XmacsLabs
/
planet
mirror of https://gitee.com/XmacsLabs/planet.git
1
0
Fork 0
Code

SICP 03: 递归

This commit is contained in:
沈浪熊猫儿 2024-02-28 06:05:13 +00:00
parent dca9acc9f6
commit ac591ff030
1 changed files with 361 additions and 51 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

412
SICP/slide03.tm
View File

@ -1,6 +1,6 @@
<TeXmacs|2.1.2>
<style|<tuple|beamer|no-page-numbers|chinese>>
<style|<tuple|beamer|no-page-numbers|chinese|python>>
<\body>
<\hide-preamble>
@ -57,7 +57,359 @@
Tree Recursion
</cell>>>>
</wide-tabular>
</shown>>
</shown>|<\hidden>
<tit|\<#6761\>\<#4EF6\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#548C\>\<#8C13\>\<#8BCD\>\V\<#77ED\>\<#8DEF\>\<#8FD0\>\<#7B97\>>
<\itemize>
<item>\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>\<#FF08\>Scheme\<#4F7F\>\<#7528\>\<#7684\>\<#662F\>\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>\<#FF09\>
<item>\<#6B63\>\<#5219\>\<#5E8F\>\<#6C42\>\<#503C\>
</itemize>
<subparagraph|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#5B9E\>\<#73B0\>\<#6C42\>\<#7EDD\>\<#5BF9\>\<#503C\>\<#7684\>\<#591A\>\<#79CD\>\<#65B9\>\<#5F0F\>>
<\with|par-columns|2>
<\equation*>
<around|\||x|\|>=<around*|{|<tabular|<tformat|<cwith|1|-1|1|1|cell-halign|r>|<cwith|1|-1|2|2|cell-halign|l>|<cwith|1|-1|3|3|cell-halign|l>|<table|<row|<cell|x>|<cell|<with|mode|text|if>>|<cell|x\<gtr\>0,>>|<row|<cell|0>|<cell|<with|mode|text|if>>|<cell|x=0,>>|<row|<cell|-x>|<cell|<with|mode|text|if>>|<cell|x\<less\>0.>>>>>|\<nobracket\>>
</equation*>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define (abs1 x)
\ \ (cond ((\<gtr\> x 0) x)
\ \ \ \ \ \ \ \ ((= x 0) 0)
\ \ \ \ \ \ \ \ (else (- x))))
<|unfolded-io>
abs1
</unfolded-io>
<\unfolded-io|Scheme] >
(define (abs2 x)
\ \ (if (\<gtr\> x 0)
\ \ \ \ \ \ x
\ \ \ \ \ \ (- x)))
<|unfolded-io>
abs2
</unfolded-io>
<\unfolded-io|Scheme] >
(define (abs3 x)
\ \ (or (and (\<gtr\> x) x) (- x)))
<|unfolded-io>
abs3
</unfolded-io>
<\unfolded-io|Scheme] >
(abs1 1)
<|unfolded-io>
1
</unfolded-io>
<\unfolded-io|Scheme] >
(abs1 -1)
<|unfolded-io>
1
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
</with>
<\folded>
<\question>
\<#4E3A\>\<#4EC0\>\<#4E48\><scm|if>\<#548C\><scm|cond>\<#662F\>\<#5FC5\>\<#987B\>\<#7684\>\<#FF1F\>
</question>
<|folded>
<\exercise>
\<#4F7F\>\<#7528\><scm|if>\<#5B9E\>\<#73B0\><scm|and>\<#548C\><scm|or>\<#3002\>
</exercise>
\<#53C2\>\<#8003\>\<#6587\>\<#6863\>\<#FF1A\><slink|https://www.scheme.com/tspl2d/grammar.html>
</folded>
\;
</hidden>|<\hidden>
<tit|\<#5FAA\>\<#73AF\>\<#FF1A\>\<#6C42\>\<#548C\>>
<paragraph|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#6C42\>\<#548C\>>
<\with|par-columns|2>
<\equation*>
<big|sum><rsub|i=1><rsup|n>i=1+2+\<cdots\>+n
</equation*>
\;
<\render-code>
result := 0
<algo-for|i \<leftarrow\> 1 <render-to> n|result := result + i>
</render-code>
</with>
<hrule>
<\with|par-columns|2>
<\session|scheme|default>
<\folded-io|Scheme] >
(define result 0)
<|folded-io>
0
</folded-io>
<\input|Scheme] >
(for (x (list 1 2 3 4))
\ \ (set! result (+ result x)))
</input>
<\folded-io|Scheme] >
result
<|folded-io>
10
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
<\session|python|default>
<\input>
\<gtr\>\<gtr\>\<gtr\>\
<|input>
def sum_n(n):
\ \ \ \ result= 0
\ \ \ \ for i in range(n):
\ \ \ \ \ \ \ \ result= result + (i + 1)
\ \ \ \ return result
</input>
<\folded-io>
\<gtr\>\<gtr\>\<gtr\>\
<|folded-io>
sum_n(3)
<|folded-io>
6
</folded-io>
<\folded-io>
\<gtr\>\<gtr\>\<gtr\>\
<|folded-io>
list(range(3))
<|folded-io>
[0, 1, 2]
</folded-io>
<\input>
\<gtr\>\<gtr\>\<gtr\>\
<|input>
\;
</input>
</session>
</with>
<\exercise>
\<#4F7F\>\<#7528\>Scheme\<#5B9E\>\<#73B0\>range\<#3002\>
</exercise>
</hidden>|<\hidden>
<tit|\<#7EBF\>\<#6027\>\<#9012\>\<#5F52\>\<#FF1A\>\<#6C42\>\<#548C\>>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define (sum start end)
\ \ (cond ((\<gtr\> start end) 0)
\ \ \ \ \ \ \ \ ((= start end) end)
\ \ \ \ \ \ \ \ (else (+ start (sum (+ start 1) end)))))
\;
<|unfolded-io>
sum
</unfolded-io>
<\unfolded-io|Scheme] >
(sum 2 3)
<|unfolded-io>
5
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
<\with|par-columns|2|par-left|1fn|par-right|4fn|par-columns-sep|0fn>
<\eqnarray*>
<tformat|<table|<row|<cell|<big|sum><rsup|100><rsub|i=1>i>|<cell|=>|<cell|1+<big|sum><rsup|100><rsub|i=2>i>>|<row|<cell|>|<cell|=>|<cell|1+<around*|(|2+<big|sum><rsub|i=3><rsup|100>i|)>>>|<row|<cell|>|<cell|=>|<cell|1+<around*|(|2+<around*|(|3+<big|sum><rsub|i=4><rsup|100>i|)>|)>>>|<row|<cell|>|<cell|=>|<cell|\<ldots\>>>|<row|<cell|>|<cell|=>|<cell|<with|math-display|false|1+<around*|(|2+\<cdots\>+<around*|(|99+<big|sum><rsub|i=100><rsup|100>i|)>|)>>>>|<row|<cell|>|<cell|=>|<cell|1+<around*|(|2+<around*|(|3+\<cdots\>+<around*|(|99+100|)>|)>|)>>>|<row|<cell|>|<cell|=>|<cell|1+<around*|(|2+<around*|(|3+\<cdots\>+<around*|(|98+199|)>|)>|)>>>|<row|<cell|>|<cell|=>|<cell|\<ldots\>>>|<row|<cell|>|<cell|=>|<cell|1+5049>>|<row|<cell|>|<cell|=>|<cell|5050>>>>
</eqnarray*>
</with>
\;
</hidden>|<\hidden>
<tit|\<#6811\>\<#5F62\>\<#9012\>\<#5F52\>\<#FF1A\>\<#6590\>\<#6CE2\>\<#90A3\>\<#5951\>\<#6570\>\<#5217\>>
<\folded>
<\equation*>
<with|mode|text|Fib><around*|(|n|)>=<around*|{|<tabular|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|2|2|cell-halign|l>|<table|<row|<cell|0>|<cell|<with|mode|text|if>
n=0,>>|<row|<cell|1>|<cell|<with|mode|text|if>
n=1,>>|<row|<cell|<with|mode|text|Fib><around*|(|n-1|)>+<with|mode|text|Fib><around*|(|n-2|)>>|<cell|<with|mode|text|otherwise>.>>>>>|\<nobracket\>>
</equation*>
<|folded>
<scm|<\with|par-mode|center>
<tree|fib 5|<tree|fib 4|<tree|fib 3|<tree|fib 2|<tree|fib
1|1>|<tree|fib 0|0>>>|<tree|fib 2|<tree|fib 1|1>|<tree|fib
0|0>>>|<tree|fib 3|<tree|fib 2|<tree|fib 1|1>|<tree|fib 0|0>>>>
</with>>
</folded>
<\session|scheme|default>
<\folded-io|Scheme] >
(define (fib n)
\ \ (cond ((= n 0) 0)
\ \ \ \ \ \ \ \ ((= n 1) 1)
\ \ \ \ \ \ \ \ (else (+ (fib (- n 1)) (fib (- n 2))))))
<|folded-io>
fib
</folded-io>
<\folded-io|Scheme] >
(fib 2)
<|folded-io>
1
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
</hidden>|<\hidden>
<tit|\<#6811\>\<#5F62\>\<#9012\>\<#5F52\>\<rightarrow\>\<#8FED\>\<#4EE3\>>
<\equation*>
<with|mode|text|Fib><around*|(|n|)>=<around*|{|<tabular|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|2|2|cell-halign|l>|<table|<row|<cell|0>|<cell|<with|mode|text|if>
n=0,>>|<row|<cell|1>|<cell|<with|mode|text|if>
n=1,>>|<row|<cell|<with|mode|text|Fib><around*|(|n-1|)>+<with|mode|text|Fib><around*|(|n-2|)>>|<cell|<with|mode|text|otherwise>.>>>>>|\<nobracket\>>
</equation*>
<\equation*>
<tabular|<tformat|<table|<row|<cell|0>|<cell|1>|<cell|2>|<cell|3>|<cell|4>|<cell|5>|<cell|\<ldots\>>|<cell|n-2>|<cell|n-1>|<cell|n>>|<row|<cell|0>|<cell|1>|<cell|2>|<cell|3>|<cell|5>|<cell|8>|<cell|\<ldots\>>|<cell|f<around*|(|n-2|)>>|<cell|f<around*|(|n-1|)>>|<cell|f<around*|(|n-1|)>+f<around*|(|n-2|)>>>|<row|<cell|a<rsub|0>=0>|<cell|b<rsub|0>=1>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>>|<row|<cell|>|<cell|a<rsub|1>=1>|<cell|b<rsub|1>=2>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>>|<row|<cell|>|<cell|>|<cell|a<rsub|2>=2>|<cell|b<rsub|2>=3>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>>|<row|<cell|>|<cell|>|<cell|>|<cell|a<rsub|3>=b<rsub|2>>|<cell|b<rsub|3>=a<rsub|2>+b<rsub|2>>|<cell|>|<cell|>|<cell|>|<cell|>|<cell|>>>>>
</equation*>
<\with|par-columns|2>
<\algorithm>
<\math>
a<rsub|0>\<leftarrow\> 0
b <rsub|0>\<leftarrow\> 1
<\algo-for|i \<leftarrow\> 1 <render-to> n>
a<rsub|i> \<leftarrow\> b<rsub|i-1>
b <rsub|i>\<leftarrow\> a<rsub|i-1> + b<rsub|i-1>
</algo-for>
<render-result>b<rsub|n>
</math>
</algorithm>
<\algorithm>
a \<leftarrow\> 0
b <math|\<leftarrow\>> 1
<\algo-for|i \<leftarrow\> 1 <render-to> n>
old_b \<leftarrow\> b
b \<leftarrow\> a + b
a \<leftarrow\> old_b
</algo-for>
<render-result> b
</algorithm>
</with>
\;
</hidden>|<\hidden>
<tit|\<#5206\>\<#6CBB\>\<#6CD5\>\<#FF1A\>\<#627E\>\<#96F6\>\<#95EE\>\<#9898\>>
<\itemize>
<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E00\>\<#5143\>\<#7EB8\>\<#5E01\>
<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E94\>\<#5143\>\<#7EB8\>\<#5E01\>
<item>\<#65E0\>\<#9650\>\<#591A\>\<#5341\>\<#5143\>\<#7EB8\>\<#5E01\>
<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E94\>\<#5341\>\<#5143\>\<#7EB8\>\<#5E01\>
</itemize>
<\folded-documentation>
<\question>
\<yen\>6\<#6709\>\<#51E0\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
</question>
<|folded-documentation>
\<yen\>6=6\<times\>\<yen\>1, \<yen\>6=1\<times\>\<yen\>5+1
</folded-documentation>
<\folded-documentation>
<\question>
\<yen\>16\<#6709\>\<#51E0\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
</question>
<|folded-documentation>
\;
</folded-documentation>
<\folded-documentation>
<\question>
\<#5BF9\>\<#4E8E\>\<yen\>n\<#FF0C\>\<#4E00\>\<#5171\>\<#6709\>\<#591A\>\<#5C11\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
</question>
<|folded-documentation>
<\equation*>
f<around*|(|n,<around*|[|1,5,10,50|]>|)>=f<around*|(|n,<around*|(|1|)>|)>+f<around*|(|n,<around*|(|5|)>|)>+f<around*|(|n,<around*|(|10|)>|)>+f<around*|(|n,<around*|(|50|)>|)>+f<around*|(|n,<around*|(|1,5|)>|)>+f<around*|(|n,<around*|(|1,10|)>|)>+f<around*|(|n,<around*|(|1,50|)>|)>+f<around*|(|n,<around*|(|5,10|)>|)>+f<around*|(|n,<around*|(|5,50|)>|)>+f<around*|(|n,<around*|(|10,50|)>|)>+f<around*|(|n,<around*|(|1,5,10|)>|)>+f<around*|(|n,<around*|(|1,5,50|)>|)>+f<around*|(|n,<around*|(|5,10,50|)>|)>+f<around*|(|n,<around*|(|1,5,10,50|)>|)>
</equation*>
<\equation*>
f<around*|(|n,<around*|[|1,5,10,50|]>|)>=f<around*|(|n,<around*|[|5,10,50|]>|)>+f<around*|(|n-1,<around*|[|1,5,10,50|]>|)>
</equation*>
</folded-documentation>
</hidden>|<\hidden>
<tit|\<#603B\>\<#7ED3\>>
<\itemize>
<item>\<#56DE\>\<#987E\>\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>\<#548C\>\<#6B63\>\<#5219\>\<#5E8F\>\<#6C42\>\<#503C\>
<item>\<#6DF1\>\<#5165\>\<#7406\>\<#89E3\><scm|if>\<#548C\><scm|cond>
<item>\<#7F16\>\<#7A0B\>\<#4E2D\>\<#6700\>\<#57FA\>\<#7840\>\<#7684\>\<#6982\>\<#5FF5\>\<#4E4B\>\<#4E00\>\<#FF1A\>\<#5FAA\>\<#73AF\>
<item>\<#4F7F\>\<#7528\>\<#9012\>\<#5F52\>\<#5B9E\>\<#73B0\>\<#5FAA\>\<#73AF\>\<#FF0C\>\<#57FA\>\<#4E8E\>\<#5FAA\>\<#73AF\>\<#7406\>\<#89E3\>\<#9012\>\<#5F52\>
<item>\<#5B9E\>\<#6218\>\<#FF1A\>\<#7EBF\>\<#6027\>\<#9012\>\<#5F52\>\<#548C\>\<#6811\>\<#5F62\>\<#9012\>\<#5F52\>
<item>\<#6280\>\<#5DE7\>\<#FF1A\>\<#5C06\>\<#9012\>\<#5F52\>\<#5B9E\>\<#73B0\>\<#6539\>\<#4E3A\>\<#8FED\>\<#4EE3\>\<#5B9E\>\<#73B0\>
<item>\<#62BD\>\<#8C61\>\<#FF1A\>\<#5229\>\<#7528\>\<#9012\>\<#5F52\>\<#89E3\>\<#51B3\>\<#73B0\>\<#5B9E\>\<#4E2D\>\<#7684\>\<#627E\>\<#96F6\>\<#95EE\>\<#9898\>
</itemize>
</hidden>>
</body>
<\initial>
@ -66,70 +418,28 @@
<associate|marked-color|pastel yellow>
<associate|page-medium|beamer>
<associate|page-screen-margin|false>
<associate|par-columns|1>
<associate|preamble|false>
</collection>
</initial>
<\references>
<\collection>
<associate|auto-1|<tuple|?|?|slide01.tm>>
<associate|auto-10|<tuple|2|?|slide01.tm>>
<associate|auto-11|<tuple|1|?|slide01.tm>>
<associate|auto-12|<tuple|applicative order evaluation|?|slide01.tm>>
<associate|auto-13|<tuple|2|?|slide01.tm>>
<associate|auto-14|<tuple|normal order evaluation|?|slide01.tm>>
<associate|auto-15|<tuple|2|?|slide01.tm>>
<associate|auto-2|<tuple|normal order evaluation|?|slide01.tm>>
<associate|auto-3|<tuple|2|?|slide01.tm>>
<associate|auto-4|<tuple|2|?|slide01.tm>>
<associate|auto-5|<tuple|normal order evaluation|?|slide01.tm>>
<associate|auto-6|<tuple|2|?|slide01.tm>>
<associate|auto-7|<tuple|2|?|slide01.tm>>
<associate|auto-8|<tuple|2|?|slide01.tm>>
<associate|auto-9|<tuple|normal order evaluation|?|slide01.tm>>
<associate|auto-1|<tuple|1|?>>
<associate|auto-2|<tuple|1|?>>
</collection>
</references>
<\auxiliary>
<\collection>
<\associate|figure>
<tuple|normal|<surround|<hidden-binding|<tuple>|1>||\<#64CD\>\<#4F5C\>\<#7B26\>\<#548C\>\<#64CD\>\<#4F5C\>\<#6570\>>|<pageref|auto-7>>
<tuple|normal|<surround|<hidden-binding|<tuple>|2>||\<#4E00\>\<#4E2A\>\<#5177\>\<#4F53\>\<#7684\>\<#4F8B\>\<#5B50\>>|<pageref|auto-8>>
</associate>
<\associate|gly>
<tuple|normal|primitive|\<#539F\>\<#8BED\>|<pageref|auto-1>>
<tuple|normal|expression|\<#8868\>\<#8FBE\>\<#5F0F\>|<pageref|auto-2>>
<tuple|normal|procedure|\<#51FD\>\<#6570\>|<pageref|auto-3>>
<tuple|normal|combination|\<#7EC4\>\<#5408\>|<pageref|auto-4>>
<tuple|normal|abstraction|\<#62BD\>\<#8C61\>|<pageref|auto-5>>
<tuple|normal|combinations|\<#7EC4\>\<#5408\>\<#5F0F\>|<pageref|auto-6>>
<tuple|normal|compound procedure|\<#590D\>\<#5408\>\<#51FD\>\<#6570\>|<pageref|auto-9>>
<tuple|normal|substitution model|\<#4EE3\>\<#6362\>\<#6A21\>\<#578B\>|<pageref|auto-10>>
<tuple|normal|applicative order evaluation|\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>|<pageref|auto-12>>
<tuple|normal|normal order evaluation|\<#6B63\>\<#5219\>\<#5E8F\>\<#6C42\>\<#503C\>|<pageref|auto-14>>
</associate>
<\associate|toc>
<with|par-left|<quote|3tab>|\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>
<with|par-left|<quote|4tab>|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#5B9E\>\<#73B0\>\<#6C42\>\<#7EDD\>\<#5BF9\>\<#503C\>\<#7684\>\<#591A\>\<#79CD\>\<#65B9\>\<#5F0F\>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-11>>
<no-break><pageref|auto-1>>
<with|par-left|<quote|3tab>|\<#6B63\>\<#5219\>\<#5E8F\>\<#6C42\>\<#503C\>
<with|par-left|<quote|3tab>|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#6C42\>\<#548C\>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-13>>
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|\<#672F\>\<#8BED\>\<#8868\>>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-15><vspace|0.5fn>
<no-break><pageref|auto-2>>
</associate>
</collection>
</auxiliary>