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<link rel="prev" href="../time_complexity/">
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2.3.4. &nbsp; 权衡时间与空间
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<li class="md-nav__item">
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2.4. &nbsp; 权衡时间与空间
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2.5. &nbsp; 小结
2.4. &nbsp; 小结
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6.1. &nbsp; 哈希表
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6.3. &nbsp; 小结
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6.1. &nbsp; 二分查找
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7.1. &nbsp; 二叉树
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7.1. &nbsp; 哈希表
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7.2. &nbsp; 二叉树遍历
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7.2. &nbsp; 哈希冲突处理
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7.3. &nbsp; 小结
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8.1. &nbsp; 堆
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8.2. &nbsp; 二叉树遍历
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8.3. &nbsp; 小结
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8.3. &nbsp; 二叉搜索树
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8.4. &nbsp; AVL 树 *
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8.5. &nbsp; 小结
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9. &nbsp; &nbsp; 图
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9. &nbsp; &nbsp; 图
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9.1. &nbsp; 图
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9.1. &nbsp; 堆
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<li class="md-nav__item">
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9.2. &nbsp; 图基础操作
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9.2. &nbsp; 建堆操作 *
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9.3. &nbsp; 图的遍历
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9.4. &nbsp; 小结
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9.3. &nbsp; 小结
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10. &nbsp; &nbsp; 查找算法
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10. &nbsp; &nbsp; 查找算法
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10.1. &nbsp; 线性查找
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10.1. &nbsp; 图
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
10.2. &nbsp; 二分查找
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10.2. &nbsp; 图基础操作
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<li class="md-nav__item">
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
10.3. &nbsp; 哈希查找
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10.3. &nbsp; 图的遍历
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10.4. &nbsp; 小结
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<li class="md-nav__item">
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
11.6. &nbsp; 桶排序（New）
11.6. &nbsp; 桶排序
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11.7. &nbsp; 计数排序（New）
11.7. &nbsp; 计数排序
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11.8. &nbsp; 基数排序（New）
11.8. &nbsp; 基数排序
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12. &nbsp; &nbsp; 回溯算法
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<p>对数阶常见于分治算法和数据类型转换等。</p>
<p>例如“归并排序”算法，输入长度为 <span class="arithmatex">\(n\)</span> 的数组，每轮递归将数组从中点划分为两半，形成高度为 <span class="arithmatex">\(\log n\)</span> 的递归树，使用 <span class="arithmatex">\(O(\log n)\)</span> 栈帧空间。</p>
<p>再例如“数字转化为字符串”，输入任意正整数 <span class="arithmatex">\(n\)</span> ，它的位数为 <span class="arithmatex">\(\log_{10} n\)</span> ，即对应字符串长度为 <span class="arithmatex">\(\log_{10} n\)</span> ，因此空间复杂度为 <span class="arithmatex">\(O(\log_{10} n) = O(\log n)\)</span> 。</p>
<h2 id="234">2.3.4. &nbsp; 权衡时间与空间<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
<p>理想情况下，我们希望算法的时间复杂度和空间复杂度都能达到最优。然而在实际情况中，同时优化时间复杂度和空间复杂度通常是非常困难的。</p>
<p><strong>降低时间复杂度通常需要以提升空间复杂度为代价，反之亦然</strong>。我们将牺牲内存空间来提升算法运行速度的思路称为“以空间换时间”；反之，则称为“以时间换空间”。</p>
<p>选择哪种思路取决于我们更看重哪个方面。在大多数情况下，时间比空间更宝贵，因此以空间换时间通常是更常用的策略。当然，在数据量很大的情况下，控制空间复杂度也是非常重要的。</p>
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