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实际测试
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理论估算
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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3. 数据结构
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3.1. 数据结构分类
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3.2. 基本数据类型
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3.3. 数字编码 *
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3.4. 字符编码 *
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3.5. 小结
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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4.3. 列表
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4.4. 小结
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5. 栈与队列
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5.1. 栈
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5.2. 队列
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5.3. 双向队列
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5.4. 小结
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6. 散列表
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6.1. 哈希表（ ）
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6.2. 哈希冲突（ ）
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6.3. 哈希算法（ ）
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6.4. 小结
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7. 树
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7.1. 二叉树
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7.2. 二叉树遍历
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7.3. 二叉树数组表示
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7.4. 二叉搜索树
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7.5. AVL 树 *
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< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.6. 小结
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8. 堆
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8.1. 堆
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< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作
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8.3. Top-K 问题（ ）
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8.4. 小结
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9. 图
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9.1. 图
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9.2. 图基础操作
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9.3. 图的遍历
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9.4. 小结
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10. 搜索
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10.1. 二分查找
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
10.2. 二分查找边界
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10.3. 哈希优化策略
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10.4. 重识搜索算法
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10.5. 小结
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11. 排序
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11.1. 排序算法
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11.2. 选择排序
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11.3. 冒泡排序
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11.4. 插入排序
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11.5. 快速排序
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11.6. 归并排序
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11.7. 堆排序
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11.8. 桶排序
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11.9. 计数排序
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11.10. 基数排序
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11.11. 小结
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12.1. 分治算法（ ）
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13.1. 回溯算法
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13.2. 全排列问题
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13.3. 子集和问题
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13.4. N 皇后问题
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13.5. 小结
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14. 动态规划
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14.1. 初探动态规划（ ）
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14.2. DP 问题特性（ ）
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14.3. DP 解题思路（ ）
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14.4. 0-1 背包问题（ ）
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14.6. 编辑距离问题（ ）
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14.7. 小结（ ）
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15. 附录
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15.1. 编程环境安装
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2.1.1. 算法评价维度
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2.1.2. 效率评估方法
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实际测试
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理论估算
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2.1.3. 复杂度分析重要性
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< h1 id = "21" > 2.1. 算法效率评估< a class = "headerlink" href = "#21" title = "Permanent link" > ¶ < / a > < / h1 >
< h2 id = "211" > 2.1.1. 算法评价维度< a class = "headerlink" href = "#211" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 从总体上看，算法设计追求以下两个层面的目标：< / p >
< ol >
< li > < strong > 找到问题解法< / strong > 。算法需要在规定的输入范围内，可靠地求得问题的正确解。< / li >
< li > < strong > 寻求最优解法< / strong > 。同一个问题可能存在多种解法，我们希望找到尽可能高效的算法。< / li >
< / ol >
< p > 因此，在能够解决问题的前提下，算法效率成为主要的评价维度，主要包括：< / p >
< ul >
< li > < strong > 时间效率< / strong > ，即算法运行速度的快慢。< / li >
< li > < strong > 空间效率< / strong > ，即算法占用内存空间的大小。< / li >
< / ul >
< p > 简而言之，< strong > 我们的目标是设计“既快又省”的数据结构与算法< / strong > 。掌握评估算法效率的方法则至关重要，因为只有了解评价标准，我们才能进行算法之间的对比分析，从而指导算法设计与优化过程。< / p >
< h2 id = "212" > 2.1.2. 效率评估方法< a class = "headerlink" href = "#212" title = "Permanent link" > ¶ < / a > < / h2 >
< h3 id = "_1" > 实际测试< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 假设我们现在有算法 A 和算法 B， ， ， ， ， < / p >
< p > < strong > 难以排除测试环境的干扰因素< / strong > 。硬件配置会影响算法的性能表现。例如，在某台计算机中，算法 A 的运行时间比算法 B 短；但在另一台配置不同的计算机中，我们可能得到相反的测试结果。这意味着我们需要在各种机器上进行测试，而这是不现实的。< / p >
< p > < strong > 展开完整测试非常耗费资源< / strong > 。随着输入数据量的变化，算法会表现出不同的效率。例如，输入数据量较小时，算法 A 的运行时间可能短于算法 B； ， ， ， ， < / p >
< h3 id = "_2" > 理论估算< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 由于实际测试具有较大的局限性，我们可以考虑仅通过一些计算来评估算法的效率。这种估算方法被称为「复杂度分析 Complexity Analysis」或「渐近复杂度分析 Asymptotic Complexity Analysis」。< / p >
< p > < strong > 复杂度分析评估的是算法运行效率随着输入数据量增多时的增长趋势< / strong > 。这个定义有些拗口，我们可以将其分为三个重点来理解：< / p >
< ul >
< li > “算法运行效率”可分为“运行时间”和“占用空间”，因此我们可以将复杂度分为「时间复杂度 Time Complexity」和「空间复杂度 Space Complexity」； < / li >
< li > “随着输入数据量增多时”表示复杂度与输入数据量有关，反映了算法运行效率与输入数据量之间的关系；< / li >
< li > “增长趋势”表示复杂度分析关注的是算法时间与空间的增长趋势，而非具体的运行时间或占用空间；< / li >
< / ul >
< p > < strong > 复杂度分析克服了实际测试方法的弊端< / strong > 。首先，它独立于测试环境，因此分析结果适用于所有运行平台。其次，它可以体现不同数据量下的算法效率，尤其是在大数据量下的算法性能。< / p >
< p > 如果你对复杂度分析的概念仍感到困惑，无需担心，我们会在后续章节详细介绍。< / p >
< h2 id = "213" > 2.1.3. 复杂度分析重要性< a class = "headerlink" href = "#213" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 复杂度分析为我们提供了一把评估算法效率的“标尺”，告诉我们执行某个算法所需的时间和空间资源，并使我们能够对比不同算法之间的效率。< / p >
< p > 复杂度是个数学概念，对于初学者可能比较抽象，学习难度相对较高。从这个角度看，复杂度分析可能不太适合作为第一章的内容。然而，当我们讨论某个数据结构或算法的特点时，我们难以避免要分析其运行速度和空间使用情况。< strong > 因此，在深入学习数据结构与算法之前，建议读者先对复杂度建立初步的了解，并能够完成简单案例的复杂度分析< / strong > 。< / p >
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