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<TMU|<tuple|1.0.1|2.1.2>>
<style|<tuple|beamer|no-page-numbers|chinese|python|s7|maxima>>
<\body>
<\hide-preamble>
<assign|dfn|<macro|x|<strong|<arg|x>>>>
</hide-preamble>
<\slideshow>
<\slide>
\;
\;
\;
<doc-data|<doc-title|零基础SICP 12：集合、列表和二叉树>|<doc-author|<author-data|<author-name|>>>|<doc-author|<author-data|<author-name|沈浪熊猫儿（Dē老师）>>>|<doc-author|<author-data|<author-name|MathAgape（ē老师）>|<\author-affiliation>
\;
\;
\;
\;
\;
\;
\;
</author-affiliation>>>|<doc-subtitle|>>
</slide>
<\slide>
<tit|零基础SICP：第12课>
<\wide-tabular>
<tformat|<cwith|2|-1|1|-1|cell-height|40px>|<cwith|2|-1|1|-1|cell-vmode|exact>|<table|<row|<\cell>
<\large>
<strong|数据抽象导引>
</large>
</cell>|<\cell>
<\large>
<strong|Introduction to Data Abstraction>
</large>
</cell>>|<row|<\cell>
<large|<strong|层次性数据和闭包性质>>
</cell>|<\cell>
<large|<strong|Hierarchical Data and the Closure Property>>
</cell>>|<row|<\cell>
<large|<strong|符号数据>>
</cell>|<\cell>
<large|<strong|Symbolic Data>>
</cell>>|<row|<\cell>
实例：符号求导
</cell>|<\cell>
Example: Symbolic Differentiation
</cell>>|<row|<\cell>
实例：集合的表示
</cell>|<\cell>
Example: Representing Sets
</cell>>>>
</wide-tabular>
\;
回顾：通过定义一组<strong|逻辑自洽>的选择函数和构造函数，定义数据。
\;
今天，我们定义集合。
\;
</slide>
<\slide>
<tit|定义集合（课本版）>
<\description>
<item*|构造函数>
<\description>
<item*|adjoin-set>接受集合和元素作为参数，返回一个插入了元素的新集合。
<item*|intersection-set>接受两个集合<math|set1>和<math|set2>，返回两个集合的交集<math|set1\<cap\>set2>。
<item*|union-set>接受两个集合<math|set1>和<math|set2>，返回两个集合的并集<math|set1\<cup\>set2>。
</description>
<item*|选择函数>
<\description>
<item*|element-of-set?>判断元素x是否在集合中。
</description>
</description>
\;
<\question>
上述构造函数中是否有冗余或者缺失？
</question>
<\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？
</question>
</slide>
<\slide>
<tit|定义集合（der老师版）>
<\description>
<item*|构造函数>
<\description>
<with|color|dark green|<item*|empty-set>无参数，直接返回空集。>
<item*|adjoin-set>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>
<item*|intersection-set>接受两个集合<math|set1>和<math|set2>，返回两个集合的交集<math|set1\<cap\>set2>。
<item*|union-set>接受两个集合<math|set1>和<math|set2>，返回两个集合的并集<math|set1\<cup\>set2>。
</marked>
</description>
<item*|选择函数>
<\description>
<item*|element-of-set?>判断元素x是否在集合中。
</description>
</description>
\;
<\question>
在定义集合时，是否可以不定义集合的交集和并集？
</question>
</slide>
<\slide>
<tit|借助列表定义集合>
借助列表，实现<scm|empty-set>、<scm|adjoin-set>和<scm|element-of-set?>
<\with|par-columns|2>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (empty-set) ‘())
<|folded-io>
empty-set
</folded-io>
<\input>
\<gtr\>\
<|input>
(define (adjoin-set x set)
\ \ (if (element-of-set? x set)
\ \ \ \ \ \ set
\ \ \ \ \ \ (cons x set)))
</input>
<\folded-io>
\<gtr\>\
<|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>
\<gtr\>\
<|folded-io>
\;
<|folded-io>
adjoin-set
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(empty-set)
<|folded-io>
()
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(adjoin-set 1 (empty-set))
<|folded-io>
(1)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(adjoin-set 2 (adjoin-set 1 (empty-set)))
<|folded-io>
(2 1)
</folded-io>
<\folded-io>
\<gtr\>\
<|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>
\<gtr\>\
<|folded-io>
(element-of-set? 3 两个元素的集合)
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(element-of-set? 2 两个元素的集合)
<|folded-io>
#t
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</with>
</slide>
<\slide>
<tit|借助树定义集合—先定义二叉树>
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>
\<gtr\>\
<|folded-io>
(define (make-tree entry left right)
\ \ (list entry left right))
<|folded-io>
make-tree
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (entry tree) (car tree))
<|folded-io>
entry
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (left-branch tree) (cadr tree))
<|folded-io>
left-branch
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (right-branch tree) (caddr tree))
<|folded-io>
right-branch
</folded-io>
</session>
<tree|7|6|8> <tree|20|10|21>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define l-t (make-tree 7
\ \ (make-tree 6 () ())
\ \ (make-tree 8 () ())))
<|folded-io>
(7 (6 () ()) (8 () ()))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define r-t (make-tree 20
\ \ (make-tree 10 () ())
\ \ (make-tree 21 () ())))
<|folded-io>
(20 (10 () ()) (21 () ()))
</folded-io>
</session>
<tree|9|<tree|7|6|8>|<tree|20|10|21>>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(make-tree 9 l-t r-t)
<|folded-io>
(7 (6 () ()) (8 () ()))
</folded-io>
</session>
</with>
</slide>
<\slide>
<tit|借助树定义集合之adjoin-set>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (adjoin-set x set)
\ \ (cond ((null? set) (make-tree x '() '()))
\ \ \ \ \ \ \ \ ((= x (entry set)) set)
\ \ \ \ \ \ \ \ ((\<less\> x (entry set))
\ \ \ \ \ \ \ \ \ (make-tree (entry set)\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (adjoin-set x (left-branch set))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (right-branch set)))
\ \ \ \ \ \ \ \ ((\<gtr\> x (entry set))
\ \ \ \ \ \ \ \ \ (make-tree (entry set)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (left-branch set)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (adjoin-set x (right-branch set))))))
<|unfolded-io>
adjoin-set
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</slide>
<\slide>
<tit|借助树定义集合之element-of-set?>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (element-of-set? x set)
\ \ (cond ((null? set) #f)
\ \ \ \ \ \ \ \ ((= x (entry set)) #t)
\ \ \ \ \ \ \ \ ((\<less\> x (entry set))
\ \ \ \ \ \ \ \ \ (element-of-set? x (left-branch set)))
\ \ \ \ \ \ \ \ ((\<gtr\> x (entry set))
\ \ \ \ \ \ \ \ \ (element-of-set? x (right-branch set)))))
<|unfolded-io>
element-of-set?
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</slide>
<\slide>
<tit|借助树定义集合之实战>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(empty-set)
<|folded-io>
()
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(adjoin-set 1 (empty-set))
<|folded-io>
(1 () ())
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(adjoin-set 2 (adjoin-set 1 (empty-set)))
<|folded-io>
(1 () (2 () ()))
</folded-io>
<\folded-io>
\<gtr\>\
<|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>
\<gtr\>\
<|folded-io>
(element-of-set? 3 两个元素的集合)
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(element-of-set? 2 两个元素的集合)
<|folded-io>
#t
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</slide>
<\slide>
<tit|番外：如何显示二叉树>
墨干V1.2.7的S7 Scheme插件的隐藏功能：
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
‘(document (tree "7"))
<|folded-io>
<tree|7>
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
‘(document (tree "7" "6" "8"))
<|folded-io>
<tree|7|6|8>
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
‘(document (tree "9" (tree "7" "6" "8") (tree "20" "10" "21")))
<|folded-io>
<tree|9|<tree|7|6|8>|<tree|20|10|21>>
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<\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。
</exercise>
</slide>
<\slide>
<tit|总结>
<\itemize>
<item>回顾：如何定义数据
<item>集合：如何定义集合
<item>集合：借助列表定义集合
<item>二叉树：借助列表定义二叉树
<item>集合：借助二叉树定义集合
<item>二叉树：S7 Scheme中显示二叉树的隐藏功能
</itemize>
</slide>
</slideshow>
</body>
<\initial>
<\collection>
<associate|info-flag|minimal>
<associate|marked-color|#faa>
<associate|page-medium|paper>
<associate|page-screen-margin|false>
<associate|par-columns|1>
<associate|preamble|false>
</collection>
</initial>
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