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<article id="post-动态规划——简单的密码" class="h-entry article article-type-post" itemprop="blogPost" itemscope itemtype="https://schema.org/BlogPosting">
<div class="article-meta">
<a href="/2023/09/27/%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E2%80%94%E2%80%94%E7%AE%80%E5%8D%95%E7%9A%84%E5%AF%86%E7%A0%81/" class="article-date">
<time class="dt-published" datetime="2023-09-27T14:15:25.000Z" itemprop="datePublished">2023-09-27</time>
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<a class="article-category-link" href="/categories/%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/">学习笔记</a>
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<a class="p-name article-title" href="/2023/09/27/%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E2%80%94%E2%80%94%E7%AE%80%E5%8D%95%E7%9A%84%E5%AF%86%E7%A0%81/">动态规划——简单的密码</a>
</h1>
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<div class="e-content article-entry" itemprop="articleBody">
<blockquote>
<p>今天实验课上了强度,抓耳挠腮,无不惊叹敬爱的老师下手之厉害。细细思量,请教百度谷歌之先贤,终得解出此题,大呼过瘾 </p>
</blockquote>
<p><img src="/../imgs/%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E9%97%AE%E9%A2%98--%E7%AE%80%E5%8D%95%E7%9A%84%E5%AF%86%E7%A0%81.png" alt="简单的密码"></p>
<h2 id="思路"><a href="#思路" class="headerlink" title="思路"></a>思路</h2><blockquote>
<p>把一个大问题拆分为几个小问题。 </p>
</blockquote>
<p>对于位数大于5位的密码,有如下表格关系。<br>pwd(n)是个伪函数,用来表示n位密码的可能值。</p>
<table>
<thead>
<tr>
<th>密码前导</th>
<th align="center">剩余部分</th>
</tr>
</thead>
<tbody><tr>
<td>000</td>
<td align="center">pow(2,n-3)</td>
</tr>
<tr>
<td>001</td>
<td align="center">pwd(n-3)</td>
</tr>
<tr>
<td>01</td>
<td align="center">pwd(n-2)</td>
</tr>
<tr>
<td>1</td>
<td align="center">pwd(n-1)</td>
</tr>
</tbody></table>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><cmath></span></span></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">fun</span><span class="params">(<span class="type">int</span> n)</span></span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> n;</span><br><span class="line"> <span class="keyword">while</span> (<span class="number">1</span>)</span><br><span class="line"> {</span><br><span class="line"> std::cin >> n;</span><br><span class="line"> std::cout << <span class="built_in">fun</span>(n) << std::endl;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">fun</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (n < <span class="number">3</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (n == <span class="number">3</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (n == <span class="number">4</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">3</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (n == <span class="number">5</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">8</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (n == <span class="number">6</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">20</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">fun</span>(n - <span class="number">1</span>) + <span class="built_in">fun</span>(n - <span class="number">2</span>) + <span class="built_in">fun</span>(n - <span class="number">3</span>) + <span class="built_in">pow</span>(<span class="number">2</span>, n - <span class="number">3</span>);</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<blockquote>
<p>下面是Python实现的另一种方法</p>
</blockquote>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line">result=[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>,<span class="number">1</span>,<span class="number">3</span>,<span class="number">8</span>,<span class="number">20</span>]</span><br><span class="line"><span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="number">7</span>,<span class="number">31</span>):</span><br><span class="line"> count=<span class="number">0</span></span><br><span class="line"> count+=<span class="number">2</span>**(i-<span class="number">3</span>)+<span class="number">2</span>**(i-<span class="number">4</span>)+<span class="number">2</span>**(i-<span class="number">5</span>)*<span class="number">2</span>+<span class="number">2</span>**(i-<span class="number">6</span>)*<span class="number">4</span></span><br><span class="line"> <span class="keyword">for</span> n <span class="keyword">in</span> <span class="built_in">range</span>(<span class="number">4</span>,i-<span class="number">2</span>):</span><br><span class="line"> count+=<span class="number">2</span>**(i-n-<span class="number">3</span>)*(<span class="number">2</span>**(n-<span class="number">1</span>)-result[n-<span class="number">1</span>])</span><br><span class="line"> result.append(count)</span><br><span class="line"> <span class="built_in">print</span>(<span class="string">f'<span class="subst">{i}</span>:<span class="subst">{count}</span>'</span>)</span><br></pre></td></tr></table></figure>
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