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<input type="text" id="local-search-input"><div id="local-search-result"></div><span class="popup-btn-close">close</span></div></div></nav></div></header><main id="main" class="main"><div class="main-inner"><div class="content-wrap"><div id="content" class="content"><div id="posts" class="posts-expand"><article class="post post-type-normal" itemscope itemtype="http://schema.org/Article"><link itemprop="mainEntityOfPage" href="http://www.shenzekun.cn/蓝桥杯-四平方和问题.html"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="name" content="shenzekun"><meta itemprop="description" content=""><meta itemprop="image" content="https://blog-1257878287.cos.ap-chengdu.myqcloud.com/avatar1.jpg"></span><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Moorez"></span><header class="post-header"><h1 class="post-title" itemprop="name headline">蓝桥杯-四平方和问题</h1><div class="post-meta"><span class="post-time"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">发表于</span> <time itemprop="dateCreated" datetime="2017-03-04T23:09:54+08:00" content="2017-03-04">2017-03-04</time></span> <span class="post-category"> | <span class="post-meta-item-icon"><i class="fa fa-folder-o"></i></span> <span class="post-meta-item-text">分类于</span> <span itemprop="about" itemscope itemtype="https://schema.org/Thing"><a href="/categories/c-c/" itemprop="url" rel="index"><span itemprop="name">c-c++</span></a></span></span> <span id="/蓝桥杯-四平方和问题.html" class="leancloud_visitors" data-flag-title="蓝桥杯-四平方和问题"> | <span class="post-meta-item-icon"><i class="fa fa-eye"></i></span> <span class="post-meta-item-text">热度</span><span class="leancloud-visitors-count"></span> <span>℃</span></span><div class="post-wordcount"><span class="post-meta-divider">|</span><span class="post-meta-item-icon"><i class="fa fa-file-word-o"></i></span> <span class="post-meta-item-text">字数统计</span> <span title="字数统计">642 字</span> <span class="post-meta-divider">|</span><span class="post-meta-item-icon"><i class="fa fa-clock-o"></i></span> <span class="post-meta-item-text">阅读时长</span> <span title="阅读时长">3 分钟</span></div></div></header><div class="post-body" itemprop="articleBody"><h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a>问题：</h2><p>四平方和定理，又称为拉格朗日定理：<br>每个正整数都可以表示为至多4个正整数的平方和。<br>如果把0包括进去，就正好可以表示为4个数的平方和。</p><a id="more"></a><p>比如：<br>5 = 0^2 + 0^2 + 1^2 + 2^2<br>7 = 1^2 + 1^2 + 1^2 + 2^2<br>（ ^ 符号表示乘方的意思）</p><p>对于一个给定的正整数，可能存在多种平方和的表示法。<br>要求你对4个数排序：<br>0 <= a <= b <= c <= d<br>并对所有的可能表示法按 a,b,c,d 为联合主键升序排列，最后输出第一个表示法</p><p>程序输入为一个正整数N (N<5000000)<br>要求输出4个非负整数，按从小到大排序，中间用空格分开</p><p>例如，输入：<br>5<br>则程序应该输出：<br>0 0 1 2</p><p>再例如，输入：<br>12<br>则程序应该输出：<br>0 2 2 2</p><p>再例如，输入：<br>773535<br>则程序应该输出：<br>1 1 267 838</p><p>资源约定：<br>峰值内存消耗 < 256M<br>CPU消耗 < 3000ms</p><p>请严格按要求输出，不要画蛇添足地打印类似：“请您输入…” 的多余内容。</p><p>所有代码放在同一个源文件中，调试通过后，拷贝提交该源码。</p><p>注意: main函数需要返回0<br>注意: 只使用ANSI C/ANSI C++ 标准，不要调用依赖于编译环境或操作系统的特殊函数。<br>注意: 所有依赖的函数必须明确地在源文件中 #include<xxx>， 不能通过工程设置而省略常用头文件。</xxx></p><p>提交时，注意选择所期望的编译器类型。</p><h2 id="思路："><a href="#思路：" class="headerlink" title="思路："></a>思路：</h2><p>这题我是用暴力输出的，用四个循环，我先前用四个循环是从小加到大，但是超时了。我发现，输入的数越大，输出的前两个数是比较小的，但是后面两个数比较大，于是我把后面两个循环变成从大减到小，于是成功了╮(￣▽￣)╭</p><h2 id="实现代码（用C语言实现）"><a href="#实现代码（用C语言实现）" class="headerlink" title="实现代码（用C语言实现）"></a>实现代码（用C语言实现）</h2><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string"><stdio.h></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string"><math.h></span></span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">solve</span><span class="params">(<span class="keyword">long</span> n)</span></span>{</div><div class="line"> <span class="keyword">int</span> a[<span class="number">4</span>];</div><div class="line"> <span class="keyword">for</span> (a[<span class="number">0</span>]=<span class="number">0</span>; a[<span class="number">0</span>]<<span class="built_in">sqrt</span>(n); a[<span class="number">0</span>]++) {</div><div class="line"> <span class="keyword">for</span> (a[<span class="number">1</span>]=a[<span class="number">0</span>];a[<span class="number">1</span>]<<span class="built_in">sqrt</span>(n) ; a[<span class="number">1</span>]++) {</div><div class="line"> <span class="keyword">for</span> (a[<span class="number">2</span>]=<span class="built_in">sqrt</span>(n-a[<span class="number">1</span>]*a[<span class="number">1</span>]-a[<span class="number">0</span>]*a[<span class="number">0</span>]); a[<span class="number">2</span>]>=a[<span class="number">1</span>]; a[<span class="number">2</span>]--) {</div><div class="line"> <span class="keyword">for</span> (a[<span class="number">3</span>]=<span class="built_in">sqrt</span>(n-a[<span class="number">1</span>]*a[<span class="number">1</span>]-a[<span class="number">2</span>]*a[<span class="number">2</span>]-a[<span class="number">0</span>]*a[<span class="number">0</span>])+<span class="number">1</span>; a[<span class="number">3</span>]>=a[<span class="number">2</span>]; a[<span class="number">3</span>]--) {<span class="comment">//其实这里加1不加1都一样</span></div><div class="line"> <span class="keyword">if</span> (a[<span class="number">0</span>]*a[<span class="number">0</span>]+a[<span class="number">1</span>]*a[<span class="number">1</span>]+a[<span class="number">2</span>]*a[<span class="number">2</span>]+a[<span class="number">3</span>]*a[<span class="number">3</span>]==n) {</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%d %d %d %d\n"</span>,a[<span class="number">0</span>],a[<span class="number">1</span>],a[<span class="number">2</span>],a[<span class="number">3</span>]);</div><div class="line"> <span class="keyword">return</span> ;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }</div><div class="line">}</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</div><div class="line"> <span class="keyword">long</span> n;</div><div class="line"> <span class="built_in">scanf</span>(<span class="string">"%ld"</span>,&n);</div><div class="line"> solve(n);</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure></div><div><div><div style="text-align:center;color:#ccc;font-size:14px">-------------本文结束<i class="fa fa-paw"></i>感谢您的阅读-------------</div></div></div><div><div class="my_post_copyright"><script src="//cdn.bootcss.com/clipboard.js/1.5.10/clipboard.min.js"></script><script src="https://cdn.bootcss.com/jquery/2.0.0/jquery.min.js"></script><script src="https://unpkg.com/sweetalert/dist/sweetalert.min.js"></script><p><span>本文标题:</span><a href="/蓝桥杯-四平方和问题.html">蓝桥杯-四平方和问题</a></p><p><span>文章作者:</span><a href="/" title="访问 shenzekun 的个人博客">shenzekun</a></p><p><span>发布时间:</span>2017年03月04日 - 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