left-tree 
                 (car left-result))
                (non-left-elts 
                 (cdr left-result))
                (right-size 
                 (- n (+ left-size 1))))
            (let ((this-entry 
                   (car non-left-elts))
                  (right-result 
                   (partial-tree 
                    (cdr non-left-elts)
                    right-size)))
              (let ((right-tree 
                     (car right-result))
                    (remaining-elts 
                     (cdr right-result)))
                (cons (make-tree this-entry 
                                 left-tree 
                                 right-tree)
                      remaining-elts))))))))

;; Tests
(partial-tree '(1 3 5 7 9 11) 6)

;; Write a short paragraph explaining as clearly as you can how partial-tree works.

;; cut the elts from middle, use the middle element as an entry, and do the same thing for left and right branch

;; Draw the tree produced by list->tree for the list (1 3 5 7 9 11). 

;;       5
;;     /   \
;;    1     9
;;     \   / \
;;      3 7  11
;;

;; What is the order of growth in the number of steps required by list->tree to convert a list of n elements? 

;; O(n)