2-64.scm

#lang sicp

(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))))))))

(list->tree '(1 3 5 7 9 11))

;a)
;Takes a list then gets median element of list and create a node with an entry as this median element,
;left branch is partial-tree called recursively but with half length, and because of the length
;it will also return right part (all the remaining elements) untouched as a cdr
;which will be used to create the right branch

;b)
;First from the fact that list->tree uses length it cannot be better than O(n),
;lets check partial-tree implementation
;the fact that it splits array in 2 parts recursively makes it O(logn),
;but it also goes through each and every element of list and set them as tree entry,
;hence it's O(n) too, and the whole algorithm is O(n)