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10.1. &nbsp; 线性查找
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11.6. &nbsp; 桶排序（New）
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11.7. &nbsp; 计数排序（New）
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12. &nbsp; &nbsp; 回溯算法
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<h1 id="104">10.4. &nbsp; 小结<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
<h1 id="123">12.3. &nbsp; 小结<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
<ul>
<li>线性查找通过遍历数据结构并进行条件判断来完成查找任务。</li>
<li>二分查找依赖于数据的有序性，通过循环逐步缩减一半搜索区间来实现查找。它要求输入数据有序，且仅适用于数组或基于数组实现的数据结构。</li>
<li>哈希查找利用哈希表实现常数阶时间复杂度的查找操作，体现了空间换时间的算法思维。</li>
<li>下表概括并对比了三种查找算法的特性和时间复杂度。</li>
<li>暴力搜索通过遍历数据结构来定位数据。线性搜索适用于数组和链表，广度优先搜索和深度优先搜索适用于图和树。此类算法通用性好，无需对数据预处理，但时间复杂度 <span class="arithmatex">\(O(n)\)</span> 较高。</li>
<li>哈希查找、树查找和二分查找属于高效搜索方法，可在特定数据结构中快速定位目标元素。此类算法效率高，时间复杂度可达 <span class="arithmatex">\(O(\log n)\)</span> 甚至 <span class="arithmatex">\(O(1)\)</span> ，但通常需要借助额外数据结构。</li>
<li>实际中，我们需要对数据体量、搜索性能要求、数据查询和更新频率等因素进行具体分析，从而选择合适的搜索方法。</li>
<li>线性搜索适用于小型或频繁更新的数据；二分查找适用于大型、排序的数据；哈希查找适合对查询效率要求较高且无需范围查询的数据；树查找适用于需要维护顺序和支持范围查询的大型动态数据。</li>
<li>用哈希查找替换线性查找是一种常用的优化运行时间的策略，可将时间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。 </li>
</ul>
<div class="center-table">
<table>
<thead>
<tr>
<th></th>
<th>线性查找</th>
<th>二分查找</th>
<th>哈希查找</th>
</tr>
</thead>
<tbody>
<tr>
<td>适用数据结构</td>
<td>数组、链表</td>
<td>有序数组</td>
<td>数组、链表</td>
</tr>
<tr>
<td>时间复杂度</br>（查找，插入，删除）</td>
<td><span class="arithmatex">\(O(n)\)</span> , <span class="arithmatex">\(O(1)\)</span> , <span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(\log n)\)</span> , <span class="arithmatex">\(O(n)\)</span> , <span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span> , <span class="arithmatex">\(O(1)\)</span> , <span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td>空间复杂度</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
<td><span class="arithmatex">\(O(n)\)</span></td>
</tr>
</tbody>
</table>
</div>
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