sicp-solutions/chapter-2/ex-2.65.scm

101 lines
No EOL
3.3 KiB
Scheme

#lang sicp
; the helper functions:
(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 (element-of-set? x set)
(cond ((null? set) false)
((= x (entry set)) true)
((< x (entry set))
(element-of-set? x (left-branch set)))
((> x (entry set))
(element-of-set? x (right-branch set)))))
(define (adjoin-set x set)
(cond ((null? set) (make-tree x '() '()))
((= x (entry set)) set)
((< x (entry set))
(make-tree (entry set)
(adjoin-set x (left-branch set))
(right-branch set)))
((> x (entry set))
(make-tree (entry set) (left-branch set)
(adjoin-set x (right-branch set))))))
(define (tree->list-2 tree)
(define (copy-to-list tree result-list)
(if (null? tree)
result-list
(copy-to-list (left-branch tree)
(cons (entry tree)
(copy-to-list
(right-branch tree)
result-list)))))
(copy-to-list tree '()))
(define tree->list tree->list-2)
(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))))))))
; the exercise itself
(define (union-olist set1 set2)
(cond ((null? set1) set2)
((null? set2) set1)
((< (car set1) (car set2)) (cons (car set1)
(union-olist (cdr set1) set2)))
((= (car set1) (car set2)) (cons (car set1)
(union-olist (cdr set1) (cdr set2))))
((> (car set1) (car set2)) (cons (car set2)
(union-olist set1 (cdr set2))))))
(define (intersection-olist set1 set2)
(if (or (null? set1) (null? set2))
'()
(let ((x1 (car set1)) (x2 (car set2)))
(cond ((= x1 x2)
(cons x1 (intersection-olist (cdr set1)
(cdr set2))))
((< x1 x2)
(intersection-olist (cdr set1) set2))
((< x2 x1)
(intersection-olist set1 (cdr set2)))))))
(define (union-set set1 set2)
(list->tree
(union-olist (tree->list set1)
(tree->list set2))))
(define (intersection-set set1 set2)
(list->tree
(intersection-olist (tree->list set1)
(tree->list set2))))