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<ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E7%A4%BA%E4%BE%8B"><span class="toc-number">1.</span> <span class="toc-text">示例</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%80%9D%E8%B7%AF"><span class="toc-number">2.</span> <span class="toc-text">思路</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E8%A7%A3%E7%AD%94"><span class="toc-number">3.</span> <span class="toc-text">解答</span></a></li></ol>
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Leetcode 74.搜索二维矩阵
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<p>编写一个高效的算法来判断 m x n 矩阵中，是否存在一个目标值。该矩阵具有如下特性：</p>
<ul>
<li>每行中的整数从左到右按升序排列。</li>
<li>每行的第一个整数大于前一行的最后一个整数。<br><img src="/img/leetcode74.png" alt="Leetcode74"><span id="more"></span></li>
</ul>
<h2 id="示例"><a href="#示例" class="headerlink" title="示例"></a>示例</h2><blockquote>
<p>输入：matrix = [<br> [1, 3, 5, 7],<br> [10,11,16,20],<br> [23,30,34,60]<br> ], target = 16<br>输出：true</p>
</blockquote>
<h2 id="思路"><a href="#思路" class="headerlink" title="思路"></a>思路</h2><p>有序，查找类任务，想到二分查找</p>
<ol>
<li>利用每一列，每一行有序的特性，先对第一列进行查找，再对那一行进行查找,时间复杂度为 O(lg mn)<br><img src="/img/leetcode741.png" alt="解法1"><blockquote>
<p>先查找第一列，找到第二行，再查找第二行</p>
</blockquote>
</li>
<li>利用有序的条件，从左下角开始查找，时间复杂度为O(m + n)</li>
</ol>
<ul>
<li>当当前元素大于 target时, 向上查找</li>
<li>当当前元素小于 target时, 向右查找<br><img src="/img/leetcode74.png" alt="解法2"></li>
</ul>
<h2 id="解答"><a href="#解答" class="headerlink" title="解答"></a>解答</h2><figure class="highlight c++"><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></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Solution</span></span><br><span class="line">{</span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line"> <span class="function"><span class="type">bool</span> <span class="title">searchMatrix</span><span class="params">(vector<vector<<span class="type">int</span>>> &matrix, <span class="type">int</span> target)</span></span></span><br><span class="line"><span class="function"> </span>{</span><br><span class="line"> <span class="keyword">auto</span> p = <span class="built_in">upper_bound</span>(matrix.<span class="built_in">begin</span>(), matrix.<span class="built_in">end</span>(),target, []( <span class="type">const</span> <span class="type">int</span> a, <span class="type">const</span> vector<<span class="type">int</span>>& b){</span><br><span class="line"> <span class="keyword">return</span> a < b[<span class="number">0</span>];</span><br><span class="line"> });</span><br><span class="line"> <span class="keyword">if</span>(p != matrix.<span class="built_in">begin</span>()) { </span><br><span class="line"> -- p;</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">binary_search</span>(p-><span class="built_in">begin</span>(), p-><span class="built_in">end</span>(),target);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>; <span class="comment">// 默认找不到</span></span><br><span class="line"> }</span><br><span class="line">};</span><br></pre></td></tr></table></figure>
<figure class="highlight c++"><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></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Solution</span></span><br><span class="line">{</span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line"> <span class="function"><span class="type">bool</span> <span class="title">searchMatrix</span><span class="params">(vector<vector<<span class="type">int</span>>> &matrix, <span class="type">int</span> target)</span></span></span><br><span class="line"><span class="function"> </span>{</span><br><span class="line"> <span class="type">int</span> m = matrix.<span class="built_in">size</span>();</span><br><span class="line"> <span class="type">int</span> n = matrix[<span class="number">0</span>].<span class="built_in">size</span>();</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = m - <span class="number">1</span>, j = <span class="number">0</span>; i >= <span class="number">0</span> &&j < n;)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (matrix[i][j] < target)</span><br><span class="line"> ++j;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (matrix[i][j] > target)</span><br><span class="line"> --i;</span><br><span class="line"> <span class="keyword">else</span> </span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>; <span class="comment">// 默认找不到</span></span><br><span class="line"> }</span><br><span class="line">};</span><br></pre></td></tr></table></figure>
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<ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E7%A4%BA%E4%BE%8B"><span class="toc-number">1.</span> <span class="toc-text">示例</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%80%9D%E8%B7%AF"><span class="toc-number">2.</span> <span class="toc-text">思路</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E8%A7%A3%E7%AD%94"><span class="toc-number">3.</span> <span class="toc-text">解答</span></a></li></ol>
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