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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_preface/installation/" class="md-nav__link">
|
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编程环境安装
|
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</a>
|
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</li>
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_preface/contribution/" class="md-nav__link">
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一起参与创作
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|
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|
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</ul>
|
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_2">
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="引言" data-md-level="1">
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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算法无处不在
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</ul>
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_3">
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<nav class="md-nav" aria-label="计算复杂度" data-md-level="1">
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数据与内存
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小结
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数组与链表
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数组与链表
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|
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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数组（Array）
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
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链表（LinkedList）
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
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列表（List）
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<label class="md-nav__link" for="__nav_6">
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栈与队列
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="栈与队列" data-md-level="1">
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<label class="md-nav__title" for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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栈与队列
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
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栈（Stack）
|
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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队列（Queue）
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</a>
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
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双向队列（Deque）
|
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|
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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小结
|
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</ul>
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</nav>
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<label class="md-nav__link" for="__nav_7">
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散列表
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="散列表" data-md-level="1">
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散列表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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|
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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哈希表（HashMap）
|
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</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<label class="md-nav__link" for="__nav_8">
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二叉树
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" aria-label="二叉树" data-md-level="1">
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<label class="md-nav__title" for="__nav_8">
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<span class="md-nav__icon md-icon"></span>
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二叉树
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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二叉树（Binary Tree）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree_types/" class="md-nav__link">
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二叉树常见类型
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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二叉搜索树
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
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AVL 树 *
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<h1 id="_1">小结<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
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<h3 id="_2">算法效率评估<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
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<li>「复杂度分析」克服了实际测试的弊端，分析结果适用于所有运行平台，并且可以体现不同数据大小下的算法效率。</li>
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<h3 id="_3">时间复杂度<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
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<ul>
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<li>「时间复杂度」统计算法运行时间随着数据量变大时的增长趋势，可以有效评估算法效率，但在某些情况下可能失效，比如在输入数据量较小或时间复杂度相同时，无法精确对比算法效率的优劣性。</li>
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<li>「最差时间复杂度」使用大 <span class="arithmatex">\(O\)</span> 符号表示，即函数渐近上界，其反映当 <span class="arithmatex">\(n\)</span> 趋于正无穷时，<span class="arithmatex">\(T(n)\)</span> 处于何种增长级别。</li>
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<li>推算时间复杂度分为两步，首先统计计算操作数量，再判断渐近上界。</li>
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<li>常见时间复杂度从小到大排列有 <span class="arithmatex">\(O(1)\)</span> , <span class="arithmatex">\(O(\log n)\)</span> , <span class="arithmatex">\(O(n)\)</span> , <span class="arithmatex">\(O(n \log n)\)</span> , <span class="arithmatex">\(O(n^2)\)</span> , <span class="arithmatex">\(O(2^n)\)</span> , <span class="arithmatex">\(O(n!)\)</span> 。</li>
|
||
<li>某些算法的时间复杂度不是恒定的，而是与输入数据的分布有关。时间复杂度分为「最差时间复杂度」和「最佳时间复杂度」，后者几乎不用，因为输入数据需要满足苛刻的条件才能达到最佳情况。</li>
|
||
<li>「平均时间复杂度」可以反映在随机数据输入下的算法效率，最贴合实际使用情况下的算法性能。计算平均时间复杂度需要统计输入数据的分布，以及综合后的数学期望。</li>
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<h3 id="_4">空间复杂度<a class="headerlink" href="#_4" title="Permanent link">¶</a></h3>
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|
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<p>与时间复杂度的定义类似，「空间复杂度」统计算法占用空间随着数据量变大时的增长趋势。</p>
|
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|
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<li>
|
||
<p>算法运行中相关内存空间可分为输入空间、暂存空间、输出空间。通常情况下，空间复杂度不计入输入空间。暂存空间可分为指令空间、数据空间、栈帧空间，其中栈帧空间一般在递归函数中才会影响到空间复杂度。</p>
|
||
</li>
|
||
<li>我们一般只关心「最差空间复杂度」，即统计算法在「最差输入数据」和「最差运行时间点」下的空间复杂度。</li>
|
||
<li>常见空间复杂度从小到大排列有 <span class="arithmatex">\(O(1)\)</span> , <span class="arithmatex">\(O(\log n)\)</span> , <span class="arithmatex">\(O(n)\)</span> , <span class="arithmatex">\(O(n^2)\)</span> , <span class="arithmatex">\(O(2^n)\)</span> 。</li>
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