> <\body> <\hide-preamble> >>> <\slideshow> <\slide> \<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>5\<#8BFE\>> <\wide-tabular> || \<#7F16\>\<#7A0B\>\<#7684\>\<#57FA\>\<#672C\>\<#539F\>\<#7406\> > |<\cell> Elements of Programming > >| \<#7EBF\>\<#6027\>\<#9012\>\<#5F52\>\<#548C\>\<#8FED\>\<#4EE3\> |<\cell> Linear Recursion and Iteration >| \<#6811\>\<#5F62\>\<#9012\>\<#5F52\> |<\cell> Tree Recursion >| \<#589E\>\<#957F\>\<#7684\>\<#9636\> |<\cell> Orders of Growth >| \<#6C42\>\<#5E42\> |<\cell> Exponentiation >| \<#6700\>\<#5927\>\<#516C\>\<#7EA6\>\<#6570\> |<\cell> Greatest Common Divisors >>> <\slide> \<#8BED\>\<#56DE\>\<#987E\>> <\itemize> \<#5E94\>\<#7528\>\<#4E00\>\<#4E2A\>\<#51FD\>\<#6570\>\<#7684\>\<#4EE3\>\<#6362\>\<#6A21\>\<#578B\>\<#FF1A\> <\itemize> \<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\> \<#6B63\>\<#5219\>\<#5E8F\>\<#6C42\>\<#503C\> \<#9012\>\<#5F52\>\<#7684\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\> \<#8FED\>\<#4EE3\>\<#7684\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\> \<#9012\>\<#5F52\>\<#51FD\>\<#6570\>\<#7684\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\>\<#4E0D\>\<#4E00\>\<#5B9A\>\<#662F\>\<#9012\>\<#5F52\>\<#7684\>\<#FF0C\>\<#4E5F\>\<#6709\>\<#53EF\>\<#80FD\>\<#662F\>\<#8FED\>\<#4EE3\>\<#7684\>\<#3002\> \; <\quote-env> \<#4E4E\>\<#7528\>\<#6237\>\<#9AD8\>\<#82F1\>\<#607A\>|https://www.zhihu.com/question/21056295/answer/17030255>\<#FF1A\> \<#6B63\>\<#5219\>\<#7684\>\<#82F1\>\<#8BED\>\<#539F\>\<#6587\>\<#662F\>regular\<#FF0C\>\<#53EF\>\<#4EE5\>\<#7406\>\<#89E3\>\<#4E3A\>\<#6709\>\<#89C4\>\<#5F8B\>\<#7684\>\<#FF0C\>\<#6709\>\<#89C4\>\<#5219\>\<#7684\>\<#3002\>\<#5728\>\<#82F1\>\<#8BED\>\<#91CC\>\<#9762\>\<#88AB\>\<#63CF\>\<#8FF0\>\<#4E3A\>regular\<#7684\>\<#5BF9\>\<#8C61\>\<#5176\>\<#5B9E\>\<#662F\>\<#6BD4\>\<#8F83\>\<#7B80\>\<#5355\>\<#7684\>\<#FF0C\>\<#5BB9\>\<#6613\>\<#638C\>\<#63E1\>\<#7684\>\<#5BF9\>\<#8C61\>\<#3002\>\<#6BD4\>\<#5982\>\<#8BF4\>\<#6B63\>\<#5219\>\<#8BED\>\<#8A00\>\<#53EA\>\<#6709\>\<#51E0\>\<#6761\>\<#7B80\>\<#5355\>\<#7684\>\<#5B9A\>\<#4E49\>\<#FF0C\>\<#9664\>\<#4E86\>\<#539F\>\<#5B50\>\<#FF08\>atom\<#FF09\>\<#7684\>\<#5B9A\>\<#4E49\>\<#5C31\>\<#662F\>\<#5404\>\<#79CD\>\<#8FDE\>\<#63A5\>\<#FF08\>concatenation\<#FF09\>\<#548C\>\<#6C42\>\<#5E76\>\<#FF08\>union\<#FF09\>\<#FF0C\>\<#5E76\>\<#4E14\>\<#53EF\>\<#4EE5\>\<#7B80\>\<#5355\>\<#7684\>\<#7528\>\<#786E\>\<#5B9A\>\<#72B6\>\<#6001\>\<#6709\>\<#9650\>\<#81EA\>\<#52A8\>\<#673A\>\<#8868\>\<#8FBE\>\<#FF1B\>\<#76F8\>\<#5BF9\>\<#800C\>\<#8A00\>\<#FF0C\>\<#4E0A\>\<#4E0B\>\<#6587\>\<#65E0\>\<#5173\>\<#4EE5\>\<#53CA\>\<#4E0A\>\<#4E0B\>\<#6587\>\<#76F8\>\<#5173\>\<#8BED\>\<#8A00\>\<#5C31\>\<#8981\>\<#590D\>\<#6742\>\<#7684\>\<#591A\>\<#4E86\>\<#FF0C\>\<#9700\>\<#8981\>\<#4E0B\>\<#63A8\>\<#81EA\>\<#52A8\>\<#673A\>\<#548C\>\<#7EBF\>\<#6027\>\<#6709\>\<#9650\>\<#81EA\>\<#52A8\>\<#673A\>\<#6765\>\<#8868\>\<#793A\>\<#4E86\>\<#3002\> <\slide> \<#957F\>\<#7684\>\<#9636\>\V>\<#8BB0\>\<#6CD5\>> <\definition> \<#4EE4\>n\<#662F\>\<#4E00\>\<#4E2A\>\<#53C2\>\<#6570\>\<#FF0C\>\<#4F5C\>\<#4E3A\>\<#95EE\>\<#9898\>\<#89C4\>\<#6A21\>\<#7684\>\<#4E00\>\<#79CD\>\<#5EA6\>\<#91CF\>\<#FF0C\>\<#4EE4\>>\<#662F\>\<#4E00\>\<#4E2A\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\>\<#5728\>\<#5904\>\<#7406\>\<#89C4\>\<#6A21\>\<#4E3A\>n\<#7684\>\<#95EE\>\<#9898\>\<#6240\>\<#9700\>\<#8981\>\<#7684\>\<#8D44\>\<#6E90\>\<#91CF\>\<#3002\>\<#5982\>\<#679C\>\<#5B58\>\<#5728\>\<#4E0E\>\<#65E0\>\<#5173\>\<#7684\>\<#6574\>\<#6570\>>\<#548C\>>\<#FF0C\>\<#4F7F\>\<#5F97\> <\equation*> k*f\R\k*f \<#5BF9\>\<#4EFB\>\<#4F55\>\<#8DB3\>\<#591F\>\<#5927\>\<#7684\>\<#503C\>\<#90FD\>\<#6210\>\<#7ACB\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#79F0\>>\<#5177\>\<#6709\>|)>>\<#7684\>\<#957F\>\<#9636\>>\<#3002\> <\example> \<#67D0\>\<#67D0\>\<#7B97\>\<#6CD5\>\<#7684\>\<#65F6\>\<#95F4\>\<#590D\>\<#6742\>\<#5EA6\>\<#4E3A\>|)>> <\equation*> \<#7B97\>\<#8FC7\>\<#7A0B\>\<#6240\>\<#9700\>\<#7684\>\<#6B65\>\<#9AA4\>\<#6570\>>||\<#957F\>\<#9636\>>>|>||>|>|>||)>>>|+10*n+17>||>>>> \; \; <\slide> \<#6CD5\>\<#5BFC\>\<#8BBA\>\<#5BF9\>>\<#8BB0\>\<#53F7\>\<#7684\>\<#5B9A\>\<#4E49\>> <\definition> For a given function >, we denote by |)>> <\equation*> \|)>=: \c\0,c\0,n,\n\n,0\c*g\f\c*g|}> <\definition> For a given function >, we denote the set of funtions by |)>> <\equation*> O|)>=:\c,n,\n\n,0\f\c*g|}> <\definition> For a given function , we denote the set of fuctions by |)>> <\equation*> \|)>=:\c,n,\n\n,0\c*g\f|}> <\slide> \<#8868\>\<#7684\>\<#5B9A\>\<#4E49\>> |gr-frame|>|gr-geometry||gr-grid||gr-edit-grid-aspect|||>|gr-edit-grid||gr-arrow-end|\|gr-auto-crop|true|gr-grid-old||1>|gr-edit-grid-old||1>|gr-transformation||||>|magnify|0.840896415|gr-snap|||||>>||||>>|>|>||||>>||||>>||||>>|>|>|>||||>>|>||||>>||||>>|>||||>>||||>>||||>>||||>>||||>>||||>>||>>||>>||>>||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>||magnify|0.8408964147443614|line-width|2ln||>>>> <\scm-code> (cons 1 (cons 2 (cons 3 (cons 4 ())))) <\session|scheme|default> <\unfolded-io|Scheme] > () <|unfolded-io> () <\unfolded-io|Scheme] > (list 1 2 3 4) <|unfolded-io> (1 2 3 4) <\unfolded-io|Scheme] > (cons 0 (list 1 2 3 4 5)) <|unfolded-io> (0 1 2 3 4 5) <\unfolded-io|Scheme] > (cdr (list 1 2 3 4 5)) <|unfolded-io> (2 3 4 5) <\input|Scheme] > \; <\slide> \<#94FE\>\<#8868\>\<#957F\>\<#5EA6\>\<#7684\>\<#65F6\>\<#95F4\>\<#590D\>\<#6742\>\<#5EA6\>> <\session|scheme|default> <\unfolded-io|Scheme] > (eq? () (list )) <|unfolded-io> #t <\unfolded-io|Scheme] > (define (list-length l) \ \ (if (eq? () l) \ \ \ \ \ \ 0 \ \ \ \ \ \ (+ 1 (list-length (cdr l))))) <|unfolded-io> list-length <\unfolded-io|Scheme] > (list-length (list 1 2 3 4)) <|unfolded-io> 4 <\unfolded-io|Scheme] > (define (list-min l) \ \ (if (= (list-length l) 1) \ \ \ \ \ \ (car l) \ \ \ \ \ \ (min (car l) (list-min (cdr l))))) <|unfolded-io> list-min <\input|Scheme] > \; <\equation*> \ <\equation*> O <\slide> \<#7684\>\<#65F6\>\<#95F4\>\<#590D\>\<#6742\>\<#5EA6\>> <\session|scheme|default> <\unfolded-io|Scheme] > (define (range n) \ \ (define (range-iter k n) \ \ \ \ (if (= k n) \ \ \ \ \ \ \ \ (list n) \ \ \ \ \ \ \ \ (cons k (range-iter (+ k 1) n)))) \ \ (range-iter 1 n)) <|unfolded-io> range <\unfolded-io|Scheme] > (range 3) <|unfolded-io> (1 2 3) <\input|Scheme] > (define (range n) \ \ (append (range (- n 1) (list n)))) <\slide> \<#5E42\>> <\equation*> b=b>|1>>|>|>>>> \; <\slide> \<#5927\>\<#516C\>\<#7EA6\>\<#6570\>> <\session|scheme|default> <\input> Scheme]\ <|input> (define (gcd a b) \ \ (if (= b 0) \ \ \ \ \ \ a \ \ \ \ \ \ (gcd b (remainder a b)))) \<#8FD9\>\<#4E2A\>\<#4F8B\>\<#5B50\>\<#7684\>\<#7279\>\<#70B9\>\<#5728\>\<#4E8E\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#4E0D\>\<#77E5\>\<#9053\>\<#6C42\>\<#4E24\>\<#4E2A\>\<#6570\>\<#7684\>\<#6700\>\<#5927\>\<#516C\>\<#7EA6\>\<#6570\>\<#FF0C\>\<#5230\>\<#5E95\>\<#9700\>\<#8981\>\<#51E0\>\<#4E2A\>\<#8FED\>\<#4EE3\>\<#6B65\>\<#9AA4\>\<#3002\> <\exercise> \<#7ED3\>\<#5408\>\<#4E66\>\<#672C\>\<#4E0A\>\<#7684\>\<#8BB2\>\<#89E3\>\<#FF0C\>\<#81EA\>\<#5DF1\>\<#6574\>\<#7406\>\<#4E00\>\<#4E0B\>\<#6B27\>\<#51E0\>\<#91CC\>\<#5F97\>\<#7B97\>\<#6CD5\>\<#7684\>\<#589E\>\<#957F\>\<#9636\>\<#4E3A\>>\<#7684\>\<#8BC1\>\<#660E\>\<#3002\> <\initial> <\collection>