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<h1 id="75">7.5. &nbsp; 小结<a class="headerlink" href="#75" title="Permanent link">&para;</a></h1>
<ul>
<li>二叉树是一种非线性数据结构，体现“一分为二”的分治逻辑。每个二叉树节点包含一个值以及两个指针，分别指向其左子节点和右子节点。</li>
<li>对于二叉树中的某个节点，其左（右）子节点及其以下形成的树被称为该节点的左（右）子树。</li>
<li>二叉树的相关术语包括根节点、叶节点、层、度、边、高度和深度等。</li>
<li>二叉树的初始化、节点插入和节点删除操作与链表操作方法类似。</li>
<li>常见的二叉树类型有完美二叉树、完全二叉树、满二叉树和平衡二叉树。完美二叉树是最理想的状态，而链表是退化后的最差状态。</li>
<li>二叉树可以用数组表示，方法是将节点值和空位按层序遍历顺序排列，并根据父节点与子节点之间的索引映射关系来实现指针。</li>
<li>二叉树的层序遍历是一种广度优先搜索方法，它体现了“一圈一圈向外”的分层遍历方式，通常通过队列来实现。</li>
<li>前序、中序、后序遍历皆属于深度优先搜索，它们体现了“走到尽头，再回头继续”的回溯遍历方式，通常使用递归来实现。</li>
<li>二叉搜索树是一种高效的元素查找数据结构，其查找、插入和删除操作的时间复杂度均为 <span class="arithmatex">\(O(\log n)\)</span> 。当二叉搜索树退化为链表时，各项时间复杂度会劣化至 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li>AVL 树，也称为平衡二叉搜索树，它通过旋转操作，确保在不断插入和删除节点后，树仍然保持平衡。</li>
<li>AVL 树的旋转操作包括右旋、左旋、先右旋再左旋、先左旋再右旋。在插入或删除节点后，AVL 树会从底向顶执行旋转操作，使树重新恢复平衡。</li>
</ul>


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