二叉搜索树常被简写为BST是一种特殊的二叉树。它继承了二叉树的基本特性并在此基础上实现了有序线性表的特性即所有节点的值都保持有序。这种树形结构在计算机科学中有着广泛的应用是数据结构中的一种重要类型。因此二叉搜索树BST的严格定义是每个节点的值必须大于其左子树中的任何节点并且小于其右子树中的任何节点。同时不允许有重复的节点值存在。这是二叉搜索树BST的形态示意图▲ BST的增删查操作对于二叉搜索树BST来说查找和插入操作简单但删除操作需要处理不同情况以确保不破坏BST性质。以删除关键码为69的节点为例这种情况相对简单因为该节点只有一个分支。但即使如此也需要我们谨慎处理。删除情况二删除关键码为36的节点此节点具有两个分支在进行删除操作时我们需要分两步来处理这种双分支节点。首先将36与右子树中的最小节点即最左节点进行交换。这一步的目的是确保在删除过程中BST的性质不会受到破坏。通过这样的交换我们可以将问题简化为删除一个分支较少的节点从而更易于理解和处理。第二步经过第一步的交换后36节点已转化为单分支状态此时可参照第一种情况的处理方式进行后续操作。02二叉搜索树的平衡策略▲ 二叉树的高度与平衡在讨论二叉树的高度时我们特别关注了BST二叉搜索树的平均高度。通常BST的平均高度约为n的平方根其中n为节点总数。然而我们期望的理想情况是树的理想高度能达到对数级别即logn。那么如何才能实现这一目标呢▲ 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