mirror of https://gitee.com/XmacsLabs/planet.git
181 lines
3.5 KiB
Tcl
181 lines
3.5 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|generic|no-page-numbers|british|reduced-margins|s7>>
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<\body>
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<section*|Orders of Growth>
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<\session|s7|default>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(define (expt-1 b n)
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\ \ (if (= n 0)
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\ \ \ \ \ \ 1
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\ \ \ \ \ \ (* b (expt-1 b (- n 1)))))
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<|unfolded-io>
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expt-1
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(expt-1 1 0)
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<|unfolded-io>
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1
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(expt-1 2 3)
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<|unfolded-io>
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8
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(define (expt-2 b n)
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\ \ (define (expt-iter b counter product)
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\ \ \ \ (if (= counter 0)
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\ \ \ \ \ \ \ \ product
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\ \ \ \ \ \ \ \ (expt-iter b
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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (- counter 1)
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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (* b product))))
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\ \
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\ \ (expt-iter b n 1))
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<|unfolded-io>
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expt-2
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(expt-2 3 3)
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<|unfolded-io>
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27
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</unfolded-io>
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<\input>
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\<gtr\>\
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<|input>
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\;
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</input>
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</session>
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<section*|Exponentiation>
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<\session|s7|default>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(define (fast-expt b n)
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\ \ (define (even? n)
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\ \ \ \ (= (remainder n 2) 0))
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\ \ (define (square x) (* x x))
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\ \
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\ \ (cond ((= n 0) 1)
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\ \ \ \ \ \ \ \ ((even? n) (square (fast-expt b (/ n 2))))
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\ \ \ \ \ \ \ \ (else (* b (fast-expt b (- n 1))))))
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<|unfolded-io>
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fast-expt
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(fast-expt 3 3)
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<|unfolded-io>
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27
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</unfolded-io>
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<\input>
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\<gtr\>\
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<|input>
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\;
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</input>
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</session>
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<section*|Greatest Common Divisors>
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<\session|s7|default>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(define (gcd a b)
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\ \ (if (= b 0)
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\ \ \ \ \ \ a
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\ \ \ \ \ \ (gcd b (remainder a b))))
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<|unfolded-io>
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gcd
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</unfolded-io>
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<\unfolded-io>
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\<gtr\>\
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<|unfolded-io>
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(gcd 10 20)
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<|unfolded-io>
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10
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</unfolded-io>
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<\input>
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\<gtr\>\
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<|input>
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\;
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</input>
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</session>
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</body>
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<\initial>
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<\collection>
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<associate|page-screen-margin|true>
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</collection>
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</initial>
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<\references>
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<\collection>
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<associate|auto-1|<tuple|?|?>>
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<associate|auto-2|<tuple|?|?>>
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<associate|auto-3|<tuple|?|?>>
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</collection>
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</references>
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<\auxiliary>
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<\collection>
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<\associate|toc>
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<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Orders
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of Growth> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-1><vspace|0.5fn>
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<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Exponentiation>
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<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-2><vspace|0.5fn>
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<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Greatest
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Common Divisors> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-3><vspace|0.5fn>
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</associate>
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</collection>
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</auxiliary> |