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obsidian-sync/日常学习/数据结构/二叉查找（排序）树.md

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二叉排序树又称二叉排序树。它或者是一个空树，或者是一个具有下列性质的二叉树：

  • 若它的左子树不空，则左子树上所有节点的值均小于它的根结构的值
  • 若它的右子树不空，则右子树上所有结点的值均大于它的根节点的值
  • 它的左、右子树也分别是二叉排序树

!20190311150104225.png

BST以链接方式存储，保持了链接存储结构在执行插入或删除操作时不用移动元素的优点，只要找到合适的插入和删除位置后，仅需要修改链接指针即可。插入删除的时间性能比较好。而对于BST的查找，其比较次数等于给定值的结点在二叉排序树的层数，极端情况下，最少为1次，最多不会超过树的深度。也就是说BST的查找性能取决于BST的形状。
我们希望二叉排序树是比较平衡的，其深度与完全二叉树相同，均为\log_{2}nlog2​n + 1，那么查找的时间复杂度也就为O(logn)，近似于折半查找。这就引申出一个问题，即如何让BST平衡化。

模拟AVL树插入及自平衡过程 AVL Tree Visualzation (usfca.edu)