# sicp-ex-2.65

``` (define (union-set tree1 tree2)
(list->tree (union-set-list (tree->list tree1)
(tree->list tree2))))

(define (intersection-set tree1 tree2)
(list->tree (intersection-set-list (tree->list tree1)
(tree->list tree2))))
```

tig

leafac's algorithm for union-set does not work properly. If, for instance, the entry of one tree is bigger than the other, it won't compare the right branch of the tree with the bigger entry with the tree with the smaller entry. Try this:

``` (union-set (list->tree '(1 2 3 5 7 9 46))
(list->tree '(5 6 10 11 20 23 46)))

;; => (11 (6 (5 (2 (1 () ()) (3 () ())) (9 (7 () ()) (46 () ()))) (10 () ())) (23 (20 () ()) (46 () ())))
```

46 shows up twice.

leafac

If you want to avoid the conversions back and forth from representations, you can choose to don't use the results of exercises 2.63 and 2.64:

``` (define (union-set a b)
(cond ((null? a) b)
((null? b) a)
(else
(let ((a-entry (entry a))
(a-left-branch (left-branch a))
(a-right-branch (right-branch a))
(b-entry (entry b))
(b-left-branch (left-branch b))
(b-right-branch (right-branch b)))
(cond ((= a-entry b-entry)
(make-tree a-entry
(union-set a-left-branch b-left-branch)
(union-set a-right-branch b-right-branch)))
((< a-entry b-entry)
(make-tree b-entry
(union-set a b-left-branch)
b-right-branch))
((> a-entry b-entry)
(make-tree a-entry
(union-set a-left-branch b)
a-right-branch)))))))

(union-set (list->tree '(1 3 5))
(list->tree '(2 3 4)))
;; => (3 (2 (1 () ()) ()) (5 (4 () ()) ()))

;warning this algo has wrong output
;; check input as bst1 bst2 as:
; (define bst1 (list->tree '(1 2 3 4 5 6 7)))
; (define bst2 (list->tree '(6 7 8 9)))
(define (intersection-set a b)
(cond ((null? a) ())
((null? b) ())
(else
(let ((a-entry (entry a))
(a-left-branch (left-branch a))
(a-right-branch (right-branch a))
(b-entry (entry b))
(b-left-branch (left-branch b))
(b-right-branch (right-branch b)))
(cond ((= a-entry b-entry)
(make-tree a-entry
(intersection-set a-left-branch b-left-branch)
(intersection-set a-right-branch b-right-branch)))
((< a-entry b-entry)
(union-set
(intersection-set a-right-branch
(make-tree b-entry () b-right-branch))
(intersection-set (make-tree a-entry a-left-branch ())
b-left-branch)))
((> a-entry b-entry)
(union-set
(intersection-set (make-tree a-entry () a-right-branch)
b-right-branch)
(intersection-set a-left-branch
(make-tree b-entry b-left-branch ())))))))))

(intersection-set (list->tree '(3 5 10))
(list->tree '(1 2 3 4 5 7)))
;; => (5 (3 () ()) ())

```

anohter solution

```
(define (addjoin x set)
(cond ((null? set) (make-tree x '() '()))
((= x (entry set)) set)
((< x (entry set)) (make-tree (entry set) (addjoin x (left-branch set)) (right-branch set)))
((> x (entry set)) (make-tree (entry set) (left-branch set) (addjoin x (right-branch set))))))
(define (element-of? x set)
(cond ((null? set) false)
((= x (entry set)) true)
((< x (entry set)) (element-of? x (left-branch set)))
((> x (entry set)) (element-of? x (right-branch set)))))
(define (union-set set1 set2)
(cond ((null? set1) set2)
(else
(let ((result-entry (addjoin (entry set1) set2)))
(let ((left-result (union-set (left-branch set1) result-entry)))
(union-set (right-branch set1) left-result))))))
(define (intersection-set set1 set2)
(cond ((null? set1) '())
((null? set2) '())
((element-of? (entry set1) set2)
(make-tree (entry set1)
(intersection-set (left-branch set1) set2)
(intersection-set (right-branch set1) set2)))
(else
(union-set (intersection-set (left-branch set1) set2)
(intersection-set (right-branch set1) set2)))))

;next is annother list->tree
(define (sub-lst lst a b)
(define (iter lst index a b result)
(cond ((or (null? lst) (> index b)) result)
((< index a) (iter (cdr lst) (+ index 1) a b result))
(else
(iter (cdr lst) (+ index 1) a b (append result (list (car lst)))))))
(iter lst 0 a b '()))
(define (list->tree2 lst)
(let* ((n (length lst))
(part (quotient (- n 1) 2)))
(cond ((= n 0) '())
((= n 1) (make-tree (car lst) '() '()))
(else
(let ((left-part (sub-lst lst 0 (- part 1)))
(right-part (sub-lst lst part n)))
(let ((entry (car right-part)))
(make-tree entry
(list->tree2 left-part)
(list->tree2 (cdr right-part)))))))))

```