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    <title>DEV Community: mengqinyuan</title>
    <description>The latest articles on DEV Community by mengqinyuan (@mengqinyuan).</description>
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    <item>
      <title>My github projects</title>
      <dc:creator>mengqinyuan</dc:creator>
      <pubDate>Fri, 25 Oct 2024 07:54:56 +0000</pubDate>
      <link>https://dev.to/mengqinyuan/my-gihub-projects-56d9</link>
      <guid>https://dev.to/mengqinyuan/my-gihub-projects-56d9</guid>
      <description>&lt;p&gt;Recent I make a project on github:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://github.com/mengqinyuan/RedHorse" rel="noopener noreferrer"&gt;https://github.com/mengqinyuan/RedHorse&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;You can make some PR or give me some suggestions.&lt;/p&gt;

</description>
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    <item>
      <title>Speed up `shutil.copytree` !</title>
      <dc:creator>mengqinyuan</dc:creator>
      <pubDate>Tue, 27 Aug 2024 06:36:09 +0000</pubDate>
      <link>https://dev.to/mengqinyuan/add-multithreading-to-shutil--2lm1</link>
      <guid>https://dev.to/mengqinyuan/add-multithreading-to-shutil--2lm1</guid>
      <description>&lt;h1&gt;
  
  
  Discuss of speeding up shutil.copytree
&lt;/h1&gt;

&lt;h2&gt;
  
  
  Write here
&lt;/h2&gt;

&lt;p&gt;This is a discussion on , see: &lt;a href="https://discuss.python.org/t/speed-up-shutil-copytree/62078" rel="noopener noreferrer"&gt;https://discuss.python.org/t/speed-up-shutil-copytree/62078&lt;/a&gt;. If you have any ideas, send me please !&lt;/p&gt;

&lt;h2&gt;
  
  
  Background
&lt;/h2&gt;

&lt;p&gt;shutil is a very useful moudle in Python. You can find it in github: &lt;a href="https://github.com/python/cpython/blob/master/Lib/shutil.py" rel="noopener noreferrer"&gt;https://github.com/python/cpython/blob/master/Lib/shutil.py&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;shutil.copytree is a function that copies a folder to another folder.&lt;/p&gt;

&lt;p&gt;In this function, it calls &lt;code&gt;_copytree&lt;/code&gt; function to copy.&lt;/p&gt;

&lt;p&gt;What does &lt;code&gt;_copytree&lt;/code&gt; do ?&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Ignoring specified files/directories.&lt;/li&gt;
&lt;li&gt;Creating destination directories.&lt;/li&gt;
&lt;li&gt;Copying files or directories while handling symbolic links.&lt;/li&gt;
&lt;li&gt;Collecting and eventually raising errors encountered (e.g., permission issues).&lt;/li&gt;
&lt;li&gt;Replicating metadata of the source directory to the destination directory.&lt;/li&gt;
&lt;/ol&gt;

&lt;h2&gt;
  
  
  Problems
&lt;/h2&gt;

&lt;p&gt;&lt;code&gt;_copytree&lt;/code&gt; speed is not very fast when the numbers of files are large or the file size is large.&lt;/p&gt;

&lt;p&gt;Test here:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;shutil&lt;/span&gt;

&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;mkdir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;mkdir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;time&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;time&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;__name__&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; takes &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; seconds&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;

&lt;span class="c1"&gt;# write in 3000 files
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;write_in_5000_files&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5000&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="k"&gt;with&lt;/span&gt; &lt;span class="nf"&gt;open&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/source/&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;.txt&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;w&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Hello World&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;urandom&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;24&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;hex&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;
            &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;close&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;write_in_5000_files&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/destination&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;copy&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;The result is:&lt;/p&gt;

&lt;p&gt;write_in_5000_files takes 4.084963083267212 seconds&lt;br&gt;
copy takes 27.12768316268921 seconds&lt;/p&gt;
&lt;h2&gt;
  
  
  What I done
&lt;/h2&gt;
&lt;h3&gt;
  
  
  Multithreading
&lt;/h3&gt;

&lt;p&gt;I use multithread to speed up the copying process. And I rename the funtion &lt;code&gt;_copytree_single_threaded&lt;/code&gt; add a new function &lt;code&gt;_copytree_multithreaded&lt;/code&gt;. Here is the &lt;code&gt;copytree_multithreaded&lt;/code&gt;:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;_copytree_multithreaded&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;copy2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                            &lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;max_workers&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="sh"&gt;"""&lt;/span&gt;&lt;span class="s"&gt;Recursively copy a directory tree using multiple threads.&lt;/span&gt;&lt;span class="sh"&gt;"""&lt;/span&gt;
    &lt;span class="n"&gt;sys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;audit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;shutil.copytree&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="c1"&gt;# get the entries to copy
&lt;/span&gt;    &lt;span class="n"&gt;entries&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;scandir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

    &lt;span class="c1"&gt;# make the pool
&lt;/span&gt;    &lt;span class="k"&gt;with&lt;/span&gt; &lt;span class="nc"&gt;ThreadPoolExecutor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_workers&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;max_workers&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;executor&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# submit the tasks
&lt;/span&gt;        &lt;span class="n"&gt;futures&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
            &lt;span class="n"&gt;executor&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;submit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;_copytree_single_threaded&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                            &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                            &lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                            &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;entries&lt;/span&gt;
        &lt;span class="p"&gt;]&lt;/span&gt;

        &lt;span class="c1"&gt;# wait for the tasks
&lt;/span&gt;        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;future&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;as_completed&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;futures&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="n"&gt;future&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;result&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
            &lt;span class="k"&gt;except&lt;/span&gt; &lt;span class="nb"&gt;Exception&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Failed to copy: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
                &lt;span class="k"&gt;raise&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I add a judgement to choose use multithread or not.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt; &lt;span class="ow"&gt;or&lt;/span&gt; &lt;span class="nf"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getsize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;1024&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;1024&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# multithreaded version
&lt;/span&gt;        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;_copytree_multithreaded&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# single threaded version
&lt;/span&gt;    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;_copytree_single_threaded&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;copy_function&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;ignore_dangling_symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                                        &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Test
&lt;/h4&gt;

&lt;p&gt;I write 50000 files in the source folder. Bench Mark:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;__name__&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; costs &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;s&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Write in:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;
&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;mkdir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Test&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;mkdir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# write in 50000 files
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;write_in_file&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;50000&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
         &lt;span class="k"&gt;with&lt;/span&gt; &lt;span class="nf"&gt;open&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Test/source/&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;.txt&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;w&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
             &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
             &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;close&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Two comparing:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy1&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;shutil&lt;/span&gt;
    &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/destination1&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy2&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;my_shutil&lt;/span&gt;
    &lt;span class="n"&gt;my_shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;test/destination2&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;"my_shutil" is my modified version of shutil.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;copy1 costs 173.04780609999943s&lt;br&gt;
copy2 costs 155.81321870000102s&lt;/p&gt;

&lt;p&gt;&lt;code&gt;copy2&lt;/code&gt; is faster than &lt;code&gt;copy1&lt;/code&gt; a lot. You can run many times.&lt;/p&gt;
&lt;h4&gt;
  
  
  Advantages &amp;amp; Disadvantages
&lt;/h4&gt;

&lt;p&gt;Use multithread can speed up the copying process. But it will increase the memory usage. But we do not need to rewrite the multithread in the code.&lt;/p&gt;
&lt;h3&gt;
  
  
  Async
&lt;/h3&gt;

&lt;p&gt;Thanks to "Barry Scott". I will follow his/her suggestion :&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;You might get the same improvement for less overhead by using async I/O.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;I write these code:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;shutil&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;asyncio&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;concurrent.futures&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;ThreadPoolExecutor&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;


&lt;span class="c1"&gt;# create directory
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;create_target_directory&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;makedirs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# copy 1 file
&lt;/span&gt;&lt;span class="k"&gt;async&lt;/span&gt; &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy_file_async&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;loop&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;asyncio&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;get_event_loop&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="n"&gt;loop&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;run_in_executor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;copy2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# copy directory
&lt;/span&gt;&lt;span class="k"&gt;async&lt;/span&gt; &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy_directory_async&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;entries&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;scandir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;create_target_directory&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;tasks&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;src_path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;
        &lt;span class="n"&gt;dst_path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;join&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;is_dir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;follow_symlinks&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;copy_directory_async&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src_path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst_path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;symlinks&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dirs_exist_ok&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;copy_file_async&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src_path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst_path&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

    &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="n"&gt;asyncio&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;gather&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c1"&gt;# choose copy method
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;choose_copy_method&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;kwargs&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt; &lt;span class="ow"&gt;or&lt;/span&gt; &lt;span class="nf"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getsize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;path&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;1024&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;1024&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# async version
&lt;/span&gt;        &lt;span class="n"&gt;asyncio&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;run&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;copy_directory_async&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;kwargs&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# single thread version
&lt;/span&gt;        &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dst&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;kwargs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c1"&gt;# test function
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;__name__&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; costs &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;s&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# write in 50000 files
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;write_in_50000_files&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;50000&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="k"&gt;with&lt;/span&gt; &lt;span class="nf"&gt;open&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Test/source/&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;.txt&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;w&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;makedirs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;exist_ok&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;write_in_50000_files&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

    &lt;span class="c1"&gt;# 单线程复制
&lt;/span&gt;    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy1&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
        &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/destination1&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy2&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
        &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copytree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/destination2&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="c1"&gt;# async
&lt;/span&gt;    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;copy3&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
        &lt;span class="n"&gt;entries&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;scandir&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
        &lt;span class="nf"&gt;choose_copy_method&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/source&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test/destination3&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;copy1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;copy2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;copy3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;shutil&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;rmtree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;__name__&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;__main__&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;p&gt;Output:&lt;/p&gt;

&lt;p&gt;copy1 costs 187.21s&lt;br&gt;
copy2 costs 244.33s&lt;br&gt;
copy3 costs 111.27s&lt;/p&gt;




&lt;p&gt;You can see that the async version is faster than the single thread version. But the single thread version is faster than the multi-thread version. ( Maybe my test environment is not very good, you can try and send your result as a reply to me )&lt;/p&gt;

&lt;p&gt;Thank you Barry Scott !&lt;/p&gt;

&lt;h4&gt;
  
  
  Advantages &amp;amp; Disadvantages
&lt;/h4&gt;

&lt;p&gt;Async is a good choice. But no solution is perfect. If you find some problem, you can send me as a reply.&lt;/p&gt;

&lt;h2&gt;
  
  
  End
&lt;/h2&gt;

&lt;p&gt;This is my first time to write discussion on python.org. If there is any problem, please let me know. Thank you.&lt;/p&gt;

&lt;p&gt;My Github: &lt;a href="https://github.com/mengqinyuan" rel="noopener noreferrer"&gt;https://github.com/mengqinyuan&lt;/a&gt;&lt;br&gt;
My Dev.to: &lt;a href="https://dev.to/mengqinyuan"&gt;https://dev.to/mengqinyuan&lt;/a&gt;&lt;/p&gt;

</description>
      <category>python</category>
      <category>programming</category>
    </item>
    <item>
      <title>How Far You Can Optimize a Program to Compute the Fibonacci Sequence?</title>
      <dc:creator>mengqinyuan</dc:creator>
      <pubDate>Wed, 21 Aug 2024 05:31:31 +0000</pubDate>
      <link>https://dev.to/mengqinyuan/how-far-can-you-optimize-a-program-to-compute-the-fibonacci-sequence-oa2</link>
      <guid>https://dev.to/mengqinyuan/how-far-can-you-optimize-a-program-to-compute-the-fibonacci-sequence-oa2</guid>
      <description>&lt;h2&gt;
  
  
  How Far Can You Optimize a Program to Compute the Fibonacci Sequence?
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Introduction
&lt;/h3&gt;

&lt;blockquote&gt;
&lt;p&gt;When I was learning Python, our teacher gave us a homework -- calculate the Nth number of Fibonacci Sequence.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;I think it's very easy, so I write this code:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
    &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Later, I know this kind of solution cost too much time.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;When you read here, you may think of the &lt;em&gt;Binet&lt;/em&gt;, but we need to consider the float problems.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;$$ [ F(n) = \frac{1}{\sqrt{5}} \left( \left(\frac{1 + \sqrt{5}}{2}\right)^n - \left(\frac{1 - \sqrt{5}}{2}\right)^n \right) ] $$&lt;/p&gt;

&lt;h3&gt;
  
  
  Optimize a Program
&lt;/h3&gt;

&lt;p&gt;I change the solution to iteration.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I use &lt;code&gt;matplotlib&lt;/code&gt; draw the time it cost:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;plt&lt;/span&gt;


&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="c1"&gt;# calculate the time
&lt;/span&gt;    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;  &lt;span class="c1"&gt;# return the time and the result
&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="n"&gt;mark_list&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;mark&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;mark_list&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;mark&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;size : &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; , time : &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;mark&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;mark_list&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Input Size&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Execution Time (seconds)&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;title&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Test fot fibonacci&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;show&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Here is the result:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F3x4q52nyh2vjuvt798co.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F3x4q52nyh2vjuvt798co.png" alt="Image description" width="640" height="480"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;The time it cost is very short.&lt;/p&gt;

&lt;p&gt;But I write &lt;code&gt;fib(300000)&lt;/code&gt;, cost 5.719049899998936 seconds. It's too long.&lt;/p&gt;

&lt;p&gt;When I grow up, I learn &lt;strong&gt;CACHE&lt;/strong&gt;, so I change the solution to use &lt;code&gt;dict&lt;/code&gt; to store the result.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;lru_cache&lt;/span&gt;
&lt;span class="nd"&gt;@lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxsize&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Or we can write the CACHE by ourself.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="p"&gt;{}):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="n"&gt;next_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
            &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;next_value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next_value&lt;/span&gt;
        &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I compare two kinds of fib with cache, and one without cache:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;lru_cache&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;plt&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;sys&lt;/span&gt;
&lt;span class="n"&gt;sys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;set_int_max_str_digits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;7500&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;sys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;setrecursionlimit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;190000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="nd"&gt;@lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxsize&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib_with_lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;fib_with_lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;fib_with_lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib_with_hand_writing_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="p"&gt;{}):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="n"&gt;next_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
            &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;next_value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next_value&lt;/span&gt;
        &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib_with_no_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="n"&gt;next_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;next_value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;__name__&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; took &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; seconds to run.&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;

&lt;span class="n"&gt;lru_cache_time&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;hand_writing_cache_time&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;no_cache_time&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;18000&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;lru_cache_time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fib_with_lru_cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="n"&gt;hand_writing_cache_time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fib_with_hand_writing_cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="n"&gt;no_cache_time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;bench_mark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fib_with_no_cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lru_cache_time&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;label&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;lru_cache&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;hand_writing_cache_time&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;label&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;hand_writing_cache&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;no_cache_time&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;label&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;no_cache&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;span class="n"&gt;plt&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;show&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;I calculate from fib(1) to fib(18000) in order to see the difference clearly.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Here is the result:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F5eptzkuz5jlo701k8f7h.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F5eptzkuz5jlo701k8f7h.png" alt="Image description" width="800" height="322"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;Later, I know the &lt;strong&gt;MATRIX EXPONENTIAL&lt;/strong&gt;, so I change the solution to use matrix.&lt;br&gt;
Here is the code:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;matrix_power&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;power&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;power&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;
    &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;power&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;half_power&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;matrix_power&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;power&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;matrix_multiply&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;half_power&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;half_power&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;matrix_multiply&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;matrix_power&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;power&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;matrix_multiply&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;a11&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a12&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a21&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a22&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;
    &lt;span class="n"&gt;b11&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b12&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b21&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b22&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;
    &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="n"&gt;a11&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b11&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;a12&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b21&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="n"&gt;a11&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b12&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;a12&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b22&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="n"&gt;a21&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b11&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;a22&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b21&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="n"&gt;a21&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b12&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;a22&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b22&lt;/span&gt;
    &lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fibonacci&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;
    &lt;span class="n"&gt;fib_matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;result_matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;matrix_power&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fib_matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result_matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;result_matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;


&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I make the compare with the previous solution:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F89gr9daf20klftg63v5s.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F89gr9daf20klftg63v5s.png" alt="Image description" width="640" height="480"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;h3&gt;
  
  
  What is the next step?
&lt;/h3&gt;

&lt;p&gt;There are many kinds of solution to solve this problem. I think the next step is to learn more about the algorithm.&lt;br&gt;
And do not give up finding the solution. Maybe you can have more ideas.&lt;/p&gt;
&lt;h3&gt;
  
  
  Additional
&lt;/h3&gt;

&lt;p&gt;A person named "Jon Randy 🎖️" add my idea, here is the reply :&lt;/p&gt;

&lt;p&gt;JS function to calculate Nth Fibonacci number in O(1) - well, maybe O(log N) - depends on how the system implements some of the underlying maths functions:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fibonacci&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;r5&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;((((&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="nx"&gt;r5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;r5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="nx"&gt;r5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;And HE/SHE gives a explanation (very detailed) :&lt;br&gt;
&lt;a href="https://akuli.github.io/math-tutorial/fib.html" rel="noopener noreferrer"&gt;https://akuli.github.io/math-tutorial/fib.html&lt;/a&gt;&lt;/p&gt;

&lt;h3&gt;
  
  
  End
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;My Github : &lt;a href="https://github.com/mengqinyuan" rel="noopener noreferrer"&gt;https://github.com/mengqinyuan&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;My Dev.to : &lt;a href="https://dev.to/mengqinyuan"&gt;https://dev.to/mengqinyuan&lt;/a&gt;
&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>python</category>
      <category>learning</category>
      <category>discuss</category>
      <category>softwaredevelopment</category>
    </item>
    <item>
      <title>Python PDB Code Review Report</title>
      <dc:creator>mengqinyuan</dc:creator>
      <pubDate>Wed, 07 Aug 2024 10:30:37 +0000</pubDate>
      <link>https://dev.to/mengqinyuan/python-pdb-code-review-report-3f51</link>
      <guid>https://dev.to/mengqinyuan/python-pdb-code-review-report-3f51</guid>
      <description>&lt;h1&gt;
  
  
  Python PDB Code Review Report
&lt;/h1&gt;

&lt;ul&gt;
&lt;li&gt;TIME: 2024/08/07&lt;/li&gt;
&lt;li&gt;AUTHOR: QINYUAN MENG&lt;/li&gt;
&lt;li&gt;EMAIL: &lt;a href="mailto:njbj1210@sina.com"&gt;njbj1210@sina.com&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;GITHUB: &lt;a href="https://github.com/mengqinyuan/" rel="noopener noreferrer"&gt;https://github.com/mengqinyuan/&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;DEV.TO： &lt;a href="https://dev.to/mengqinyuan/"&gt;https://dev.to/mengqinyuan/&lt;/a&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Code Review Report
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;FILE_LOCATION: C:\Program Files\WindowsApps\PythonSoftwareFoundation.Python.3.11_3.11.2544.0_x64__qbz5n2kfra8p0\Lib\bdb.py&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  USAGE
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;enable, disable: Toggle a breakpoint's activity.&lt;/li&gt;
&lt;li&gt;bpprint: Print breakpoint information.&lt;/li&gt;
&lt;li&gt;bpformat: Format breakpoint details as a string.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;__str__&lt;/code&gt;: Return a concise breakpoint description.&lt;/li&gt;
&lt;li&gt;checkfuncname: Determine if a breakpoint should be set based on function name or line number.&lt;/li&gt;
&lt;li&gt;effective: Decide if a breakpoint should be set at a given file and line, and if it's temporary.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I find some problems in the code.&lt;/p&gt;

&lt;h2&gt;
  
  
  Problems
&lt;/h2&gt;

&lt;p&gt;The provided code snippet defines a &lt;code&gt;Breakpoint&lt;/code&gt; class for managing breakpoints, along with helper functions and a test case. Here are the translations and refinements for the identified potential issues and optimization directions:&lt;/p&gt;

&lt;h2&gt;
  
  
  Potential Issues and Optimization Directions
&lt;/h2&gt;

&lt;h3&gt;
  
  
  1. &lt;code&gt;del self.bplist[index]&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;bplist&lt;/code&gt; is a class attribute, and directly deleting elements from it may lead to unexpected results, especially in multi-threaded environments.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Ensure that access to and modification of &lt;code&gt;bplist&lt;/code&gt; are thread-safe, or explicitly state that the class does not support multi-threading.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  2. &lt;code&gt;bpprint&lt;/code&gt; method using &lt;code&gt;sys.stdout&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Directly using &lt;code&gt;sys.stdout&lt;/code&gt; can cause output to be mixed with that of external callers.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Provide an option to specify the output stream, allowing users to direct the output to a specific location.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  3. Static Methods and Class Attributes
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Static methods and class attributes like &lt;code&gt;Breakpoint.clearBreakpoints()&lt;/code&gt; and &lt;code&gt;Breakpoint.next&lt;/code&gt; can lead to shared state issues between different instances of &lt;code&gt;Bdb&lt;/code&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Consider using instance attributes and methods instead of static methods and class attributes to avoid shared state issues.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  4. Exception Handling in &lt;code&gt;effective&lt;/code&gt; Function
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The exception handling in the &lt;code&gt;effective&lt;/code&gt; function catches all exceptions, which might not be ideal.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Catch specific exceptions to handle them appropriately, and log the exception details for debugging purposes.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  5. Use of &lt;code&gt;sys.settrace&lt;/code&gt; and &lt;code&gt;BdbQuit&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The use of &lt;code&gt;sys.settrace&lt;/code&gt; and raising &lt;code&gt;BdbQuit&lt;/code&gt; can interfere with the normal flow of the program.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Document the implications of using these mechanisms and provide guidance on how to properly integrate the debugger into applications.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  6. Test Case Implementation
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Potential Issue:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The test case (&lt;code&gt;test&lt;/code&gt;) uses a global &lt;code&gt;Tdb&lt;/code&gt; instance, which might not be suitable for all scenarios.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Optimization Suggestion:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Encapsulate the test case within a function or a class to ensure that the test environment is isolated and does not affect other parts of the application.&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  New Code
&lt;/h2&gt;

&lt;p&gt;bpformat function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;bpformat&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="sh"&gt;"""&lt;/span&gt;&lt;span class="s"&gt;Return a string with information about the breakpoint.&lt;/span&gt;&lt;span class="sh"&gt;"""&lt;/span&gt;
    &lt;span class="n"&gt;disp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;del  &lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;temporary&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;keep &lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="n"&gt;disp&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;yes  &lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;enabled&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;no   &lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="n"&gt;ret&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;breakpoint   &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;disp&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;at &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;file&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt;:&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;line&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;cond&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;ret&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="se"&gt;\n\t&lt;/span&gt;&lt;span class="s"&gt;stop only if &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;cond&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;ret&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="se"&gt;\n\t&lt;/span&gt;&lt;span class="s"&gt;ignore next &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; hits&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hits&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;ss&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;s&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hits&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="sh"&gt;''&lt;/span&gt;
        &lt;span class="n"&gt;ret&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="se"&gt;\n\t&lt;/span&gt;&lt;span class="s"&gt;breakpoint already hit &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hits&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s"&gt; time&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;ss&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ret&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;effective function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;effective&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;file&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;line&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;frame&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="sh"&gt;"""&lt;/span&gt;&lt;span class="s"&gt;Return (active breakpoint, delete temporary flag) or (None, None) as
       breakpoint to act upon.
    &lt;/span&gt;&lt;span class="sh"&gt;"""&lt;/span&gt;
    &lt;span class="n"&gt;possibles&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;Breakpoint&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;bplist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;file&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;line&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;possibles&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;enabled&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;continue&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="nf"&gt;checkfuncname&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;frame&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="k"&gt;continue&lt;/span&gt;
        &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hits&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;cond&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt; &lt;span class="o"&gt;-=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
                &lt;span class="k"&gt;continue&lt;/span&gt;
            &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;cond&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;frame&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;f_globals&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;frame&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;f_locals&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
                &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                        &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ignore&lt;/span&gt; &lt;span class="o"&gt;-=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
                        &lt;span class="k"&gt;continue&lt;/span&gt;
                    &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="k"&gt;except&lt;/span&gt; &lt;span class="nb"&gt;NameError&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Error evaluating condition: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
                &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  Summary
&lt;/h2&gt;

&lt;p&gt;This analysis provides insights into potential issues and optimization directions for the &lt;code&gt;Breakpoint&lt;/code&gt; class and related functionalities. Implementing the suggested optimizations can improve the robustness and maintainability of the code.&lt;/p&gt;

</description>
      <category>python</category>
      <category>pdb</category>
      <category>codereview</category>
    </item>
    <item>
      <title>“Be wary of time complexity pitfalls"</title>
      <dc:creator>mengqinyuan</dc:creator>
      <pubDate>Thu, 01 Aug 2024 09:57:57 +0000</pubDate>
      <link>https://dev.to/mengqinyuan/be-wary-of-time-complexity-pitfalls-13jf</link>
      <guid>https://dev.to/mengqinyuan/be-wary-of-time-complexity-pitfalls-13jf</guid>
      <description>&lt;h1&gt;
  
  
  Be wary of time complexity pitfalls
&lt;/h1&gt;

&lt;h2&gt;
  
  
  Write Here
&lt;/h2&gt;

&lt;p&gt;A bilibili vedio also shows this : &lt;a href="https://www.bilibili.com/video/BV16u4m1c7cU/?spm_id_from=333.999.0.0" rel="noopener noreferrer"&gt;https://www.bilibili.com/video/BV16u4m1c7cU/?spm_id_from=333.999.0.0&lt;/a&gt; and I think it's a good vedio, but its language is Chinese.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fdawqc8to0r2aew4khwi3.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media.dev.to/cdn-cgi/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fdawqc8to0r2aew4khwi3.png" alt="Image description" width="800" height="450"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;h2&gt;
  
  
  time complexity
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;What does time complexity mean?&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Time complexity is a measure of how much time an algorithm takes to run as a function of the size of its input. It is a way to describe the efficiency of an algorithm, and it is used to compare different algorithms and determine which one is the most efficient.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;How to calculate time complexity?&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;To calculate time complexity, we need to consider the number of operations performed by the algorithm as a function of the size of the input. The most common way to measure the number of operations is by counting the number of times a particular operation is performed.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;What are some common pitfalls when calculating time complexity?&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;ol&gt;
&lt;li&gt;Not considering the &lt;strong&gt;input size&lt;/strong&gt;: If we only consider the number of operations performed by the algorithm, we may underestimate the time complexity. For example, if we count the number of times a loop runs, but we don't take into account the size of the input, then the time complexity may be too high.&lt;/li&gt;
&lt;/ol&gt;&lt;/li&gt;
&lt;li&gt;&lt;ol&gt;
&lt;li&gt;Not considering the &lt;strong&gt;algorithm's efficiency&lt;/strong&gt;: Some algorithms may perform many operations even when the input size is small, which can lead to high time complexity. For example, sorting algorithms like bubble sort and selection sort have quadratic time complexity, even though they may only need to swap two elements in a small array.&lt;/li&gt;
&lt;/ol&gt;&lt;/li&gt;
&lt;li&gt;&lt;ol&gt;
&lt;li&gt;Not considering the &lt;strong&gt;algorithm's worst-case scenario&lt;/strong&gt;: Some algorithms have a best-case scenario where they perform fewer operations than the worst-case scenario. For example, searching algorithms like binary search have a best-case scenario where they find the target element in logarithmic time, but they have a worst-case scenario where they need to examine all elements in the array.&lt;/li&gt;
&lt;/ol&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Let's see some examples of time complexity
&lt;/h3&gt;

&lt;p&gt;Here is a question:&lt;br&gt;
    Find the max 10 integers in a list.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;random&lt;/span&gt;
&lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;random&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;randint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Here is the test function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;float&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# bench mark for testing
&lt;/span&gt;    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Solution1: Use heap
&lt;/h3&gt;

&lt;p&gt;Here is the solution which uses the heapq module:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_max_n&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;nlargest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Or we write it in the python way:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_largest_n&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

    &lt;span class="n"&gt;max_heap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="c1"&gt;# call sift_down
&lt;/span&gt;            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
                &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt;
            &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;
    &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Solution2: Use sort
&lt;/h3&gt;

&lt;p&gt;Here is the solution which uses the sort function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_max_n&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;reverse&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)[:&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Testing
&lt;/h3&gt;

&lt;p&gt;Almost everyone know that The time complexity of the heap, is &lt;em&gt;O(n log k)&lt;/em&gt;, and the time complexity of the sort function is &lt;em&gt;O(n log n)&lt;/em&gt;.&lt;/p&gt;

&lt;p&gt;It seems that the First solution is better than the second one. But it is &lt;strong&gt;not true&lt;/strong&gt; in python.&lt;/p&gt;

&lt;p&gt;Look at the final code:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;float&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="nf"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_max_n_heapq&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;nlargest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_max_n_python_heap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

    &lt;span class="n"&gt;max_heap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="c1"&gt;# call sift_down
&lt;/span&gt;            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
                &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt;
            &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;
    &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;


&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;find_max_n_sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;reverse&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)[:&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# test
&lt;/span&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;random&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;random&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;randint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;n = &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Use    Heapq: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;find_max_n_heapq&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Python Heapq: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;find_max_n_python_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Sorted      : &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;find_max_n_sorted&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I run it in &lt;strong&gt;Python3.11 VScode&lt;/strong&gt;, Here is the result:&lt;/p&gt;

&lt;h3&gt;
  
  
  n is not big
&lt;/h3&gt;

&lt;p&gt;n = 900&lt;br&gt;
Use    Heapq: 0.002430099993944168&lt;br&gt;
Python Heapq: 0.06343129999004304&lt;br&gt;
Sorted      : 9.280000813305378e-02&lt;br&gt;
n = 910&lt;br&gt;
Use    Heapq: 9.220000356435776e-05&lt;br&gt;
Python Heapq: 0.07715500006452203&lt;br&gt;
Sorted      : 9.360001422464848e-05&lt;br&gt;
n = 920&lt;br&gt;
Use    Heapq: 9.440002031624317e-05&lt;br&gt;
Python Heapq: 0.06573969998862594&lt;br&gt;
Sorted      : 0.00012450001668185&lt;br&gt;
n = 930&lt;br&gt;
Use    Heapq: 9.689992293715477e-05 &lt;br&gt;
Python Heapq: 0.06760239996947348&lt;br&gt;
Sorted      : 9.66999214142561e-05 &lt;br&gt;
n = 940&lt;br&gt;
Use    Heapq: 9.600003249943256e-05&lt;br&gt;
Python Heapq: 0.07372559991199523&lt;/p&gt;

&lt;h2&gt;
  
  
  Sorted      : 9.680003859102726e-05
&lt;/h2&gt;

&lt;p&gt;n = 950&lt;br&gt;
Use    Heapq: 9.770004544407129e-05&lt;br&gt;
Python Heapq: 0.07306570000946522&lt;br&gt;
Sorted      : 0.000119799980893731&lt;br&gt;
n = 960&lt;br&gt;
Use    Heapq: 9.980006143450737e-05 &lt;br&gt;
Python Heapq: 0.0771204000338912&lt;br&gt;
Sorted      : 0.00022829999215900898&lt;br&gt;
n = 970&lt;br&gt;
Use    Heapq: 0.0001601999392732978&lt;br&gt;
Python Heapq: 0.07493270002305508&lt;br&gt;
Sorted      : 0.00010840001050382853&lt;br&gt;
n = 980&lt;br&gt;
Use    Heapq: 9.949994273483753e-05&lt;br&gt;
Python Heapq: 0.07698320003692061&lt;br&gt;
Sorted      : 0.00010300008580088615&lt;br&gt;
n = 990&lt;br&gt;
Use    Heapq: 9.979994501918554e-05&lt;br&gt;
Python Heapq: 0.0848745999392122&lt;br&gt;
Sorted      : 0.00012620002962648869&lt;/p&gt;

&lt;h3&gt;
  
  
  if n is big ?
&lt;/h3&gt;

&lt;p&gt;n = 10000&lt;br&gt;
Use    Heapq: 0.003642000025138259&lt;br&gt;
Python Heapq: 9.698883199947886&lt;br&gt;
Sorted      : 0.0010799999581649&lt;br&gt;
n = 11000&lt;br&gt;
Use    Heapq: 0.0014836000045761466&lt;br&gt;
Python Heapq: 10.537632800056599&lt;br&gt;
Sorted      : 0.0012236000038683414&lt;br&gt;
n = 12000&lt;br&gt;
Use    Heapq: 0.001384599949233234&lt;br&gt;
Python Heapq: 12.328411899972707&lt;br&gt;
Sorted      : 0.001322699943557381&lt;br&gt;
n = 13000&lt;br&gt;
Use    Heapq: 0.0020017001079395413&lt;br&gt;
Python Heapq: 15.637207800056785&lt;br&gt;
Sorted      : 0.0015075999544933438&lt;br&gt;
n = 14000&lt;br&gt;
Use    Heapq: 0.0017026999266818166&lt;br&gt;
Python Heapq: 17.298848500009626&lt;br&gt;
Sorted      : 0.0016967999981716275&lt;br&gt;
n = 15000&lt;br&gt;
Use    Heapq: 0.0017773000290617347&lt;br&gt;
Python Heapq: 20.780625900020823&lt;br&gt;
Sorted      : 0.0017105999868363142&lt;/p&gt;

&lt;h3&gt;
  
  
  What I find &amp;amp; how to improve it
&lt;/h3&gt;

&lt;p&gt;When n is big, Sorted costs a little time (sometimes even better than use heapq), but Python Heapq costs a lot of time.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Why Sorted costs a little time, but Python Heap costs a lot of time? &lt;/li&gt;
&lt;li&gt;Because &lt;code&gt;sorted()&lt;/code&gt; is a &lt;code&gt;bulit-in function&lt;/code&gt; in Python, you can find python office document about it.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Bulit-in function is faster than heapq because it is written in C, which is a compiled language.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;How to improve it?&lt;/li&gt;
&lt;li&gt;You can use the built-in function sorted() instead of &lt;code&gt;heapq.nlargest()&lt;/code&gt; to improve the performance of your code. The sorted() function is a built-in function in Python, which is implemented in C and is therefore much faster than &lt;code&gt;heapq.sort()&lt;/code&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Maybe heapq.nlargest is faster in some situatios, but I cannot make sure that.&lt;/p&gt;

&lt;h3&gt;
  
  
  What about use other language?
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;Use other language like C++, C#, Java, etc.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;iostream&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;vector&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;algorithm&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;chrono&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;random&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// C++ benchmark function&lt;/span&gt;
&lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;chrono&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;high_resolution_clock&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;now&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;chrono&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;high_resolution_clock&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;now&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;chrono&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;duration&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;double&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Using std::partial_sort to find the n largest elements&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;find_max_n_sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;partial_sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;greater&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
    &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;resize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Manual heap implementation&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
        &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;swap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="n"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;find_max_n_python_heap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;

    &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
                &lt;span class="n"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="nf"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;mt19937&lt;/span&gt; &lt;span class="n"&gt;gen&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;random_device&lt;/span&gt;&lt;span class="p"&gt;{}());&lt;/span&gt;
    &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;uniform_int_distribution&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;dis&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;generate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;dis&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;gen&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="p"&gt;});&lt;/span&gt;

        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls_copy1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls_copy2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;cout&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;"n = "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;endl&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;cout&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;"Use    Heapq: "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;find_max_n_sorted&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls_copy1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;endl&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;cout&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;"Python Heapq: "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;benchmark&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;find_max_n_python_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls_copy2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;endl&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="c1"&gt;// Note: C++ std::nth_element or std::partial_sort could be used here for comparison&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.util.*&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.time.Duration&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.time.Instant&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;MaxElementsBenchmark&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="nf"&gt;benchmark&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Runnable&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;Instant&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Instant&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;now&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
        &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;run&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
        &lt;span class="nc"&gt;Instant&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Instant&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;now&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nc"&gt;Duration&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;between&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;).&lt;/span&gt;&lt;span class="na"&gt;toNanos&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="n"&gt;e9&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="nc"&gt;List&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;findMaxNHeap&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;minHeap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;();&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;offer&lt;/span&gt;&lt;span class="o"&gt;(-&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(-&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;peek&lt;/span&gt;&lt;span class="o"&gt;())&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;poll&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
                &lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;offer&lt;/span&gt;&lt;span class="o"&gt;(-&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="nc"&gt;List&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;(&lt;/span&gt;&lt;span class="n"&gt;minHeap&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="nc"&gt;Collections&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;sort&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="nc"&gt;Collections&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;reverse&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="nc"&gt;List&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;findMaxNManualHeap&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;();&lt;/span&gt;

        &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;maxHeap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;();&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;add&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
                &lt;span class="n"&gt;siftDown&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;))&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;set&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
                &lt;span class="n"&gt;siftDown&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;maxHeap&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;private&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;siftDown&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="o"&gt;))&lt;/span&gt;
            &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="o"&gt;))&lt;/span&gt;
            &lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;largest&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="nc"&gt;Collections&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;swap&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="n"&gt;siftDown&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;largest&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="nc"&gt;List&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;findMaxNSorted&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;Collections&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;sort&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="nc"&gt;Collections&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;reverseOrder&lt;/span&gt;&lt;span class="o"&gt;());&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;subList&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="nc"&gt;Math&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;min&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;size&lt;/span&gt;&lt;span class="o"&gt;()));&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;String&lt;/span&gt;&lt;span class="o"&gt;[]&lt;/span&gt; &lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;Random&lt;/span&gt; &lt;span class="n"&gt;rand&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Random&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;10000&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;ls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;ArrayList&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&amp;gt;();&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;add&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rand&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;nextInt&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt;

            &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"n = "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
            &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Use    Heapq: "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;benchmark&lt;/span&gt;&lt;span class="o"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;findMaxNHeap&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)));&lt;/span&gt;
            &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Python Heapq: "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;benchmark&lt;/span&gt;&lt;span class="o"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;findMaxNManualHeap&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)));&lt;/span&gt;
            &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Sorted      : "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;benchmark&lt;/span&gt;&lt;span class="o"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;findMaxNSorted&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ls&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;)));&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;The result is different from the C++ version. The C++ version is faster than the Java version. This is because the C++ version uses a built-in function, while the Java version uses a manual heap implementation.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Conclusion
&lt;/h3&gt;

&lt;p&gt;When we are dealing with large data, we should use built-in function instead of &lt;code&gt;heapq.sort()&lt;/code&gt; to improve the performance of our code. We must be wary of time complexity pitfalls when dealing with large data. Sometimes time complexity pitfalls are unavoidable, but we should try to avoid them as much as possible.&lt;/p&gt;

&lt;h3&gt;
  
  
  About Me
&lt;/h3&gt;

&lt;p&gt;Hello, I'm mengqinyuan. I'm a student. I love to learn new things.&lt;br&gt;
You can see my github: [MengQinYuan's Github][&lt;a href="https://github.com/mengqinyuan" rel="noopener noreferrer"&gt;https://github.com/mengqinyuan&lt;/a&gt;]&lt;/p&gt;

&lt;h3&gt;
  
  
  Other things
&lt;/h3&gt;

&lt;p&gt;Eight Queens Problem: [&lt;a href="https://www.geeksforgeeks.org/8-queen-problem/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/8-queen-problem/&lt;/a&gt;]&lt;br&gt;
Time &amp;amp; Space Complexity: [&lt;a href="https://www.geeksforgeeks.org/time-complexity-and-space-complexity/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/time-complexity-and-space-complexity/&lt;/a&gt;]&lt;br&gt;
Heap: [&lt;a href="https://www.geeksforgeeks.org/heap-data-structure/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/heap-data-structure/&lt;/a&gt;]&lt;/p&gt;

</description>
      <category>python</category>
      <category>development</category>
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