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<small><time class="date dt-published" datetime="2019-10-21T00:00:00+08:00">21 October 2019</time> - 字数统计：1350 - 阅读大约需要5分钟 - Hits: <span id="/2019/10/21/python.html" class="visitors">Loading...</span></small>
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<h1 class="p-name">Python学习笔记 - 求质数</h1>
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<p class="view">by <a class="p-author h-card" href="//github.com/Mabbs">mayx</a></p>
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<div id="outdate" style="display:none;">
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<hr /><p>
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这是一篇创建于 <span id="outime"></span> 天前的文章，其中的信息可能已经有所发展或是发生改变。
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<b>AI摘要</b>
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<p id="ai-output">这篇文章是作者在学习Python过程中，针对生成质数的任务分享了自己的实现方法，使用了埃氏筛法，但发现效率相比在学校资源中看到的原生Python埃氏筛和欧拉筛法实现低很多，他们的代码能在更短的时间内处理大量质数。作者虽然感到沮丧，但也意识到这是一个学习过程，且随后了解到欧拉筛法的原理较复杂。</p>
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<hr />
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<ul><li><a href="#起因">起因</a></li><li><a href="#使用python做一个">使用Python做一个</a></li><li><a href="#结局">结局</a></li></ul>
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<hr />
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<main class="post-content e-content" role="main"><p>讲真，我酸了……<!--more--></p>
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<h1 id="起因">
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<a href="#起因"><svg class='octicon' viewBox='0 0 16 16' version='1.1' width='16' height='32' aria-hidden='true'><path fill-rule='evenodd' d='M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z'></path></svg></a> 起因
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</h1>
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<p>在学习Python的过程中，我和同学举行了一个比赛，大概内容是用Python做一个时间复杂度最低的质数生成器。 </p><p>
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在学校里就是有个好处，学校网络上知网下论文是免费的，我大概的查了一下，好像用埃氏筛法的效率比较高。 </p><p>
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以前我用Linux Shell也写过一个：</p>
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<div class="language-shell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c">#!/system/bin/sh</span>
|
||
<span class="nv">max</span><span class="o">=</span>1000
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||
<span class="nv">list</span><span class="o">=</span><span class="s2">"2"</span>
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||
<span class="nv">rlist</span><span class="o">=</span><span class="s2">"2"</span>
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||
<span class="nv">i</span><span class="o">=</span>3
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||
<span class="k">while</span> <span class="o">[</span> <span class="nv">$i</span> <span class="nt">-lt</span> <span class="nv">$max</span> <span class="o">]</span>
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<span class="k">do</span>
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<span class="o">[</span> <span class="s2">"</span><span class="si">$(</span>
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<span class="nb">echo</span> <span class="s2">"</span><span class="nv">$list</span><span class="s2">"</span>|while <span class="nb">read </span>a
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<span class="k">do</span>
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||
<span class="o">[</span> <span class="s2">"</span><span class="k">$((</span><span class="nv">$i</span><span class="o">%</span><span class="nv">$a</span><span class="k">))</span><span class="s2">"</span> <span class="o">==</span> <span class="s2">"0"</span> <span class="o">]&&{</span>
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<span class="nb">echo</span> <span class="s2">"1"</span>
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<span class="nb">break </span>1
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||
<span class="o">}</span>
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<span class="k">done</span>
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||
<span class="si">)</span><span class="s2">"</span> <span class="o">==</span> <span class="s2">"1"</span> <span class="o">]||</span><span class="nv">c</span><span class="o">=</span><span class="nv">$i</span>
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||
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||
<span class="o">[</span> <span class="s2">"</span><span class="nv">$bj</span><span class="s2">"</span> <span class="o">==</span> <span class="s2">""</span> <span class="nt">-a</span> <span class="s2">"</span><span class="nv">$c</span><span class="s2">"</span> <span class="o">!=</span> <span class="s2">""</span> <span class="o">]&&{</span>
|
||
<span class="o">[</span> <span class="s2">"</span><span class="k">$((${</span><span class="nv">c</span><span class="k">}</span><span class="o">*</span><span class="k">${</span><span class="nv">c</span><span class="k">}))</span><span class="s2">"</span> <span class="nt">-gt</span> <span class="s2">"</span><span class="nv">$max</span><span class="s2">"</span> <span class="o">]&&</span><span class="nv">bj</span><span class="o">=</span><span class="s2">"1"</span>
|
||
<span class="o">}</span>
|
||
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||
<span class="o">[</span> <span class="s2">"</span><span class="nv">$c</span><span class="s2">"</span> <span class="o">==</span> <span class="s2">""</span> <span class="o">]||{</span>
|
||
<span class="o">[</span> <span class="s2">"</span><span class="nv">$bj</span><span class="s2">"</span> <span class="o">==</span> <span class="s2">"1"</span> <span class="o">]||{</span>
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||
<span class="nv">list</span><span class="o">=</span><span class="s2">"</span><span class="nv">$list</span><span class="s2">
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</span><span class="nv">$c</span><span class="s2">"</span>
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||
<span class="o">}</span>
|
||
<span class="nb">echo</span> <span class="s2">"</span><span class="nv">$c</span><span class="s2">"</span>
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||
<span class="o">}</span>
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||
<span class="nv">c</span><span class="o">=</span><span class="s2">""</span>
|
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<span class="nv">i</span><span class="o">=</span><span class="s2">"</span><span class="k">$((</span><span class="nv">$i</span><span class="o">+</span><span class="m">1</span><span class="k">))</span><span class="s2">"</span>
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<span class="k">done</span>
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</code></pre></div></div>
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<p>不过效率极低……因为原生Shell是不支持数组之类的东西，所以其实并不能完全使用埃氏筛法……</p>
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<h1 id="使用python做一个">
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||
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||
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<a href="#使用python做一个"><svg class='octicon' viewBox='0 0 16 16' version='1.1' width='16' height='32' aria-hidden='true'><path fill-rule='evenodd' d='M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z'></path></svg></a> 使用Python做一个
|
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</h1>
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<p>当然Python还是可以用的，于是我理解了一下，做了一个出来：</p>
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<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">maxprime</span><span class="o">=</span><span class="mi">100000</span>
|
||
<span class="n">rprimeset</span><span class="o">=</span><span class="nb">set</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">maxprime</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
|
||
<span class="n">lprimeset</span><span class="o">=</span><span class="nb">set</span><span class="p">()</span>
|
||
<span class="n">lastprime</span><span class="o">=</span><span class="mi">0</span>
|
||
<span class="k">while</span> <span class="n">lastprime</span><span class="o"><=</span><span class="n">maxprime</span><span class="o">**</span><span class="mf">0.5</span><span class="p">:</span>
|
||
<span class="n">lastprime</span><span class="o">=</span><span class="nb">min</span><span class="p">(</span><span class="n">rprimeset</span><span class="p">)</span>
|
||
<span class="n">rprimeset</span><span class="o">=</span><span class="n">rprimeset</span><span class="o">-</span><span class="nb">set</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">lastprime</span><span class="p">,</span><span class="n">maxprime</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">lastprime</span><span class="p">))</span>
|
||
<span class="n">lprimeset</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">lastprime</span><span class="p">)</span>
|
||
<span class="n">primelist</span><span class="o">=</span><span class="nb">sorted</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">rprimeset</span><span class="o">|</span><span class="n">lprimeset</span><span class="p">))</span>
|
||
<span class="k">print</span><span class="p">(</span><span class="n">primelist</span><span class="p">)</span>
|
||
<span class="c1">#print(primelist,file=open(__file__[:__file__.rfind("/")]+"/prime.txt",'w+'))
|
||
</span></code></pre></div></div>
|
||
<p>这个效率确实比Shell做的好太多了，而且看起来也清晰易懂。在我的电脑上，1000000的质数只需要4s就能算出来</p>
|
||
<h1 id="结局">
|
||
|
||
|
||
<a href="#结局"><svg class='octicon' viewBox='0 0 16 16' version='1.1' width='16' height='32' aria-hidden='true'><path fill-rule='evenodd' d='M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z'></path></svg></a> 结局
|
||
|
||
|
||
</h1>
|
||
|
||
<p>不过我后来在某百科上查了一下他们用埃氏筛做的Python版本……然后我就酸了……他们的代码在我的电脑上只需要0.6s就能跑完1000000的质数……而且我估计他们的空间复杂度还比我小……</p>
|
||
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="c1"># python 原生实现
|
||
</span>
|
||
<span class="k">def</span> <span class="nf">primes</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<span class="n">P</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<span class="n">f</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">i</span><span class="o">%</span><span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<span class="n">f</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="n">f</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="n">i</span> <span class="o">=</span> <span class="mi">3</span>
|
||
<span class="k">while</span> <span class="n">i</span><span class="o">*</span><span class="n">i</span> <span class="o"><=</span> <span class="n">n</span><span class="p">:</span>
|
||
<span class="k">if</span> <span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<span class="n">j</span> <span class="o">=</span> <span class="n">i</span><span class="o">*</span><span class="n">i</span>
|
||
<span class="k">while</span> <span class="n">j</span> <span class="o"><=</span> <span class="n">n</span><span class="p">:</span>
|
||
<span class="n">f</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
|
||
<span class="n">j</span> <span class="o">+=</span> <span class="n">i</span><span class="o">+</span><span class="n">i</span>
|
||
<span class="n">i</span> <span class="o">+=</span> <span class="mi">2</span>
|
||
|
||
<span class="n">P</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
|
||
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="n">f</span><span class="p">[</span><span class="n">x</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<span class="n">P</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
|
||
<span class="k">return</span> <span class="n">P</span>
|
||
|
||
<span class="n">n</span> <span class="o">=</span> <span class="mi">1000000</span>
|
||
<span class="n">P</span> <span class="o">=</span> <span class="n">primes</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<span class="k">print</span><span class="p">(</span><span class="n">P</span><span class="p">)</span>
|
||
</code></pre></div></div>
|
||
<p>感觉好难受，每次在网上搜的代码都比我写的好……算了，反正我也是在学习嘛。 </p><p>
|
||
后来我听说用欧拉筛法的效率更高……可惜我看完后不太理解……质数算法可真是复杂啊……</p></main>
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