scheme 学习:红黑树
这几天继续学习scheme，scheme中虽然有hashtable但没有类似C++中的map,于是把C版本中的红黑树移植到scheme(中间也发现了C版本中的一些问题，暂时懒得调整了^()^)
以作为后序set和表格驱动设计中表格的基础数据结构.
虽说这个红黑树在C版本中是调试好的了，但移植过来还是花费了我一天多的时间，中间出现各种小问题，苦于并不熟悉如何调试scheme程序，所以进度十分缓慢.
(注：代码中大量使用set-car!所以无法再racket中运行，当然也可以调整rbnode的表示形式，不使用list来表示各字段，只使用set!修改字段的内容以使得可以被
racket支持)
(begin (define nil-node (list 0 0 'black '() '() '())) ;红黑树节点的定义 ;节点结构如下 ;(key (val (color (parent (left (right nil)))))) (define (make-rb-node key val) (list key val 'red '() '() '()) ) (define (get-key rbnode) (car rbnode)) (define (get-val rbnode) (cadr rbnode)) (define (set-val! rbnode val) (set-car! (cdr rbnode) val)) (define (get-color rbnode) (caddr rbnode)) (define (set-color! rbnode color) (set-car! (cddr rbnode) color)) (define (get-parent rbnode) (cadddr rbnode)) (define (set-parent! rbnode parent) (if (not (equal? rbnode nil-node)) (set-car! (cdddr rbnode) parent))) (define (get-left rbnode) (car (cddddr rbnode))) (define (set-left! rbnode left) (if (not (equal? rbnode nil-node)) (set-car! (cddddr rbnode) left))) (define (get-right rbnode) (cadr (cddddr rbnode))) (define (set-right! rbnode right) (if (not (equal? rbnode nil-node)) (set-car! (cdr (cddddr rbnode)) right))) (define (color-flip rbnode) (if (and (not (null? (get-left rbnode))) (not (null? (get-right rbnode)))) (begin (set-color! rbnode 'red) (set-color! (get-left rbnode) 'black) (set-color! (get-right rbnode) 'black) #t) #f) ) ;红黑树定义 ;(root (size nil)) (define (make-rbtree comp-function) ;(let ((rbtree (list nil 0 nil))) (let ((root nil-node)(size 0)(cmp-function comp-function)) (define (rbtree-get-root) root) (define (rbtree-set-root! new-root) (set! root new-root)) (define (rbtree-get-size) size) (define (rbtree-insert key val) (define rbnode (make-rb-node key val)) (define child_link '()) (define parent nil-node) (define cmp cmp-function) (define (iter cur) (if (equal? cur nil-node) #t (begin (set! parent cur) (let ((ret (cmp key (get-key cur)))) (cond ((= 0 ret) #f) (else (if (< ret 0) (begin (set! child_link (cddddr cur)) (set! cur (get-left cur))) (begin (set! child_link (cdr (cddddr cur))) (set! cur (get-right cur)))) (iter cur)))) ))) (if (not (iter (rbtree-get-root))) #f (begin (set-left! rbnode nil-node) (set-right! rbnode nil-node) (set-parent! rbnode parent) (if (not (null? child_link)) (set-car! child_link rbnode)) (set! size (+ 1 size)) (if (= 1 size)(rbtree-set-root! rbnode)) (insert-fix-up rbnode) #t )) ) (define (rbtree-find-imp key) (define (iter node) (define cmp cmp-function) (if (equal? node nil-node)'() (let ((ret (cmp key (get-key node)))) (cond ((= 0 ret) node) ((= -1 ret) (iter (get-left node))) (else (iter (get-right node))))))) (if (= 0 size) '() (iter root)) ) (define (rbtree-find key) (define ret (rbtree-find-imp key)) (if (null? ret) ret (get-val ret)) ) (define (rbtree-remove key) (define rbnode (rbtree-find-imp key)) (if (null? rbnode)'() (rbtree-delete rbnode)) rbnode ) ;获取用于代替将被删除节点的节点 (define (get-replace-node rbnode) (cond ((and (equal? (get-left rbnode) nil-node) (equal? (get-right rbnode) nil-node))rbnode) ((not (equal? (get-right rbnode) nil-node)) (minimum (get-right rbnode))) (else (maxmum (get-left rbnode)))) ) (define (rbtree-delete rbnode) (define x (get-replace-node rbnode));用x替代rbnode的位置 (define rb-parent (get-parent rbnode));rbnode的父亲 (define x-parent (get-parent x));x的父亲 (define x-old-color (get-color x)) (define fix-node nil-node) (if (equal? nil-node (get-left x))(set! fix-node (get-right x)) (set! fix-node (get-left x))) (if (not (equal? x rbnode));如果x与rbnode不是同一个节点 (begin ;x的父亲不是rbnode,将x的孩子交给它的父亲 (if (not (equal? x-parent rbnode)) (let ((child (if (not (equal? nil-node (get-left x)))(get-left x) (get-right x)))) (set-parent! child x-parent) (if (equal? x (get-left x-parent)) (set-left! x-parent child) (set-right! x-parent child)))) (if (not (equal? nil-node rb-parent)) ;如果rb-parent不为nil让x成为rb-parent的孩子 (begin (if (equal? rbnode (get-left rb-parent))(set-left! rb-parent x) (set-right! rb-parent x)) (set-parent! x rb-parent) ) ;否则将x父亲设为nil (set-parent! x nil-node)) ;将rbnode的孩子移交给x (let ((rb-left (get-left rbnode))(rb-right (get-right rbnode))) (if (not (equal? nil-node rb-left)) (begin (set-left! x rb-left)(set-parent! rb-left x))) (if (not (equal? nil-node rb-right)) (begin (set-right! x rb-right)(set-parent! rb-right x)))) )) ;将rbnode的所有关系清除 (set-left! rbnode nil-node)(set-right! rbnode nil-node)(set-parent! rbnode nil-node) (if (equal? root rbnode) (rbtree-set-root! x)) (set! size (- size 1)) (if (and (equal? nil-node fix-node) (eq? x-old-color 'black)) (delete-fix-up fix-node)) ) (define (rotate-left rbnode) (define parent (get-parent rbnode)) (define right (get-right rbnode)) (if (not (equal? nil-node right)) (begin (set-right! rbnode (get-left right)) (set-parent! (get-left right) rbnode) (if (equal? root rbnode) (rbtree-set-root! right) (begin (if (equal? rbnode (get-left parent))(set-left! parent right) (set-right! parent right)))) (set-parent! right parent) (set-parent! rbnode right) (set-left! right rbnode) #t) #f) ) (define (rotate-right rbnode) (define parent (get-parent rbnode)) (define left (get-left rbnode)) (if (not (equal? nil-node left)) (begin (set-left! rbnode (get-right left)) (set-parent! (get-right left) rbnode) (if (equal? root rbnode) (rbtree-set-root! left) (begin (if (equal? rbnode (get-left parent))(set-left! parent left) (set-right! parent left)))) (set-parent! left parent) (set-parent! rbnode left) (set-right! left rbnode) #t) #f) ) (define (insert-fix-up rbnode) (define (iter n) (if (eq? (get-color (get-parent n)) 'black) (set-color! root 'black) (begin (let ((parent (get-parent n))(grand_parent (get-parent (get-parent n)))) (if (equal? parent (get-left grand_parent)) (begin (let ((ancle (get-right grand_parent))) (if (eq? (get-color ancle) 'red) (begin (color-flip grand_parent) (set! n grand_parent)) (begin (if (equal? n (get-right parent)) (begin (set! n parent)(rotate-left n))) (set-color! (get-parent n) 'black) (set-color! (get-parent (get-parent n)) 'red) (rotate-right (get-parent (get-parent n)))))) ) (begin (let ((ancle (get-left grand_parent))) (if (eq? (get-color ancle) 'red) (begin (color-flip grand_parent) (set! n grand_parent)) (begin (if (equal? n (get-left parent)) (begin (set! n parent)(rotate-right n))) (set-color! (get-parent n) 'black) (set-color! (get-parent (get-parent n)) 'red) (rotate-left (get-parent (get-parent n)))))) ))) (iter n)))) (iter rbnode) ) (define (delete-fix-up rbnode) (define (iter n) (if (not (and (not (equal? n root)) (not (equal? (get-color n) 'red)))) (set-color! n 'black) (begin (let ((parent (get-parent n))) (if (equal? n (get-left parent)) (begin (let ((w (get-right parent))) (if (eq? 'red (get-color w)) (begin (set-color! w 'black) (set-color! parent 'red) (rotate-left parent) (set! w (get-right parent)))) (if (and (eq? 'black (get-color (get-left w))) (eq? 'black (get-color (get-right w)))) (begin (set-color! w 'red)(set! n parent)) (begin (if (eq? (get-color (get-right w)) 'black) (begin (set-color! (get-left w) 'black) (set-color! w 'red) (rotate-right w) (set! w (get-right parent)) )) (set-color! w (get-color parent)) (set-color! parent 'black) (set-color! (get-right w) 'black) (rotate-left parent) (set! n root) )))) (begin (let ((w (get-left parent))) (if (eq? 'red (get-color w)) (begin (set-color! w 'black) (set-color! parent 'red) (rotate-right parent) (set! w (get-left parent)))) (if (and (eq? 'black (get-color (get-left w))) (eq? 'black (get-color (get-right w)))) (begin (set-color! w 'red)(set! n parent)) (begin (if (eq? (get-color (get-left w)) 'black) (begin (set-color! (get-right w) 'black) (set-color! w 'red) (rotate-left w) (set! w (get-left parent)) )) (set-color! w (get-color parent)) (set-color! parent 'black) (set-color! (get-left w) 'black) (rotate-right parent) (set! n root) )))))) (iter n)))) (iter rbnode) ) (define (minimum rbnode) (define (minimum-imp rbnode) (if (equal? (get-left rbnode) nil-node) rbnode (minimum-imp (get-left rbnode)))) (minimum-imp rbnode)) (define (maxmum rbnode) (define (maxmum-imp rbnode) (if (equal? (get-right rbnode) nil-node) rbnode (maxmum-imp (get-right rbnode)))) (maxmum-imp rbnode)) (define (successor rbnode) (define (iter parent node) (if (and (not (equal? parent nil-node)) (equal? (get-right parent) node)) (iter (get-parent parent) parent) parent)) (if (not (equal? (get-right rbnode) nil-node)) (minimum (get-right rbnode)) (iter (get-parent rbnode) rbnode))) (define (node-next rbnode) (display (get-key rbnode))(newline) (if (null? rbnode) '() (begin (let ((succ (successor rbnode))) (if (equal? succ nil-node) '() succ)) ))) (define (rbtree->array) (define (iter rbnode ret) (if (null? rbnode) ret (iter (node-next rbnode) (cons (get-val rbnode) ret))) ) (iter (minimum root) '()) ) (lambda (op . arg) (cond ((eq? op 'find) (rbtree-find (car arg))) ((eq? op 'remove) (rbtree-remove (car arg))) ((eq? op 'insert) (rbtree-insert (car arg) (cadr arg))) ((eq? op 'size) size) ((eq? op 'root) (get-key root)) ((eq? op 'tree->array-desc) (rbtree->array)) ((eq? op 'tree->array-asc) (reverse (rbtree->array))) (else "bad op"))) )) (define (default-cmp a b) (cond ((= a b) 0) ((< a b) -1) (else 1))) (define r (make-rbtree default-cmp)) (r 'insert 1 1) (r 'insert 4 4) (r 'insert 5 5) (r 'insert 11 11) (r 'insert 15 15) (r 'insert 8 8) (r 'insert 2 2) (r 'insert 3 3) (r 'insert 6 6) (r 'insert 7 7) )
