> > <\body> <\hide-preamble> >>> <\slideshow> <\slide> \; \; \; |>>|>>||<\author-affiliation> \; \; \; \; \; \; \; >>|> <\slide> <\wide-tabular> || <\large> |<\cell> <\large> >| > |<\cell> > >| > |<\cell> > >| 实例：符号求导 |<\cell> Example: Symbolic Differentiation >| 实例：集合的表示 |<\cell> Example: Representing Sets >>> \; 回顾：通过定义一组的选择函数和构造函数，定义数据。 \; 今天，我们定义集合。 \; <\slide> <\description> <\description> 接受集合和元素作为参数，返回一个插入了元素的新集合。 接受两个集合和，返回两个集合的交集set2>。 接受两个集合和，返回两个集合的并集set2>。 <\description> 判断元素x是否在集合中。 \; <\question> 上述构造函数中是否有冗余或者缺失？ <\question> 目前只有一个选择函数，只能判断一个元素是否在集合中，那么这样的选择函数是否还能定义集合这种数据？ <\slide> <\description> <\description> 无参数，直接返回空集。> 接受集合和元素作为参数，返回一个插入了元素的新集合。 <\marked> 接受两个集合和，返回两个集合的交集set2>。 接受两个集合和，返回两个集合的并集set2>。 <\description> 判断元素x是否在集合中。 \; <\question> 在定义集合时，是否可以不定义集合的交集和并集？ <\slide> 借助列表，实现、和 <\with|par-columns|2> <\session|s7|default> <\folded-io> \\ <|folded-io> (define (empty-set) ‘()) <|folded-io> empty-set <\input> \\ <|input> (define (adjoin-set x set) \ \ (if (element-of-set? x set) \ \ \ \ \ \ set \ \ \ \ \ \ (cons x set))) <\folded-io> \\ <|folded-io> (define (element-of-set? x set) \ \ (cond ((null? set) #f) \ \ \ \ \ \ \ \ ((equal? x (car set)) #t) \ \ \ \ \ \ \ \ (else (element-of-set? x (cdr set))))) <|folded-io> element-of-set? <\folded-io> \\ <|folded-io> \; <|folded-io> adjoin-set <\folded-io> \\ <|folded-io> (empty-set) <|folded-io> () <\folded-io> \\ <|folded-io> (adjoin-set 1 (empty-set)) <|folded-io> (1) <\folded-io> \\ <|folded-io> (adjoin-set 2 (adjoin-set 1 (empty-set))) <|folded-io> (2 1) <\folded-io> \\ <|folded-io> (define 两个元素的集合 (adjoin-set 2 (adjoin-set 1 (empty-set)))) <|folded-io> (2 1) <\folded-io> \\ <|folded-io> (element-of-set? 3 两个元素的集合) <|folded-io> #f <\folded-io> \\ <|folded-io> (element-of-set? 2 两个元素的集合) <|folded-io> #t <\input> \\ <|input> \; <\slide> 先借助列表定义二叉树，熟悉二叉树的性质，再定义集合 <\with|par-columns|2> <\session|s7|default> <\folded-io> \\ <|folded-io> (define (make-tree entry left right) \ \ (list entry left right)) <|folded-io> make-tree <\folded-io> \\ <|folded-io> (define (entry tree) (car tree)) <|folded-io> entry <\folded-io> \\ <|folded-io> (define (left-branch tree) (cadr tree)) <|folded-io> left-branch <\folded-io> \\ <|folded-io> (define (right-branch tree) (caddr tree)) <|folded-io> right-branch <\session|s7|default> <\folded-io> \\ <|folded-io> (define l-t (make-tree 7 \ \ (make-tree 6 () ()) \ \ (make-tree 8 () ()))) <|folded-io> (7 (6 () ()) (8 () ())) <\folded-io> \\ <|folded-io> (define r-t (make-tree 20 \ \ (make-tree 10 () ()) \ \ (make-tree 21 () ()))) <|folded-io> (20 (10 () ()) (21 () ())) |> <\session|s7|default> <\folded-io> \\ <|folded-io> (make-tree 9 l-t r-t) <|folded-io> (7 (6 () ()) (8 () ())) <\slide> <\session|s7|default> <\unfolded-io> \\ <|unfolded-io> (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)))))) <|unfolded-io> adjoin-set <\input> \\ <|input> \; <\slide> <\session|s7|default> <\unfolded-io> \\ <|unfolded-io> (define (element-of-set? x set) \ \ (cond ((null? set) #f) \ \ \ \ \ \ \ \ ((= x (entry set)) #t) \ \ \ \ \ \ \ \ ((\ x (entry set)) \ \ \ \ \ \ \ \ \ (element-of-set? x (left-branch set))) \ \ \ \ \ \ \ \ ((\ x (entry set)) \ \ \ \ \ \ \ \ \ (element-of-set? x (right-branch set))))) <|unfolded-io> element-of-set? <\input> \\ <|input> \; <\slide> <\session|s7|default> <\folded-io> \\ <|folded-io> (empty-set) <|folded-io> () <\folded-io> \\ <|folded-io> (adjoin-set 1 (empty-set)) <|folded-io> (1 () ()) <\folded-io> \\ <|folded-io> (adjoin-set 2 (adjoin-set 1 (empty-set))) <|folded-io> (1 () (2 () ())) <\folded-io> \\ <|folded-io> (define 两个元素的集合 (adjoin-set 2 (adjoin-set 1 (empty-set)))) <|folded-io> (1 () (2 () ())) <\folded-io> \\ <|folded-io> (element-of-set? 3 两个元素的集合) <|folded-io> #f <\folded-io> \\ <|folded-io> (element-of-set? 2 两个元素的集合) <|folded-io> #t <\input> \\ <|input> \; <\slide> 墨干V1.2.7的S7 Scheme插件的隐藏功能： <\session|s7|default> <\folded-io> \\ <|folded-io> ‘(document (tree "7")) <|folded-io> <\folded-io> \\ <|folded-io> ‘(document (tree "7" "6" "8")) <|folded-io> <\folded-io> \\ <|folded-io> ‘(document (tree "9" (tree "7" "6" "8") (tree "20" "10" "21"))) <|folded-io> |> <\input> \\ <|input> \; <\exercise> 利用S7 Scheme插件的隐藏功能实现二叉树（本次课程中利用列表定义的）的可视化。 <\slide> <\itemize> 回顾：如何定义数据 集合：如何定义集合 集合：借助列表定义集合 二叉树：借助列表定义二叉树 集合：借助二叉树定义集合 二叉树：S7 Scheme中显示二叉树的隐藏功能 <\initial> <\collection>