SICP 05 Draft 2

2024-03-14 00:40:08 +08:00 · 2024-03-14 00:40:08 +08:00 · d430afb0d7
parent 571d624afd
commit d430afb0d7
1 changed files with 279 additions and 89 deletions
--- a/SICP/slide05.tm
+++ b/SICP/slide05.tm
@ -7,7 +7,8 @@
    <assign|dfn|<macro|x|<strong|<arg|x>>>>
  </hide-preamble>

-  <screens|<\shown>
+  <\slideshow>
+    <\slide>
      <tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>5\<#8BFE\>>

      <\wide-tabular>
@ -19,34 +20,6 @@
          <very-large|<\sectional-normal-bold>
            Elements of Programming
          </sectional-normal-bold>>
-      </cell>>|<row|<\cell>
-        \<#8868\>\<#8FBE\>\<#5F0F\>
-      </cell>|<\cell>
-        Expressions
-      </cell>>|<row|<\cell>
-        \<#547D\>\<#540D\>\<#4E0E\>\<#73AF\>\<#5883\>
-      </cell>|<\cell>
-        Naming and the Evironment
-      </cell>>|<row|<\cell>
-        \<#7EC4\>\<#5408\>\<#5F0F\>\<#7684\>\<#6C42\>\<#503C\>
-      </cell>|<\cell>
-        Evaluating Combinations
-      </cell>>|<row|<\cell>
-        \<#590D\>\<#5408\>\<#51FD\>\<#6570\>
-      </cell>|<\cell>
-        Compound Procedures
-      </cell>>|<row|<\cell>
-        \<#51FD\>\<#6570\>\<#5E94\>\<#7528\>\<#7684\>\<#4EE3\>\<#6362\>\<#6A21\>\<#578B\>
-      </cell>|<\cell>
-        The Subsitution Model for Procedure Application
-      </cell>>|<row|<\cell>
-        \<#6761\>\<#4EF6\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#548C\>\<#8C13\>\<#8BCD\>
-      </cell>|<\cell>
-        Conditional Expressions and Predicates
-      </cell>>|<row|<\cell>
-        \;
-      </cell>|<\cell>
-        \;
        </cell>>|<row|<\cell>
          \<#7EBF\>\<#6027\>\<#9012\>\<#5F52\>\<#548C\>\<#8FED\>\<#4EE3\>
        </cell>|<\cell>
@ -69,7 +42,9 @@
          Greatest Common Divisors
        </cell>>>>
      </wide-tabular>
-  </shown>|<\hidden>
+    </slide>
+
+    <\slide>
      <tit|\<#672F\>\<#8BED\>\<#56DE\>\<#987E\>>

      <\itemize>
@ -95,28 +70,243 @@

        \<#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\>
      </quote-env>
-  </hidden>|<\hidden>
+    </slide>
+
+    <\slide>
      <tit|\<#589E\>\<#957F\>\<#7684\>\<#9636\>\V<math|\<Theta\>>\<#8BB0\>\<#6CD5\>>

      <\definition>
-      \<#4EE4\>n\<#662F\>\<#4E00\>\<#4E2A\>\<#53C2\>\<#6570\>\<#FF0C\>\<#4F5C\>\<#4E3A\>\<#95EE\>\<#9898\>\<#89C4\>\<#6A21\>\<#7684\>\<#4E00\>\<#79CD\>\<#5EA6\>\<#91CF\>\<#FF0C\>\<#4EE4\><math|R<around*|(|n|)>>\<#662F\>
+        \<#4EE4\>n\<#662F\>\<#4E00\>\<#4E2A\>\<#53C2\>\<#6570\>\<#FF0C\>\<#4F5C\>\<#4E3A\>\<#95EE\>\<#9898\>\<#89C4\>\<#6A21\>\<#7684\>\<#4E00\>\<#79CD\>\<#5EA6\>\<#91CF\>\<#FF0C\>\<#4EE4\><math|R<around*|(|n|)>>\<#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\><math|n>\<#65E0\>\<#5173\>\<#7684\>\<#6574\>\<#6570\><math|k<rsub|1>>\<#548C\><math|k<rsub|2>>\<#FF0C\>\<#4F7F\>\<#5F97\>
+
+        <\equation*>
+          k<rsub|1>*f<around*|(|n|)>\<leqslant\>R<around*|(|n|)>\<leqslant\>k<rsub|2>*f<around*|(|n|)>
+        </equation*>
+
+        \<#5BF9\>\<#4EFB\>\<#4F55\>\<#8DB3\>\<#591F\>\<#5927\>\<#7684\><math|n>\<#503C\>\<#90FD\>\<#6210\>\<#7ACB\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#79F0\><math|R<around*|(|n|)>>\<#5177\>\<#6709\><math|\<Theta\><around*|(|f<around*|(|n|)>|)>>\<#7684\><dfn|\<#589E\>\<#957F\>\<#9636\>>\<#3002\>
      </definition>
-  </hidden>|<\hidden>
-    <tit|\<#6C42\>\<#5E42\>\<#7684\>\<#65F6\>\<#7A7A\>\<#590D\>\<#6742\>\<#5EA6\>>
+
+      <\example>
+        \<#67D0\>\<#67D0\>\<#7B97\>\<#6CD5\>\<#7684\>\<#65F6\>\<#95F4\>\<#590D\>\<#6742\>\<#5EA6\>\<#4E3A\><math|\<Theta\><around*|(|n<rsup|2>|)>>
+      </example>
+
+      <\equation*>
+        <tabular*|<tformat|<table|<row|<cell|\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\>\<#6240\>\<#9700\>\<#7684\>\<#6B65\>\<#9AA4\>\<#6570\>>|<cell|>|<cell|\<#589E\>\<#957F\>\<#9636\>>>|<row|<cell|n<rsup|2>>|<cell|>|<cell|>>|<row|<cell|1000n<rsup|2>>|<cell|\<Rightarrow\>>|<cell|\<Theta\><around*|(|n<rsup|2>|)>>>|<row|<cell|3*n<rsup|2>+10*n+17>|<cell|>|<cell|>>>>>
+      </equation*>

      \;
-  </hidden>|<\hidden>
+
+      \;
+    </slide>
+
+    <\slide>
+      <tit|\<#7B97\>\<#6CD5\>\<#5BFC\>\<#8BBA\>\<#5BF9\><math|\<Theta\>>\<#8BB0\>\<#53F7\>\<#7684\>\<#5B9A\>\<#4E49\>>
+
+      <\definition>
+        For a given function <math|g<around*|(|n|)>>, we denote <samp|the set
+        of funtions> by <math|\<Theta\><around*|(|g<around*|(|n|)>|)>>
+
+        <\equation*>
+          \<Theta\><around*|(|g<around*|(|n|)>|)>=<around*|{|f<around*|(|n|)>:
+          \<exists\>c<rsub|1>\<gtr\>0,c<rsub|2>\<gtr\>0,n<rsub|0>,\<forall\>n\<geqslant\>n<rsub|0>,0\<leqslant\>c<rsub|1>*g<around*|(|n|)>\<leqslant\>f<around*|(|n|)>\<leqslant\>c<rsub|2>*g<around*|(|n|)>|}>
+        </equation*>
+      </definition>
+
+      <\definition>
+        For a given function <math|g<around*|(|n|)>>, we denote the set of
+        funtions by <math|O<around*|(|g<around*|(|n|)>|)>>
+
+        <\equation*>
+          O<around*|(|g<around*|(|n|)>|)>=<around*|{|f<around*|(|n|)>:\<exists\>c,n<rsub|0>,\<forall\>n\<gtr\>n<rsub|0>,0\<leqslant\>f<around*|(|n|)>\<leqslant\>c*g<around*|(|n|)>|}>
+        </equation*>
+      </definition>
+
+      <\definition>
+        For a given function <math|g(n)>, we denote the set of fuctions by
+        <math|\<Omega\><around*|(|g<around*|(|n|)>|)>>
+
+        <\equation*>
+          \<Omega\><around*|(|g<around*|(|n|)>|)>=<around*|{|f<around*|(|n|)>:\<exists\>c,n<rsub|0>,\<forall\>n\<geqslant\>n<rsub|0>,0\<leqslant\>c*g<around*|(|n|)>\<leqslant\>f<around*|(|n|)>|}>
+        </equation*>
+      </definition>
+    </slide>
+
+    <\slide>
+      <tit|\<#94FE\>\<#8868\>\<#7684\>\<#5B9A\>\<#4E49\>>
+
+      <with|gr-mode|<tuple|group-edit|edit-props>|gr-frame|<tuple|scale|0.707097cm|<tuple|0.420873gw|0.443453gh>>|gr-geometry|<tuple|geometry|0.986667par|0.6par|center>|gr-grid|<tuple|empty>|gr-edit-grid-aspect|<tuple|<tuple|axes|none>|<tuple|1|none>|<tuple|10|none>>|gr-edit-grid|<tuple|empty>|gr-arrow-end|\<gtr\>|gr-auto-crop|true|gr-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-edit-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-transformation|<tuple|<tuple|0.9950041652780258|0.0|-0.09983341664682815|0.0>|<tuple|0.0|1.0|0.0|0.0>|<tuple|0.09983341664682815|0.0|0.9950041652780258|0.0>|<tuple|0.0|0.0|0.0|1.0>>|magnify|0.840896415|gr-snap|<tuple|control
+      point|grid point|grid curve point|curve-grid
+      intersection>|<graphics||<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|-4|3>|<point|-4.0|2.0>|<point|-3.0|2.0>|<point|-3.0|3.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|-3|3>|<point|-2.0|3.0>|<point|-2.0|2.0>|<point|-3.0|2.0>>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|-3.50102|2.52259>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|-2.5|2.5>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|-4|1>|<point|-4.0|0.0>|<point|-3.0|0.0>|<point|-3.0|1.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|-1|3>|<point|-1.0|2.0>|<point|0.0|2.0>|<point|0.0|3.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|0|3>|<point|0.0|2.0>|<point|1.0|2.0>|<point|1.0|3.0>>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|-0.5|2.5>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|0.5|2.5>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|3.5|2.5>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|3.0|3.0>|<point|3.9999999999999987|3.0>|<point|3.9999999999999987|2.0>|<point|3.0|2.0>>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|2.5|2.5>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|1.9999999999999996|3.0>|<point|1.9999999999999996|2.0>|<point|3.0|2.0>|<point|3.0|3.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|5.999999999999999|3.0000000000000004>|<point|6.999999999999997|3.0000000000000004>|<point|6.999999999999997|2.0>|<point|5.999999999999999|2.0>>>|<with|magnify|0.8408964147443614|point-size|4ln|<point|5.499999999999999|2.5000000000000004>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|4.999999999999998|3.0000000000000004>|<point|4.999999999999998|2.0>|<point|5.999999999999999|2.0>|<point|5.999999999999999|3.0000000000000004>>>|<with|magnify|0.8408964147443614|<cline|<point|-1.0000000000000004|1.0>|<point|-1.0000000000000004|-5.551115123125784e-17>|<point|4.579669976578771e-16|-5.551115123125784e-17>|<point|4.579669976578771e-16|1.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|-1.0000000000000004|1.0>|<point|-1.0000000000000004|-5.551115123125784e-17>|<point|4.579669976578771e-16|-5.551115123125784e-17>|<point|4.579669976578771e-16|1.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|2.0|1.0>|<point|2.0|-3.885780586188048e-16>|<point|3.0|-3.885780586188048e-16>|<point|3.0|1.0>>>|<with|magnify|0.8408964147443614|<cline|<point|5.0|1.0>|<point|5.0|-8.326672684688674e-17>|<point|6.000000000000001|-8.326672684688674e-17>|<point|6.000000000000001|1.0>>>|<with|magnify|0.8408964147443614|line-width|2ln|<cline|<point|5.0|1.0>|<point|5.0|-8.326672684688674e-17>|<point|6.000000000000001|-8.326672684688674e-17>|<point|6.000000000000001|1.0>>>|<with|magnify|0.8408964147443614|<text-at|<with|font-base-size|14|1>|<point|-3.593097631961901|0.3682762270141557>>>|<with|magnify|0.8408964147443614|<text-at|<with|font-base-size|14|2>|<point|-0.6449913157577223|0.3075032520986105>>>|<with|magnify|0.8408964147443614|<text-at|<with|font-base-size|14|3>|<point|2.348511608144202|0.3075048443957941>>>|<with|magnify|0.8408964147443614|<text-at|<with|font-base-size|14|4>|<point|5.342030339128242|0.2775770710333033>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|-3.501024677268475|2.5225909878829595>|<point|-3.501024677268475|1.0225909878829582>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|-0.48894846585593915|2.561781411894845>|<point|-0.48894846585593915|1.061781411894845>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|2.495524431244153|2.5459183332822795>|<point|2.495524431244153|1.0459183332822821>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|5.5123046324007365|2.5369012998207285>|<point|5.5123046324007365|1.0369012998207283>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|-2.5203512558408128|2.51236>|<point|-1.020351255840812|2.51236>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|0.4725050759228232|2.48776>|<point|1.9725050759228244|2.48776>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|3.464129235987035|2.51236>|<point|4.964129235987034|2.51236>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|-5|2.5>|<point|-4.0|2.5>>>|<with|arrow-end|\<gtr\>|magnify|0.8408964147443614|line-width|2ln|<line|<point|7|3>|<point|6.0|2.0>>>>>
+
+      <\scm-code>
+        (cons 1 (cons 2 (cons 3 (cons 4 ()))))
+      </scm-code>
+
+      <slink|https://srfi.schemers.org/srfi-1/srfi-1.html>
+
+      <\session|scheme|default>
+        <\unfolded-io|Scheme] >
+          ()
+        <|unfolded-io>
+          ()
+        </unfolded-io>
+
+        <\unfolded-io|Scheme] >
+          (list 1 2 3 4)
+        <|unfolded-io>
+          (1 2 3 4)
+        </unfolded-io>
+
+        <\unfolded-io|Scheme] >
+          (cons 0 (list 1 2 3 4 5))
+        <|unfolded-io>
+          (0 1 2 3 4 5)
+        </unfolded-io>
+
+        <\unfolded-io|Scheme] >
+          (cdr (list 1 2 3 4 5))
+        <|unfolded-io>
+          (2 3 4 5)
+        </unfolded-io>
+
+        <\input|Scheme] >
+          \;
+        </input>
+      </session>
+    </slide>
+
+    <\slide>
+      <tit|\<#6C42\>\<#94FE\>\<#8868\>\<#957F\>\<#5EA6\>\<#7684\>\<#65F6\>\<#95F4\>\<#590D\>\<#6742\>\<#5EA6\>>
+
+      <\session|scheme|default>
+        <\unfolded-io|Scheme] >
+          (eq? () (list ))
+        <|unfolded-io>
+          #t
+        </unfolded-io>
+
+        <\unfolded-io|Scheme] >
+          (define (list-length l)
+
+          \ \ (if (eq? () l)
+
+          \ \ \ \ \ \ 0
+
+          \ \ \ \ \ \ (+ 1 (list-length (cdr l)))))
+        <|unfolded-io>
+          list-length
+        </unfolded-io>
+
+        <\unfolded-io|Scheme] >
+          (list-length (list 1 2 3 4))
+        <|unfolded-io>
+          4
+        </unfolded-io>
+
+        <\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
+        </unfolded-io>
+
+        <\input|Scheme] >
+          \;
+        </input>
+      </session>
+
+      <\equation*>
+        \<Theta\><around*|(|n|)>
+      </equation*>
+
+      <\equation*>
+        O<around*|(|c*n|)>
+      </equation*>
+    </slide>
+
+    <\slide>
+      <tit|<scm|range(n)>\<#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>
+
+        <\unfolded-io|Scheme] >
+          (range 3)
+        <|unfolded-io>
+          (1 2 3)
+        </unfolded-io>
+
+        <\input|Scheme] >
+          (define (range n)
+
+          \ \ (append (range (- n 1) (list n))))
+        </input>
+      </session>
+    </slide>
+
+    <\slide>
+      <tit|\<#6C42\>\<#5E42\>>
+
+      <\equation*>
+        b<rsup|n>=<choice|<tformat|<table|<row|<cell|b\<cdot\>b<rsup|n-1>>|<cell|,n\<gtr\>1>>|<row|<cell|b<rsup|0>>|<cell|,n=0>>>>>
+      </equation*>
+
+      \;
+    </slide>
+
+    <\slide>
      <tit|\<#6700\>\<#5927\>\<#516C\>\<#7EA6\>\<#6570\>>

-    \;
-  </hidden>>
+      <\session|scheme|default>
+        <\input>
+          Scheme]\ 
+        <|input>
+          (define (gcd a b)
+
+          \ \ (if (= b 0)
+
+          \ \ \ \ \ \ a
+
+          \ \ \ \ \ \ (gcd b (remainder a b))))
+        </input>
+      </session>
+
+      \<#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\><math|\<Theta\><around*|(|log
+        n|)>>\<#7684\>\<#8BC1\>\<#660E\>\<#3002\>
+      </exercise>
+    </slide>
+  </slideshow>
 </body>

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