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<h2 class="post-title" itemprop="name headline">Leetcode 939: Minimum Area Rectangle
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<p><strong>难度：Medium</strong></p>
<h3 id="题目描述"><a href="#题目描述" class="headerlink" title="题目描述"></a>题目描述</h3><p>给定xy平面的一些点的集合，找出这些点能组成的最小面积的矩形，矩形的边要平行于x，y轴。</p>
<p>如果不能组成矩形，返回0.</p>
<h3 id="示例"><a href="#示例" class="headerlink" title="示例"></a>示例</h3><p><strong>示例1</strong><br><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入: [[1,1],[1,3],[3,1],[3,3],[2,2]]</span><br><span class="line">输出: 4</span><br></pre></td></tr></table></figure></p>
<a id="more"></a>
<p><strong>示例2</strong><br><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入: [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]</span><br><span class="line">输出: 2</span><br></pre></td></tr></table></figure></p>
<h3 id="注意"><a href="#注意" class="headerlink" title="注意"></a>注意</h3><blockquote>
<ul>
<li>1 <= points.length <= 500</li>
<li>0 <= points[i][0] <= 40000</li>
<li>0 <= points[i][1] <= 40000</li>
<li>所有点都不相同</li>
</ul>
</blockquote>
<h3 id="解题思路"><a href="#解题思路" class="headerlink" title="解题思路"></a>解题思路</h3><p>主要还是从题目中要构成矩形的点的特征出发，题目要求矩形的边要和x，y轴平行，那么如果x = $x<em>{0}$有多个点，x=$x</em>{1}$也有多个点，那么能构成矩形的是$x=x<em>{0}, x=x</em>{1}$这些点的y坐标的交集，才能满足题目的要求。</p>
<p>比如在示例1中，x = 1的点有两个[1, 1], [1, 3]，x = 3的点有两个[3, 1], [3, 3]，那么共同的y坐标有1， 3，那么面积可以由x的差值乘以y的差值计算得出。</p>
<p>可以利用hashmap来存储具有共同x坐标的y，然后对不同x的y坐标求交集，得到最小的面积即可。具体见下面的代码。</p>
<h3 id="解题代码"><a href="#解题代码" class="headerlink" title="解题代码"></a>解题代码</h3><p><strong>Python3</strong><br><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><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></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span>:</span></span><br><span class="line"> <span class="function"><span class="keyword">def</span> <span class="title">minAreaRect</span><span class="params">(self, points)</span>:</span></span><br><span class="line"> <span class="string">"""</span></span><br><span class="line"><span class="string"> :type points: List[List[int]]</span></span><br><span class="line"><span class="string"> :rtype: int</span></span><br><span class="line"><span class="string"> """</span></span><br><span class="line"> pdict = collections.defaultdict(list)</span><br><span class="line"> <span class="keyword">for</span> x, y <span class="keyword">in</span> points:</span><br><span class="line"> pdict[x].append(y)</span><br><span class="line"> keys = [key <span class="keyword">for</span> key <span class="keyword">in</span> pdict.keys() <span class="keyword">if</span> len(pdict[key]) >= <span class="number">2</span>]</span><br><span class="line"> minArea = sys.maxsize</span><br><span class="line"> <span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">0</span>, len(keys)):</span><br><span class="line"> <span class="keyword">for</span> j <span class="keyword">in</span> range(i+<span class="number">1</span>, len(keys)):</span><br><span class="line"> y = sorted([e1 <span class="keyword">for</span> e1 <span class="keyword">in</span> pdict[keys[i]] <span class="keyword">if</span> e1 <span class="keyword">in</span> pdict[keys[j]]])</span><br><span class="line"> <span class="keyword">if</span> len(y) >= <span class="number">2</span>:</span><br><span class="line"> miny = sys.maxsize</span><br><span class="line"> <span class="keyword">for</span> k <span class="keyword">in</span> range(<span class="number">1</span>, len(y)):</span><br><span class="line"> miny = min(miny, y[k]-y[k<span class="number">-1</span>])</span><br><span class="line"> minArea = min(minArea, abs(keys[i]-keys[j]) * miny)</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span> <span class="keyword">if</span> minArea == sys.maxsize <span class="keyword">else</span> minArea</span><br></pre></td></tr></table></figure></p>
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