<rss xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title>大数运算 - 标签 - 菠菜眾長</title><link>https://lruihao.cn/tags/%E5%A4%A7%E6%95%B0%E8%BF%90%E7%AE%97/</link><description>大数运算 - 标签 - 菠菜眾長</description><generator>Hugo -- gohugo.io</generator><language>zh-CN</language><managingEditor>1024@lruihao.cn (Lruihao)</managingEditor><webMaster>1024@lruihao.cn (Lruihao)</webMaster><lastBuildDate>Thu, 28 Mar 2019 22:50:43 +0000</lastBuildDate><atom:link href="https://lruihao.cn/tags/%E5%A4%A7%E6%95%B0%E8%BF%90%E7%AE%97/" rel="self" type="application/rss+xml"/><item><title>大数乘法</title><link>https://lruihao.cn/posts/dacheng/</link><pubDate>Thu, 28 Mar 2019 22:50:43 +0000</pubDate><author>Lruihao</author><guid>https://lruihao.cn/posts/dacheng/</guid><description><![CDATA[<blockquote>
<p>大数乘法 c 版(基础写法)</p>
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<pre tabindex="0" class="chroma"><code class="language-cpp" data-lang="cpp"><span class="line"><span class="cl"><span class="cp">#include</span><span class="cpf">&lt;stdio.h&gt;</span><span class="cp">
</span></span></span><span class="line"><span class="cl"><span class="cp">#include</span><span class="cpf">&lt;string.h&gt;</span><span class="cp">
</span></span></span><span class="line"><span class="cl"><span class="cp">#define N 202
</span></span></span><span class="line"><span class="cl"><span class="cp"></span>
</span></span><span class="line"><span class="cl"><span class="kt">int</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">  <span class="kt">int</span> <span class="n">a</span><span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">},</span> <span class="n">b</span><span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">},</span> <span class="n">c</span><span class="p">[</span><span class="mi">404</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">},</span> <span class="n">la</span><span class="p">,</span> <span class="n">lb</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span><span class="n">k</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">;</span><span class="c1">//202位数相乘，最长404位数
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>  <span class="kt">int</span> <span class="n">get</span><span class="p">(</span><span class="kt">int</span> <span class="o">*</span><span class="n">p</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">  <span class="kt">void</span> <span class="n">change</span><span class="p">(</span><span class="kt">int</span> <span class="o">*</span><span class="n">a</span><span class="p">,</span> <span class="kt">int</span> <span class="o">*</span><span class="n">b</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">  <span class="n">la</span> <span class="o">=</span> <span class="n">get</span><span class="p">(</span><span class="n">a</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">  <span class="n">lb</span> <span class="o">=</span> <span class="n">get</span><span class="p">(</span><span class="n">b</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">  <span class="n">n1</span> <span class="o">=</span> <span class="n">la</span> <span class="o">&gt;</span> <span class="n">lb</span> <span class="o">?</span> <span class="nl">la</span> <span class="p">:</span> <span class="n">lb</span><span class="p">;</span><span class="c1">//较长的数长
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>  <span class="n">n2</span> <span class="o">=</span> <span class="n">la</span> <span class="o">&lt;</span> <span class="n">lb</span> <span class="o">?</span> <span class="nl">la</span> <span class="p">:</span> <span class="n">lb</span><span class="p">;</span><span class="c1">//较短的数长
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>
</span></span><span class="line"><span class="cl">  <span class="k">if</span> <span class="p">(</span><span class="n">la</span> <span class="o">&lt;</span> <span class="n">lb</span><span class="p">)</span>
</span></span><span class="line"><span class="cl">    <span class="n">change</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">lb</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">  <span class="c1">//模拟乘法运算过程（进位等考虑）
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>  <span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">n2</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">    <span class="k">for</span> <span class="p">(</span><span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="n">n1</span><span class="p">;</span> <span class="n">j</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">      <span class="n">c</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">d</span><span class="p">)</span><span class="o">%</span><span class="mi">10</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">      <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">d</span><span class="p">)</span> <span class="o">/</span> <span class="mi">10</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">      <span class="k">if</span> <span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="n">i</span><span class="p">]</span><span class="o">&gt;</span><span class="mi">9</span><span class="p">){</span>
</span></span><span class="line"><span class="cl">        <span class="n">d</span><span class="o">++</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">        <span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="n">i</span><span class="p">]</span><span class="o">%=</span><span class="mi">10</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">      <span class="p">}</span>
</span></span><span class="line"><span class="cl">      <span class="k">if</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">==</span><span class="mi">0</span><span class="o">&amp;&amp;</span><span class="n">d</span><span class="o">!=</span><span class="mi">0</span><span class="p">){</span>
</span></span><span class="line"><span class="cl">        <span class="n">k</span><span class="o">=</span><span class="n">j</span><span class="o">+</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">        <span class="n">c</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="o">=</span><span class="n">d</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">      <span class="p">}</span>
</span></span><span class="line"><span class="cl">    <span class="p">}</span>
</span></span><span class="line"><span class="cl">    <span class="n">d</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="p">}</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">  <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="o">&gt;</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="mi">2</span><span class="p">)</span><span class="o">?</span><span class="nl">k</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="mi">2</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="n">k</span><span class="p">;</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="c1">//将倒序装入的结果打印
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>    <span class="n">printf</span><span class="p">(</span><span class="s">&#34;%d&#34;</span><span class="p">,</span> <span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">  <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
</span></span><span class="line"><span class="cl"><span class="p">}</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl"><span class="c1">//输入字符串作为数字，并返回数字去除前导0后的长度
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="kt">int</span> <span class="nf">get</span><span class="p">(</span><span class="kt">int</span> <span class="o">*</span><span class="n">p</span><span class="p">)</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">  <span class="kt">char</span> <span class="n">x</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
</span></span><span class="line"><span class="cl">  <span class="kt">int</span> <span class="n">l</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">ex</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">  <span class="n">scanf</span><span class="p">(</span><span class="s">&#34;%s&#34;</span><span class="p">,</span> <span class="n">x</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">  <span class="n">l</span> <span class="o">=</span> <span class="n">strlen</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
</span></span><span class="line"><span class="cl">  <span class="k">while</span> <span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">ex</span><span class="p">]</span> <span class="o">==</span> <span class="sc">&#39;0&#39;</span><span class="p">)</span>
</span></span><span class="line"><span class="cl">    <span class="n">ex</span><span class="o">++</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="n">ex</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">l</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="c1">//提取字符串数字到int数组，倒序排列
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>    <span class="o">*</span><span class="p">(</span><span class="n">p</span> <span class="o">+</span> <span class="n">l</span> <span class="o">-</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="sc">&#39;0&#39;</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="k">return</span> <span class="n">l</span> <span class="o">-</span> <span class="n">ex</span><span class="p">;</span>
</span></span><span class="line"><span class="cl"><span class="p">}</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl"><span class="kt">void</span> <span class="nf">change</span><span class="p">(</span><span class="kt">int</span> <span class="o">*</span><span class="n">a</span><span class="p">,</span> <span class="kt">int</span> <span class="o">*</span><span class="n">b</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">)</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">  <span class="kt">int</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">n</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
</span></span><span class="line"><span class="cl">    <span class="n">t</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
</span></span><span class="line"><span class="cl">    <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
</span></span><span class="line"><span class="cl">    <span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span><span class="p">;</span>
</span></span><span class="line"><span class="cl">  <span class="p">}</span>
</span></span><span class="line"><span class="cl"><span class="p">}</span></span></span></code></pre></td></tr></table>
</div>
</div><p>程序运行结果</p>
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<pre tabindex="0" class="chroma"><code><span class="lnt">1
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<pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback"><span class="line"><span class="cl">1234567890123456789
</span></span><span class="line"><span class="cl">98765432109876543210
</span></span><span class="line"><span class="cl">121932631124517831023715309991126352690</span></span></code></pre></td></tr></table>
</div>
</div>]]></description></item></channel></rss>