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SICP/slide03.tm
345
SICP/slide03.tm
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@ -1,13 +1,13 @@
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<TeXmacs|2.1.2>
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<TeXmacs|2.1.2>
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<style|<tuple|beamer|no-page-numbers|chinese>>
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<style|<tuple|beamer|no-page-numbers|chinese|python>>
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<\body>
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<\body>
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<\hide-preamble>
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<\hide-preamble>
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<assign|dfn|<macro|x|<strong|<arg|x>>>>
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<assign|dfn|<macro|x|<strong|<arg|x>>>>
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</hide-preamble>
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</hide-preamble>
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<screens|<\shown>
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<screens|<\hidden>
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<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>3\<#8BFE\>>
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<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>3\<#8BFE\>>
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<\wide-tabular>
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<\wide-tabular>
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@ -57,7 +57,7 @@
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Tree Recursion
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Tree Recursion
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</cell>>>>
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</cell>>>>
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</wide-tabular>
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</wide-tabular>
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</shown>|<\hidden>
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</hidden>|<\hidden>
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<tit|\<#6761\>\<#4EF6\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#548C\>\<#8C13\>\<#8BCD\>\V\<#77ED\>\<#8DEF\>\<#8FD0\>\<#7B97\>>
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<tit|\<#6761\>\<#4EF6\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#548C\>\<#8C13\>\<#8BCD\>\V\<#77ED\>\<#8DEF\>\<#8FD0\>\<#7B97\>>
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<\itemize>
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<\itemize>
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@ -137,7 +137,329 @@
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</folded>
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</folded>
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\;
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\;
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</hidden>>
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</hidden>|<\hidden>
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<tit|\<#5FAA\>\<#73AF\>\<#FF1A\>\<#6C42\>\<#548C\>>
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<paragraph|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#6C42\>\<#548C\>>
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<\with|par-columns|2>
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<\equation*>
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<big|sum><rsub|i=1><rsup|n>i=1+2+\<cdots\>+n
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</equation*>
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\;
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<\render-code>
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result := 0
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<algo-for|i \<leftarrow\> 1 <render-to> n|result := result + i>
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</render-code>
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</with>
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<hrule>
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<\with|par-columns|2>
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<\session|scheme|default>
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<\folded-io|Scheme] >
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(define result 0)
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<|folded-io>
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0
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</folded-io>
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<\input|Scheme] >
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(for (x (list 1 2 3 4))
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\ \ (set! result (+ result x)))
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</input>
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<\folded-io|Scheme] >
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result
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<|folded-io>
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10
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</folded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|python|default>
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<\input>
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\<gtr\>\<gtr\>\<gtr\>\
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<|input>
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def sum_n(n):
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\ \ \ \ result= 0
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\ \ \ \ for i in range(n):
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\ \ \ \ \ \ \ \ result= result + (i + 1)
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\ \ \ \ return result
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</input>
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<\folded-io>
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\<gtr\>\<gtr\>\<gtr\>\
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<|folded-io>
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sum_n(3)
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<|folded-io>
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6
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</folded-io>
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<\folded-io>
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\<gtr\>\<gtr\>\<gtr\>\
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<|folded-io>
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list(range(3))
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<|folded-io>
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[0, 1, 2]
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</folded-io>
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<\input>
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\<gtr\>\<gtr\>\<gtr\>\
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<|input>
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\;
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</input>
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</session>
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</with>
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<\exercise>
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\<#4F7F\>\<#7528\>Scheme\<#5B9E\>\<#73B0\>range\<#3002\>
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</exercise>
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</hidden>|<\hidden>
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<tit|\<#7EBF\>\<#6027\>\<#9012\>\<#5F52\>\<#FF1A\>\<#6C42\>\<#548C\>>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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(define (sum start end)
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\ \ (cond ((\<gtr\> start end) 0)
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\ \ \ \ \ \ \ \ ((= start end) end)
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\ \ \ \ \ \ \ \ (else (+ start (sum (+ start 1) end)))))
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\;
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<|unfolded-io>
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sum
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(sum 2 3)
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<|unfolded-io>
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5
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\with|par-columns|2|par-left|1fn|par-right|4fn|par-columns-sep|0fn>
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<\eqnarray*>
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<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>>>>
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</eqnarray*>
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</with>
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\;
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</hidden>|<\hidden>
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<tit|\<#6811\>\<#5F62\>\<#9012\>\<#5F52\>\<#FF1A\>\<#6590\>\<#6CE2\>\<#90A3\>\<#5951\>\<#6570\>\<#5217\>>
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<\folded>
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<\equation*>
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<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>
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n=0,>>|<row|<cell|1>|<cell|<with|mode|text|if>
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n=1,>>|<row|<cell|<with|mode|text|Fib><around*|(|n-1|)>+<with|mode|text|Fib><around*|(|n-2|)>>|<cell|<with|mode|text|otherwise>.>>>>>|\<nobracket\>>
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</equation*>
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<|folded>
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<scm|<\with|par-mode|center>
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<tree|fib 5|<tree|fib 4|<tree|fib 3|<tree|fib 2|<tree|fib
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1|1>|<tree|fib 0|0>>>|<tree|fib 2|<tree|fib 1|1>|<tree|fib
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0|0>>>|<tree|fib 3|<tree|fib 2|<tree|fib 1|1>|<tree|fib 0|0>>>>
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</with>>
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</folded>
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<\session|scheme|default>
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<\folded-io|Scheme] >
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(define (fib n)
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\ \ (cond ((= n 0) 0)
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\ \ \ \ \ \ \ \ ((= n 1) 1)
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\ \ \ \ \ \ \ \ (else (+ (fib (- n 1)) (fib (- n 2))))))
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<|folded-io>
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fib
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</folded-io>
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<\folded-io|Scheme] >
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(fib 2)
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<|folded-io>
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1
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</folded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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</hidden>|<\hidden>
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<tit|\<#6811\>\<#5F62\>\<#9012\>\<#5F52\>\<rightarrow\>\<#8FED\>\<#4EE3\>>
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<\equation*>
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<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>
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n=0,>>|<row|<cell|1>|<cell|<with|mode|text|if>
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n=1,>>|<row|<cell|<with|mode|text|Fib><around*|(|n-1|)>+<with|mode|text|Fib><around*|(|n-2|)>>|<cell|<with|mode|text|otherwise>.>>>>>|\<nobracket\>>
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</equation*>
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<\equation*>
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<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|>>>>>
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</equation*>
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<\with|par-columns|2>
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<\algorithm>
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<\math>
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a<rsub|0>\<leftarrow\> 0
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b <rsub|0>\<leftarrow\> 1
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<\algo-for|i \<leftarrow\> 1 <render-to> n>
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a<rsub|i> \<leftarrow\> b<rsub|i-1>
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b <rsub|i>\<leftarrow\> a<rsub|i-1> + b<rsub|i-1>
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</algo-for>
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<render-result>b<rsub|n>
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</math>
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</algorithm>
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<\algorithm>
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a \<leftarrow\> 0
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b <math|\<leftarrow\>> 1
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<\algo-for|i \<leftarrow\> 1 <render-to> n>
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old_b \<leftarrow\> b
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b \<leftarrow\> a + b
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a \<leftarrow\> old_b
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</algo-for>
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<render-result> b
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</algorithm>
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</with>
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\;
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\;
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</hidden>|<\hidden>
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<tit|\<#5206\>\<#6CBB\>\<#6CD5\>\<#FF1A\>\<#627E\>\<#96F6\>\<#95EE\>\<#9898\>>
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<\itemize>
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<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E00\>\<#5143\>\<#7EB8\>\<#5E01\>
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<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E94\>\<#5143\>\<#7EB8\>\<#5E01\>
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<item>\<#65E0\>\<#9650\>\<#591A\>\<#5341\>\<#5143\>\<#7EB8\>\<#5E01\>
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<item>\<#65E0\>\<#9650\>\<#591A\>\<#4E94\>\<#5341\>\<#5143\>\<#7EB8\>\<#5E01\>
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</itemize>
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<\folded-documentation>
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<\question>
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\<yen\>6\<#6709\>\<#51E0\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
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</question>
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<|folded-documentation>
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\<yen\>6=6\<times\>\<yen\>1, \<yen\>6=1\<times\>\<yen\>5+1
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</folded-documentation>
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<\folded-documentation>
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<\question>
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\<yen\>16\<#6709\>\<#51E0\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
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</question>
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<|folded-documentation>
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\;
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</folded-documentation>
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<\folded-documentation>
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<\question>
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||||||
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\<#5BF9\>\<#4E8E\>\<yen\>n\<#FF0C\>\<#4E00\>\<#5171\>\<#6709\>\<#591A\>\<#5C11\>\<#79CD\>\<#627E\>\<#96F6\>\<#65B9\>\<#5F0F\>\<#FF1F\>
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</question>
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<|folded-documentation>
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<\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*>
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||||||
|
|
||||||
|
<\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|]>|)>
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||||||
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</equation*>
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</folded-documentation>
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</hidden>|<\shown>
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||||||
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<tit|\<#5206\>\<#6CBB\>\<#6CD5\>\<#FF1A\>\<#627E\>\<#96F6\>\<#95EE\>\<#9898\>>
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|
|
||||||
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<\equation*>
|
||||||
|
f<around*|(|n,<around*|[|1,5,10,50|]>|)>=<choice|<tformat|<table|<row|<cell|f<around*|(|n,<around*|[|5,10,50|]>|)>+f<around*|(|n-1,<around*|[|1,5,10,50|]>|)>>|<cell|,n\<geqslant\>2>>|<row|<cell|1>|<cell|,n\<longequal\>1>>|<row|<cell|1>|<cell|,n=0>>>>>
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</equation*>
|
||||||
|
|
||||||
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<\session|scheme|default>
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||||||
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<\unfolded-io|Scheme] >
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||||||
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(define (\<#53D6\>\<#53EF\>\<#7528\>\<#6700\>\<#5C0F\>\<#9762\>\<#503C\>
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n)
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||||||
|
|
||||||
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\ \ (cond ((= n 4) 1)
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\ \ \ \ \ \ \ \ ((= n 3) 5)
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\ \ \ \ \ \ \ \ ((= n 2) 10)
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\ \ \ \ \ \ \ \ ((= n 1) 50)
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||||||
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\ \ \ \ \ \ \ \ (else 0)))
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<|unfolded-io>
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||||||
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\<#53D6\>\<#53EF\>\<#7528\>\<#6700\>\<#5C0F\>\<#9762\>\<#503C\>
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</unfolded-io>
|
||||||
|
|
||||||
|
<\unfolded-io|Scheme] >
|
||||||
|
(define (\<#627E\>\<#96F6\>\<#65B9\>\<#6CD5\>\<#6570\> n k)
|
||||||
|
|
||||||
|
\ \ (if (or (\<less\> n 2) (\<less\>= k 1))
|
||||||
|
|
||||||
|
\ \ \ \ \ \ (if (and (\<gtr\>= n (\<#53D6\>\<#53EF\>\<#7528\>\<#6700\>\<#5C0F\>\<#9762\>\<#503C\>
|
||||||
|
k)) (= (% n (\<#53D6\>\<#53EF\>\<#7528\>\<#6700\>\<#5C0F\>\<#9762\>\<#503C\>
|
||||||
|
k)) 0))
|
||||||
|
|
||||||
|
\ \ \ \ \ \ \ \ \ \ 1
|
||||||
|
|
||||||
|
\ \ \ \ \ \ \ \ \ \ 0)
|
||||||
|
|
||||||
|
\ \ \ \ \ \ (+ (\<#627E\>\<#96F6\>\<#65B9\>\<#6CD5\>\<#6570\> n (- k
|
||||||
|
1)) (\<#627E\>\<#96F6\>\<#65B9\>\<#6CD5\>\<#6570\> (- n
|
||||||
|
(\<#53D6\>\<#53EF\>\<#7528\>\<#6700\>\<#5C0F\>\<#9762\>\<#503C\> k))
|
||||||
|
k))))
|
||||||
|
<|unfolded-io>
|
||||||
|
\<#627E\>\<#96F6\>\<#65B9\>\<#6CD5\>\<#6570\>
|
||||||
|
</unfolded-io>
|
||||||
|
|
||||||
|
<\unfolded-io|Scheme] >
|
||||||
|
(\<#627E\>\<#96F6\>\<#65B9\>\<#6CD5\>\<#6570\> 50 1)
|
||||||
|
<|unfolded-io>
|
||||||
|
<errput|unbound variable % in (% n ((symbol
|
||||||
|
"å\\x8f;\\x96;å\\x8f;¯ç\\x94;¨æ\\x9c;\\x80;å°\\x8f;é\\x9d;¢å\\x80;¼")
|
||||||
|
k))>
|
||||||
|
</unfolded-io>
|
||||||
|
|
||||||
|
<\unfolded-io|Scheme] >
|
||||||
|
(/ 10 5)
|
||||||
|
<|unfolded-io>
|
||||||
|
2
|
||||||
|
</unfolded-io>
|
||||||
|
|
||||||
|
<\input|Scheme] >
|
||||||
|
\;
|
||||||
|
</input>
|
||||||
|
</session>
|
||||||
|
|
||||||
|
\;
|
||||||
|
</shown>>
|
||||||
</body>
|
</body>
|
||||||
|
|
||||||
<\initial>
|
<\initial>
|
||||||
|
|
@ -154,5 +476,20 @@
|
||||||
<\references>
|
<\references>
|
||||||
<\collection>
|
<\collection>
|
||||||
<associate|auto-1|<tuple|1|?>>
|
<associate|auto-1|<tuple|1|?>>
|
||||||
|
<associate|auto-2|<tuple|1|?>>
|
||||||
</collection>
|
</collection>
|
||||||
</references>
|
</references>
|
||||||
|
|
||||||
|
<\auxiliary>
|
||||||
|
<\collection>
|
||||||
|
<\associate|toc>
|
||||||
|
<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-1>>
|
||||||
|
|
||||||
|
<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-2>>
|
||||||
|
</associate>
|
||||||
|
</collection>
|
||||||
|
</auxiliary>
|
||||||
Loading…
Reference in New Issue