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obsidian-sync/日常学习/数据结构/B-树.md

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为弥补红黑树高度不可控问题，提出多叉搜索树，即为B-树 B树满足一下条件：

  1. 树中每个节点至多有M个孩子节点（即至多有m-1个关键字）
  2. 除根节点外，其他节点至少有m/2个孩子节点
  3. 若根节点不是叶子节点，则根节点至少有2个孩子节点
  4. 所有叶子节点都在同一层上，即B树是所有结点的平衡因子均等于0的多路查找树。

如下图所示一颗3阶b树： !微信截图_20221216171144.png

每个节点都会存储key、data、指针(如图5阶B树) !1446087-bc023e47bc74cfa1.webp

B-tree的插入：

与BST相同，比较大小后判断放在左还是右

B-tree的删除：

需要先判断节点是否富有，富有：删除一个key，剩余key的数量大于等于(m/2)向上取整-1。 节点如果不富有需要从兄弟、父亲节点借。如果都不富有，只能降低树的高度。具体过程参考B站：站长数据结构

B-tree模拟 B-Tree Visualization (usfca.edu)