蓝桥杯算法训练 ALGO-1004 无聊的逗（C++详解）_算法训练无聊的逗 - wpsshop博客

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src="https://cdn.wpsshop.cn/public/wpsshopindex/js/mid_detail_last.js?v=33890"></script><style type="text/css"></style><script type="text/javascript"></script><div class="interactive_info" id="body-data-0098" attrv="45594"></div><div class="article_box" style="overflow: hidden;"><div class="article_channel"><div class="channel_top_line"><div class="cn_t_l"></div><div class="cn_t_r"></div></div><div class="article_channel_info">当前位置: <a href="/article/list/1">article</a> > 正文 </div></div><div class="article_title"><h1>蓝桥杯算法训练 ALGO-1004 无聊的逗（C++详解）_算法训练无聊的逗</h1></div><div class="article_info"><div class="article_c_info"> 作者：凡人多烦事01 | 2024-05-30 06:09:52</div><div class="article_click" style="width: 140px;"><p class="operation-b-img operation-b-img-active"><i class="img-up txclick" attc="upclick" attn="0"></i><span class="num"> 赞</span></p><p class="operation-b-img operation-b-img-active"><i class="img-down txclick" attc="downclick" attn="0"></i><span class="num">踩</span></p></div></div><div class="article_intro">算法训练无聊的逗</div><div class="article_content article_contentheight"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/kdoc_html_views-1a98987dfd.css"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/ck_htmledit_views-044f2cf1dc.css"> <div id="content_views" class="htmledit_views"> <h4 id="输入样例："><a name="t0"></a>资源限制：</h4> <p>时间限制：1.0s 内存限制：256.0MB</p> <h4 id="输出样例："><a name="t1"></a>问题描述：</h4> <p>逗志芃在干了很多事情后终于闲下来了，然后就陷入了深深的无聊中。不过他想到了一个游戏来使他更无聊。他拿出n个木棍，然后选出其中一些粘成一根长的，然后再选一些粘成另一个长的，他想知道在两根一样长的情况下长度最长是多少。</p> <h4><a name="t2"></a>输入格式：</h4> <p>第一行一个数n，表示n个棍子。第二行n个数，每个数表示一根棍子的长度。</p> <h4><a name="t3"></a>输出格式：</h4> <p>一个数，最大的长度。</p> <h4><a name="t4"></a>样例输入：</h4> <pre data-index="0" class="set-code-show" name="code"><code class="hljs language-cobol"><ol class="hljs-ln" style="width:100%"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">4</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">1</span> <span class="hljs-number">2</span> <span class="hljs-number">3</span> <span class="hljs-number">1</span></div></div></li></ol></code><div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}" onclick="hljs.signin(event)"></div></pre> <h4><a name="t5"></a> 样例输出：</h4> <pre data-index="1" class="set-code-show" name="code"><code class="hljs language-cobol"><span class="hljs-number">3</span></code><div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}" onclick="hljs.signin(event)"></div></pre> <h4><a name="t6"></a>数据规模和约定：</h4> <p>n<=15</p> <h4><a name="t7"></a>代码示例（含详细注释）：</h4> <pre data-index="2" class="set-code-hide" name="code"><code class="language-cpp hljs"><ol class="hljs-ln" style="width:1072px"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#<span class="hljs-keyword">include</span> <span class="hljs-string"><bits/stdc++.h></span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> std;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-type">int</span> a[<span class="hljs-number">15</span>];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-type">int</span> b[<span class="hljs-number">1</span> << <span class="hljs-number">15</span>]; <span class="hljs-comment">//2^15</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-comment">//假设有四根木棍，则 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-comment">// 1代表取，0代表不取，即每根木棍取与不取的所有组合情况，共2^4种组合</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-function"><span class="hljs-type">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-type">int</span> n;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> cin >> n;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = n - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) { <span class="hljs-comment">//让木棍在数组中以倒序排列，这样取0010 = 2^1 即取a[1] = 3</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> cin >> a[i];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//原：1 2 3 1</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//倒序：1 3 2 1</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//求每一个组合的木棍的长度</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i < (<span class="hljs-number">1</span> << n); i++) { <span class="hljs-comment">//0 ~ 2^n的所有数，即所有组合取用木棍的情况（不要用pow(2,n)，效率比二进制移位低，会超时）</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> j = <span class="hljs-number">0</span>; j < n; j++) { <span class="hljs-comment">//n根木棍</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">if</span> (i & (<span class="hljs-number">1</span> << j)) <span class="hljs-comment">//i分别按位与 0001 0010 0100 1000，说明这个组合选用了这根木棒</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> b[i] += a[j];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//木棍分别为 1 2 3 1</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 //i：所有组合取用木棍的情况，0不选；1选</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//0000 0001 0030 0031 0200 0201 0230 0231 1000 1001 1030 1031 1200 1201 1230 1231 //实际的木棍选用情况</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">// 0 1 3 4 2 3 5 6 1 2 4 5 3 4 6 7 //b[i]：每种组合的长度</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="26"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-type">int</span> ans = <span class="hljs-number">0</span>;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="27"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-comment">//将这个组合和其它组合进行比较，如果其它组合和这个组合中没有选用相同的木棍，并且这两个组合长度相等，则符合条件，进而与最大长度比较和替换。</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="28"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i < (<span class="hljs-number">1</span> << n); i++) {</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="29"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> j = <span class="hljs-number">0</span>; j < (<span class="hljs-number">1</span> << n); j++) {</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="30"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">if</span> (!(i & j) && b[i] == b[j]) {</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="31"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> ans = <span class="hljs-built_in">max</span>(ans, b[i]);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="32"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="33"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="34"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="35"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> cout << ans;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="36"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="37"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">}</div></div></li></ol></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}" onclick="hljs.signin(event)"></div></pre> <p></p> 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